CN105259599A - Double-sided Fresnel lens - Google Patents

Abstract

The invention discloses a double-sided Fresnel lens, which comprises an incident surface and an emergent surface. Both the incident surface and the emergent surface are tooth grooves with multiple depressions; the corresponding tooth surface for light concentrating in each tooth groove has an arc surface structure; and the arc surface contour shape of each tooth groove at the lower part changes along with changes of the contour shape of the corresponding tooth groove at the upper part. Through double-sided structure design, the ratio of the focus of the light concentrator to a caliber of the light concentrator is compressed to 0.7; as the tooth surface in each tooth groove adopts an arc surface structure, a tooth distance can be selected randomly, a small light spot can be acquired, and that is, high light concentrating times can be met while a larger tooth distance is used for improving light effects.

Description

A double-sided Fresnel lens

technical field

The invention belongs to the technical field of solar energy utilization, in particular to a double-sided Fresnel lens.

Background technique

The current Fresnel lenses are all single-sided structures, that is, the incident surface is a planar structure, and the outgoing surface is a multi-sink alveolar structure. This structure design makes the thickness of the light-condensing component relatively thick. The caliber ratio (F/#) is usually 1.1, and the tooth surfaces in the tooth grooves of the existing Fresnel lenses are all set as planes, so the Fresnel lens itself must be very thin, that is, the tooth spacing is extremely small, usually It is required to be below 0.5mm. If the tooth spacing is too large, the spot size will be too large. However, due to the process, each tooth tip and tooth bottom, that is, the segment of each tooth surface, will form a rounded corner, and there will be light loss in the rounded part, and the smaller the tooth, the more light will be lost. The greater the efficiency loss.

Contents of the invention

The purpose of the present invention is to provide a double-sided Fresnel lens that satisfies a higher light-gathering factor while improving the light efficiency.

The technical solution of the present invention is achieved as follows: a double-sided Fresnel lens, including an incident surface and an outgoing surface, is characterized in that: both the incident surface and the outgoing surface are provided with a plurality of concave alveoli, each The tooth surfaces corresponding to the light concentrating in the tooth grooves are all arc-shaped structures, and the shape of the arc surface of the lower tooth groove changes with the change of the contour shape of the corresponding upper tooth groove, discretizing the light and from Numbering from right to left, respectively 0, 1, 2, 3 to N, and assuming that the distance between two adjacent rays is ΔX, the optical path through each ray determines the upper and lower parts of the corresponding alveolar. The curve equation of the profile shape of the curved tooth surface;

First, determine the equation of the upper tooth surface, whose curve equation satisfies:

$\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}$

y _n ＝y _n-1 +△x*tanβ

x _n ＝x _n-1 -△x

$\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>}$

sinβ=nsinθ

$\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}$

Among them, x _n is the X value of the Nth ray, m is the X value at the focal point after the Nth ray passes through the curve, a is the semi-diameter of the lens, b is the radius of the focal point, and y _n is the Nth ray and the curve The Y value of the intersection point, ΔX is the distance between two adjacent rays, β is the incident angle of the ray, θ is the incident angle, α is the angle between the refracted ray and the X-axis, h is the vertical distance between the x-axis and the focus, and n is material refractive index;

Where a, b, ΔX, h, n are known, and Y ₀ =0, through the above formula, select the appropriate value of x, the curve point of each tooth can be obtained;

Secondly, after the curve equation of the upper tooth surface is determined, the equation of the lower tooth surface is determined, and the curve equation satisfies:

