JP3006611B2 - Design method of lens and optical system - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of designing a lens and an optical system which are easy to manufacture. When designing a lens system or the like, an optical equation is established and solved by some means to obtain values of all optical parameters that determine the lens system. We need to evaluate whether this is a suitable solution. We use an evaluation function for evaluation. This is the sum of the squares of some error at each point, such as a position error at the image point and a wavefront aberration, following the ray. The smaller this is, the smaller the error is as a whole. Therefore, a parameter that minimizes the evaluation function is obtained and is set as a design value. Since the function can evaluate the quality of the design value, it is called an evaluation function. Design values that minimize the cost function should give the best performance.

However, there are actually manufacturing errors. It cannot be made as designed due to errors. Therefore, the range of the maximum error that the error must be less than this in order to give at least this performance is determined. This is the allowable range of the error. This is the tolerance (TOLERANCE). No matter how good the performance can be when manufactured as designed, manufacturing is difficult if the tolerance is small. It is important to find a set of parameters that have good design performance and large tolerances. SUMMARY OF THE INVENTION It is an object of the present invention to provide a method of designing an easily manufactured optical system having a large tolerance.

[0003] Terms will be described. There are various parameters for defining a lens and an optical system. In designing, the present invention will explain that there are two aspects in how the parameters are handled. One aspect is that in designing a lens or an optical system having desired characteristics, some parameters are treated as variables in optimization calculation processing and some are treated as constants. When considering an optical system composed of a plurality of lenses, parameters such as the thickness of each lens, the radius of curvature of each surface, and the interval between the lenses are calculated by calculating an optimal value so as to satisfy the target performance. Done. At this time, parameters of other constants that are not variables are kept at predetermined values with the default values. For example, when the distance from the light source to the lens, the thickness and curvature of the window (= 0), the shape of some lenses, and the distance between the lenses are fixed to predetermined values, they are treated as constants. Physical properties such as refractive index and dispersion determined by the material of the lens and the number of lenses are usually constants, not variables, because values cannot be changed as variables during optimization calculations (preconditions for calculation processing). It is possible to change the material and number of sheets as a precondition change).

[0004] Another aspect is, as will be described later, parameters that give an error and those that do not. The term “giving error” is a fundamental idea of the present invention, and its meaning will be described later. It is not a known concept. It is a completely new concept. However, since it is convenient to describe the types of parameters here, the classification of parameters based on applied errors will also be described in advance. All parameters will have greater or lesser manufacturing errors when they are manufactured after design. Parameters that become variables such as lens thickness, radius of curvature, lens spacing, etc., even if optimal values are obtained as described above, when actually manufactured,
It has a thickness error, a curvature radius error, and a lens interval error. On the other hand, parameters treated as constants also have errors. The wedge (wedge angle), decenter (axis deviation, eccentricity), tilt (tilt), surface accuracy (surface distortion), non-uniformity of refractive index, etc. of a lens are parameters that are purely manufacturing errors, and are generally This parameter is assumed to be completely zero in design. In the present invention, a parameter having a large manufacturing error and affecting optical performance is selected from all of these parameters, and an optimization process is performed by positively giving an error to the parameter. The parameter giving the giving error may or may not be a parameter treated as a variable in design. Alternatively, a parameter that originally represents an error, such as a wedge or decenter, may be used. A parameter given an award error will typically have three values. Assuming that a given error ± δ is given to the value P of a certain parameter, that parameter has a central value P and three values of a maximum value P + δ and a minimum value P−δ. Whether this parameter is a constant or a variable, there is no difference in how the giving error is given. If the value of a variable changes during the optimization calculation, an error is given based on the new value. For example, when the thickness of a certain lens is a variable and gives an error of ± 0.5 mm to the lens, and if the value of the thickness is 10 mm in the middle of the optimization calculation process, the thickness is a central value of 10 mm. Maximum value 10mm +
0.5 mm = 10.5 mm, minimum value 10 mm 0-0.
It is treated as having three values of 5 mm = 9.5 mm. Even if the calculation proceeds and the thickness value is changed to 11 mm, the same application error of ± 0.5 mm is given, and at that time, the three values of 11 mm, 11.5 mm, and 10.5 mm are provided. Is treated as In the above sense, the present invention can classify the parameters into four. 1. A parameter that is a variable and gives an award error. 2. A parameter that is a constant and gives the award error. 3. A parameter that is a variable and does not give an award error. 4. A parameter that is constant and does not give an award error.

[0005]

2. Description of the Related Art An outline of a method of designing an optical system will be described with reference to FIG. To design an optical system consisting of a lens system, the lens material (refractive index, dispersion, absorption coefficient), the number of lenses, the shape selection such as spherical and aspherical surfaces, and the relative arrangement of lenses (distance between lenses, lens Initial values for parameters such as image plane distance) must be determined. In addition, what is used as a variable among those parameters to determine a solution is determined. This is the basic configuration setting. There are some other constraints such as the wavelength of the light source, the thickness of the lens, the material, and the overall dimensions. Taking these constraints into account, formulate an equation that gives refraction on the lens surface, impose conditions that give the desired output, and calculate the solution of variables such as lens thickness, curvature, aspheric coefficient, and spacing by calculation. . That is, the value of a variable that solved the equation is a solution, and an optical system can be defined by a set of solutions.

[0006] In many cases, however, equations that provide a given purpose are abstract and cannot be uniquely solved. Even with constraints, there are not enough equations and there are many solutions. In addition, these equations cannot be solved analytically in most cases because the equations themselves are nonlinear, and when using an aspherical lens, there are many variables that determine the lens itself. In that case, various approximate expressions are used or ray analysis is performed to find solutions for the variables of the optical system. There can be many approximate solutions.
There are often countless solutions that satisfy the equations giving the desired refraction and reflection by the lens and mirror, and it is unlikely that one solution will immediately give the appropriate parameters. Many solutions are found, but it is necessary to find the most appropriate solution set.

An evaluation function is considered as a function for determining whether a solution is appropriate. This is generally the sum of the squares of the error. In general, the smaller the error, the higher the performance, so that the performance of the product can be evaluated. Further, a variable can be obtained under the condition that the evaluation function is minimized. In the present invention, the evaluation function is obtained by adding the squares of optical errors (aberrations) at some points on the image plane with appropriate weights. Of course, there are many types of aberration. An evaluation function is defined by using an appropriate type of optical error (aberration). As an optical system evaluation function including a lens, for example, wavefront aberration is adopted as an error of the evaluation function. Alternatively, a deviation (ray aberration) of a light ray at a test point on an image plane may be used as an error.
An appropriate error of the evaluation function is adopted as needed.

