CN101493584B - Shaped non-corrective eyewear lenses and methods for providing same - Google Patents

Abstract

The disclosure relates to shaped ophthalmic lenses and methods for providing such lenses, including non-powered lenses having non-quadratic surfaces of complementary curvature. Such lenses may have a curvature maximum away from an axis of symmetry and a substantially constant wall thickness. Equations describing and methods of designing such lenses are disclosed including embodiments where two spheres of substantially different curvature are merged in accordance with a weighting function, and adjusted using merit functions.

Description

Shaped non-corrective goggle lens and method of providing the same

This application is a divisional application based on the patent application with the application number 200480041156.9, the application date is December 2, 2004, and the invention title is "Shaped non-corrective goggle lens and method for providing the same".

technical field

The present invention relates to optical lenses and lens blanks for use in non-corrective goggles, including sunglasses, sports goggles, safety glasses, safety glasses, and sun visors.

Background technique

It is well known in the art to manufacture non-corrective eyewear, such as sunglasses or safety glasses, with a face wrapping portion to protect the eyes from incident light, wind, and external spectacles in the wearer's temporal field of view. designed for objects. These face goggles bend horizontally around the eye sockets, "wrapping the face" and closing the eyes up to 100° from the line of sight. The vertical profile of the inner lower area of the lens towards the cheeks is variously called "pantoscopic tilt" or "rake" depending on how this effect is achieved. Lenses can be designed to fit into a pair of lens frames, or the lenses can be an integral shield type. Wrapping and/or cupping the face aesthetically creates pleasing eyewear that is comfortable for the wearer, but also introduces optical distortions that make precise visual work difficult for the wearer. To improve the seal provided by wrapping and wrapping the face, various surface forms and arrangements have been employed. While some arrangements have been able to achieve accurate imaging on the frontal line of sight of the wearer's far-field vision, the lack of spatial alignment between the optical axis of the lens and the frontal line of sight when worn introduces inherent oblique refractive errors. The prior art in the early 20th century employed spherical and elliptical dual designs of approximately constant thickness, so there was no optical axis, but these designs had negative optical power and exhibited a Basic refraction and prism distortion. In order to function as a dual lens goggle, the lens must have an exceptionally high base curve (-16 to 21D) so that it can be donned approximately concentrically with the movement of the wearer's eyes. Alternatively, the overall lens should have a base curve with a low D value so that the distance between the frontal line of sight of one eye and the optical axis in the wearer's median plane is much smaller than the apex radius of the curved portion, e.g. , in the range 1 to 2D. Most goggles use a basic curve between these conditions.

The prior art introduced by Rayton 75 years ago (US Patent 1,741,536) attempted to tilt the nominally zero power lens outward and/or downward and align the optical center of the lens with the frontal line of sight of the wearer to obtain Wrap the face and/or pull the face effect. This method was abandoned due to prism distortion in the wearing position. More recent techniques, for pairs of low negative lenses, teach a way to overcome this prismatic error. Reichow and Citek disclose in their U.S. Patent 6,129,435 (U.S. Patent 6,129,435) that by displacing the geometric center of the lens inwardly and/or outwardly, an apparent wrapping and/or huddling of the face can be achieved by The center of curvature rotates the lens to position the optical axis inwardly and/or upwardly, correcting wear-induced prismatic errors without altering the physical appearance of the lens. However, there is still negative power error on frontal sight. It can be shown that for pairs of low positive lenses, a set of opposite rotations can correct for prism errors during wear. However, most non-corrective goggles are fitted according to Prentice's Rule (1888), which is an approximate analysis that predicts the distance between an optical prism on a line of sight that is decentered relative to the lens, and the rear vertex power of that lens. linear relationship. Most commonly, the lens is designed so that it gives zero rear vertex power. Their optical axes and the wearer's frontal line of sight when worn, can be displaced laterally relative to each other when required, while remaining parallel between them. This arrangement is shown in Figure 1A, where line 2-2' is the frontal line of sight and 1-1' is the displaced optical axis.

Rayton in U.S. Patent 1,741,536 (U.S. Patent 1,741,536), and Jannard in U.S. Patents 4,674,851 and 4,859,048 (U.S. Patent 4,674,851 and 4,859,048), disclose cylindrical lenses. Jannard (U.S. Patent 4,867,550) and Burn (U.S. Patent 4,741,611) describe toroidal lenses. Integral goggles described by Montesi and King (U.S. Patent 4,271,538) and Conway (U.S. Patent 5,555,038) have left and right spherical lens portions whose optical axes are displaced nasally from the frontal line of sight when worn. Houston et al. (U.S. Patents 5,648,832, 5,689,323, and 6,010,218) describe spherical lenses that are centrifugal relative to the frontal line of sight in both the horizontal and vertical planes. Fecteau et al. (U.S. Patents 5,825,455, 6,019,469, and 6,254,236) describe integral lenses consisting of surfaces formed by rotation of an ellipse, parabola, or hyperbola about a horizontal axis near the wearer's eye. Davis and Waido (U.S. Patent 5,604,547) describe integral lenses whose surfaces are paraboloids curved in the lateral region to form a side wrap outside the wearer's point of gaze. They also describe overall style sunglasses or eye protection glasses whose lenses have oblate spherical inner and outer surfaces. The surfaces they discuss also have regions of maximum surface astigmatism on the lens surface. Tackles (U.S. Patent 5,774,201) describes two types of lenses, an integral lens style and a double lens style, wherein the horizontal arc of the lens section has a middle portion and a side end portion, and the side end portion has a gradual tightening relative to the curvature of the middle portion. The curved portion basically coincides with the elliptical portion with an eccentricity ranging from 0.1 to 0.85. The vertical bends can take any desired form.

For a spherical lens to have zero posterior vertex power, its anterior and posterior radii, R ₁ and R ₂ , are related by R ₁ -R ₂ =t(n-1)/n, where t is the lens center thickness and n is the material refractive index. This relationship states that the caliper thickness of the lens (measured perpendicular to each surface) has a maximum at the center of the lens and then tapers off away from the optical axis of the lens, a fact long known in ophthalmic optics. For example, the lenses described by Rayton have wall thicknesses that taper away from the optical axis of the lens. Conway noted that lenses that taper outward from the point of greatest thickness (the optical center) often have zero optical power and low prism imbalance at 20° eye saccadic angles, whereas similar constant wall thickness lenses, There is negative optical power and relatively higher prism imbalance. Others, including Montesi, Jannard, Tackles, and Houston et al., make claims specifically for noncorrective lenses characterized by progressively thinning thickness.

In an apparently contrary view, Davis and Waido claim a noncorrective integral lens of "substantially all uniform thickness." They state that the purpose of the development is "to provide improved sunglasses and safety goggles having a relatively uniform thickness throughout without sacrificing optical performance". In particular, the design task is to correct for unwanted thinning of the lens in the outer curvature zone and to avoid any need to manufacture an unnecessarily heavy lens. Each of these designs disclosed in U.S. Patent No. 5,604,547 has been analyzed and the corresponding lenses have been found to have a gradually thinning thickness from the optical center across the field of view to the lateral curvature, in which region the lens wall thickens locally . In the same region, there is a consequent negative refractive error. Therefore, the content disclosed by this patent does not contradict the prior knowledge.

表1。非矫正镜片佩戴时，正面视线折射误差和棱镜误差的一些指标。The design of non-corrective lenses has been greatly simplified by the industry's focus on far-field visual quality in forward gaze. Optical testing is usually performed with a telescope aligned on the geometric axis, evaluating the optics in frontal view while worn. Tilt refractive errors, which are important to ophthalmic lens design, are often overlooked in the analysis of noncorrective lenses. Industry standards usually only quote tolerances for refractive and prismatic errors in the "worn" position. See Table 1 below.

Table 1. Some indicators of refractive and prismatic errors in frontal vision when noncorrective lenses are worn.

These tolerances allow for significantly different lens characteristics in oblique fields of view relative to base curve, material, and lens center thickness. The prior art layouts and devices described above all result in placing the optical axis of the lens in a space that does not coincide with the frontal line of sight. The two vectors can intersect in some plane, they can be strictly parallel, or they can be oblique. All of these arrangements lead to aberrations for simple object fields that are asymmetric to monocular rotation, increasing the magnitude of the tilt error experienced. It also subjects the wearer's left and right eyes to a specular aberration field, introducing binocular parallax to lateral movement. These are fundamental optical requirements in far-field vision, and this parallax is an obvious shortcoming of current designs. Ophthalmic lenses, on the other hand, are conventionally placed in front of the eye so that the optical axis is closely aligned with the frontal line of sight. The design of the tilt field should be basically rotationally symmetric to the monocular, and there should be basically no binocular parallax in the lateral rotation and vergence movement, unless required by the scheme.

Therefore, what is highly needed is the design of methods and devices by which an aesthetically pleasing and usefully shaped non-corrective lens is presented to the wearer to fit the shape of the face to achieve: The wearer's frontal line of sight is substantially aligned, or: the field of view is symmetrical to the monocular rotation, and preferably: both can be achieved. Given the state of the art in the art, it should be expected that lenses satisfying our purposes exhibit unusual physical characteristics, especially in the conformity of their surfaces. An embodiment of a pair of lenses according to the present invention is shown in FIG. 2 .

Reshef et al. describe highly curved non-corrective goggles with spherical surfaces (under 35mm radius) and tapering thickness (U.S. Patent 5,094,520). Applicants have also developed novel solutions for lenses, sun lenses, and goggles that feature sharply curved surfaces (~16 to 18D) that are nearly spherical and concentric with the centroid of the eye's rotation. These purposes are specified in U.S. Patent 6,142,624 of Sola Internatonal, the entire disclosure of which is incorporated herein by reference. This type of lens departs substantially from the conventional, relatively flat lens shape. However, the shape of such lenses is based on the generally spherical reference surfaces that have been used, and their optical properties in tilted fields are sensitive to lens position errors.

Sola Internatonal has developed improved aspheric solution lenses for face wrap frames as described in their US Patent 6,361,166, the entire disclosure of which patent is incorporated herein by reference. Sola Internatonal has developed other novel optical lenses suitable for use in face wrapping or protective goggles. These lenses are described in US Patents 6,334,681 and 6,454,408 to SolaInternatonal, the entire disclosures of these patents are incorporated herein by reference. These applications describe close-fitting scheme shields, visors, or dual-lens scheme sunglasses whose physical form is obtained by forcing the curvature of the Rx lens to change locally, especially in the wearer's forward field of view, so that A significant departure from the conventional (quadratic) conical form is also achieved by employing a significant shape asymmetry between the horizontal and vertical meridians of the lens. However, these surface forms lack a complete and comprehensive definition, making it difficult to optimize the lens appearance and wide field of view function from the wearer's point of view. The configuration of lens surfaces is mathematically complex, even for lenses with simple axial symmetry. Also, at the limit of the wearer's field of vision, the resulting oblique optical errors may be less desirable than those of more classical configurations, referring to standard optical surfaces according to the quadratic type, with or without Aspheric correction of surfaces. technical noun

Some of the technical terms and descriptors used in the discussion of the invention below either have a specialized meaning in this text or are unfamiliar in the field of non-corrective lens design. For the sake of clarity and understanding, we enumerate those terms and their meanings used below in this article. Mathematical terms and meanings, follow CRC Concise Encyclopedia of Mathematics, by E.W. Weisstein, Chapman&Hall, New York 1999. Mathematical terms and principles, follow Optical Society of America Handbook of Optics, Volume I, Part 1, M.Bass (Ed), Second Edition, McGraw Hill, New York 1995, or The Principles of Ophthalmic Lenses, M.Jalie, Fourth Edition, London 1994.

The term "optical lens unit", in a context commensurate with the specific embodiments of the present application, refers to a completed optical or spectacle lens, a semi-finished lens that needs to be trimmed and assembled into a frame assembly, or to provide left and right lenses and suitable for A light-transmitting article that is ultimately formed as an integral optical unit or shield for non-corrective goggles.

The term "monocular field of view", in a context commensurate with the specific embodiments of the present application, refers to the portion of the solid angle that the human eye is capable of receiving and discerning an image from in front of the wearer. It is generally believed that the temporal (temporally) can be extended to about 90°, while the nose can reach 60°, the lesser is 70°, and the better is 50°, depending on the individual face structure, lighting, and the size of the stimulus , duration, and color.

The term "binocular field of view", in a context commensurate with specific embodiments of the present application, refers to the overlapping region of the left and right monocular fields of view, separated from the center by the wearer's median plane.

The term "version movement", in a context commensurate with specific embodiments of the present application, refers to binocular tracking in the object plane in which both eyes make the same movement in the same direction.

The term "vergence movement", in a context commensurate with the specific embodiments of this application, refers to binocular tracking at different distances from the observer, in which the two eyes make identical movements in opposite directions.

The term "visual fixation field", in a context commensurate with the specific embodiments of this application, refers to the area on the surface of the lens defined by the collection of points on the lens surface that when the wearer fixates on an object in the central plane, he or she The point where the line of sight intersects the lens surface. This field of view typically accompanies the eye rotation by about 40 to 50°.

The term "peripheral field of vision", in a context commensurate with the specific embodiments of this application, means the area on the surface of a lens defined by a collection of points that are defined when the wearer is generally looking at objects in the frontal line of sight. , the point at which light rays entering his or her pupil intersect the surface of the lens. The eyes are usually static, exhibiting only small rotations.

The term "quadratic standard form" refers to any of the 17 general standard form quadratic surfaces in a text commensurate with the specific embodiments of the present application, as shown in CRC Concise Encyclopedia of Mathematics, by E.W. As illustrated in Weisstein, Chapman & Hall, New York 1999, p.1485.

The term "standard optical surface of the quadratic type", in the context commensurate with the specific embodiments of the present application, means any biconvex or plano-convex surface that is part of a cone, cylinder, sphere, sphere, or quadric The generative family of ellipsoids or toruses formed by the rotation of an ordinary conic arc about an axis, which may be a normal to a surface, or a line parallel to and away from a tangent to a surface. The surface is continuous up to at least the third derivative and has explicit symmetry about at least one reference normal vector.

The term "axis of symmetry", in a context commensurate with the specific embodiments of the present application, refers to the normal vector with respect to which the lobes of the surface have at least reflective symmetry and the sagittal centers of curvature of individual surface elements are located at on the normal vector.

The term "vertex", in a context commensurate with a particular embodiment of the present application, refers to the point of intersection of a surface with its axis of symmetry. The term "apex" we use to mean the most forward point on the lens surface when worn.

The term "optical axis", in a context consistent with the specific embodiments of the present application, refers to the axis where the centers of sagittal curvature of the two surfaces lie. It forms when the axes of symmetry are collinear. The lobe of a surface is usually defined in cylindrical coordinates (r, □, z), where the origin of the coordinates is the vertex of the surface, the optical axis is the axis Oz, and the radial distance r is the tangent plane passing through the vertex of the surface, i.e., the "vertex measured in the plane". The orientation distance z(r) from the vertex plane to the surface, also known as the "curvature" of the surface. The lenses according to the invention are preferably worn in front of the wearer so that the optical axis of the lens substantially coincides with the wearer's frontal vision for far field vision.

The term "optical center", in a context commensurate with particular embodiments of the present application, means the point where the optical axis intersects the front surface of the lens. It can actually be determined as the position of the null optical prism of the lens, while the orientation of the optical axis can be found by identifying the normal vector of the plane tangent to the surface at that position.