△x=[x _n-1 -ctgα _n-1 *(y _n-1 +h ₀ )]-[x _n -ctgα _n (y _n +h ₀ )]... Formula 1

△x'＝△x-ctg(α _n-1 )*(y' _n-1 -h ₀ )+ctgα _n (y' _n -h ₀ )………Formula 2

y' ₀ ＝y' _n-1 -△x'*tgφ _n-1 ………Formula 3

${\mathrm{tg\&phi;}}_{\mathrm{no}}=\frac{\mathrm{no}{\mathrm{cos\&alpha;}}_{\mathrm{no}}-{\mathrm{sin\&beta;}}_{\mathrm{no}}}{{\mathrm{cos\&beta;}}_{\mathrm{no}}-\mathrm{no}{\mathrm{sin\&alpha;}}_{\mathrm{no}}}$ ………Formula 4

x' _n ＝x' _n-1 -△x'……Formula 5

${\mathrm{tg\&beta;}}_{\mathrm{no}}=\frac{x_0^{\&prime;}-b+\frac{N}{d}*b}{h^{\&prime;}-{\mathrm{the\; y}}_{\mathrm{no}}^{\&prime;}}$ ……Formula 6

Among them, h ₀ is the thickness of the glass, b is the vertical distance between the intersection point of the first incident ray and the y=h' line and the Y axis, h' is the distance from the light spot to the upper surface of the glass, x ₀ is the first incident ray at The starting point of the upper light-gathering refraction surface, α0 is the angle between the first incident ray and the X-axis after passing through the upper light-gathering refraction surface, and _β0 is the _refraction angle of the first incident ray on the cross-section of the lower light-gathering refraction surface, _θ0 is the incident angle of the first incident ray on the cross-section of the lower light-gathering refraction surface, and φ0 is the acute angle between the curve normal and the y-axis _at the intersection of the first incident ray and the cross-section of the lower light-gathering refraction surface, △x is the distance between the first incident ray and the second incident ray and the intersection point of the lower surface of the glass respectively, △x′ is the horizontal distance between the first incident ray and the second incident ray and the refraction point of the lower concentrating refraction surface , n is the refractive index of the material; N is a natural number, that is, the cross-section of the entire surface is divided into N equal parts, and d is the ratio of light equal ratio compression, which is numerically equal to Formula 1 can be obtained from the upper tooth surface. Substituting Formula 2 into Formula 3, combining Formula 1 to obtain y' _n , substituting y' _n into Formula 6 to obtain β _n , substituting y' _n into Formula 2 to obtain △x', Substitute △x' into formula 5 to obtain x' _n , so that the coordinates (y' _n , x' _n ) of each point on the lower tooth surface are obtained, that is, the curve of the lower tooth surface is obtained;

Among them, the upper and lower tooth surfaces corresponding to the upper and lower tooth grooves are equivalent to forming an independent lens. Assuming that the radius of the entire Fresnel lens is R, that is, X ₀ =R, the upper and lower two can be obtained through the above equation Continuous curve, cut off the continuous curve at a reasonable height position H, the X value of the cut-off position is X ₁ , and the intercepted tooth surface width is W ₁ , then X ₁ = RW ₁ , which is used as the initial calculation point of the next tooth surface, When the height of the next tooth surface is close to H, the curve is truncated; by analogy, until X _n =0, the calculation of the entire Fresnel lens is completed.

In the double-sided Fresnel lens of the present invention, the tooth grooves on the incident surface and the tooth grooves on the outgoing surface are respectively arranged symmetrically with the axis of the lens, and the tooth grooves on the incident surface are The number is equal to the number of slots on the exit surface.

The present invention can compress the ratio of the focal length of the concentrator to the caliber of the concentrator to 0.7 through the double-sided structural design, and at the same time, the tooth surface in the tooth groove adopts an arc surface structure, which can realize that the tooth spacing can be selected arbitrarily while still being able to Obtain a smaller spot, that is, use a larger tooth spacing to meet a higher concentration factor while improving light efficiency.

Description of drawings

Fig. 1 is a structural schematic diagram of the present invention.

Fig. 2 is a schematic diagram of light concentrating in the present invention.

Fig. 3 is a sectional view of the present invention.

Fig. 4 is a partial enlarged view of the section of the present invention.

Fig. 5 is a principle diagram of the tooth surface curve equation of the upper alveolar in the present invention.