FIG. 2 shows a diagram in which a plane wave is converged by a lens and forms an image at one point. In a plane wave, the wavefront is flat, but when converged by a lens, the wavefront becomes spherical. However, it may not actually be an exact spherical wave. FIG. 3 shows this. The ideal wavefront and the actual wavefront differ. This difference is the wavefront aberration. The image deviates from a perfect circle at the image forming point due to the wavefront aberration. Also, the spot diameter deviates from the ideal case. A discrepancy in roundness is also a type of error. The difference in spot diameter is also an error. Therefore, these errors can be adopted as errors of the evaluation function.

An aberration generated by the solution obtained above is obtained, an evaluation function is created, and a value of the evaluation function is obtained. The value evaluates the validity of the solution. The value of the evaluation function is determined for some solutions. Among them, a set of solutions that minimizes the evaluation function is defined as an optimal design value. This is called optimization calculation.
For example, assuming that the aberration coefficient is s _j , the target value is s _j0 , the weight is w _j , and the evaluation function Φ is Φ = jw _j
(S _j −s _j0 ) ² in some cases. An evaluation function is defined as a square error of the aberration and is minimized. The original evaluation function is to obtain a solution from the optical equation and enter the evaluation function to evaluate the solution.

However, a solution may be obtained by an evaluation function from the beginning without obtaining a solution from an optical equation. Given a certain initial value of the optical system variables (refractive index, thickness, curvature, aspheric coefficient, etc.), find its evaluation function, and give a slight change to the variable from the initial value to find its evaluation function. There is also an asymptotic method of giving a change in a variable in the direction of decreasing. Assuming specific values for the optical variables,
Ray tracing can be performed, and ray aberration and wavefront aberration can be calculated. For the initial values, wavefront aberration, ray aberration and the like are calculated, and from the result, an evaluation function composed of errors such as wavefront aberration and ray aberration is calculated. Ray tracing is possible because the solution is assumed from the beginning, not the solution. Then, a slight deviation is given to the initial value, and ray tracing is performed in the same manner to obtain a wavefront aberration, a ray aberration and the like, and an evaluation function is calculated. In this way, assuming solutions one after another, the quality is evaluated by an evaluation function.

In this way, a set of variables that minimizes the evaluation function is obtained. This is the optimization calculation. Next, what happens to the ray and wavefront aberrations depending on this value, and what happens to the spot shape at each point? Simulate that. Now that the optimal design value has been determined, the parameters are shifted from the design value, and a decrease in performance from the ideal state is examined.
The maximum error within a range in which performance degradation can be tolerated is determined as a tolerance. This is the tolerance analysis. Basic configuration settings so far,
Optical design includes optimization calculation, simulation, and tolerance analysis.

An optical system is actually manufactured based on the result obtained in this manner. And actually check the performance. This is the prototype evaluation. Evaluate products in terms of actual performance, manufacturing cost, ease of production, etc. In the method based on the evaluation function, the value is selected based only on the performance, and the cost, ease of manufacturing, and the like are not considered. Therefore, prototype evaluation is indispensable.

If a satisfactory result is not obtained by the evaluation of the prototype, the process returns to the beginning and starts over from the stage of the basic configuration setting. The same is repeated to finally obtain an optimal set of variable values (optimal solutions). Since similar steps up to this stage are repeated, the development period becomes longer if the number of repetitions is large. Development costs increase. Not a good thing. You want to find the optimal variables faster.

[0014]

In evaluating the performance of a lens system, not only aberration but also cost and manufacturability must be taken into consideration. In the conventional evaluation method, even if a variable is calculated as optimum, it is not always easy to manufacture. The required lens parameters should give optimal performance if they are realized. This is called design performance. However, in practice, variables and parameters cannot be produced as calculated because of manufacturing errors. Actual performance is lower than design performance due to manufacturing errors.

Here, the term performance is defined. An optical system has various characteristics, but the term performance is used as a set of individual characteristics. Individual properties are measurable, but are not, of course, performance because they are a set. Performance cannot be measured unless it is decided which of the characteristics should be emphasized and which should be neglected. Since the weight of the property is appropriately determined, the performance as a set property can be considered to be measurable here. So here, performance is an integrated variable that can be measured.

Each characteristic is determined by parameters and variables of the optical system. The number of variables, such as the thickness of the lens, the curvature of the front and back surfaces, the coefficient of the curved surface, and the distance between the lenses, is large. Design is about determining the optimal values of these variables for a given purpose. A variable that satisfies the equation is simply called a "solution" here. There is one solution for each variable, and given a set of solutions, the design has been made.

The optical system has a predetermined purpose, and the solution of the variable is obtained by setting an equation for the variable that achieves the purpose and solving the equation. However, because there are often fewer equations than variables, there are several sets of solutions that satisfy the equations. In other words, since there are few constraints,
There are several solution sets. Therefore, just finding a set of solutions does not end the design. We must find a more optimal set from a set of solutions that may be infinite.
This is not determined solely by the equations giving the desired effect. Rather, a set of optimum values is often determined from a different viewpoint independently of the individual optical equations.

The means for that is an evaluation function. The sum of the squares of optical errors such as ray aberration and optical path difference is calculated at each point. The smaller this value is, the better the performance is. Current evaluation functions focus on the evaluation of aberrations. That is, assuming that the appropriate values of the variables are known, the solution that minimizes the aberration among them is determined by the evaluation function. Since the aberration is a deviation of the actual performance from the performance when the optical system completely achieves the predetermined purpose, it is reasonable to evaluate the solution by the aberration.
In other words, it is a direct evaluation method because the solution that evaluates the performance and gives the best performance is selected as one of the myriad solutions that is outstanding.

However, it has not been evaluated from the viewpoint of ease of manufacture. Even if the lens shape given by the set of optimum values can be actually produced, even if excellent performance is obtained, since there is always a manufacturing error in the manufacture of the parts, the performance is reduced due to the manufacturing error. Often, the manufacturing error for a given parameter is fatal and a slight manufacturing error can result in significant degradation in performance. Care must then be taken to minimize manufacturing errors for that parameter. Even if careful, there is a manufacturing error, so products that are not inspected and within an allowable error range must be rejected. Then, the yield is low and the cost is high.