The term "sagittal center of curvature", in context consistent with specific embodiments of the present application, refers to the center of curvature of rotation defined by the inclination of a surface in any meridian. It is located on the concave side of the surface and the distance from the vertex is given by $R=z+\frac{r}{z^{\′}}$ here $z^{\′}\≡\frac{\∂z}{\∂r}$

The term "standard optical reference surface", in a context commensurate with the specific embodiments of the present application, refers to a quadratic surface, including aspheric correction terms if present, which scales with tangential and sagittal surface curvature as Characterized by monotonic variation away from the axis of symmetry, with no local maxima or minima.

The term "significant deviation from a standard optical reference surface", in a context commensurate with the specific embodiments of this application, refers to surfaces with quadratic and higher order components, including aspheric correction terms if present , the entire surface is characterized by a maximum value of at least the tangential or mean curvature at an oblique position along at least one meridian.

The term "significant deviation from the quadratic standard optical reference surface in terms of surface curvature", in a context consistent with the specific embodiments of the present application, refers to the tangential curvature and/or sagittal curvature of each surface element, when leaving The symmetry axis first exhibits an increasing difference, and then a decreasing difference when moving further away from the symmetry axis.

The term "significant deviation in surface astigmatism from a standard optical surface", in a context commensurate with the specific embodiments of the application, means that the tangential and sagittal surface curvature deviations are large enough to introduce large optical astigmatism distortion.

The term "static prism", in a context commensurate with the specific embodiments of the present application, refers to the sensory prism that enters his or her pupils when the wearer gazes at an object in the straight-ahead position and the eyes do not move. The prism component of the sampled ray. This prism is often associated with peripheral vision.

The term "spin prism", in the context commensurate with the specific embodiments of the present application, refers to the prismatic component of the sampled light rays that are perceived along his or her line of sight when the wearer rotates his or her eyes. This prism is usually associated with about 40 to 50 degrees of eye rotation.

The term "sagittal depth", in a context consistent with specific embodiments of the present application, refers to the distance between the surface tangent plane at the anterior apex of the lens and the point of the anterior surface closest to the temporal edge. The term "difference in sagittal depth," as we use it, refers to the difference between the sagittal depth at the point on the anterior surface closest to the temporal margin, and the point on the anterior surface closest to the nasal margin.

The term "mean through power" is the average of the through power along one principal meridian along a given line of sight and the mean through power along the other principal meridian along that line of sight. "Mean Power Error" (MPE) is the arithmetic mean of the actual error in the passing power of the lens within the principal meridian along a given line of sight compared to the required refractive correction. "RMS Power Error" (RMSPE) is the root mean square error of the actual lens passing power within the principal meridian along a given line of sight compared to the required refractive correction. The term "substantially zero average passing optical power", in a context consistent with the specific embodiments of the present application, means that the average passing optical power is in the field of vision of the wearer, in the range of -0.50D to +0.125D, preferably The best is -0.30D to +0.05D, more preferable is ±0.09D, and most preferable is ±0.05D.

The term "surface Q-value", in a context commensurate with specific embodiments of the present application, refers to a measure of the degree to which a curve or surface can be described as quadratic. For curves, it is determined by the first and second derivatives along the length of the curve. For surfaces, it is determined by the tangential and sagittal curvatures, or by the radius of curvature.

The terms "eccentricity" and "shape factor", in the context commensurate with the specific embodiments of the present application, refer to a standard measure of the degree to which the section of a cone deviates from that of an ideal circle.

The term "surface curve" according to the preferred embodiment of the present invention, in the context commensurate with the specific embodiments of the application, refers to a plane curve which has: an axis of symmetry; relatively low curvature in the center and relatively high side ends curvature; the curvature at the intermediate position between the central part and the side ends is locally maximum, and it is also characterized in that the normal vectors of the curve are mutually angularly directed towards each other in the two opposite regions of its maximum tangential curvature skewed.

The term "osculating surface", in a context commensurate with particular embodiments of the present application, means a pair of surfaces that are co-tangent to each other on the closed curves where they intersect. These two surfaces have equal sagittal curvatures at their intersection.

Contents of the invention

Today, most corrective and non-corrective lenses are built with a pair of quadratic surfaces whose geometry is derived in some way from the rotation or translation of circular or conical sections. In the field of single vision lens design, there is very little experience with the use of surfaces that deviate significantly across the wearer's field of view from standard quadratic forms. Even with experience in this area, there is still a lack of comprehensive design methods by which the required surface forms can be established. Thus, if a face-wrapping non-corrective goggle is provided that deviates substantially from a standard quadratic surface across the lens aperture, and wraps the face both horizontally (near the eyebrows) and vertically, a wide range of styles can be chosen, It would be a significant advance in the art to maximize the interest of the wearer. It would be an even more significant advance in the art if the lenses could match the optical properties of secondary lenses over the entire field of view, if necessary, from the center to the periphery of the field of view.

Another object of the present invention is to overcome, or at least mitigate, the errors that occur with prior art non-standard surfaces in oblique fields of view as well as in peripheral fields of view. It is also an object of the present invention to provide superior optical properties as measured by a figure of merit function; to simplify the mathematical structure of the surface; and to facilitate the surface adjustments necessary to provide such improved oblique optical properties. Visualization of Surface Curves

Prior art non-corrective surfaces are generally convex shapes, or shapes very close thereto, created by rotating the conical section about the axis of symmetry of the cone, or about an axis perpendicular to the axis of symmetry. For cylindrical, conical, and toroidal lens forms, the axis of rotation is positioned perpendicular to the wearer. The axis of rotation for lenses whose surfaces are elliptical, parabolic, hyperbolic, and spherical may be horizontal or parallel to the wearer's frontal line of sight when worn. The conical section is easy to imagine, and belongs to the range of shapes formed by the intersection of an upright cone and a plane.

The surface of current interest is generated by curves that do not belong to any of the above categories. They cannot be classified in a strict mathematical form, except in very few special cases. However, their general properties are easy to imagine. Figure 2B shows a perspective view of a cylindrical dome having a circular base of symmetry in mid-section and a mid-section of substantially flat vertical section. The curve of intersection produced by the intersection of the base-sloping plane with the dome is strongly influenced by the vertical curvature of the dome and the height of the intersection. These curves have an axis of symmetry 3-3' and have the shape shown in the set of curves (a) of Figure 2B. They necessarily have a non-quadratic form characteristically different from the elliptical shape that an oblique crossing with a right cylinder would find elliptical, such as that shown in the set of curves (c) in Fig. 2B. According to an embodiment of the present invention, these curves and other similar features, rather than conic sections, are used to create lens surfaces.

The optical surface that deviates from the regular form is described by the surface height relative to the vertex plane, and is described by the Taylor series of the radial distance item from the vertex. Therefore, the aspheric surface can be regarded as a spherical surface and the deviation from the spherical surface is treated by convention. The spherical surface An asphere that matches the curvature of this asphere at the vertex, rather than a conic, can be treated as a cone matched at the vertex and a deviation from the cone. See, eg, Optical Society of America Handbook of Optics, Volume I, Part 1, M. Bass (Ed), Second Edition, McGraw Hill, NewYork 1995 p.1.39. It is assumed here that the deviation is small and that the surface height curve occurring along the surface meridian is either an ordinary circle or an ordinary cone. This characteristic of the surface curve can be tested by the variation of the physical curve and the variation of the involute of the curve, which is the locus along the center of tangential curvature of the physical curve unit.

The involute of a circle is a point on the unique center of curvature. An ellipse obeying the equation $\frac{x^2}{a^2}+\frac{{(\mathrm{the\; y}-b)}^2}{b^2}=1$ There is the Lamé curve involute (ax) ^2/3 + (b(yb)) ^2/3 = c ^4/3 here $c\&equiv;\sqrt{a^2-{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="H2009100021083E00011.png,H2009100021083E00031.png"\; state="\{\{state\}\}">b</figure-callout>}}^2}\&equiv;\mathrm{ae}$ and $p\&equiv;{\left(\frac{a}{b}\right)}^2$ An ellipse with shape factor p = 4 (eccentricity e = 0.87) and its involute are drawn as curves (c) and (cc) in Fig. 2B. Note that the cycloid has four cusps and is symmetrical about both the minor and major axes of the ellipse.

The involute of any curve can be determined by the trajectory analysis of the tangential curvature center, and the coordinates of the involute to the moving point (x, y) are (X, Y), where X=x-{1+(y') ² }y′/y″ and Y=y+{1+(y′) ² }/y″

Therefore, we find that the curve (a) in Fig. 2B has an involute as shown in (aa). If a portion of a circle merges with its close circle, as in curve (b) of Fig. 2B, then its involute takes the form of curve (bb). This is an irregular circular cycloid with a toothed apex on the minor axis of the surface curve, corresponding to the outer region of the curve close to a circle. A pair of horizontally configured cusps correspond to the maximum positions of the tangential curvature, as they are in the case of an ellipse. But this situation occurs without the formation of vertices, which is necessary for ellipses, because the inclination of the curve remains limited in the region of highest curvature, and the normal vector is skewed towards the minor axis rather than perpendicular to it (i.e., φ < π /2). See Figures 2C and 2D.

One surface embodiment of the present invention, illustrated in Table 4C below, has an extended region in which the representative surface curve approximates a cone with an outer region of maximum tangential curvature. The surface curve and its involute are drawn in Fig. 2C(b). The involute shape, that is, curve 1 of FIG. 2C(c), is very close to the involute of an ellipse in the inner region, that is, curve 2 of FIG. 2C(c), where a=34.5mm, b=9.25mm. This fact indicates that the surface curves from its center to the maximum tangential curvature, generally elliptical, with shape factor p = 13.9 and eccentricity e = 0.963. The ellipse thus derived closely matches the physical curve in the aperture. See Figure 2C(a).

Such a high eccentricity value on the inside of the surface curve is derived from the design idea of slowly changing the curvature around the apex and then imposing a rapid rate of change on the outside curvature. This phenomenon is not unique to vertex curvature itself. A high eccentricity ellipse has a>>b and can be likened to an expanding arc with an abrupt and shallow outer curvature. Various surfaces according to embodiments of the present invention, as described in Table 3A below, are constructed using a pair of 2nd and 4th order polynomial coefficients. It has a very sudden abrupt change in lateral curvature starting with dimensions a = 10.95 mm and b = 0.28 mm, corresponding to eccentricity e = 0.9997 (or p = 1530). Its characteristics are drawn in Figure 2D. The use of such high eccentricity curves is impractical unless some measures are taken to prevent the surface curve from turning inward from the front plane over small distances. Our method makes the curve spiral outward from the ellipse in the lateral end region.

Accordingly, in an aspect of an embodiment of the present invention there is provided a lens having inner and outer convex surfaces with a thickness therebetween, wherein at least one of said surfaces has a curved form in cross-section at least along a horizontal meridian such that The section curve: has a central portion and lateral ends spaced from the central portion, has an axis of symmetry; curvature increases from the central portion to the lateral ends, and; midway between the central portion and the lateral ends, has a maximum curvature value.

In a more preferable aspect: the shape of the curve in the central area is close to an ellipse, and; the curve in the side end areas is helically spiraling outward from the ellipse.

In a preferred aspect, the involute in the central region of the curve approximately corresponds to an ellipse with an eccentricity greater than about e=0.95 (shape factor about p=10); the involute of the curve has a pair of regions of maximum tangential curvature The corresponding horizontal cusp, the normal vector from the curve to said cusp, is skewed toward the minor axis of the curve at an angle other than 90°, and the involute near the side end of the curve to shift from the horizontally shifted cusp to Branch points with minor axis extensions on the concave side of the curve are featured.

Preferably, the normal vector of the curve at the position opposite the highest tangential curvature is deflected to the axis of symmetry by an angle less than φ = 75 degrees, more preferably less than 60 degrees, and most preferably less than 45 degrees. In a preferred aspect, the involute in the central region of the curve corresponds approximately to an ellipse having an eccentricity of about e=0.96 (shape factor of about p=14) or greater. Further Aspects of the Disclosed Embodiments

A convex sheet surface according to one embodiment of the invention may be produced by rotation of symmetry arcs of the general type described above about their own symmetry axes, or about a coplanar axis perpendicular to the curve symmetry axes and located at the rear of the surface elements. In another arrangement, the horizontal meridians of the lens surface may be surface curves according to embodiments of the invention, while the vertical curves may have any suitable form.

In a second aspect of an embodiment of the present invention, there is provided an optical lens unit comprising a first surface with an axis of symmetry; and a second surface with a complementary curvature to the axis of symmetry; In astigmatism, exhibiting significant deviations from the quadratic standard optical reference surface; deviations of surface astigmatism starting locally around the apex on the lens aperture, generally extending across the entire surface, and forming the largest surface image on the lens surface an annular region of divergence; and the first and second surfaces, in combination, define an optical center, an optical axis, and an optical zone exhibiting substantially zero mean passing power.

The surface of the lens according to the present embodiment of the present invention is preferably designed such that the tangential and sagittal curvatures of the surface converge in the transverse direction so as to define an umbilicus on the surface within or near the peripheral region of the lens aperture. Preferably, the surface tangential power is generally higher than the sagittal curvature across the lens aperture and the lens surface is oblate. The average focal power of the lens surface can be changed by 1.0D in a 40° field of view, preferably by 3.0D, more preferably by 5.0D in a 50° field of view, and the most preferable is , can change 6.0D in 50° field of view.

Preferably, there is a sloped region of maximum astigmatism within or near the edge of the wearer's field of gaze. Preferably, the surface astigmatism drops to zero in the peripheral region of the lens aperture. The astigmatism of the lens surface can vary by 1.0D, preferably by 3.0D in a 40° field of view, more preferably by 5.0D in a 50° field of view, and most preferably in a 50° field of view Change in 6.0D. Because the tangential and sagittal surface curvatures converge to the umbilicus near the periphery of the lens aperture, the surface astigmatism will decrease in the peripheral region of the lens aperture. Preferably, the surface astigmatism is less than 3.0D over a 75° field of view, more preferably less than 2.0D over a 75° field of view, and most preferably less than 1.0D.

Preferably, lenses according to the present embodiment of the invention will exhibit a sagittal depth of at least 10mm, more preferably 15mm, and most preferably 20mm over a radial distance of 40mm. Preferably, the lenses according to the invention enclose the wearer's entire field of gaze, preferably at least over a field angle of 60° relative to the center of rotation of the eye, and most preferably in the range of 70 to 75°.

Accordingly, in a third aspect of an embodiment of the present invention, an optical lens is provided, comprising a first surface with an axis of symmetry; and a second surface with a complementary curvature of the axis of symmetry; in surface astigmatism exhibiting significant deviations from a quadratic standard optical reference surface; deviations in surface astigmatism starting locally around an apex on the lens aperture and generally extending across the entire surface by means of maximum, and form an outer band of low surface astigmatism at the periphery of the lens, the lens surfaces are approximately umbilicus-shaped around the periphery of the lens, and; the first and second surfaces, combined, define the optical axis and exhibit substantially zero mean passing focus degrees of optical band.

Obviously, the optical lens according to the present invention allows the manufacture of non-corrective lenses with surfaces that are completely radially shaped relative to standard ophthalmic lenses, but the invention still provides a lens body having an average passing power of Within normal ophthalmic standards, the tilt from the optical axis to the field of gaze boundary is relatively constant. This deviated surface can exhibit significant optical distortions, such as a high degree of surface astigmatism over a large portion of the lens aperture. However, refractive mean power, RMS power, and astigmatism errors, from the optical axis to oblique to the field-of-view boundary, are still small within normal ophthalmic standards.