Fig. 6 is a principle diagram of the tooth surface curve equation of the middle and lower tooth grooves of the present invention.

Marks in the figure: 1 is the incident surface, 2 is the outgoing surface, 3 is the tooth groove, 4 is the tooth surface, and 5 is the central axis of symmetry.

detailed description

Below in conjunction with accompanying drawing, the present invention is described in detail.

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

As shown in Figures 1-4, a double-sided Fresnel lens includes an incident surface 1 and an outgoing surface 2, the incident surface 1 and the outgoing surface 2 are provided with a plurality of recessed tooth grooves 3, each tooth The corresponding tooth surfaces 4 in the grooves for concentrating light are arc-shaped structures, and the tooth grooves on the incident surface 1 and the tooth grooves on the outgoing surface 2 are respectively arranged symmetrically with the axis of the lens as the central axis 5 , for one-to-one correspondence of light rays, the number of alveoli on the incident surface 1 is equal to the number of alveoli on the outgoing surface 2 .

The difficulty of the double-sided Fresnel lens is that in order to obtain a smaller spot, the upper and lower layers of the Fresnel lens need to match each other, that is, the contour shape of the arc surface of the lower alveolar follows the contour shape of the corresponding upper alveolar In order to make the upper and lower layers of Fresnel lenses match, the light is discretized in the design, and because the concentrator is centrally symmetrical, only a cross section passing through the center of symmetry is considered in the design, and finally the cross section along the This center of symmetry is selected to obtain the desired concentrator.

The specific method is: on the cross section shown in Figure 4, the rays are discretized and numbered from right to left, respectively 0, 1, 2, 3 to N, and the distance between two adjacent rays is assumed is ΔX, and the optical path through each ray determines the curve equation of the contour shape of the upper and lower arc tooth surfaces in the corresponding tooth slot.

As shown in Fig. 5, firstly, the equation of the upper tooth surface is determined, and its curve equation satisfies:

$\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}$

y _n ＝y _n-1 +△x*tanβ

x _n ＝x _n-1 -△x

$\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>}$

sinβ=nsinθ

$\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}$

Among them, x _n is the X value of the Nth ray, m is the X value at the focal point after the Nth ray passes through the curve, a is the semi-diameter of the lens, b is the radius of the focal point, and y _n is the Nth ray and the curve The Y value of the intersection point, ΔX is the distance between two adjacent rays, β is the incident angle of the ray, θ is the incident angle, α is the angle between the refracted ray and the X-axis, h is the vertical distance between the x-axis and the focus, and n is material refractive index;

Where a, b, ΔX, h, n are known, and Y ₀ =0, through the above formula, select the appropriate value of x, the curve point of each tooth can be obtained. In addition, the curve equation of the upper tooth surface can also be obtained by the design method disclosed in the patent CN201210534148.4.

As shown in Figure 6, secondly, after the curve equation of the upper tooth surface is determined, the corresponding equation of the lower tooth surface is determined, and the contour shape of the lower tooth surface is in the plane coordinate system forming the contour shape of the upper tooth surface The curve equation in satisfies:

△x=[x _n-1 -ctgα _n-1 *(y _n-1 +h ₀ )]-[x _n -ctgα _n (y _n +h ₀ )]... Formula 1

△x'＝△x-ctg(α _n-1 )*(y' _n-1 -h ₀ )+ctgα _n (y' _n -h ₀ )………Formula 2

y' ₀ ＝y' _n-1 -△x'*tgφ _n-1 ………Formula 3

${\mathrm{tg\&phi;}}_{\mathrm{no}}=\frac{\mathrm{no}{\mathrm{cos\&alpha;}}_{\mathrm{no}}-{\mathrm{sin\&beta;}}_{\mathrm{no}}}{{\mathrm{cos\&beta;}}_{\mathrm{no}}-\mathrm{no}{\mathrm{sin\&alpha;}}_{\mathrm{no}}}$ ………Formula 4

x' _n ＝x' _n-1 -△x'……Formula 5

${\mathrm{tg\&beta;}}_{\mathrm{no}}=\frac{x_0^{\&prime;}-b+\frac{N}{d}*b}{h^{\&prime;}-{\mathrm{the\; y}}_{\mathrm{no}}^{\&prime;}}$ ……Formula 6