FIG. 4 is a graph showing the optical system variables on the horizontal axis and the performance on the vertical axis. There are many optical variables that determine the performance, but only one for simplicity. Although the performance is abstract, it is measurable. When finding the optimal solution using the evaluation function, for example, if the point B is the initial value,
If the variable is biased to the right to lower the evaluation function, a point C is reached. This gives the minimum value of the evaluation function, so it is an optimal solution. However, if the two points are set as the initial values, a variable is gradually changed to a point E where the evaluation function is minimized. This is the optimal solution. When the initial point is the initial point, the variable is changed little by little to reach the initial point. This is the optimal solution. As described above, since the number of variables is large and the constraint conditions and refraction conditions are small, there are several optimal solutions to be obtained by minimizing the evaluation function. Moreover, the optimal solution depends on the initial value. Then the choice of the initial value is important. However, there is no way to know the optimal initial value.

Another problem is that it is not only performance that determines the order between the optimum values. E point is superior to G point in terms of performance. However, point E is a very narrow valley. If the point E is determined, even if there is a slight manufacturing error, the performance is significantly reduced. The performance of point G is inferior to that of point E. However, since it is in a wide valley, when a design value is determined at the point G, the performance does not decrease even if there is a considerable manufacturing error. Further, when the initial value is at B, the optimal value reached by lowering the evaluation function is the point C. The manufacturing error-performance relationship at the point C is more moderate. When an optical system is actually manufactured, some manufacturing error is involved. Therefore, when the point E is set as a design value, the tolerance is small, and it is difficult to produce a product having desired performance. On the other hand, when the point G is set to the design value, even if there is a slight manufacturing error, the performance is not greatly reduced, so that the manufacturing is easy. The point E is difficult to manufacture because of a small tolerance or tolerance. The point G and the point C have a large tolerance and are easy to manufacture. From the viewpoint of ease of manufacture, it is better to set the point G and point C, which have a wide tolerance, to the design value than the point E, which has the best performance.

What is the optimal value? That depends on the initial value. However, it depends not only on the initial value but also on the order in which the variables are moved from the initial value. Different orders of changing variables lead to different minima. The selection of the initial value is arbitrary, and the order of variable changes has various degrees of freedom. Just minimizing the cost function cannot lead to a solution with wide tolerances. Even if a solution with excellent performance is obtained, it is difficult to manufacture if the tolerance is narrow.

FIG. 5 shows the relationship between the manufacturing error and the performance in an abstract manner. When the optimum value x _0, maximum performance (design performance) yl are obtained. If there is a manufacturing error from the optimum value, the performance drops. Assume that the lowest permissible performance (reference performance) is null. The error at the point ヲ where the reference value crosses the performance curve is the tolerance ±
Δ is assumed. That is, the manufacturing error e corresponding to the allowable performance drop is the tolerance ± Δ. Because there are many parameters and variables that affect performance, some parameters have large tolerances and some have small tolerances. Relative = deviation e from the optimum value _{x 0 (x-x 0)} , in some cases performance swoop. When such a parameter exists, processing of the parameter requires careful attention, and even if it is done, a large number of defective products appear. That is, the yield is poor and the production is difficult.

Performance drop dS / de for unit manufacturing error
It is easy to understand the story of assuming something like this in an abstract manner. An optical system with a large parameter
Unless an ideal value can be obtained, the performance is remarkably reduced, which is not preferable in practice. The effect of the manufacturing error is not understood simply by evaluating the solution based on the aberration. Then, after the optimal solution is determined, the tolerance or tolerance of each parameter is given. Similarly, even if the lens has a thickness of 10 mm, the difficulty in manufacturing the lens is completely different between a case where the tolerance is 100 μm and a case where the tolerance is 3 μm.

If there is an optimal solution and there is a set of tolerances for each parameter, and if there is a particularly small tolerance, it is difficult to manufacture a product conforming to the optimal solution. Such a viewpoint of evaluating the solution due to the difficulty of manufacturing has not existed in the conventional optical design evaluation. In the conventional evaluation method, a solution that is small in aberration and has a high performance is determined as an optimal solution without using a solution that is actually easy to manufacture as an optimal solution.

According to the present invention, unlike the evaluation function used in the conventional design method, it is also possible to know whether or not it is easy to manufacture, and as a result, it is necessary to obtain the parameters of the lens system and the optical system that are easy to manufacture. Give design methods to enable.

[0027]

Means for Solving the Problems] Evaluation All parameters for the parameter sets of the state S ₀ no error function E
_0, at least one state S ₁ has an error of error ± [delta] in the parameter, S ₂ ... evaluation function E ₁ for parameter group, E ₂ ... a multiplying an appropriate weighting added evaluation function E =
w ₀ E ₀ + w ₁ E ₁ + w ₂ E ₂ ... = Σw _k E _k
The optical system design method of the present invention finds a set of parameters that minimizes this. It is preferable to select a parameter which gives an error and which is difficult to manufacture with high precision. Further, the applied error ± δ given to the error state is preferably set to a value larger than a normal manufacturing error.

The present invention considers states S ₁ , S ₂ ,... In which parameters are positively assumed to have errors, rather than manufacturing errors that appear naturally in the manufacturing process. This error is tentatively called an applied error to distinguish it from the former manufacturing error. A state including a plurality of application errors is referred to as an error state S ₁ . The state S _{0 in} which no error is given is called an error-free state. The weighted sum 評 価 w _k E _k of the evaluation functions will be referred to as an integrated evaluation function.

The general idea of the present invention will be described with reference to FIG. The state S ₀ is an ideal state in which no giving error is given (no error state). The evaluation function is E ₀ . In addition to the state that gave error + [delta] in the parameter P _i of this is S ₁ (error state). The evaluation function of this and E _1. State S
₂ is a state that gave error of -δ to the same parameter P _i. The evaluation function of this and E _2. If the parameter P _i is treated as a variable, the parameter P _i differs in these three states as P _i , P _i ± δ, but the other parameters are changed in common. An error may be given to two or more parameters.
In that case, many states such as S ₃ , S _4, etc. and the evaluation function E
_3, E _4, ... can. Determine the values of all the variables to determine the wavefront aberration or ray aberration, etc., and obtain an integrated evaluation function E = Σw _k
Calculate the value of E _k and find the set of variables that minimizes E. This is the optimization calculation. An appropriate set of variables is given as an initial value, aberration is calculated, E is calculated, and the variable is minutely changed to determine a variable that minimizes E.

Once the optical variables have been determined, the results are evaluated.
These are performance analysis and tolerance analysis. In the present invention, the variables are optimized so as to minimize the integrated evaluation function to which the evaluation functions of the states S ₁ , S _2, ... To which the error has been added, so that the tolerance for the parameter to which the error has been added becomes large. Manufacturing is facilitated due to large tolerances. Productivity can be increased and manufacturing costs can be reduced.