We have found that when optimizing the optical properties of a non-corrective lens limited by the surface form described herein, the lens thickness shows no signs of gradual thinning or thickening in the aperture corresponding to the approximate field of gaze when worn. The appearance of this phenomenon is different from that expected for a quadratic surface, without the accompanying development of negative refractive power errors or enlarged prismatic errors. See, eg, Houston et al. (U.S. Patent 5,648,832, 5,689,323, and 6,010,218) and Conway (U.S. Patent 5,555,038). These lenses exhibit optical errors across a 50° field of view that are indeed lower than true spherical lenses with equivalent sagittal depth at the outer edge. Lens thickness generally has a shallow minimum on the optical axis that deepens slightly in the oblique field and persists to or beyond the edge of the field of view before tapering off in the peripheral region of the lens.

In yet another aspect of an embodiment of the present invention, a pair of non-corrective lenses is provided in a face-wrapping frame or structure that positions the lenses accurately in front of the wearer such that the frontal line of sight substantially coincides with the optical axis of the corresponding lenses , the lenses rely on their physical shape and sagittal depth to conform to the shape of the face and close at least the forward field of view, wherein each lens is characterized by the following: a first lens surface having an axis of symmetry; and a second lens surface having a complementary curvature and axis of symmetry Lens surface; at least one surface exhibiting a significant deviation in surface height from a quadratic standard optical reference surface; deviation in surface height locally around the apex on the lens aperture and generally extending across the entire surface; deviated surface A sloped region exhibiting high astigmatism, and optionally an outer band of low surface astigmatism in the periphery around which the surface region is approximately umbilicus-shaped; the first and second surfaces combine to define the optical axis and the optical a band in which the lens thickness is substantially constant (maintained without thinning) across the aperture corresponding to the field of fixation when worn; no significant refractive or prismatic errors in the frontal line of sight when worn; and; when the eye Tilt-refractive power errors remain small and symmetrical when rotated across the field of view and into the periphery of the field of view.

Preferably, the oblique refractive power error and the prism error vary symmetrically at least over a pair of orthogonal meridians of the field of view.

Preferably, the average passing power of the lens on the frontal line of sight is in the range of -0.25 to +0.125D, more preferably in the range of ±0.09D, and most preferably in the range of ±0.05D. Desirably, the refractive and prismatic errors on the frontal line of sight are at least as small as 0.125D, more preferably less than 0.09D, and most preferably less than 0.05D.

Optical errors generally increase in oblique fields and have varying degrees of acceptability to the wearer depending on their position within the field of view. Preferably, the average pass power in the oblique field is in the range -0.50 to +0.125D, more preferably in the range -0.30 to +0.05D in the aperture corresponding to the near fixation field, and most preferably is in the aperture, in the -0.125 to +0.05D range. Preferably, the magnitude of the oblique refractive error is less than 0.60D, more preferably less than 0.25D in the aperture corresponding to the near fixation field, still more preferably less than 0.125D in said aperture, and most preferably Less than 0.05D in the pore size.

Preferably, the average angular rate of increase in magnitude of both rotational and static effects in the optical prism is at least as slow as 40 mD/degree of field of view, preferably slower than 25 mD/degree, more preferably, As slow as 12.5 mD/degree across the aperture substantially corresponding to the field of gaze, and preferably as slow as 20 mD/degree within the angular field of 30° around the frontal line of sight. Still more preferably, the average rate of change in magnitude of the static optical prism remains at least as slow as 80 mD/degree, and even more preferably less than 40 mD, within the outward peripheral field of view from about 50° to 80° field angle /degree, and the most desirable is less than 25mD/degree.

These and other objects and features will be apparent from this application including the accompanying drawings. One or more objects and advantages (but not necessarily all) can be achieved by the various aspects and embodiments of the invention described herein.

Description of drawings

Figure 1A depicts a pair of prior art face-wrapping spectacles, where aesthetic requirements are achieved by moving the lens optical axis 1-1' upwardly at the nose and relative to the wearer's frontal line of sight 2-2'.

figure 2

Figure 2A: Draws a front perspective view (viewed from above, directly in front, and below) of a lens according to one embodiment of the present invention. These lenses give the geometry necessary to fit the shape of the face while keeping the axis collinear with the frontal line of sight when worn.

Figure 2B: Drawing the cylindrical dome and its oblique intersection with the skewed plane yields an intersection curve with an axis of symmetry 3-3'. By varying the skewness of the planes, a family of such intersecting curves is produced, as shown in the set of curves (a) on the figure, and the involutes of the accentuated curves, as shown in curves (aa). A closed curve (b) formed by merging part of the curve (a) with its close circle has an involute (bb). A family of nested ellipses is drawn on the figure for comparison with the set of curves (c), while an ellipse with shape factor p=4 and its involutes are drawn as curves (cc).

Figure 2C: Sectional properties through the surface meridian of an embodiment of the invention are plotted and described in Table 4C. The surface curve and its involute are drawn as part (b) of the figure, while part (c) of the figure shows the involute curve (1) and the pseudo Conjoint ellipse (2) involute. The physical curve (solid line) is used for comparison with the ellipse (dashed line) derived in part (a) of the figure.

Figure 2D: Sectional properties through the surface meridian of an embodiment of the invention are plotted and described in Table 3A. The surface curve, and its involute, are drawn as part (b) of the figure, while part (c) of the figure shows the involute curve (1) and the curve (1) on the surface

Figure 3 illustrates the prior art integral lens described by Davis and Waido.

Figure 3A: Draw an elliptical monolithic lens with apex curvature 3.78D and eccentricity e = 0.866 (shape factor p = 4.0). Its refractive properties are asymmetric to the rotation of the eye on either side of the frontal vision.

Figure 3B: Draw a nearly parabolic overall lens form with higher order coefficients producing temporal curvature. It is asymmetrical to the rotation of the eye on either side of the frontal sight, and the curvilinear involute (1) does not resemble the involute of any regular form curve. The closest elliptical involute (2) has a shape factor of p = 4.0, but is not a satisfactory match.

Figure 4 depicts a spherical non-corrective double lens goggle of a prior art design.

Figure 4A: Draw a spherical lens with a 9D basic curve whose optical axis is collinear with the frontal line of sight.

Figure 4B: Draw the 8D basic curve lens that wraps/closes the face obtained according to the method of Houston et al. It is a spherical lens with an axis offset of 15mm in the analysis plane. The refractive properties are asymmetric to the rotation of the eye on either side of the front view.

Figure 5 depicts the properties of non-corrected surfaces having a spherical apex and a lateral umbilicus (Fig. 5A), one of which has a lateral umbilicus (Fig. 5B), in accordance with an embodiment of the present invention. The properties of the surfaces are summarized in Tables 3A and 3B.

Figures 6A and 6B illustrate the properties of two surfaces formed mathematically as a weighted combination of a pair of spherical surfaces with different curvatures. Both are umbilical in the outer zone and have bulbous points at the apex. Their properties are summarized in Tables 4A and 4B.

Fig. 7 compares the interior angle of the incident characteristic of the surface shown in Table 4A relating to the center of rotation of the wearer's eye, with that of a spherical surface of equal surface height, at a radius of 35 mm (Fig. 7A), and with an ellipsoid Equal sagittal depths and those with eccentricity e=0.75 were compared (Fig. 7B). The properties determined with reference to the pupil diaphragm of the wearer's forward gaze are plotted in Figures 7C and 7D.

Figures 8A and 8B plot the optical properties of a pair of 4th order rotationally symmetric non-corrective lenses with curvatures at the top of the axis of symmetry of 1.75 and 3.5D. The set of front surface parameters is given in Table 5 (Type 5B and Type 5C).

Figures 9A and 9B plot the optical properties of a pair of 4th order rotationally symmetric non-corrective lenses with curvatures at the top of the axis of symmetry of 3.5 and 5.0D. The set of front surface parameters is given in Table 5 (Type 5D and Type 5E).

Figure 10 depicts the optical properties of a 4th order non-corrective lens having a donut-shaped apex with a curvature of 3.5D in the horizontal direction and a curvature of 0.0D in the vertical direction.

Fig. 11 draws the contour map of the optical properties of the lens in Fig. 10 in the monocular 40° rotation range, and the contour map of the physical properties of the lens within the 40mm aperture of the lens. Isolines are spaced as follows: optic prisms, in 0.25D steps; refractive powers, in 0.025D steps around a field of ±0.005D; lens prisms, in 1D increments; surface height, in steps around a field of -0.25mm Amplitude 5mm; lens thickness step +0.025mm relative to center; and surface astigmatism, step 4D around a field of 1.25D.

Fig. 12 draws the contour map of the optical properties of the lens in Fig. 13 in the monocular 40° rotation range, and the contour map of the physical properties of the lens within the 40mm aperture of the lens. Isolines are spaced as follows: optic prisms, in 0.25D steps; refractive powers, in 0.025D steps around a field of ±0.005D; lens prisms, in 1D increments; surface height, in steps around a field of -0.25mm Amplitude 5mm; lens thickness step +0.025mm relative to center; and surface astigmatism, step 4D around a field of 1.25D.

Figure 13 depicts the optical properties of a 4th order non-corrective lens having a donut-shaped apex with a curvature of 3.5D in the horizontal direction and a curvature of 7.0D in the vertical direction.

Figures 14A and 14B plot the optical properties of a rotationally symmetric uncorrected lens having the front surface described in Table 4C and optimized according to two figure of merit functions.

Figure 15 plots the optical properties of a non-corrective lens whose front surface is formed by a mathematical combination of two ellipsoids having an eccentricity e=0.71 in a plane perpendicular to the optical axis.

Fig. 16 draws the contour map of the optical properties of the lens in Fig. 15 in the monocular 40° rotation range, and the contour map of the physical properties of the lens within the 40mm aperture of the lens. Contours are spaced as follows: optical prisms and refractive powers, in 0.10D steps; lens prisms, in 0.25D increments; surface heights, in 2mm steps; lens thickness relative to 2mm centers, in +0.05mm steps; and Surface astigmatism, stride 4D around a 1.0D field.

Detailed ways

For lenses according to embodiments of the present invention, the first and second surfaces are continuous at least to the third derivative and exhibit no visible discontinuities, more specifically no optical discontinuities. Preferably, the lens surfaces are covariant surfaces such that the optical zone exhibits substantially zero mean passing power. Lenses according to embodiments of the invention are worn in front of the wearer with their optical axes substantially coincident with the frontal vision of each eye. The lens is characterized by an optical zone in which the lens thickness varies smoothly, though not necessarily linearly, across an aperture equal to the wearer's field of gaze from its center to its edges, with relatively greater gains in the intermediate zone , maintained at an aperture approximately corresponding to the field of fixation when worn, and then, at its outer extremities, tapered to a thinner thickness without the tendency for unwanted negative refractive powers to develop therein. Definition of lens surface

Lens surfaces are designed, often according to specific properties of their shape, such as the geometry that wraps around the wearer's face, or the inclination angle that defines the fit to the shape of the wearer's face, and also defines the reflective properties of light visible to both the wearer and the observer properties. Therefore, a mathematical procedure is required to define the physical form of the surface detailed above with specific curvature properties. Higher-order and mixed-order closed surfaces are generally involved in these designs. is a rotated egg or oval as described in CRC Concise Encyclopedia of Mathematics, by E.W. Weisstein, Chapman & Hall, New York 1999, p.1293. Except for a few special cases, they are not strictly classified mathematically, but can be obtained through many mathematical ways, as we illustrate with examples below.

A standard quadratic ophthalmic surface, most commonly a surface produced as a conic section revolution figure. The mathematics of such conic sections is of course very familiar and is illustrated, for example, in Jalie's standard textbook: The Principles of Ophthalmic Lenses, M. Jalie, Fourth Edition, London 1994, Chapter 21. A feature that ties all surfaces of this form together is the relationship between the first and second derivatives of the surface height z(r), namely ${\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="H2009100021083E00011.png,H2009100021083E00031.png"\; state="\{\{state\}\}">R</figure-callout>}}^2=z^{\&prime;\&prime;}{\left(\frac{r}{z^{\&prime;}}\right)}^3=\frac{r_S^3}{r_T}$ or ${\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="H2009100021083E00011.png,H2009100021083E00031.png"\; state="\{\{state\}\}">R</figure-callout>}}_2=\frac{K_T\left(r\right)}{{\left[K_S\left(r\right)\right]}^3}$ Here R is the apex radius of curvature; r _T and r _S are the tangential and sagittal radii of curvature; K _T (r) and K _S (r) are the tangential and sagittal curvatures. Thus, if the surface is quadratic, the "implied vertex radius" R(r), calculated from the derivative at any point of the partial curve, remains constant over any part of the surface. If the surface is non-quadratic, the implied vertex radius will increase or decrease depending on whether the surface is prolate or oblate. We name the ratio of the implied vertex radius to the true vertex radius as the "Q value" of the surface, Q(x)=R(x)/R(0).

Therefore, in another aspect of the present invention, there is provided an optical lens comprising a first surface having an axis of symmetry; and a second surface having a complementary curvature to the axis of symmetry; Significant deviation from the standard optical reference surface of the quadratic type; a deviation in the height of the surface beginning locally at the lens aperture and generally extending across the entire surface; the surface of this deviation, as the inner intimate surface of the standard optical form and the outer intimate surface of the standard optical form Formed by an inscribed surface between , the standard optical form of this outer intimate surface, has a different apex radius than the first; the tangential and sagittal radii vary across the deviated surface such that Q(r)≡r _S ³ /r _T R(0) ² is non-constant, equal to 1 at the vertex, and changes at least 0.25 away from the axis of symmetry, where r _T and r _S are the tangential and sagittal radii of curvature, respectively, and R(0) is the vertex radius of curvature ; the corresponding tangential and sagittal curvatures K _T and K _S vary across the off-surface, making Q(r)≡K _T (r)*[K _S (0)] ² /[K _S (r)] ³ non-constant , equal to 1 at the vertex, and change at least 0.25 away from the axis of symmetry, where K _S (0) is the vertex sagittal curvature; deviating surfaces may optionally exhibit an outer band of low surface astigmatism in the perimeter where wherein, the surface is approximately umbilicus-shaped; and the first and second surfaces, in combination, define an optical axis and an optical band exhibiting substantially zero mean passing power.

Preferably, the inner oscillating surface is a conical surface rotated relative to the optical axis, while the apex of the deviating surface is umbilical and is a spherical point. The inner occlusal surface may be a toric surface. Preferably, the toric surface is circular in all meridians. Preferably, the inner and outer intimate surfaces have the same rotational symmetry about a common axis.

It is desirable that the surface "Q-value" be approximately constant in the central region of the lens aperture around the frontal line of sight when worn, and drop away from there, less than 0.75 in the peripheral field of view of the lens field angle ~ 60°, preferably less than 0.75 It is less than 0.75 in the field of gaze at lens field angle ~40°. Most preferably, the "Q-value" has a steady minimum on the umbilicus at the border of the wearer's field of vision, and/or into the peripheral vision zone.

A deviated surface will essentially exhibit oblique surface astigmatism that increases from the apex, experiences a maximum at an intermediate field angle, and then decreases toward the near-umbilical peripheral region. Desirably, the selected lens aperture will be located in the region of maximum surface astigmatism in the boundary of the field of view of the wearer. Preferably, the selected lens aperture will be located in the approximate umbilical region of the lens edge in the immediate peripheral field of view of the wearer.