Among them, h ₀ is the thickness of the glass, b is the vertical distance between the intersection point of the first incident ray and the y=h' line and the Y axis, h' is the distance from the light spot to the upper surface of the glass, x ₀ is the first incident ray at The starting point of the upper light-gathering refraction surface, α0 is the angle between the first incident ray and the X-axis after passing through the upper light-gathering refraction surface, and _β0 is the _refraction angle of the first incident ray on the cross-section of the lower light-gathering refraction surface, _θ0 is the incident angle of the first incident ray on the cross-section of the lower light-gathering refraction surface, and φ0 is the acute angle between the curve normal and the y-axis _at the intersection of the first incident ray and the cross-section of the lower light-gathering refraction surface, △x is the distance between the first incident ray and the second incident ray and the intersection point of the lower surface of the glass respectively, △x′ is the horizontal distance between the first incident ray and the second incident ray and the refraction point of the lower concentrating refraction surface , n is the refractive index of the material; N is a natural number, that is, the cross-section of the entire surface is divided into N equal parts, and d is the ratio of light equal ratio compression, which is numerically equal to Formula 1 can be obtained from the upper tooth surface. Substituting Formula 2 into Formula 3, combining Formula 1 to obtain y' _n , substituting y' _n into Formula 6 to obtain β _n , substituting y' _n into Formula 2 to obtain △x', Substitute △x' into formula 5 to obtain x' _n , so that the coordinates (y' _n , x' _n ) of each point on the lower tooth surface can be obtained, that is, the curve of the lower tooth surface can be obtained.

Among them, the upper and lower tooth surfaces corresponding to the upper and lower tooth grooves are equivalent to forming an independent lens. Assuming that the radius of the entire Fresnel lens is R, that is, X ₀ =R, the upper and lower two can be obtained through the above equation Continuous curve, cut off the continuous curve at a reasonable height position H, the X value of the cut-off position is X ₁ , and the intercepted tooth surface width is W ₁ , then X ₁ = RW ₁ , which is used as the initial calculation point of the next tooth surface, When the height of the next tooth surface is close to H, the curve is truncated; by analogy, until X _n =0, the calculation of the entire Fresnel lens is completed.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention should be included in the protection of the present invention. within range.

Claims (2)