[0031]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention assumes a state where an error is intentionally given to some of the optical parameters, and creates an integrated evaluation function in addition to an evaluation function having no error and minimizes the evaluation function. Design the optical system by finding the variables. As a result, tolerances can be widened and manufacturing becomes easy.

(1) The parameters giving the giving error are, for example, the following parameters.・ Radius of curvature of each surface ・ Coefficient of aspherical surface ・ Surface accuracy (surface distortion) ・ Center thickness ・ Lens spacing ・ Refractive index ・ Non-uniformity of refractive index ・ Wedge ・ Tilt ・ Decenter If the optical elements include not only lenses but also mirrors and other elements, their optical parameters are taken into account. It is assumed that one or a plurality of these parameters are selected to give an error. In particular, it is only necessary to select parameters that require strict production accuracy.

(2) The error ± δ to be given is set to an appropriate value in consideration of manufacturing accuracy. It is desirable that the value be equal to or larger than a normal manufacturing error. The manufacturing error is an actual error that occurs accidentally during manufacturing and is a random variable. In this case, the average value or an error value (such as a 2σ value) that can statistically occur with a certain probability. It is. When the state in which the applied error δ is small is set to S ₁ , S _2, ..., The tolerance is not so widened because the state is pulled and the evaluation function selects a variable with a small evaluation function. However, if the giving error δ is too large, the difference between the states of S ₀ , S ₁ , S ₂ ... Becomes too large, and the value of the integrated evaluation function does not decrease. It is necessary to select an appropriate giving error δ.

(3) Give initial values to all parameters. This may be a value close to a value that satisfies the optical equation to some extent, instead of a value that satisfies the optical equation. The initial value determines the optimal value that can be reached from it. A variable that minimizes the evaluation function is obtained by gradually changing the value of the variable in the direction in which the evaluation function decreases from the initial value.

If the evaluation function E does not become sufficiently small by the optimization, it means that the performance is still insufficient, or the influence of the manufacturing error is so strong that the tolerance is too small. This can be determined by looking at the breakdown of the integrated evaluation function. If w _k E _k / E (k = 0, 1, 2,...) is calculated for each state S _k , how much the evaluation function for each state contributes to the entire integrated evaluation function (degree of contribution) Can be requested. contribution of w ₀ E ₀ is if still greater performance insufficient. the lower the contribution of w ₀ E ₀ means that tolerance is small. Depending on which state contributes more, a parameter whose tolerance is not loose can be found. If the evaluation function E does not become small, the initial setting is bad. The initial setting is reviewed, and the variable is changed in a direction to lower the evaluation function from the new initial value, and the calculation of the evaluation function is repeated.

If the evaluation function does not become sufficiently small even by the change of the initial value, the given error δ is set to a small value and the initialization is performed to minimize the evaluation function while changing the variables in a direction to reduce the evaluation function. Ultimately, the tolerances may not be loosened. The invention does not always allow the tolerances to be relaxed at will. (The present invention does not override optical theory, that is, optical phenomena as a natural phenomenon.) If a higher performance lens or optical system is desired, the tolerance becomes larger or smaller. The present invention works effectively as a method for efficiently finding a solution which is easy to manufacture and has as close a tolerance as possible within a range satisfying desired performance. (4) When there are many error states S _k (the total number K of k is _i of P i
2 times the total number I: K = 2I) that is, when the selected number of P _i, the evaluation function becomes complicated. Optimization calculations take longer and take more time. If that is not a problem, the results of the tolerance analysis are used to limit the parameters to those that are problematic in manufacturing and to give errors. Then, the number K of error states can be reduced and the calculation time can be reduced. In other words, it is to select a parameter that makes it difficult to reduce the manufacturing error and that cannot be reduced below the required tolerance.

The above-described one gives two error states for one applied error. In order to reduce the number of error states S _k and widen the tolerance, the following means can be taken. This is a method in which two different applied errors are included in one error state. For example, the parameter P _i
And select the parameters P _j, the error state S ₁ is set to + [delta] _i, the P _j + [delta] _j for P _i, the error state S ₂ is P _i
For -δ _i, for P _j can be a -δ _j. S ₁ (+ δ _i , + δ _j ), S ₂ (−δ _i , −δ _j )
That is. In this case, there are two types of applied errors and two error states. That is, the states of (+ δ _i , −δ _j ) and (−δ _i , + δ _j ) are omitted. In this way, the number of error states can be reduced by half, and the calculation time can be shortened. However, to ensure that the effects of each error do not cancel each other,
It is necessary to select the sign of the giving error. For example, if an error of both the thickness of a certain lens and the thickness of another lens is given to one state, the effects of each error cancel each other out, and the evaluation function for that state does not have a very large value. Even so, sometimes the tolerance cannot be widened. Alternatively, the same can occur with the radius of curvature and thickness, the refractive index and radius of curvature, and the like. In such a case, it is necessary to change the combination of the signs (+ or-) of the applied errors so that the influence of each error is not canceled out and selected so as to reinforce each other. Alternatively, an axisymmetric error such as a radius of curvature, a thickness, and a refractive index may be combined with an asymmetric error such as a decenter, a tilt, or a wedge.

(5) The judgment index of the tolerance analysis is some aberration, optical path difference or performance at each point on the image plane. Wavefront aberration, ray aberration, MTF value, distortion,
f-θ linearity, focal length, etc. Is a special performance that can be used only for the f-θ lens. In the case of the wavefront aberration (), the increase in the wavefront aberration due to the increase in the error is, for example, λ / 100 or less (λ is a wavelength). The appropriate limit value is determined for the other items. The deviation (error) from the set value (design value) of the parameter giving the limit value is the tolerance.

FIG. 6 shows a design method by minimizing an evaluation function according to a conventional method. The horizontal axis represents the manufacturing error for a certain parameter, and the vertical axis represents the performance. Performance is low by default. From now on, we will change the variables so that the evaluation function becomes smaller. A circle is written upward from the initial value, but this is an asymptotically improved state. When the target parameter is treated as a variable and the value changes, as shown in FIG. 4, the reference value of the variable itself changes and the performance increases. 4 is represented by the transition of the circle from the initial value to the optimal solution in FIG. Optimal solution is the set of variables which minimizes E _0. This gives the best performance when changing variables starting from some initial value. However, the tolerance is small, and the reference performance is given only between the yota.