A suitable rotationally symmetric oblate surface, substantially different from a quadratic surface, would satisfy the following relation $z\left(r\right)=\underset{\mathrm{no}\&Greater\; Equal;2}{\overset{m}{\mathrm{\&Sigma;}}}{A}_{\mathrm{no}}{r}^{\mathrm{no}}$ here $\stackrel{\&OverBar;}{z^{\&prime;\&prime;}{\left(\frac{r}{z^{\&prime;}}\right)}^3}<<{\left(\frac{1}{2A_2}\right)}^2$

This condition states that the polynomial form will be governed by the coefficients _An , where n ≥ 3, and that these coefficients will vary in a certain order, unlike the variation of the conical surface. The numerical index n is an integer defining the "ordinal" of the surface component. In designing the lens front surface of an embodiment of the present invention, it is sufficient to use ordinal numbers from 2 to 8, with the most important being on factors in the 3 to 5 range. Sometimes it is convenient to express this surface in the form $z\left(r\right)=C\left(r\right)+\underset{\mathrm{no}\&Greater\; Equal;3}{\overset{m}{\mathrm{\&Sigma;}}}{A}_{\mathrm{no}}{r}^{\mathrm{no}}$ here $C\left(r\right)=\frac{R}{p}[1-\sqrt{1-p\frac{r^2}{R^2}}]$

The first term specifies complete quadratic surfaces. It can be a conical surface of revolution with apex radius R and shape coefficient p, whereby the polynomial only describes the deviation from the conical surface. In this case, a centered sphere is defined by the shape factor p=1, a parabola by p=0, and a hyperboloid by p<0. Other p-values define ellipsoids. In addition, the ratio can be a torus and a general ellipsoid. If necessary, weighting functions can be used to achieve specific design goals.

Therefore, in yet another aspect of the preferred embodiments of the present invention, there is provided an optical lens comprising a first surface with an axis of symmetry; and a second surface with a complementary curvature to the axis of symmetry; at least one front surface in surface height, Exhibits a significant deviation from a quadratic standard optical reference surface; a deviation in surface height that begins locally at the lens aperture and generally extends across the entire surface; the front surface of this deviation, as determined by the polynomial surface height added to the reference surface Defined surface formation with ordinal numbers of coefficients ranging from 2 to 8; the deviated surface exhibits a sloped region of high astigmatism, and optionally an outer band of low surface astigmatism in the perimeter around which, The surfaces are approximately umbilicus-shaped, and; the first and second surfaces, in combination, define an optical axis and an optical band exhibiting substantially zero mean passing power.

In an alternative approach according to an embodiment of the present invention, a pair of quadratic surfaces C ₁ (r) and C ₂ (r) of different curvatures B ₁ and B ₂ are combined with an appropriate weighting function M(r) to give the final The rotationally symmetric surface of is of the form z(r)=M(r)*C ₁ (r)+(1-M(r))*C ₂ (r)

Any suitable weighting function can be used, as an example hyperbolic secant is used: M(r)=a*sech(r/b)

This surface merges with its outer intimate surface at the outer region and with the inner intimate surface at its top. The surface "Q-value" is 1 (unity) at the top, then leaves the axis and descends smoothly towards a constant value on the outside, which corresponds to the attained curvature ratio B ₁ /B ₂ in the two conical regions. The surface astigmatism grows rapidly away from the top and then drops smoothly to a low value in the outer region where the surface can be umbilical. This property is governed by a weighting function that must drop smoothly from 1 on either side of the coordinate origin. In the present representation, parameter b controls the general rate at which the surface changes, while parameter a sets the center value. If the center value of the weighting function is less than 1, then the apex region has an intermediate curvature defining the curvature of the two surfaces, and a relatively wider navel.

Accordingly, in a different aspect of a preferred embodiment of the present invention, there is provided an optical lens comprising a first surface having an axis of symmetry; and a second surface having a complementary curvature to the axis of symmetry; at least one surface exhibiting Significant deviations from the quadratic standard optical reference surface; deviations in the height of the surface starting locally at the lens aperture, generally extending across the entire surface; the surface of the deviation, with the aid of an appropriate weighting function, by combining the height of the reference surface with The second surface is highly formed; the design of the off-surface is smooth at least up to its third derivative; the off-surface exhibits sloped regions of high astigmatism, and optionally exhibits low surface astigmatism in the periphery An outer band, around the perimeter, approximately umbilical in surface, and; the first and second surfaces in combination, define the optical axis and an optical band exhibiting substantially zero mean passing power.

The tilted optical properties of the lens are determined by performing a ray-tracing analysis of the lens, either with reference to the center of rotation of the eye when worn, or with reference to the center of the pupil stop gazing forward when worn. A simple tilt error of the quadratic surface arises because of the change in angle of incidence between the tilted surface element and the chief ray leaving the optical axis at an equiangular angle greater than 20°. To such a simple surface is added the complexity of rapidly changing surface curvature in a tilting field. However, triangulation of optical systems can be practically simplified in accordance with the surface form of embodiments of the present invention. In particular, it has been found that the surface forms described above generally act to limit the off-axis angle of incidence. The chief ray from the center of rotation of the eye to the tilted elements of the preferred surface according to an embodiment of the present invention raises the internal incidence angle in the central aperture more rapidly than for a standard optical reference surface. Then, the internal incidence angle saturates, remaining at an approximately constant value for higher field angles. Similar properties apply to the chief ray at the center of the pupil diaphragm.

A surface according to an embodiment of the invention may be specified not by the surface height itself, but by choosing an appropriate functional form of the variation in the internal incidence angle. Analysis of the basic geometric relationships yields the following differential equations involving the interior angle of refraction d(r), surface height z(r), and surface inclination z'(r): $r-z^{\&prime;}\left(r\right)(L-z\left(r\right))=\sin \left[d\left(r\right)\right]\sqrt{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="H2009100021083E00011.png,H2009100021083E00031.png"\; state="\{\{state\}\}">r</figure-callout>}}^2+{(L-z\left(r\right))}^2(1+[z^{\&prime;}\left(r\right){]}^2)}$ Here L is the distance from the surface vertex to the reference center of the analysis. This equation is easily solved by modern mathematical programs given an appropriate d(r) model function and a boundary condition such as the physical location of the vertices. A model function we have found useful is sin d(r)=sinγ*(1-exp(-nr ² /L ² )) ^1/2 which specifies that the angle is exactly constant across the tilt field, d=.y. The surface defined in this way is a quasi-spherical dome; the outer surface area does not incorporate a spherical area, but exhibits an umbilicus around which the surface astigmatism is low and varies slowly.

Therefore, in yet another aspect of a preferred embodiment of the present invention, there is provided an optical lens comprising a first surface having an axis of symmetry; and a second surface having a complementary curvature to the axis of symmetry; at least one surface exhibiting Significant deviations from the quadratic standard optical reference surface; deviations in surface height starting locally at the lens aperture and generally extending across the entire surface; the deviation surface is formed as the principal ray is inclined from the center of rotation of the eye so that the first Angle of incidence in the paraxial region rises with eye rotation, then remains approximately constant or decreases slowly from the oblique field to the lateral limit; oblique regions exhibit high astigmatism away from the surface and, alternatively, low in the periphery an outer band of surface astigmatism around which perimeter the surface is approximately umbilical, and; the first and second surfaces in combination define the optical axis and an optical band exhibiting substantially zero mean passing power.

Preferably, the angle of incidence of the chief ray from the center of rotation of the eye to the inclined surface region remains substantially constant over an angle of 30° or less, more preferably 20°, and most preferably less than 15°. Preferably, the angle of incidence of the chief ray from the center of the pupil stop to the inclined surface region remains substantially constant at a value of 45° or less, more preferably less than 35°, and most preferably less than 30°. Optimization of lens characteristics

It is therefore clear that very detailed requirements must be met in surface shape and inclination in order to produce an extremely desirable ophthalmic lens product. This is an object of the present invention. At least the aesthetic form of the front surface, the reliability of manufacture of both surfaces, and the criteria for defining a "good" lens are all issues when the designer undertakes the task of creating the front and back surfaces of the lens. Non-corrective lenses according to embodiments of the present invention are of constant thickness, or of increasing thickness across the aperture around the apex, with the lenses being relatively thin at or near the optical axis. Selection of design parameters allows control of thickness variation and aperture size, in aperture, maintained at or above lens center thickness value, has no effect on refraction and prism errors in frontal sight, which is aligned with optical axis when worn. This effect has an additional large impact on the optimization process available for lens design.

The surface correction of the (hypothetical) lens rear surface with a predetermined front surface can be done with the help of computational methods that include the use of figure of merit functions to quantify the relationship between the achieved properties and the target performance objectives. The figure of merit function is usually based on the observed refractive errors, which are mean power error MPE, RMS power error RMSPE (also known as RMS blur (blur)), and astigmatism or cylinder error, where $\mathrm{RMSPE}=\sqrt{{\left[\mathrm{MPE}\right]}^2+\frac{1}{4}{\left[\mathrm{CylError}\right]}^2}$

The following figure of merit function is often chosen to optimize the lens over the range of eye rotation θ: ${\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="H2009100021083E00011.png,H2009100021083E00031.png"\; state="\{\{state\}\}">m</figure-callout>}}_2=\underset{\mathrm{\&theta;}}{\mathrm{\&Sigma;}}{\left({\left[\mathrm{RMS\; Blur}\right]}^2\right)}_{\mathrm{\&theta;}}$ ${\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="H2009100021083E00011.png,H2009100021083E00031.png"\; state="\{\{state\}\}">m</figure-callout>}}_2=\underset{\mathrm{\&theta;}}{\mathrm{\&Sigma;}}{({\left[\mathrm{MPE}\right]}^2+{\left[\mathrm{CylError}\right]}^2)}_{\mathrm{\&theta;}}$ ${\mathrm{<figure-callout\; id="3"\; label="m"\; filenames="H2009100021083E00021.png"\; state="\{\{state\}\}">m</figure-callout>}}_3=\underset{\mathrm{\&theta;}}{\mathrm{\&Sigma;}}{(\frac{1}{16}{\left[\mathrm{MPE}\right]}^2+{\left[\mathrm{CylError}\right]}^2)}_{\mathrm{\&theta;}}$ ${\mathrm{<figure-callout\; id="4"\; label="m"\; filenames="H2009100021083E00041.png,H2009100021083E00081.png"\; state="\{\{state\}\}">m</figure-callout>}}_4=\underset{\mathrm{\&theta;}}{\mathrm{\&Sigma;}}{({\left[\mathrm{MPE}\right]}^2+\frac{1}{16}{\left[\mathrm{CylError}\right]}^2)}_{\mathrm{\&theta;}},$ The choice is strategically based on a weighting between optical power and astigmatism. In this case, other merit functions are introduced, such as measuring optical prism of lenses, and merit functions measuring the rate of change of properties such as blurring and prisms, for example: $m_{\mathrm{\&alpha;},\mathrm{\&beta;}}=\underset{\mathrm{\&theta;}}{\mathrm{\&Sigma;}}{(\mathrm{\&alpha;}{\left[\mathrm{RMS\; Blur}\right]}^2+\mathrm{\&beta;}{\left[\right|\mathrm{Static\; Prism}\left|\right]}^2)}_{\mathrm{\&theta;}},$ or $m_{a,b}=\underset{\mathrm{\&theta;}}{\mathrm{\&Sigma;}}{(a{\left[\mathrm{RMS\; Blur}\right]}^2+b{\left[\frac{\&PartialD;\left(\mathrm{Static\; Prism}\right)}{\&PartialD;\mathrm{\&theta;}}\right]}^2)}_{\mathrm{\&theta;}}$

These merit functions are used over both the gaze point and the peripheral field. However, there is a non-negative weight for each ray direction (eye rotation) that controls the relative contributions of RMS blur (a) and static prism (b) in each different field. Typically, static prisms are controlled over the outer angular range, with a more general RMS blurred part of the merit function applied to the inner field, to obtain an ideal and stable optical configuration.

In yet another aspect of an embodiment of the present invention, a pair of non-corrective lenses is provided in a frame or in a face-wrapping configuration, which enables the lenses to be worn accurately in front of the wearer so that the frontal line of sight substantially coincides with the corresponding optical axis of the lenses , the lenses conform to the shape of the face and substantially close the front and peripheral fields of view by virtue of their physical shape and sagittal depth, wherein each lens is characterized by the following: a first lens surface having an axis of symmetry; and having a complementary curvature and symmetry axis of the second lens surface; at least one surface exhibits a significant deviation in surface height from a quadratic standard optical reference surface; the deviation in surface height begins locally at the apex of the lens aperture and generally extends across the entire surface; The deviated surface exhibits a sloping region of high astigmatism, and optionally an outer band of low surface astigmatism in the periphery around which is approximately umbilical; the first and second surfaces combine to define the optical axis and Optical zone in which lens thickness is maintained without tapering from the full lens aperture to the peripheral limit closing the as-worn field of view; no significant refractive or prismatic error in frontal sight when worn; at most of the fixation field Inside, the oblique refractive powers remain small and below a set limit, outside most of the field of view they rise smoothly to a steady maximum at the edge of the field of view and near the peripheral field of view where the peripheral The field of view is defined by a clinically established troublesome blur threshold; the magnitude of the static contribution of the optical prism, across the aperture approximating the field of view, increases smoothly with increasing field angle, exhibiting this tendency of an inflection point so that the prism magnitude A steady value can be assumed, with essentially no change across the peripheral field of view; and the magnitude of the rotational contribution in the optical prism, from zero in frontal sight, increases slowly as the eye rotates across the field of view.

Preferably, the oblique refractive power varies symmetrically with the prism at least in one meridian of the field of gaze, and most preferably in at least one pair of orthogonal meridians of the field of gaze.

Preferably, both RMS power error and astigmatism error: less than 0.15D in a paraxial field with an angular width of about ±25°; less than 0.30D in about half the fixation field area; less than 0.4D, and; at least as low as 0.75D, preferably less than 0.5D, on the field of gaze corresponding to eye rotation of about 40° or more. Preferably, the average angular rate of growth is as little as 25 mD/degree in rotational prism component magnitude, preferably about 12.5 mD/degree across the field of view, and in static prism component magnitude, the growth average The angular rate is as little as 60mD/degree, preferably about 30mD/degree from the frontal line of sight to the outer peripheral limit. Alternatively, the prisms can be minimized such that the average angular rate of increase in the magnitude of both the rotating and static prism components, across the aperture substantially corresponding to the field of view, is about 40 mD/degree of field of view or less.

The invention will now be described more fully with reference to the accompanying drawings and examples. Obviously, however, the following descriptions are illustrative only and should not be viewed as generally limiting to the above-mentioned invention in any way. Example 1 (Prior Art) Non-Corrective Elliptical Lens

Tackle in US Pat. No. 5,774,201 describes non-corrective lens forms suitable for integral or dual lens goggles having a substantially elliptical cross-section in the horizontal plane and various forms in the vertical direction. A preferred horizontal arc is an ellipse with an eccentricity in the range 0.10 to 0.85, extending around the minor axis apex between the major axis reaching and the opposite apex. Thus, (1) the middle portion of the horizontal arc of the lens has a lower curvature than the rest of the arc, (2) the lateral ends have a progressively denser curvature relative to the middle portion, and (3) the horizontal direction from the middle to the outside In the region, the curvature change is smooth, which is known as the advantage of this structure.