1. A double-sided Fresnel lens, comprising an incident surface and an outgoing surface, is characterized in that: the incident surface and the outgoing surface are provided with a plurality of recessed alveoli, and each alveolar corresponding to The tooth surface of the concentrating effect is an arc surface structure, and the contour shape of the arc surface of the lower alveolar changes with the change of the contour shape of the corresponding upper alveolar. The rays are discretized and numbered from right to left, respectively: 0, 1, 2, 3 to N, and assuming that the distance between two adjacent rays is ΔX, the optical path through each ray determines the curve of the upper and lower curved tooth surface contours in the corresponding tooth groove equation; First, determine the equation of the upper tooth surface, whose curve equation satisfies: $\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}$ y _n ＝y _n-1 +△x*tanβ x _n ＝x _n-1 -△x $\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>}$ sinβ=nsinθ $\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}$ Among them, x _n is the X value of the Nth ray, m is the X value at the focal point after the Nth ray passes through the curve, a is the semi-diameter of the lens, b is the radius of the focal point, and y _n is the Nth ray and the curve The Y value of the intersection point, ΔX is the distance between two adjacent rays, β is the incident angle of the ray, θ is the incident angle, α is the angle between the refracted ray and the X-axis, h is the vertical distance between the x-axis and the focus, and n is material refractive index; Where a, b, ΔX, h, n are known, and Y ₀ =0, through the above formula, select the appropriate value of x, the curve point of each tooth can be obtained; Secondly, after the curve equation of the upper tooth surface is determined, the equation of the lower tooth surface is determined, and the curve equation satisfies: △x=[x _n-1 -ctgα _n-1 *(y _n-1 +h ₀ )]-[x _n -ctgα _n (y _n +h ₀ )]... Formula 1 △x'＝△x-ctg(α _n-1 )*(y' _n-1 -h ₀ )+ctgα _n (y' _n -h ₀ )………Formula 2 y' ₀ ＝y' _n-1 -△x'*tgφ _n-1 ………Formula 3 ${\mathrm{tg\&phi;}}_{\mathrm{no}}=\frac{\mathrm{no}{\mathrm{cos\&alpha;}}_{\mathrm{no}}-{\mathrm{sin\&beta;}}_{\mathrm{no}}}{{\mathrm{cos\&beta;}}_{\mathrm{no}}-\mathrm{no}{\mathrm{sin\&alpha;}}_{\mathrm{no}}}$ ………Formula 4 x' _n ＝x' _n-1 -△x'……Formula 5 ${\mathrm{tg\&beta;}}_{\mathrm{no}}=\frac{x_0^{\&prime;}-b+\frac{N}{d}*b}{h^{\&prime;}-{\mathrm{the\; y}}_{\mathrm{no}}^{\&prime;}}$ ……Formula 6 Among them, h ₀ is the thickness of the glass, b is the vertical distance between the intersection point of the first incident ray and the y=h' line and the Y axis, h' is the distance from the light spot to the upper surface of the glass, x ₀ is the first incident ray at The starting point of the upper light-gathering refraction surface, α0 is the angle between the first incident ray and the X-axis after passing through the upper light-gathering refraction surface, and _β0 is the _refraction angle of the first incident ray on the cross-section of the lower light-gathering refraction surface, _θ0 is the incident angle of the first incident ray on the cross-section of the lower light-gathering refraction surface, and φ0 is the acute angle between the curve normal and the y-axis _at the intersection of the first incident ray and the cross-section of the lower light-gathering refraction surface, △x is the distance between the first incident ray and the second incident ray and the intersection point of the lower surface of the glass respectively, △x′ is the horizontal distance between the first incident ray and the second incident ray and the refraction point of the lower concentrating refraction surface , n is the refractive index of the material; N is a natural number, that is, the cross-section of the entire surface is divided into N equal parts, and d is the ratio of light equal ratio compression, which is numerically equal to Formula 1 can be obtained from the upper tooth surface. Substituting Formula 2 into Formula 3, combining Formula 1 to obtain y' _n , substituting y' _n into Formula 6 to obtain β _n , substituting y' _n into Formula 2 to obtain △x', Substitute △x' into formula 5 to obtain x' _n , so that the coordinates (y' _n , x' _n ) of each point on the lower tooth surface are obtained, that is, the curve of the lower tooth surface is obtained; Among them, the upper and lower tooth surfaces corresponding to the upper and lower tooth grooves are equivalent to forming an independent lens. Assuming that the radius of the entire Fresnel lens is R, that is, X ₀ =R, the upper and lower two can be obtained through the above equation Continuous curve, cut off the continuous curve at a reasonable height position H, the X value of the cut-off position is X ₁ , and the intercepted tooth surface width is W ₁ , then X ₁ = RW ₁ , which is used as the initial calculation point of the next tooth surface, When the height of the next tooth surface is close to H, the curve is truncated; by analogy, until X _n =0, the calculation of the entire Fresnel lens is completed. 2. double-sided Fresnel lens according to claim 1, is characterized in that: the alveolar on the incident surface and the alveolar on the outgoing surface are respectively arranged symmetrically with the axis of the lens as the central axis of symmetry, and the The number of alveoli on the incident face is equal to the number of alveoli on the outgoing face.