FIG. 7 shows a design method by minimizing the integrated evaluation function according to the method of the present invention. The initial value is arbitrarily selected. Variables are varied so that the integrated evaluation function is reduced from the initial value. It is the optimum value that gives the minimum value. Since the integrated evaluation function including the error state is handled, the tolerance is increased. Satisfactory performance can be provided even if there is a wide manufacturing error between the reflexes.

The parameters that determine the optical system there is also a number, gives only an error ± [delta] of which the parameters of the P _i. The evaluation function E ₁ of the state S ₁ to which an error of + δ is given is included in the integrated evaluation function. When minimizing the integrated evaluation function E
_One should of course be smaller. That E ₁ is small is that you are choosing variables set as even performance degradation when there errors + [delta] is less. So tolerance of parameters P _i is widened. That's intuitive. But this cannot be proved rigorously. This is because the parameters are various and the degree of involvement in the optical equation is also various. With respect to other parameters, it is not known in advance whether the tolerance is widened or narrowed. That is something that cannot be understood without actually calculating it. The tolerances of the other parameters are large, some are small, and some are not very different. Other parameters that are larger or do not change much are perfectly fine. Further, even if other parameters, which were originally large tolerances, are slightly reduced, no manufacturing problem occurs. The problem is,
This is the case where the tolerances of other parameters become smaller and the manufacturing accuracy cannot satisfy the tolerances.If the tolerances of other parameters become stricter, a state where an error is given to that parameter is added. A new integrated evaluation function can be created and optimized again.

[0042]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The optical system of interest may be of any type. Here, for the f-θ lens as an example, plus and minus deviations are given for various parameters,
Find the optimal solution that minimizes the evaluation function, and show that the tolerance increases.

(A) Initial lens setting ○ Number of lenses 2 Material ZnSe (refractive index n = 2.40)
3) 1st lens 1st surface is aspherical surface, 2nd surface is spherical 2nd lens 1st surface is spherical surface, 2nd surface is aspherical surface 波長 wavelength 10.6 μm 入射 entrance pupil position The first lens 1st surface is the object field Side 50mm F-number 6 Incident angles 0 °, 8 °, 16 ° An f-θ lens forms an image of light rays incident at an angle of θ from the optical axis at a position fθ away from the center of the image plane. Such a lens. FIG. 18 shows an optical system. Two lenses are used. The parallel light is converted into a lens 1 at an inclination angle of θ
, The ray coming out of the lens 2 is f
It converges to a point θ away. For example, a parallel light of θ = 0 °,
F and f converge to a point J on the optical axis. The parallel light beams 、, サ, and ゜ of θ = 8 ° form an image at a position K of 8 × L on the image plane. θ =
The 16 ° parallel light beams M, M and C form an image at a position M of 16 × L on the image plane. Here, L is a constant. Although only three rays are written in each case, countless parallel rays actually converge at one point.

(B) Variable setting The radius of curvature, thickness (interval), aspheric coefficient, and image plane position of each surface (there are four surfaces). Since there are two lenses, four radii of curvature exist as variables. Regarding the thickness, there are the thicknesses of the two lenses and the distance between the lenses. Since the first surface of the first lens and the second surface of the second lens are aspheric, the aspheric coefficient is a variable for each. this is

[0045]

(Equation 1)

The conic constant
An even-order power coefficient αj of k and radius r. c is the vertex curvature. For example, the fourth order of r, 6
If it is next, eighth, or tenth, α is four parameters. The image plane position is the distance of the image plane from the second lens. As described above, since the number of variables is large, it is necessary to judge the suitability of the variables using an evaluation function.

(C) Constraint conditions: focal length 127 mm, lens thickness 3.5 mm or more and 15 mm or less

(D) Setting of Error 1. Decenter: The deviation of the center axis of the lens from the optical axis. 2. Tilt: lens tilt 3. The radius of curvature of each surface: the radius of curvature of the spherical surface on the front and rear surfaces. 4. Aspheric coefficient: coefficient of two aspheric surfaces 5. Surface accuracy (surface distortion) 6. Refractive index: deviation of the overall refractive index of the ZnSe lens from a predetermined value Refractive index non-uniformity: local refractive index fluctuation Wedge

And so on. Parameters to which errors should be added
Is selected from one or more of them. For example
If we give an error only to the decenter,
become that way. That is, when there is no lens displacement (S₀ )of
Evaluation function E₀ And the case where there is an axis deviation of ± δ (S
₁ ) (S_Two ) And each evaluation function E₁ , E _Two 
Is calculated for each set of variables to minimize the sum of the evaluation functions.
Find a set of variables. The overall evaluation function E is weight w₀ , W₁,
w_Two And multiply by the sum. E = w₀ E₀ + W₁ E₁ + W_Two E_Two (2) Weight w₀ , W₁ , W_Two Can be freely decided.

Here, it is assumed that w ₀ = w ₁ = w ₂ = 1. Therefore, the evaluation function is simply E = E ₀ + E ₁ + E ₂ (3). The decenter error ± δ to be given is given an appropriate value in consideration of the level of manufacturing accuracy. It is better that the giving error is larger than the manufacturing error.

An error may be given to other parameters in addition to the decenter error. For example, an error of ± 1% is given to the radius of curvature of the first surface of the first lens. Then, the states of S ₃ and S ₄ increase. Since a sum of five evaluation functions can be obtained, a set of variables that minimizes the sum is obtained. When the set of optimal variables is obtained in this way, when the decenter tolerance and the curvature radius tolerance are obtained, the tolerances are larger than those at S ₀ . Manufacturing is facilitated due to large tolerances.

As the evaluation function, for example, ray aberration is adopted. Of course, other optical errors such as wavefront aberration may be used for the evaluation function. If there is an aberration in the lens, a group of rays, which should ideally converge on a single point on the image plane, scatter to points and reach the image plane. The sum of squares of the deviation of each ray is taken and used as an evaluation function.

FIG. 19 is an example showing the distribution of light rays on the entrance pupil. Here, the entrance pupil may be considered as a cross section of light incident on the lens. One point in the entrance pupil means one ray. Any position on the pupil (P _x ,
Any number of rays may be used for P _y ), but in order to increase the calculation accuracy, the number of rays is preferably large and distributed over the entire pupil. Here, (P _x , P _y ) indicates coordinates on the pupil. The size of the pupil is normalized and represented by a circle having a radius of 1. However, the number of rays must not be too large in order to reduce the amount of calculation and perform the optimization quickly. FIG. 19 shows an example in which 18 rays are taken. Take six straight lines extending radially from the center of the pupil (each 0
Degrees, 60 degrees, 120 degrees, 180 degrees, 240 degrees, and 300 degrees), and take three rings of different sizes. The radii R of the three rings are R = 0.3357, 0.707, respectively.
1, 0.9420. A total of 18 rays are taken at the intersection of these 6 radiations and 3 rings. The weight of each ray is w _j = 0.048481 (12 lines) for a black circle and w _{j for} a black and white circle.
= 0.07757 (six lines).