Tackle specifically allows the length of the major axis of the ellipse to vary along the length of the arcuate portion, as long as the section substantially conforms to the ellipse. While some deviations from the ellipse in cross-sectional profile are permissible, the above-mentioned favorable characteristics must be maintained. One such feature is that the curvature varies monotonically with the middle portion of the lens, which has less curvature than the end portions. The second is the ability to shift the optical axis of the lens significantly from the frontal line of sight when worn without introducing optical errors to the frontal line of sight, especially with optical prisms. Lens surface curves according to embodiments of the present invention do not provide these properties as described hereinafter. In particular, these lens surface curves exhibit a maximum value of tangential surface curvature between the central region of the meridian and the side ends (i.e., in the middle of the lens), and these lens surface curves are substantially unsuitable to allow frontal vision from Optical axis offset.

An uncorrected ellipsoidal lens is described in US Patent 5,604,547 (Davis and Waido), the properties of which are plotted in Figure 3A. The front surface of the lens has an eccentricity e=0.866 (shape factor p=4.0) and is positioned such that the optical axis is on the Cyclopean axis in the wearer's median plane. The frontal sight is moved 34mm from the center, the semi-major axis length of the front surface is 70mm, and the prolate edge of the surface appears 36mm to the side of the frontal sight. Note first that the anterior surface tangential power increases smoothly towards the prolate edge. The anterior surface astigmatism, which is small in frontal sight, also increases smoothly toward the prolate edge. Note next that the lens thickness tapers off smoothly from a maximum on the optical axis, as Tackle requires for less decentered elliptical lenses. Finally, the refractive properties and prism magnitudes indicated no significant errors in frontal sight. There is relatively greater tilt error at the side than at the nose, producing significant left/right eye binocular parallax for lateral movement.

The involute of the front surface ellipse is drawn in part (bb) of Figure 2B. As discussed above, the normal vector from the surface to the cusp of the horizontal displacement of the involute of the ellipse, which corresponds to the vertex of the curve, is perpendicular to the minor axis of the ellipse. The angle φ cannot be too different from 90 degrees. Example 2 (Prior Art) Aspherical Sunglasses

In U.S. Patent 5,604,547, Davis and Waido describe an integral face wrap style non-corrective sunglass or eye protection polycarbonate lens comprising a pair of surfaces forming a lens of "substantially uniform" thickness throughout, each surface being produced by a conical section rotation graphics. The axis of rotation is the optical axis of the lens. This axis is located in the middle of the wearer's frontal line of sight when worn and corresponds to the central axis in the wearer's median plane. Davis and Waido specifically disclose (claim 18) a method by combining the front and back surfaces with central regions of curvature between 1.0 and 6.0D, and other polynomial terms with indices between 10 and 30, according to the downcurvature equation Combination, so that the peripheral limit of the overall protective cover is bent outside the binocular field of view in front of the wearer (that is to say, at the angle of view outside the wearer's front line of sight 40° or 50°), the downward bending equation is as follows z=Ar ² +Br ^C where A and B are coefficients and C is an even integer index and controls wrapping. The radial distance r is measured from the optical axis, or from the wearer's central axis.

(表2A)表2A。根据Davis和Waido美国专利5,604,547的镜片设计系数，和在光学中心t_O及在正面视线t_E上的镜片厚度。   x  (mm)   θ  (Deg)   ¹/₂(K-  _S+K_T)  (D)   |K_S-K_T|  (D)   K_T  (D)   Φ(x)  (Deg)  R(x)/R(0)   35.0  30.0  25.0  20.0  15.0  10.0  5.0  0.0  -5.0  -10.0  -15.0  -20.0  -25.0  -30.0  -35.0  -40.0   49.4  45.1  40.1  34.4  27.6  19.8  10.6  0.0  -11.6  -23.8  -35.7  -46.7  -56.7  -66.3  -77.0  -88.4   4.0  4.0  4.0  4.0  3.9  3.9  3.8  3.8  3.7  3.8  4.1  5.1  7.6  11.4  12.3  8.0   0.0  0.0  0.0  0.0  0.1  0.1  0.2  0.2  0.2  0.1  0.5  2.3  6.6  12.6  12.3  2.6   4.00  3.99  3.97  3.93  3.88  3.81  3.73  3.65  3.60  3.72  4.34  6.29  10.88  17.71  18.46  9.28   0.43  1.73  3.89  6.03  8.16  10.27  12.35  14.40  16.43  18.49  20.76  23.77  28.79  38.06  52.81  68.50   1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.01  1.03  1.11  1.27  1.47  1.46  1.14  0.71 To help understand the properties of the lenses, the design of each lens has been established in Table 2A. The horizontal section of the lens depicts a stable central curvature associated with the quadratic term of the downcurve equation, and a slightly abrupt curvature toward the temporal, as shown in Figure 3B. In general, the higher order terms provide the desired depth of side wrap without significantly affecting the optical properties of the front viewing portion of the lens unit. The maximum size of this inward protrusion is demonstrated by the design of the lens Hi-14#2. All of these lenses tapered smoothly from the optical axis across the field of view lateral to the frontal line of sight (see Table 2A).

(Table 2A) Table 2A. Lens design coefficients according to Davis and Waido US Patent 5,604,547, and lens thickness at optical center t _O and at frontal line of sight t _E. x (mm) θ (Deg) ¹ /₂(K- _S+K_T) (D) |K_S-K_T| (D) K_T (D) Φ(x) (Deg) R(x)/R(0) 35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0 -5.0 -10.0 -15.0 -20.0 -25.0 -30.0 -35.0 -40.0 49.4 45.1 40.1 34.4 27.6 19.8 10.6 0.0 -11.6 -23.8 -35.7 -46.7 -56.7 -66.3 -77.0 -88.4 4.0 4.0 4.0 4.0 3.9 3.9 3.8 3.8 3.7 3.8 4.1 5.1 7.6 11.4 12.3 8.0 0.0 0.0 0.0 0.0 0.1 0.1 0.2 0.2 0.2 0.1 0.5 2.3 6.6 12.6 12.3 2.6 4.00 3.99 3.97 3.93 3.88 3.81 3.73 3.65 3.60 3.72 4.34 6.29 10.88 17.71 18.46 9.28 0.43 1.73 3.89 6.03 8.16 10.27 12.35 14.40 16.43 18.49 20.76 23.77 28.79 38.06 52.81 68.50 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.01 1.03 1.11 1.27 1.47 1.46 1.14 0.71

Table 2B. Properties of the front surface of Lens Hi-14#2 as a function of horizontal distance and field angle from the frontal line of sight towards the temporal.

In the representation of the results, the axis Oz (x=0) has been placed on the frontal line of sight of the wearer's left eye, while the nasal optical axis is on x=+34mm. The part of the lens that is arranged on the temporal frontal sight corresponds to the negative value of x. For the designs studied, the anterior surface curvature remained essentially constant for most of the nasal and temporal frontal visual field. The detailed changes in the properties of the front surface are given in Table 2B and Figure 3B. Both the anterior and posterior surfaces are prolate, with no astigmatism in the central zone, so that the tangential curvature decreases from the optical axis to the zone corresponding to the temporal portion of the eye rotation about 35°, and outside this zone, the anterior Surface tangential curvature K _T , mean curvature ^1/2 (K _S +K _T ), and surface astigmatism that increase smoothly from _the outer temporal fixation field to the temporal portion of the field angle of about 70° completely outside the fixation field During bending, a maximum value is experienced. The "surface Q value" Q=R(x)/R(0) remains greater than 1 at approximately 75° from the frontal line of sight.

The involute (1) of the front surface curve changes under the influence of high-order bending coefficients, and is approximately linear until the horizontal displacement cusp, and the surface normal vector is deflected toward the optical axis at approximately φ=50°. This involute does not fit a standard form of curve. The closest fit to the elliptical involute, represented as curve (2) in Figure 3B, corresponds to a = 75 mm, b = 39 mm, e = 0.854, and p = 3.70.

The caliper thickness of the lens Hi-14#2 is not constant, but gradually thins from 1.7mm on the optical axis to 1.65mm at the frontal sight, and slightly thickens at the side curvature. Lenses have refractive properties, power errors, and prisms, which all change smoothly with eye rotation, but there is a difference between left and right eyes for lateral movement, as shown in Figure 3B. Static prisms also have left and right parallax. This is a typical disadvantage of centrifugal lens designs.

A spherical lens whose optical axis and frontal line of sight are collinear when worn (Fig. 4A) can be compared with a similar lens translated 15 mm nasally according to the method of Houston et al. (frontal line of sight at 103° to the front surface), Houston et al., described in US Patents 5,648,832 and 5,689,323 (Figure 4B). Spherical lenses that wrap/hug the face, presenting left/right eye parallax. Example 3 "Non-quadratic" polynomial

The basis of embodiments of the present invention is the ability to obtain desired and controllable surface shapes by using generated curves, which are essentially circles, ellipses, or mathematical variations of any standard conic curve. Applying the deformation function to the standard conic curve can produce the desired curve. Alternatively, the curve can be defined directly via a function or polynomial expression. Surfaces that directly form the resulting curves are often desired. One such approach is given below.

A suitable rotationally symmetric oblate spheroidal surface should satisfy the relation $z\left(r\right)=\underset{\mathrm{no}\&Greater\; Equal;2}{\overset{m}{\mathrm{\&Sigma;}}}{A}_{\mathrm{no}}{r}^{\mathrm{no}}$ here $\stackrel{\&OverBar;}{z^{\&prime;\&prime;}{\left(\frac{r}{z^{\&prime;}}\right)}^3}<<{\left(\frac{1}{2A_2}\right)}^2$

This condition states that the polynomial form will be governed by the coefficients _An , where n ≥ 3, and that these coefficients will vary in a certain order, unlike the variation of the conical surface.

  X   z(x)   θ   K_T   |K_T-K_S|   Φ(x)   Q(x)   0.0  2.5  5.0  7.5  10.0  12.5  15.0  17.5  20.0  22.5  25.0  27.5  30.0  32.5  35.0  37.5  40.0   -0.0  -0.0  -0.0  -0.1  -0.2  -0.3  -0.5  -0.9  -1.4  -2.0  -3.0  -4.2  -5.8  -7.8  -10.2  -13.3  -17.0   0.0  5.0  10.0  14.8  19.4  23.9  28.2  32.3  36.4  40.4  44.4  48.5  52.8  57.4  62.4  67.9  73.9   1.1  1.3  2.0  3.2  4.9  7.0  9.5  12.3  15.1  17.6  19.4  20.0  19.2  17.3  14.6  11.7  9.0   0.0  0.2  0.6  1.4  2.5  3.9  5.6  7.4  9.1  10.5  11.1  10.7  9.0  6.4  3.4  0.4  -2.2   0.00  0.31  0.75  1.44  2.52  4.11  6.33  9.29  13.06  17.66  23.03  28.99  35.30  41.64  47.70  53.28  58.25   1.00  0.99  0.93  0.80  0.66  0.53  0.42  0.34  0.28  0.23  0.20  0.17  0.14  0.12  0.11  0.10  0.08 I can add various boundary conditions at the vertex r = 0 and the lateral position r = ρ, so as to pre-arrange the form of the surface, for example: define the central curvature z″(0)=A ₂ =K ₀ define the lateral sagittal depth $z\left(\mathrm{\&rho;}\right)=\underset{\mathrm{no}\&Greater\; Equal;2}{\overset{m}{\mathrm{\&Sigma;}}}{A}_{\mathrm{no}}{\mathrm{\&rho;}}^{\mathrm{no}}=Z$ Define the roll angle condition $z^{\&prime;}\left(\mathrm{\&rho;}\right)=\underset{\mathrm{no}\&Greater\; Equal;2}{\overset{m}{\mathrm{\&Sigma;}}}\mathrm{no}{A}_{\mathrm{no}}{\mathrm{\&rho;}}^{\mathrm{no}-1}=S$ Lateral umbilical condition on the edge K _S (ρ) = K _T (ρ) >>K ₀ Stability of lateral umbilical condition K _S ′(ρ)=K _T ′(ρ)=0.

x z(x) θ K_T |K_T-K_S| Φ(x) Q(x) 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0 32.5 35.0 37.5 40.0 -0.0 -0.0 -0.0 -0.1 -0.2 -0.3 -0.5 -0.9 -1.4 -2.0 -3.0 -4.2 -5.8 -7.8 -10.2 -13.3 -17.0 0.0 5.0 10.0 14.8 19.4 23.9 28.2 32.3 36.4 40.4 44.4 48.5 52.8 57.4 62.4 67.9 73.9 1.1 1.3 2.0 3.2 4.9 7.0 9.5 12.3 15.1 17.6 19.4 20.0 19.2 17.3 14.6 11.7 9.0 0.0 0.2 0.6 1.4 2.5 3.9 5.6 7.4 9.1 10.5 11.1 10.7 9.0 6.4 3.4 0.4 -2.2 0.00 0.31 0.75 1.44 2.52 4.11 6.33 9.29 13.06 17.66 23.03 28.99 35.30 41.64 47.70 53.28 58.25 1.00 0.99 0.93 0.80 0.66 0.53 0.42 0.34 0.28 0.23 0.20 0.17 0.14 0.12 0.11 0.10 0.08

Table 3A. According to one embodiment of the invention, there are 1D top curvature surface design coefficients and polynomial surface properties.

  X   z(x)   θ   K_T   K_T-K_S   Φ(x)   Q(x)   0.0  2.5  5.0  7.5  10.0  12.5  15.0  17.5  20.0  22.5  25.0  27.5  30.0  32.5  35.0  37.5  40.0   -0.0  -0.0  -0.0  -0.1  -0.2  -0.4  -0.7  -1.2  -1.8  -2.7  -3.8  -5.2  -6.9  -8.9  -11.2  -13.8  -17.0   0.0  5.0  10.0  14.8  19.5  24.0  28.4  32.6  36.9  41.1  45.4  49.8  54.2  58.9  63.7  68.7  74.0   1.0  1.4  2.7  4.7  7.2  9.9  12.6  14.9  16.2  16.6  16.0  14.9  13.5  12.3  11.5  11.1  10.7   0.0  0.3  1.1  2.4  4.0  5.7  7.2  8.2  8.5  7.9  6.6  4.8  3.1  1.7  0.8  0.4  0.0   0.0  0.3  0.8  1.8  3.4  5.7  8.8  12.6  17.0  21.7  26.6  31.4  36.0  40.4  44.8  49.2  54.0   1.00  0.98  0.83  0.64  0.48  0.36  0.28  0.23  0.19  0.16  0.14  0.12  0.11  0.10  0.10  0.10  0.09 The more such conditions are imposed, the greater the number of coefficients that can be specified. However, since a suitable matching surface must provide a lens body that satisfies a specified optical figure of merit function, the more constrained surfaces make lens optimization more difficult. In general, it is sufficient to limit the highest order of the front surface polynomial to m≈8. Two examples of surfaces thus constructed according to embodiments of the present invention, and their advantageous properties, are shown in Tables 3A and 3B, also depicted in FIG. 5 .

x z(x) θ K_T K_T-K_S Φ(x) Q(x) 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0 32.5 35.0 37.5 40.0 -0.0 -0.0 -0.0 -0.1 -0.2 -0.4 -0.7 -1.2 -1.8 -2.7 -3.8 -5.2 -6.9 -8.9 -11.2 -13.8 -17.0 0.0 5.0 10.0 14.8 19.5 24.0 28.4 32.6 36.9 41.1 45.4 49.8 54.2 58.9 63.7 68.7 74.0 1.0 1.4 2.7 4.7 7.2 9.9 12.6 14.9 16.2 16.6 16.0 14.9 13.5 12.3 11.5 11.1 10.7 0.0 0.3 1.1 2.4 4.0 5.7 7.2 8.2 8.5 7.9 6.6 4.8 3.1 1.7 0.8 0.4 0.0 0.0 0.3 0.8 1.8 3.4 5.7 8.8 12.6 17.0 21.7 26.6 31.4 36.0 40.4 44.8 49.2 54.0 1.00 0.98 0.83 0.64 0.48 0.36 0.28 0.23 0.19 0.16 0.14 0.12 0.11 0.10 0.10 0.10 0.09

Table 3B. According to one embodiment of the invention, there are 1D top curvature surface design coefficients and polynomial surface properties.

  X   z(x)   θ   K_T   |K_T-K_S|   Φ(x)   Q(x)   0.0  2.5  5.0  7.5  10.0  12.5  15.0  17.5  20.0  22.5  25.0  27.5  30.0  32.5  35.0  37.5  40.0  42.5  45.0   -0.0  -0.0  -0.2  -0.4  -0.7  -1.2  -1.7  -2.3  -3.1  -4.0  -5.0  -6.2  -7.6  -9.2  -11.1  -13.3  -16.1  -20.0  -28.9   0.0  5.0  10.0  15.0  19.8  24.6  29.2  33.8  38.2  42.5  46.8  51.0  55.1  59.3  63.5  67.9  72.8  78.6  90.5   7.8  7.8  7.8  7.9  8.0  8.1  8.3  8.5  8.8  9.1  9.5  9.9  10.5  11.2  12.1  13.2  14.6  16.6  19.3   0.0  0.0  0.1  0.1  0.2  0.4  0.5  0.8  1.0  1.4  1.8  2.3  3.0  3.8  4.9  6.4  8.3  11.1  15.1   0.0  2.1  4.2  6.4  8.6  10.8  13.2  15.6  18.2  20.9  23.8  27.0  30.6  34.6  39.3  44.9  52.0  62.2  87.5   1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0 Both surfaces have an umbilical apex, a 1D top curvature and an umbilical ring located at about r=±38mm, corresponding to a field angle of about 68°. This angle cannot be achieved by eye rotation, thus placing the umbilicus in the wearer's peripheral field of view. Surfaces are remarkably flat at the top and tend towards close bulbs on their outer sides. The surface A depicted in FIG. 5A simply intersects the osmosis sphere (curve c), and as a result an umbilical ring appears on the lateral surface. The involute curve corresponding to the radial section of the surface has been discussed above in connection with Fig. 2D. The normal vector to the cusp of the horizontal displacement from the surface to the involute of the curve, skewed towards the axis of symmetry by about φ = 30°. Surface B, shown in Figure 5B, merges with the occlusive bulb and presents an extended umbilical cord at the lateral limit. The normal vector of the surface at the position of maximum tangential curvature is deflected towards the axis of symmetry by about φ = 22°. Both surfaces exhibit a maximum in surface astigmatism associated with the maximum tangential curvature of the wearer's forward gaze field. Surface astigmatism clearly disappears in the umbilical region of the surface. In each instance, the "surface Q value" is substantially less than 1 over most of the surface.

x z(x) θ K_T |K_T-K_S| Φ(x) Q(x) 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0 32.5 35.0 37.5 40.0 42.5 45.0 -0.0 -0.0 -0.2 -0.4 -0.7 -1.2 -1.7 -2.3 -3.1 -4.0 -5.0 -6.2 -7.6 -9.2 -11.1 -13.3 -16.1 -20.0 -28.9 0.0 5.0 10.0 15.0 19.8 24.6 29.2 33.8 38.2 42.5 46.8 51.0 55.1 59.3 63.5 67.9 72.8 78.6 90.5 7.8 7.8 7.8 7.9 8.0 8.1 8.3 8.5 8.8 9.1 9.5 9.9 10.5 11.2 12.1 13.2 14.6 16.6 19.3 0.0 0.0 0.1 0.1 0.2 0.4 0.5 0.8 1.0 1.4 1.8 2.3 3.0 3.8 4.9 6.4 8.3 11.1 15.1 0.0 2.1 4.2 6.4 8.6 10.8 13.2 15.6 18.2 20.9 23.8 27.0 30.6 34.6 39.3 44.9 52.0 62.2 87.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

Table 3C. Surface design coefficients and properties of prior art ellipsoidal surfaces.

Table 3C gives, for comparison, the properties of an ellipse with an eccentricity of 0.75, which has an equivalent sagittal depth at a radial distance of 37.5 mm. According to the surface of the embodiment of the present invention, there are the following outstanding characteristics: it has a tangential curvature that increases from the central area to the side edges, while the ellipse is only significantly curved at the side edges; from the central area to the edge, there is a basic surface astigmatism, Whereas the ellipsoidal surface shows progressively increasing astigmatism towards the lateral edges; midway between the central region and the lateral edges, there is a tangential curvature maximum, but not observed in the ellipse; between the central region and the lateral edges In the middle position, there is a large surface astigmatism, but not observed in the ellipse; in the outer side, there is a low astigmatism area and related umbilical conditions, but not observed in the ellipse; away from the center area, the surface Q value is significantly less than 1 , while for an elliptical surface, it is constant, and; at the position of maximum tangential curvature, the angle φ by which the surface normal deviates to the optical axis is significantly less than 90°, but in the elliptical case they are perpendicular to the axis of symmetry .

If the prior art lens of Example 2 (Table 2B and Figure 3B) is compared similarly with the surface according to the embodiment of the present invention, it has the following outstanding characteristics: it is symmetrical to the frontal vision, which is not a prior art lens The normal to the surface; its tangential and mean surface curvature and surface astigmatism, substantially increase as they approach, and approach, the frontal line of sight in all directions, whereas prior art lenses, only in the outer regions when the field of view is at This characteristic is only available when the wearer gazes outside the field of view; its lens surface Q-value is below 1 when leaving the central region, whereas for a large part of prior art lenses, this Q-value is constant, and it is It is oblate on the axis of symmetry and oblate off the axis of symmetry, whereas the prior art lens of Example 2 is prolate across most of the lens aperture. Example 4 "Non-quadratic" surface function

In another approach according to the present invention, we combine a pair of spheres with different curvatures B ₁ =530/ρ ₁ and B ₂ =530/ρ ₂ with an appropriate weighting function W(r) to give the final rotationally symmetric surface, has the following form, $z\left(r\right)=W\left(r\right)*({\mathrm{\&rho;}}_1-\sqrt{{\mathrm{\&rho;}}_1^2-r^2})+(1-W\left(r\right))*({\mathrm{\&rho;}}_2-\sqrt{{\mathrm{\&rho;}}_2^2-r^2})$

Any suitable weighting function can be used, as an example hyperbolic secant can be used; W(r)=a*(Sech(r/b)) ⁿ

Two examples of such surfaces are shown in Figure 6 and Tables 4A and 4B.

  x   z(x)   θ   K_T   |K_T-K_S|   Φ(x)   Q(x)   0.0  2.5  5.0  7.5  10.0  12.5  15.0  17.5  20.0  22.5  25.0  27.5  30.0  32.5  35.0  37.5  40.0   -0.0  -0.0  -0.1  -0.2  -0.5  -1.0  -1.7  -2.6  -3.8  -5.2  -7.0  -9.1  -11.6  -14.7  -18.5  -23.8  -33.6   0.0  5.0  10.0  14.9  19.7  24.4  29.2  34.1  39.0  44.0  49.3  54.8  60.6  66.9  74.1  82.8  97.3   2.5  3.9  7.5  11.7  14.9  16.7  17.2  16.9  16.2  15.4  14.7  14.1  13.7  13.4  13.2  13.1  13.2   0.0  1.0  3.2  5.6  7.0  7.2  6.4  5.2  3.9  2.7  1.8  1.1  0.6  0.3  0.1  0.1  0.1   0.0  0.8  2.3  4.9  8.6  13.0  17.7  22.6  27.6  32.5  37.5  42.6  47.9  53.7  60.3  68.6  83.1   1.00  0.96  0.77  0.57  0.43  0.35  0.29  0.26  0.23  0.22  0.21  0.20  0.20  0.19  0.19  0.19  0.19 The D values of the surfaces are illustrated in Figure 6A. It combines its close spheres in the lateral regions with its low curvature spheres at its top, subject to a weighting function drawn in the curve "weighted value". The surface Q value is 1 at the top, and then drops smoothly away from the axis to a constant value Q = 0.2, corresponding to the curvature ratio B ₁ /B ₂ of the two spherical regions. Moving away from the top, the surface astigmatism and surface tangential curvature increase rapidly, pass a maximum, and then decrease smoothly toward the outer umbilicus. The rate of change is governed by the hyperbolic secant function that falls smoothly from 1 on either side of the coordinate origin. Increasing the value assigned to the parameter b slows down the rate of descent and displaces the outer umbilicus; while the curvature of the umbilicus is set directly by the choice of the reference sphere; increasing the value assigned to n sharpens the central peak of the weighting function , and increases the maximum surface astigmatism encountered. The normal to the surface in its region of greatest tangential curvature is deflected by about 20° to the axis of symmetry.

x z(x) θ K_T |K_T-K_S| Φ(x) Q(x) 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0 32.5 35.0 37.5 40.0 -0.0 -0.0 -0.1 -0.2 -0.5 -1.0 -1.7 -2.6 -3.8 -5.2 -7.0 -9.1 -11.6 -14.7 -18.5 -23.8 -33.6 0.0 5.0 10.0 14.9 19.7 24.4 29.2 34.1 39.0 44.0 49.3 54.8 60.6 66.9 74.1 82.8 97.3 2.5 3.9 7.5 11.7 14.9 16.7 17.2 16.9 16.2 15.4 14.7 14.1 13.7 13.4 13.2 13.1 13.2 0.0 1.0 3.2 5.6 7.0 7.2 6.4 5.2 3.9 2.7 1.8 1.1 0.6 0.3 0.1 0.1 0.1 0.0 0.8 2.3 4.9 8.6 13.0 17.7 22.6 27.6 32.5 37.5 42.6 47.9 53.7 60.3 68.6 83.1 1.00 0.96 0.77 0.57 0.43 0.35 0.29 0.26 0.23 0.22 0.21 0.20 0.20 0.19 0.19 0.19 0.19

Table 4A. According to one embodiment of the present invention, there are surface design coefficients and surface functional properties of 2.5D top curvature.

  x   z(x)   θ   K_T   |K_T-K_S|   Φ(x)   Q(x)   0.0  2.5  5.0  7.5  10.0  12.5  15.0  17.5  20.0  22.5  25.0  27.5  30.0  32.5  35.0  37.5  40.0   -0.0  -0.0  -0.1  -0.3  -0.6  -1.0  -1.6  -2.4  -3.5  -4.9  -6.5  -8.5  -11.0  -14.0  -17.8  -22.9  -32.7   0.0  5.0  10.0  14.9  19.7  24.4  29.2  33.9  38.7  43.6  48.7  54.0  59.7  65.9  73.0  81.6  95.9   4.4  5.1  6.9  9.4  12.1  14.5  16.2  17.0  17.1  16.7  16.0  15.2  14.5  13.9  13.5  13.3  13.8   0.0  0.4  1.6  3.2  4.7  5.9  6.5  6.4  5.6  4.6  3.4  2.4  1.5  0.9  0.4  0.2  0.6   0.0  1.3  2.9  5.0  8.0  11.6  15.9  20.7  25.7  30.9  36.2  41.6  47.2  53.2  60.0  68.3  82.9   1.00  0.99  0.96  0.88  0.78  0.68  0.59  0.53  0.47  0.43  0.40  0.38  0.36  0.35  0.34  0.34  0.35 If the value of the parameter a is set to be less than 1, a close spherical component is introduced at the top, increasing the local curvature to a value close to equal to the fractional mixture a*B ₁ +(1-a)*B ₂ . This results in a wider umbilical region at the top of the surface, such as that shown in FIG. 6B corresponding to surface E. As a result of the choice of the other parameters b and n, the surface tends to merge more slowly with the occlusal sphere, and the side umbilicals start to approach the perimeter that an actual lens surface should have. The general properties of the surface are otherwise similar to those of surface D. The normal to the surface in its region of greatest tangential curvature is deflected to the axis of symmetry at an angle of about 25°.

x z(x) θ K_T |K_T-K_S| Φ(x) Q(x) 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0 32.5 35.0 37.5 40.0 -0.0 -0.0 -0.1 -0.3 -0.6 -1.0 -1.6 -2.4 -3.5 -4.9 -6.5 -8.5 -11.0 -14.0 -17.8 -22.9 -32.7 0.0 5.0 10.0 14.9 19.7 24.4 29.2 33.9 38.7 43.6 48.7 54.0 59.7 65.9 73.0 81.6 95.9 4.4 5.1 6.9 9.4 12.1 14.5 16.2 17.0 17.1 16.7 16.0 15.2 14.5 13.9 13.5 13.3 13.8 0.0 0.4 1.6 3.2 4.7 5.9 6.5 6.4 5.6 4.6 3.4 2.4 1.5 0.9 0.4 0.2 0.6 0.0 1.3 2.9 5.0 8.0 11.6 15.9 20.7 25.7 30.9 36.2 41.6 47.2 53.2 60.0 68.3 82.9 1.00 0.99 0.96 0.88 0.78 0.68 0.59 0.53 0.47 0.43 0.40 0.38 0.36 0.35 0.34 0.34 0.35

Table 4B. According to one embodiment of the present invention, there are surface design coefficients and surface functional properties of 4.4D top curvature.

  x   z(x)   θ   K_T   |K_T-K_S|   Φ(x)   Q(x)   0.0  2.5  5.0  7.5  10.0  12.5  15.0  17.5  20.0  22.5  25.0  27.5  30.0  32.5  35.0  37.5  40.0   -0.0  -0.0  -0.1  -0.2  -0.4  -0.6  -0.9  -1.3  -1.7  -2.2  -2.8  -3.6  -4.7  -6.0  -7.7  -9.9  -12.6   0.0  5.0  10.0  14.9  19.6  24.2  28.5  32.7  36.7  40.6  44.3  47.9  51.5  55.3  59.3  63.6  68.3   4.3  4.3  4.3  4.3  4.4  4.6  5.0  5.8  7.3  9.6  12.7  16.2  19.1  20.3  19.3  16.8  14.1   0.0  0.0  0.0  0.0  0.1  0.2  0.6  1.2  2.5  4.4  6.9  9.6  11.6  11.8  10.0  7.0  3.9   0.00  1.17  2.34  3.51  4.69  5.91  7.20  8.66  10.43  12.73  15.82  19.91  25.10  31.19  37.73  44.23  50.39   1.00  1.00  1.00  1.00  1.00  1.01  1.04  1.07  1.11  1.13  1.11  1.03  0.92  0.79  0.67  0.57  0.50 European design standards, such as CEN 1836 "Sunglass & Sunglass Filter for General Use" require that in a zone with a radius of 10mm, the average spherical power falls within the range of 0.00±0.09D. Therefore, it is worthwhile to build itself a wide and stable top surface of similar dimensions. "Surface F", designed with appropriately modified weighting functions, is described in Table 4C. The surface retains the basic properties of the surface, and in the middle between the central part and the side ends, there is a maximum value of tangential curvature and surface astigmatism. Note, however, that the surface Q value remains close to 1 for the expansion region corresponding to the center top. As discussed in conjunction with Figure 2C, the central region of the top is an ellipse with eccentricity e = 0.963 (shape factor p = 13.9), but the normal to its region of greatest tangential curvature is at an angle of approximately 30° to the axis of symmetry skewed.

x z(x) θ K_T |K_T-K_S| Φ(x) Q(x) 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0 32.5 35.0 37.5 40.0 -0.0 -0.0 -0.1 -0.2 -0.4 -0.6 -0.9 -1.3 -1.7 -2.2 -2.8 -3.6 -4.7 -6.0 -7.7 -9.9 -12.6 0.0 5.0 10.0 14.9 19.6 24.2 28.5 32.7 36.7 40.6 44.3 47.9 51.5 55.3 59.3 63.6 68.3 4.3 4.3 4.3 4.3 4.4 4.6 5.0 5.8 7.3 9.6 12.7 16.2 19.1 20.3 19.3 16.8 14.1 0.0 0.0 0.0 0.0 0.1 0.2 0.6 1.2 2.5 4.4 6.9 9.6 11.6 11.8 10.0 7.0 3.9 0.00 1.17 2.34 3.51 4.69 5.91 7.20 8.66 10.43 12.73 15.82 19.91 25.10 31.19 37.73 44.23 50.39 1.00 1.00 1.00 1.00 1.00 1.01 1.04 1.07 1.11 1.13 1.11 1.03 0.92 0.79 0.67 0.57 0.50

Table 4C. According to one embodiment of the present invention, there are surface design coefficients and surface functional properties of 4.3D top curvature.