What position each ray varies on the image plane
Is calculated, the positional deviations Δx and Δy are
I get it. Δx and Δy are the deviations of all the rays from the center of gravity.
x component and y component. Each ray is j (j = 1, 2,...,
18), incident angles 0 °, 8 °, and 16 ° are changed to f (f = 1,
2, 3), and the weight w for each ray_j And for each incident angle
Weight w_f Multiply by one state S_k Evaluation function E for
_k (Omit here because we are dealing with a single wavelength case)
However, when dealing with light of a plurality of wavelengths, the weight w
multiply by λ to get the sum). S_k E for_k Is E_k = ΣΣw_f w_j (Δx_fj ^Two + Δy_fj ^Two (4) This is the state S₀ , S₁ , S_Two , ... evaluation function
E₀ , E₁ , E_Two , E_Three,…give. The invention is error free
State S₀ Error state S with error and error₁ , S _Two , S
_Three Is added to each state S_k Weight of w_k 
The integrated evaluation function E is given by: E = Σw_k E_k = ΣΣΣw_k w_f w_j (Δx_kfj ^Two+ Δy_kfj ^Two(5) Vary the variables to minimize this
It is.

With the above evaluation function, the light convergence characteristic of the lens can be evaluated. However, in designing an f-θ lens, it is necessary to be able to evaluate the linearity of the f-θ relationship as another important characteristic. (4) does not include the f-θ linearity evaluation because the error is the deviation of the light ray position on the image plane. In the case of an f-θ lens, it is necessary to further optimize the evaluation function so as to obtain good linearity between f-θ.

For example, the positions h _{J of the} focal points J, K, and M on the image plane when three incident angles of 0 °, 8 °, and 16 ° are taken.
(= 0), h _K , h _M are obtained by calculation by ray tracing the parameters of the optical system at that time. At this time, since the angle of incidence is just twice as large as the angle of incidence of 8 degrees with respect to the angle of incidence of 8 degrees, it should be 2h _K = h _M if the ideal f-θ has linearity. Therefore, as a function for evaluating the linearity of the f-θ, E _L = take ^{_{(2h K -h M) 2 (}} 6). If more than three incident angles are set, a number of functions as in equation (6) are set, and their sum is taken, f−
The linearity of θ can be evaluated in detail. At the same time as Expression (5), the value of the variable is optimized so as to minimize the evaluation function as in Expression (6).

Further, constraints such as the focal length and the thickness range of the lens may be incorporated in the evaluation function.
In order to set the focal length f to a target value, for example, 127 mm, an evaluation function represented by e ₁ = (f-127) ² (7) can be taken. Set the thickness t of the lens to a target range, for example, 3.5 mm or more and 15 mm.
In order to make the following, e ₂ = α (t−3.5) ² + β (t−15) ² (8) is taken as the evaluation function. However, the coefficient α is α = 0 when t> 3.5 mm,
When t ≦ 3.5 mm, α = 1. Similarly, the coefficient β assumes a value of β = 0 when t <15 mm and a value of β = 1 when t ≧ 15 mm. So this is the thickness t
Is 0 in the range of 3.5 mm to 15 mm, and becomes a positive value outside this range. As described above, the constraint condition can also be expressed by the evaluation function. The evaluation function e _c (e ₁ , e ₂ ,...) Relating to such a constraint condition is set to an appropriate weight w _c
The by summing over, summarized in the evaluation function _{E c} for all of the constraints, the _{E c = Σw c e c (} 9).

The integrated evaluation function is completed by taking the sum of the three evaluation functions (5), (6), and (9) as described above. Multiply by the appropriate weights w _A , w _L , and w _C and take the sum. Integrated evaluation function E becomes _{E = w A Σw k E k} + w L E L + w C E C (10). The weights w _A , w _L , w _C are given by Σw _k E _k , E _L ,
It works to minimize each evaluation function of E _{C in} a well-balanced manner. Here, it is simply assumed that w _A = w _L = w _C = 1 and E = Σw _k E _k + E _L + E _c (11). Calculation for optimizing variables so as to minimize the integrated evaluation function is performed. By finding the optimal solution, the best set of parameter values is obtained for each of the f-θ linearity and the constraint condition in addition to the ray aberration in each state.

First, an optimal design for S ₀ is performed according to the conventional method. The evaluation function is E = E ₀ + E _L + E _C.
FIG. 8 illustrates this. Light emitted from the light source is deflected by a deflecting device such as a polygon mirror or a galvanometer mirror, enters a lens at an incident angle determined thereby, is converged by the lens, and converges on an image plane. Here, three deflected lights are shown as an example, but this number is arbitrary. The curvature and thickness of the lens are variables. If there are two or more lenses, the lens spacing is also a variable. Since certain restrictions are imposed on the shape, dimensions, and the like of the lens, variables are variously changed within the range. In this method, the evaluation function is calculated according to the conventional method without giving any error to the decenter and the radius of curvature. Find the (optimum) value of the variable that minimizes the evaluation function.
This is to find the tolerance of the variable. As a result, the decenter tolerance was ± 40 μm. The radius of curvature tolerance of the first lens is ± 0.066%. Both tolerances are small and difficult to manufacture.

Embodiment 1 (Decenter of ± 160 μm) In addition to the S ₀ state having no decenter error, two error giving states will be considered. FIG. 9 shows an explanatory diagram. The variables of the optical system include the curvature of the front and rear surfaces of the lens, the lens thickness, the lens interval, and the like. The case without decenter is shown on the left. Light rays from the light source are converged by the lens into three positions.
Let its evaluation function be E ₀ . In this case, ray aberration is adopted instead of wavefront aberration. The incident angle is, for example, 0
Degrees, 8 degrees and 16 degrees.

S ₁ (−160 μm) and S ₂ (+160 μm) when the decenter error ± 160 μm is given. Ray aberration is also adopted for these. The evaluation functions in each case are E ₀ , E ₁ , and E ₂ . Optical variables are given for each state. Restrictions are imposed on the shape and dimensions. By changing the variables within the restriction conditions, the integrated evaluation function E = E ₀ + E ₁ + E ₂ + E _L + E _C is calculated (w _k = 1; k = 0, 1, 2). I asked. The decenter tolerance in that case was ± 202 μm as a result of the tolerance analysis. The manufacturing becomes easy because the tolerance is increased about five times. Not only that, but performance is also improved.