Figures 5A, 5B, 6A, and 6B, include graphs of angle of incidence as a function of radial distance on the lens. Two angles are drawn on the figure, and the curve drawn in solid line is the inner incidence angle for the appropriate curve when referenced to the center of rotation of the eye at a distance of 27 mm from the posterior apex. The other angles are the internal incidence angles to the pupil diaphragm of a static eye looking forward, the pupil diaphragm being 11 mm forward of the center of rotation. It should be noted that these angular tilt fields have approximately constant values. The surface has an approximately constant deflection about two optical reference points.

Surfaces D and E have extreme sagittal extents extending to greater than 90° FOV (Tables 4A and 4B). Tackle, as well as Houston et al., called the internal incidence angle of oblique intermediate rays limited by the lens configuration, in particular by the use of elliptical forms and progressively thinner lens wall thicknesses, as the resulting optical benefit. Therefore, we compare the surface according to the embodiment of the invention, i.e. the surface E, with spherical surfaces and with elliptical surfaces with eccentricity e=0.75, these surfaces are arranged to have common vertices and have intersections in the outer field (±35.0, -17.8).

Figure 7 (A and B) plots the internal incidence angles of the chief ray for a formal ray-tracing analysis of a rotating eye. The solid lines correspond to surface E, while the dashed lines are the equivalent spherical (Fig. 7A) and ellipsoidal equivalents. ball (Fig. 7B). Figure 7 (C and D) curves plot the internal incidence angles of chief rays in a formal ray tracing analysis for a static eye, the solid line corresponds to surface E, while the dashed line is the equivalent spherical (Figure 7C) and equivalent ellipsoid balls (Fig. 7D). In both ray-tracing configurations, the spherical surface showed a steady increase in the internal incidence angle across the mirror tilt region. For extremely eccentric ellipsoids, the oblique growth of the inner incidence angle is arrested by the changing surface curvature, presenting a region of constant deflection, outside which it varies rapidly. The extension of the region of constant deflection to the corresponding chief ray is characteristic of the surface designed according to the invention. Outside the paraxial field, the internal incidence angle has a relatively low and stable value everywhere, thus helping to obtain a stable peripheral optical structure in practical lens design. This is an advantage over the elliptical form.

These properties provide yet another method of constructing lens surfaces in accordance with the preferred embodiments of the present invention. It is the functional form of the surface z(r) that defines the center of rotation of the eye or the variation of the internal angle of incidence on the pupil diaphragm, and vice versa, on the other hand. The physical surface is defined by a detailed specification of the functional form that varies the angle of incidence. Analysis of the basic geometric relations yields the following differential equations for the internal refraction angle d(r), surface height z(r), and surface slope z'(r): $r-z^{\&prime;}\left(r\right)(L-z\left(r\right))=\sin \left[d\left(r\right)\right]\sqrt{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="H2009100021083E00011.png,H2009100021083E00031.png"\; state="\{\{state\}\}">r</figure-callout>}}^2+{(L-z\left(r\right))}^2(1+{\left[z^{\&prime;}\left(r\right)\right]}^2)}$ Here L is the distance from the surface vertex to the reference center of the analysis. This equation is easily solved by modern mathematical programs, given the appropriate model function for d(r) and a boundary condition, such as the physical location of the vertices. A useful model function we have found is sin d(r)=sinγ*(1-exp(-nr ² /L ² )) ^1/2 This function is defined as the variation process in Figure 7, where the angle of is exactly constant, d=.y. The surface thus defined is a quasi-spherical dome. Their properties, except that the outer surface region does not merge into the spherical region, are very similar to Surface E, but present an umbilicus around which the surface astigmatism is low and varies slowly. Example 5 Symmetrical non-corrective lenses

The surface of the lens according to a preferred embodiment of the present invention has a dome-like shape with steeper side walls and relatively flatter regions on the axis of symmetry. We can formulate each lens surface as a quadric surface C(r) with radius of curvature _p1 and shape factor _p1 , with associated weighting functions that provide smooth control of the surface across the lens aperture. Therefore, according to the complete lens surface of this example of the embodiment of the present invention, there is the following mathematical structure; $z\left(r\right)=C\left(r\right)*\mathrm{Sech}(r/q)+\underset{\mathrm{no}\&Greater\; Equal;3}{\overset{m}{\mathrm{\&Sigma;}}}{A}_{\mathrm{no}}{r}^{\mathrm{no}}$ here $C\left(r\right)=\frac{{\mathrm{\&rho;}}_1}{p_1}(1-\sqrt{1-{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="H2009100021083E00011.png,H2009100021083E00031.png"\; state="\{\{state\}\}">p</figure-callout>}}_1*{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="H2009100021083E00011.png,H2009100021083E00031.png"\; state="\{\{state\}\}">r</figure-callout>}}^2/{\mathrm{\&rho;}}_1^2})$

表5。用于设计图8和9镜片的前表面系数。A set of lenses has been designed with the front surface constructed with the set of parameters shown in Table 5. Lens material is polycarbonate. The lens has a back vertex power of 0.00DS and a center thickness of 1.5mm. The optical properties determined by ray tracing for a back vertex distance of 27.0 mm are plotted in FIGS. 8 and 9 . The mean power error MPE, oblique astigmatism error OAE, RMS power error RMSPE, and optical prism magnitude |prism|(rotation) are plotted against the rotation of the eye in the field of view. Static Optical Prism Amplitude |prism|(Static), determined with reference to the pupil diaphragm when the wearer is gazing forward. Lens caliper thickness and sagittal depth plotted as a function of radial position relative to the axis of symmetry of the lens unit. Spherical non-corrective lens properties with equivalent sagittal depth and alignment of corrective axes at the lens edge (r = 40mm) are plotted in Fig. 4A for comparison, and those with the same spherical surface with axes offset to obtain wrapping , is drawn in Figure 4B.

table 5. The front surface coefficients used to design the lenses of Figures 8 and 9.

By defining the optical power of the posterior apex, the posterior surface corresponding to a given anterior surface is defined in the paraxial region. At least for the posterior surface, a second aspheric correction must be made to control the oblique optics over the field of view and, if appropriate, from near the edge of the field of view into the peripheral field. In doing so, there must be a clear prioritization in judging the merit of the lenses according to the particular wearer's needs. Different criteria can be applied for internal and external design fields.

In constructing the surface of the lens of Figure 8, a different operation than that used for the lens of Figure 9 has been performed. The lenses of Figures 8A and 8B, corresponding to front surface Types 5B and 5C with top curvatures of 1.75 and 3.5D respectively, are designed to minimize the optical prism amplitude experienced by the eye during rotation (±40°) within the field of fixation . The prism amplitude, and its rate of change in the central portion of the field of view, is characteristically low because of the low curvature of the lens surface in the central portion of the field of view, and the negative mean power error that grows progressively towards the edge of the field of view. This negative refractive power error is considered acceptable if it is limited to the range naturally accommodated by the average wearer and should not exceed -0.35D, preferably not more than -0.25D. The outer regions of the lens aperture have been designed to avoid adding unwanted negative mean power errors that would otherwise occur in the peripheral field. Thus, the trend of mean or RMS power error differs significantly here, while the magnitude of the optical prism experienced with eye rotation can be seen to rise rapidly once this outer design region is encountered. The shift in design focus is evident in the trends presented in optical properties.

We have traversed the center field of the lens, in particular to obtain a very low rate of change of prism amplitude. Optical prism amplitude, which exhibited increasing paraxial variation with increasing top curvature, remained low within the field of gaze. In comparison, Fig. 4 depicts a prior art spherical lens with lower refractive error over a wide field of view, but higher optical prism (both static and rotational eye effects). In the prior art lens wrapped in Fig. 4B, the left/right eye is parallaxed, but according to the lens of the preferred embodiment of the present invention, such parallax does not occur. It should also be noted that the wall thickness of prior art lenses tapers off everywhere away from the center of the optical axis. A particular characteristic of the lenses of Figure 8 is that they thicken outwardly from the apex region towards the edge, a property found in the preferred embodiment of the present invention.

The second pair of lenses in this example is designed to have the characteristics shown in Figure 9 and is based on the front surfaces Type 5D and Type 5E. These lenses have a low paraxial prism amplitude change rate. However, the essential property is the relatively low oblique refractive error encountered across the field of view, which allows for the addition of optical prisms. Maintaining this objective is to optimize the surface outside of about 35° field of view to obtain always smaller mean power error or RMS mean power error compared to a spherical surface, and to avoid any errors that do not naturally adapt. There is no significant change in the optical property trends because the same design criteria apply across the lens aperture.

These designs, for eye rotations in the field of gaze (±40°), provide low oblique mean power error MPE or oblique RMS mean power error RMSPE compared to prior art spheres, while at most apertures On the other hand, optical prisms still have lower magnitudes than equivalent spherical lenses. Again, a generally constant caliper thickness of the lens unit is preferred over a relatively localized tapering near the edge of the lens. Example 6 Asymmetric non-corrective lenses

Non-corrective goggles used for sun or other protective purposes often have a different curvature in the horizontal direction than in the vertical direction. This asymmetry of the surface form is usually introduced by invoking a suitable asymmetric quadratic surface form. See, eg, US Patents 1,741,536, 4,741,611, 4,867,550, and 5,825,455. A suitable method according to an embodiment of the invention is to describe the lens surface as follows; $z\left(r\right)=C\left(\mathrm{\&kappa;}\right)*\mathrm{Sech}(\mathrm{\&kappa;}/q)+\underset{\mathrm{no}\&Greater\; Equal;3}{\overset{m}{\mathrm{\&Sigma;}}}{A}_{\mathrm{no}}{r}^{\mathrm{no}}$ here $C\left(\mathrm{\&kappa;}\right)=\frac{{\mathrm{\&rho;}}_1}{p_1}(1-\sqrt{1-{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="H2009100021083E00011.png,H2009100021083E00031.png"\; state="\{\{state\}\}">p</figure-callout>}}_1*{\mathrm{\&kappa;}}^2/{\mathrm{\&rho;}}_1^2})$ and κ ² =x ² +τy ²

This method produces the desired asymmetry between the horizontal and vertical shapes according to the value assigned to the parameter τ. Use the parameter set 5C type and take τ=0 to make a lens with a curvature of 3.5D in the horizontal direction and a curvature of 0.0D in the vertical direction on the apex. The resulting properties vary along the horizontal and vertical meridians, as shown in Figure 10. The contours shown in Figure 11 give the visual properties in the field of 40° eye rotation, and the properties of the lens in a 40mm aperture. Vision prisms are plotted in 0.25D steps, while refractive errors are plotted in 0.025D steps around a center range of ±0.005D. Lens prisms are drawn in 1.0D increments. Surface heights are plotted in 5mm steps around the central field within 0.25mm of the apex. Lens thickness is plotted in positive increments of +0.025 nm in the inner field equal to the center value, and in steps of -0.02 mm outside this inner field. Front surface astigmatism is plotted around 1.0D bands in 4.0D steps.

Typical frame aperture shapes tend to grab only a short length of the vertical portion of the lens, so enhanced vertical bending is necessary. Therefore, we have designed the lens with the parameter set of type 5C and taking τ=0. The lens vertex has a horizontal curvature of 3.5D and a vertical curvature of 7.0D. Its features are illustrated in Figures 2A, 12, and 13. Note the lower oblique refraction errors and their symmetry to eye rotation.

These changes in symmetry have an important effect on the astigmatic characteristics of the surface, as shown by the contours in Figs. 11 and 12. Although the lenses all have zero refractive astigmatism along the optical axis, the surfaces do not have a spherical point on that axis, but are instead toric. For the lens of this example, the former spherical points on each surface are divided into a pair of umbilical points on the axis of lower curvature. In place of the outer umbilical annulus is a low surface astigmatism outer annulus consisting of four umbilicus arcs intersecting the two meridians. These arcs become closer as the mean surface curvature increases. Example 7 Optically Corrected Lenses

Houston and coworkers (US Pat. Nos. 5,648,832, 5,689,832, and 6,010,218) have specified that the lens elements of integral and dual lens face wrap sports and sun protection goggles need to be "optically corrected". They state in the first aspect that an optically correct lens must gradually thin from the center to the edge, stating: "Preferably, the lens thickness tapers smoothly, but not necessarily linearly, from a maximum thickness,. ..to a thinner thickness on the outside edge". In the second aspect, they emphasize that, for lenses worn in wrapping and face-close configurations, the optical quality of the frontal line of sight "as the term is used in this orientation as worn, measured by one or more of the following values: prismatic distortion, refractive power, and astigmatism". Target performance on frontal line of sight, for error, both prismatic and refractive errors, at least as low as 1/4D, preferably less than 1/8D, more preferably less than 1/16D, and most preferably less than 1/ 32D.

Historically, non-corrective lenses were made with the same curvature on the front and back surfaces, or at a fixed caliper thickness across the lens aperture. Modern lenses are usually made of polycarbonate, with a center thickness of about 1.5mm. In order to have enough sagittal depth to meet the needs of double lens sports and sun goggles to wrap and hold the face, they have a basic curvature of 8 or 9D. If such lenses are equally anteriorly and posteriorly curved, they thin sharply from center to edge and have a positive posterior vertex power of about +0.095D. If they are of constant thickness, they are low negative lenses with about -0.17D back vertex power. Neither lens met the criteria for a high-performance lens. For example, CEN 1836 "Sunglass & Sunglass Filter for General Use" requires that in a zone with a radius of 10mm, the average spherical power falls within the range of 0.00±0.09D. Therefore, the lens thickness must taper from the center to the edge, but not as rapidly as a lens with equally curved front and back surfaces.

Tables 6A and 6B show the properties of three noncorrective lenses with 9.0D spherical front surfaces. Lenses referred to as "9.0D spherical" have zero refractive power on the optical axis and a thinned thickness defined by the spherical surface. Lenses called "9.0D concentric spheres" have a constant thickness and are negative lenses. Lenses known as "9.0D Aspheric" have zero refractive power on the optical axis and are corrected to maintain zero average power across the wide field of view corresponding to the distance from the rear apex Vision at 27.0mm. It tapers from center to edge slightly faster than spherical lenses. In Tables 7A and 7B we present, for comparison, the properties of three lenses, ie, embodiments of the invention having the same sagittal depth up to 9D substantially spherical at the edge of the lens. These lenses have apex curvatures of 0.0, 3.5, and 5.0D, as indicated, and their optical properties are plotted in Figure 9. Like any of the lenses in the examples given above, these lenses have a caliper thickness that is substantially constant across the entire aperture of the field of view, or increases slowly away from the optical center. Their caliper thickness drops toward the edge of the lens; the caliper thickness drops below the center thickness for zero curvature tops outside the 60° field of view, 3.5D top curvatures outside 55°, and 5.0D top curvatures outside 50°. The optical center is not the point of maximum thickness.

According to prior art quadratic surface designs, lenses of embodiments of the present invention with relatively constant wall thickness will have negative average power at the optical center and increased negative tilt average power in the lateral fields error. However, they did not show any trend towards this performance (Table 7). There is no optical error on the optical axis (corresponding to the axis of rotation), and the tilt error is generally smaller than, or roughly equivalent to, a spherical lens with a field angle of 50° or more. Thus, such lens embodiments according to embodiments of the present invention obey a definition of optical correction substantially different from that understood in the prior art and in the explicit specification of Houston et al.

表6A。对三种有9.0D球面前表面的非矫正镜片：球形面、非球形面、和恒定厚度镜片，列出作为径向距离函数的物理尺寸：卡尺厚度、前表面高度(弧矢深度)、和对应的眼睛旋转角度。

表6B。表6A镜片的作为眼睛旋转角度函数的光学性质。该非球面镜片已经校正到零平均光焦度。

表7A。对按照本发明实施例有非二次前表面和0.0、3.5D和5.0D顶点曲率的三种非矫正镜片，列出作为径向距离函数的物理尺寸。

表7B。表7A镜片的作为眼睛旋转角度函数的光学性质。例8镜片特性的优化 In a defining aspect of the lens embodiments of the present invention, there is provided a non-corrective lens that conforms to the shape of the wearer's face when worn with frontal vision substantially coincident with the optical axis, wherein: when worn, transverse approximation and fixation Field-corresponding aperture that maintains lens thickness without tapering; no significant refractive or prismatic errors in frontal vision when worn, and; oblique refractive focus as the eye rotates across the field of view and into the peripheral field of view The degree error is still small.

Table 6A. For three types of noncorrective lenses with 9.0D spherical front surfaces: spherical, aspheric, and constant thickness lenses, list the physical dimensions as a function of radial distance: caliper thickness, front surface height (sagittal depth), and Corresponding eye rotation angle.

Table 6B. Table 6A Optical properties of lenses as a function of eye rotation angle. This aspheric lens has been corrected to zero average power.

Table 7A. Physical dimensions are listed as a function of radial distance for three non-corrective lenses according to an embodiment of the invention having non-quadratic front surfaces and apex curvatures of 0.0, 3.5D, and 5.0D.

Table 7B. Table 7A Optical properties of lenses as a function of eye rotation angle. Example 8 Optimization of Lens Characteristics

The surface correction of the rear surface of a lens with a predetermined front surface can be done with the aid of computational methods which include the use of figure of merit functions to quantify the relationship between the achieved properties and the target performance objectives. The figure of merit function is usually based on the observed refractive errors, which are mean power error MPE, astigmatism or cylinder error, and RMS power error RMSPE (also known as RMS blur), where $\mathrm{RMSPE}=\sqrt{{\left[\mathrm{MPE}\right]}^2+\frac{1}{4}{\left[\mathrm{CylError}\right]}^2}$

Additional figure of merit functions can also include the optical prism error of the lens, and the rate of change of properties such as blur and prism, for example:

Two examples of lenses optimized using these two figure of merit functions are shown in Figures 14A and 14B, respectively. The front surface is described by the combination of two spheres, as in Example 4, but combined with the following weighting function W(r) $W\left(r\right)=\frac{1}{1+\mathrm{no}{r}^p}.$

The front surface is that described in Table 4C. it has parameter set parameter value N 2.5e-9 P 5.32 ρ₁(B₁) 122.55mm (4.32D)

parameters value ρ₂(B₂) 50.45mm (10.51D)

The corresponding back surface is constructed by adding a 10th order polynomial to the front surface to provide the necessary optical corrections and properties associated with the chosen figure of merit function. In another embodiment, n is in the range of 1×10 ⁻¹² to 1×10 ⁻¹³ , and p is in the range of 8 to 9.

The magnitude of the RMS power error EMSPE, and the magnitude of the optical prism|prism|(rotation), expressed in terms of eye rotation angle in the field of view. Also presented is the static optical prism magnitude |prism|(static), which is determined with reference to the pupil diaphragm of the wearer looking forward. Lens caliper thickness and sagittal depth of the anterior surface, listed as a function of radial position relative to the lens symmetry axis.

A value of figure of merit -1 (FIG. 14A) has achieved significantly lower static prism amplitudes, especially in the peripheral field. However, the RMS power error rises rapidly across the field of view, especially when compared to, for example, the prior art spherical lens of FIG. 4A , reaching critical heights. The lens was obtained by optimizing with RMS blur across the field of view, and then minimizing the static prism amplitude in the peripheral field approximately 60° away from the field of view. The second figure of merit function, figure of merit-2 (FIG. 14B), revealed much lower values of RMS power error across the entire field of view, with values less than about 0.50D. Note here again that the RMS blur has been optimized for the inner angular range, but now the rate of change of the static prism is minimized at about 50° away from the field of view. A comparison of the RMS power error when the eye is rotated by 40° reveals that the RMS power error is at least three times less than the figure of merit -1 at the same point, while the static prism is only at 40 ° field of view is slightly larger. Apparently, figure of merit-2 optimizes the figure of merit function across the entire field of view, making a compromise between the magnitude of the RMS blur and the static prism. Since already in the external field of figure of merit -2, the RMS power error is chosen to be small, the static optical prism allows an increase here.

A comparison of two optimized lenses also shows that a figure of merit -2 allows for greater control over lens thickness. According to the presently described invention, there is no gradual thinning towards the peripheral field across the entire lens aperture of the closed field of view. Unlike the lens with figure of merit -1, where it can be seen that the gradual thinning increases significantly near the boundary of the fixation field into the peripheral field, the lens with figure of merit -2, near the edge of the lens, begins to decrease in thickness as it returns to the center value Before, only a slight increase.

Likewise, by combining two aspheric surfaces with vertex curvatures _B1 and _B2 , it can be used to construct lenses optimized according to a chosen figure of merit function. Using the same weighting function W(r) explained above, combine the two aspheric surfaces so that the final non-rotationally symmetric surface has the form $z(r,\mathrm{\&lambda;})=W\left(r\right)*({\mathrm{\&rho;}}_1-\sqrt{{\mathrm{\&rho;}}_1^2-{\mathrm{\&lambda;}}^2})+(1-W\left(r\right))*({\mathrm{\&rho;}}_2-\sqrt{{\mathrm{\&rho;}}_2^2-{\mathrm{\&lambda;}}^2})$ here $r=\sqrt{x^2+{\mathrm{the\; <figure-callout\; id="2"\; label="y"\; filenames="H2009100021083E00011.png,H2009100021083E00031.png"\; state="\{\{state\}\}">y</figure-callout>}}^2},$ and $\mathrm{\&lambda;}=\sqrt{{\left(\mathrm{ax}\right)}^2+{\left(\mathrm{by}\right)}^2}$

The set of parameters for the front surface is: parameter value N 2.5e-9 P 5.32 A 1 B 0.7 ρ₁(B₁) 122.55mm (4.32D) ρ₂(B₂) 50.45mm (10.51D)

Here the curvature along the vertical section is now generally flatter than along the horizontal section.

The asymmetric lens thus formed is optimized with the figure of merit-2 function. The resulting optical, surface, and lens properties, which vary along the horizontal and vertical meridians, are plotted in Figures 15 and 16. The contours of Figure 16 represent the optical properties in the field of eye rotation ±40°, and the lens and surface properties in an aperture of 40 mm radius. Optical prism and refraction errors, plotted in 0.1D steps. Front surface heights are plotted at 2mm intervals, and lens prisms are plotted at 0.25D intervals. Lens thickness is plotted at 0.05mm intervals from the 2.00mm center value, while front surface astigmatism is plotted at increments of 4D from the first contour 1D away.

The anterior surface is no longer umbilical at the geometric center of the lens, and there are only two local spherical points when viewed along the vertical meridian. The curvature along the horizontal section increases from the central part to the side ends, and the maximum value of the curvature is at a position slightly near the middle, which is consistent with other preferred embodiments of the present invention. The lens has no outer umbilical zone, but does exhibit a sloped zone of maximum surface astigmatism. No refractors or prisms.

Regarding the error on the frontal line of sight, the oblique refraction error is symmetrical in both horizontal and vertical directions on both sides of the frontal line of sight. Also, according to one aspect of the invention, the lens thickness is maintained without tapering across a substantial portion of the field of view.

Various aspects and features of embodiments of the invention have been discussed with reference to some illustrative examples and embodiments. However, the present invention is protected by what is specified in the following claims, and is not to be considered limited to aspects and features not recited in the claims.

Claims (29)

1. A method of providing an afocal optical lens unit, comprising: Select the first and second secondary reference surfaces; Combining the first and second reference surfaces mathematically with a weighting function to give a description of the front surface of the lens element such that the front surface is described by the first reference surface at the vertex of the lens element, and with increasing distance from the vertex while approaching a second reference surface, wherein the front surface is a non-quadratic surface; and The lens unit is formed with the front surface and the complementary rear surface of the lens unit. 2. A method according to claim 1, wherein the rear surface of the lens element is described by adding a polynomial to the surface described as the front surface. 3. The method according to claim 2, wherein the addition of said polynomial provided is based on a figure of merit function which at least makes power error, astigmatism error, RMS blur, prism magnitude, Either the change in RMS blur, or the change in amplitude of the prism is minimal. 4. according to the method for claim 3, wherein merit function M takes following form $\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; RMS\; Blur</span>}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}{<span\; class="notranslate">\; [</span>\frac{<span\; class="notranslate">\; \&PartialD;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Static\; Prism</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}$ where a and b are non-negative weights used to control the relative contribution of RMS Blur and Static Prism optimization in different areas of the field of view, where RMS Blur is root mean square blur and Static Prism is static prism. 5. The method of claim 3, wherein the RMS power error is minimized such that the RMS power is at least as low as 0.75D on the outer boundary of the field of gaze corresponding to eye rotation of at least 40°. 6. A method according to claim 3, wherein astigmatism error is minimized such that astigmatism error is at least as low as 0.75D on the outer boundary of the field of gaze corresponding to eye rotation of at least 40°. 7. according to the method for claim 3, wherein make prism minimum, make average angular growth rate on the amplitude of rotation and static prism component both, on the whole aperture corresponding to field of view, be 40mD/degree field angle or smaller. 8. The method of claim 3, wherein the average angular rate of increase is less than 60 mD/degree in magnitude of the static prism component from the front view of the lens unit to the outermost peripheral edge. 9. The method according to claim 1, wherein the back surface is a non-quadratic surface, described as a surface formed by combining two spheres of different curvature according to a weighting function whose value varies with distance from light defined by the centers of curvature of the two spheres Axis distance varies. 10. The method according to claim 9, wherein the surface height z(r) from the apex plane of the rear surface is described by the following equation $\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\sqrt{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\sqrt{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>$ Here W(r) is the weighting function; ρ ₁ is the first spherical radius; ρ is the _second spherical radius; and $\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; .</span>$ 11. The method according to claim 10, wherein the weighting function W(r) takes the form $\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; nr</span>}}^{\mathrm{<span\; class="notranslate">\; p</span>}}}$ Here n and p are constants for the lens unit. 12. A method according to claim 11, wherein n is in the range ^1x10-12 to ^1x10-13 and p is in the range 8-9. 13. The method according to claim 10, wherein the weighting function W(r) takes the form W(r)=a*[Sech(r/b)] ⁿ Here n, a and b are constants for the lens unit. 14. The method according to claim 10, wherein _ρ1 is in the range of 75.7mm to 530.0mm; and _ρ2 ranges from 40.8mm to 58.9mm. 15. The method according to claim 14, wherein ρ ₁ is in the range of 75.7mm to 265.0mm. 16. An afocal optical lens unit comprising: a rotationally symmetric first surface; and a rotationally symmetric second surface having a complementary curvature to the first surface, where the first surface is a non-quadratic surface, described as a surface formed by combining two spheres of different curvature according to a weighting function whose value varies with distance from the optical axis defined by the center of curvature of the two spheres, and The first and second surfaces therein give an average passing optical power of zero in the field of gaze of the wearer. 17. An optical lens unit according to claim 16, wherein the lens unit has a constant wall thickness in the field of gaze of the wearer. 18. The optical lens unit according to claim 16, wherein the rate of change of the static prism is minimum in a field of gaze of ±50°. 19. An optical lens unit according to claim 16, wherein the complementary rear surface is described as a surface formed by adding a polynomial to the front surface, said polynomial additionally giving optical correction and performance according to a selected merit function. 20. The optical lens unit according to claim 19, wherein the figure of merit function is based on making at least power error, astigmatism error, RMS blur, prism magnitude, change in RMS blur, or prism magnitude change One of the smallest. 21. An optical lens unit according to claim 20, wherein the figure of merit function comprises minimizing a combination of at least RMS blur and static prism rate of change. 22. The optical lens unit according to claim 21, wherein the merit function M takes the form $\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; RMS\; Blur</span>}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}{<span\; class="notranslate">\; [</span>\frac{<span\; class="notranslate">\; \&PartialD;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Static\; Prism</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}$ Where a and b are non-negative weights, which control the relative contribution of RMS Blur and Static Prism optimization in different areas of the field of view, where RMS Blur is root mean square blur and Static Prism is static prism. 23. An optical lens unit according to claim 20, wherein the RMS power error is minimized such that the RMS power is at least as low as 0.75D on the outer boundary of the field of gaze corresponding to an eye rotation of at least 40°. 24. An optical lens unit according to claim 20, wherein astigmatism error is minimized such that astigmatism error is at least as low as 0.75D on the outer boundary of the field of gaze corresponding to eye rotation of at least 40°. 25. according to the optical lens unit of claim 20, wherein make prism minimum, make average angular growth rate on the magnitude value of both rotating and static prism components, on the whole aperture corresponding to field of view, be 40mD/degree field of view angle or smaller. 26. The optical lens unit of claim 20, wherein the average angular growth rate is less than 60 mD/degree in magnitude of the static prism component from the front view of the lens unit to the outermost peripheral edge. 27. The optical lens unit according to claim 16, wherein, wherein the surface height Z(r) from the apex plane of the first surface is described by the following equation $\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\sqrt{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\sqrt{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>$ Here W(r) is the weighting function; ρ ₁ is the first spherical radius; ρ is the _second spherical radius; and $\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; .</span>$ 28. The optical lens unit according to claim 27, wherein the weighting function W(r) takes the following form $\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; nr</span>}}^{\mathrm{<span\; class="notranslate">\; p</span>}}}$ Here n and p are constants for the lens unit. 29. The optical lens unit according to claim 27, wherein the weighting function W(r) takes the following form W(r)=a*[Sech(r/b)] ⁿ Here n, a and b are constants for the lens unit.

Images