FIG. 20 shows an example of the result of analyzing and evaluating the characteristics of the f-θ lens determined by the optical parameters obtained by minimizing the evaluation function in the error-free state by the conventional method.

[0063]

[Table 1]

[0064]

[Table 2]

As a manufacturing error, a decenter error is 160 μm.
Is given, and the intensity distribution of the condensed spot on the image plane at that time is shown by contour lines. This is the point J, K in FIG.
Point spread function (point spread function) for points M and M, that is, when the incident angles are 0 degrees, 8 degrees, and 16 degrees.
Is the result of calculating. In FIG. 20, the intensity of the condensed spot is represented by a contour line with a sharp mountain shape that is higher at the center and lower as it spreads out. The spot at 0 degrees (point J) is a contour line almost close to a perfect circle. On the other hand,
The spot at 16 degrees (point M) is long and elliptical. This indicates that, due to the set decenter error of 160 μm, the spot is distorted as the incident angle increases, as at point M, and good characteristics cannot be obtained.

On the other hand, FIG. 21 shows an integrated evaluation function in which an error state in which a decenter error ± 160 μm is given according to the present invention is set, and the f-θ lens determined by the optical parameter obtained by minimizing the integrated evaluation function is the same as described above. Is a result of simulating characteristics by setting a decenter error of 160 μm.

[0067]

[Table 3]

[0068]

[Table 4]

This lens has a decenter tolerance of ± 2.
Since the spots are loosened to 02 μm, even if there is a decenter error of 160 μm, any of the spots at the incident angles of 0 °, 8 °, and 16 ° does not distort and draws a true circular rotationally symmetric contour. It can be seen that the present invention is superior to the conventional method shown in FIG.

Example 2 (± 160 μm decenter error and ± 1% radius of curvature error; part 1) In addition to ± 160 μm decenter error, ± 1% error in the radius of curvature of the first surface of the first lens Was given.

[0071]

[Table 5]

[0072]

[Table 6]

S ₁ (-160 μm), S ₂ (+160 μm)
m), S ₃ (−1%), S ₄ (+ 1%) and S ₀ , the evaluation function E = E ₀ + E ₁ + E ₂ + E
₃ + E ₄ + E _L + E _C was calculated, and a set of variables that minimized this was determined. In this case, the curvature radius tolerance of the first surface of the first lens was ± 0.770%. It is more easily manufactured because increasing more than 10 times that of the conventional design tolerances handle only states of S _0. In addition, the tolerance of the decenter is also ± 180 μm, which is more relaxed than ± 40 μm of the conventional design.

Example 3 (± 160 μm decenter error and ± 1% curvature radius error; part 2) Simultaneously with ± 160 μm decenter error, ± 1% error is given to the radius of curvature of the first surface of the first lens. Was.

[0075]

[Table 7]

[0076]

[Table 8]

S ₁ (-160 μm, -1%), S ₂ (+
(160 μm, + 1%) and S ₀ were added, and an evaluation function E = E ₀ + E ₁ + E ₂ + E _L + E _C was calculated, and a set of variables minimizing this was obtained. In this case, the decenter tolerance was ± 201 μm, and the curvature radius tolerance of the first surface of the first lens was ± 0.645%. The tolerance is about 5 times the decenter tolerance in the state of S ₀ , and the radius of curvature is increased to about 10 times, so that manufacturing becomes easier.

Example 4 (± 0.2 mm lens thickness,
Lens spacing error)] The above description relates to the decenter error and the error in the radius of curvature of the lens.
Next, an error was given to the lens thickness and the lens interval to create an evaluation function, which was minimized.

[0079]

[Table 9]

[0080]

[Table 10]

There are six states where an error is given. The state where an error of ± 0.2 mm is given to the thickness of the first lens is S
S ₃ and S ₄ are states where an error of ± 0.2 mm is given to ₁ , S ₂ and the lens interval. ± 0.2 mm for the thickness of the second lens
State that gave the error is S _5, S _6. Then, the integrated evaluation function E = E ₀ + E ₁ + E ₂ + E ₃ + E ₄ + E ₅ + E
A set of variables that minimized ₆ + E _L + E _C was determined.
In the case of a set of variables that only minimizes E ₀ , the tolerance of the lens thickness and the interval was ± 0.08 mm, but in the set of variables that minimizes the integrated evaluation function including six errors, The tolerance of the thickness interval has increased to ± 0.23 mm. This is easier to manufacture because the tolerance is tripled.

Example 5 (Refractive index error of ± 0.02)
For both the first lens and the second lens, a material for infrared light of ZnSe is used. The refractive index is usually set to 2.403, but a state where a refractive index error of ± 0.02 is given to this is considered.

[0083]

[Table 11]

[0084]

[Table 12]

S ₀ is a state where there is no refractive index error. S ₁
Is a state where the refractive index of the first lens has an error of +0.02,
S ₂ is a state in which the refractive index of the first lens has an error of -0.02, S ₃ state gave an error of +0.02 to the refractive index of the second lens, S ₄ are the refractive index of the second lens This is a state where an error of −0.02 is given. The evaluation functions of these five states are E _j (j = 0,..., 4). Integrated evaluation function E = E
Optical variables that minimize ₀ + E ₁ + E ₂ + E ₃ + E ₄ + E _L + E _C were determined. The refractive index tolerance was ± 0.00782 for the variable determined as the S ₀ minimum that does not give an error, while the refractive index tolerance for the variable that minimized the integrated evaluation function was ± 0.0115. It has increased by about 50%.

Example 6 (± 0.2 mm lens thickness interval error and ± 10 minute tilt error) In addition to the lens thickness and interval of Example 4, ± 1 is set as the lens tilt error.
Consider what has been given 0 minutes. In the fourth embodiment, the tolerances of the lens thickness and the interval are loosened, but the tolerance of the tilt is strictly ± 3.8 minutes in the fourth embodiment, compared with ± 10.7 minutes in the conventional method. Therefore, in the present embodiment, it is shown that an error of the tilt is given in addition to the lens thickness and the interval, and that all the tolerances are increased.

[0087]

[Table 13]

[0088]

[Table 14]

S₁ ~ S₆ Is the same as in the fourth embodiment. S
₁ , S_Two Is an error of ± 0.2 mm for the thickness of the first lens.
State with difference, S_Three , S_FourIs ± 0.2 for lens spacing
mm is given. S_Five , S₆ Is the second ren
This is a state in which an error of ± 0.2 mm has been given to the gap thickness. S₇ 
Is the first lens with a +10 minute tilt error
It is. S₈ Gives a -10 minute tilt error to the first lens
This is the state that has been granted. S ₉ Is +10 minutes for the second lens.
State with tilt error, S_TenIs -10 minutes for the second lens
Is given. Their evaluation function
As E₁ ~ E _TenAnd the integrated evaluation function E = E₀
+ E₁ + ... + E₉ + E_Ten+ E_L + E_C think of. Tea
Evaluation function E = E with no default error₀ + E₁ + ...
… + E₆ + E_L + E_C In the case of the fourth embodiment, the tilt tolerance is
± 3.8 minutes. Here, a tilt error ± 10 minutes is added.
As a result, the tilt tolerance increased to ± 8.1 minutes. About twice
It is easy to manufacture. Lens thickness, lens
The tolerance of the interval became ± 0.25 mm.

Example 7 (Wedge Error of ± 5 Minutes) ± 5 minutes was set as the wedge error of the second lens.

[0091]

[Table 15]

[0092]

[Table 16]

[0093] S ₁ is in a state of being endowed with wedge error of + 5 minutes. S ₂ is a state in which endow wedge error of -5 minutes. Wedge error in the evaluation of only the conventional method E ₀ is ±
It was 1.9 minutes. E = E ₀ + E ₁ + E ₂ + E _L + E _C
Minimizing the wedge tolerance was improved to ± 2.7 minutes. The production becomes easy because it is enlarged by 0.8 minutes.

[Embodiment 8 (Nonuniformity of refractive index distribution)] Calculations have been made on the assumption that the lens has a constant refractive index. As for the fluctuation of the entire refractive index, the example in which the error of ± 0.02 was given in the fifth embodiment was described. Here, spatial non-uniformity is treated instead of uniform refractive index fluctuation.

[0095]

[Table 17]

[0096]

[Table 18]

It is assumed that the second lens has a non-uniform refractive index depending on the radius as expressed by the following equation.

N = n ₀ + Ar ² + Br ⁴ (r = (x ² + y ² ) ^1/2 ) (12) n ₀ = 2.403 S ₀ is a state in which the refractive index is uniform at A = 0 and B = 0. (N = n
₀ ). S ₁ is a non-uniform refractive index state where A = + 5 × 10 ⁻⁷ and B = −4 × 10 ⁻¹⁰ . S ₂ is A = −5 × 10 ⁻⁷ ,
B = + 4 × 10 ⁻¹⁰ with non-uniform refractive index. S ₀
When only the evaluation function E ₀ was minimized, the tolerance of the refractive index inhomogeneity was ± 0.0000193. According to the present invention, the integrated evaluation function E = E ₀ + E ₁ +
The optimization of the variables by minimizing E ₂ + E _L + E _C improved the index non-uniformity tolerance to ± 0.0000267. This means that the tolerance has increased by about 40%.

Ninth Embodiment (Aspherical Lens) Next, taking a simple aspherical lens as an example, an evaluation function is set by giving an error to parameters different from those in the first to eighth embodiments. By finding a variable that minimizes, it is shown that the tolerance increases as in the case of the f-θ lens.

(A) Initial lens setting. Number of lenses 1 Material ZnSe (refractive index n = 2.40
3) The first surface is a convex aspheric surface, and the second surface is a concave spherical surface. Wavelength 10.6 μm Entrance pupil diameter φ50.8 mm Incident angle 0 ° (only vertical incidence) The lens is made of ZnSe and has a meniscus shape, and the first surface is aspherical. The incident light is only infrared light having a wavelength of 10.6 μm and parallel light is perpendicularly incident.

(B) Variable setting The radii of curvature of the first and second surfaces and the aspheric coefficients (k, α ₁ , α
₂ , α ₃ , α ₄ ), thickness, and image plane position are variables.

(C) Constraint Conditions Focal length 95.25 mm Lens thickness 3 mm or more and 12 mm or less The problem of surface precision error (Fringes Irregularity) is a problem.
This is a deviation from the ideal curved surface. Wavelength 0.633 μm
Can be measured using an appropriate interferometer with the He-Ne laser as a reference wavelength. The magnitude of the deviation is represented by the number of interference fringes. For example, consider a case where there is a deviation in curvature in each of the cross sections in the x-axis direction and the y-axis direction as shown in FIG. Here, the axis of the lens is the z axis, and the X axis is in a plane perpendicular to the z axis.
Take the Y axis. That is, cylindrical distortion that is not rotationally symmetric occurs. At this time, the interference fringes are as shown in FIG. The difference between the number of stripes in the vertical direction and the number of stripes in the horizontal direction is expressed as surface distortion.

[0103]

[Table 19]

[0104]

[Table 20]

In the set of variables minimizing the evaluation function E = E ₀ + E _c including only the state S ₀ not including the surface accuracy error (conventional example 2), the surface accuracy tolerance was ± 2.97 lines. .

According to the concept of the present invention, a state S having a cylindrical surface precision error such that ± 5 stripes appear.
_1, assuming S _2, it was determined these evaluation functions E _1, E ₂ integrated evaluation function _{E = E 0 + E 1 +} E 2 + E c a to minimize variables added (Example 9).

[0107]

[Table 21]

[0108]

[Table 22]

According to this, the tolerance of the surface accuracy was improved to ± 4.67 lines.

[0110]

The present invention considers states S ₁ , S ₂ ... In which an error of ± δ is included in one or a plurality of parameters P _i among the optical parameters, and evaluates these evaluation functions E ₁ , E 2.
_2, integrated assessment was added to the ... to the evaluation function E ₀ of the non-error state S ₀ function _{E 0 + E 1 + E 2} ... to make a, while changing the variable,
It looks for variables that minimize this. The parameters P _i thought the state was endowed with error is spread tolerance. Manufacturing becomes easy because the tolerance is increased.

[Brief description of the drawings]

FIG. 1 is a schematic explanatory view of a lens design method.

FIG. 2 is a diagram showing a change in wavefront when a plane wave is converted into a spherical wave by a lens.

FIG. 3 is a view for explaining that a difference between an actual wavefront and an ideal wavefront is a wavefront aberration.

FIG. 4 is a diagram for explaining that performance varies as a function of an optical system variable, but there is a case where a performance change is large even when a change of a variable is small, and a case where performance degradation is small even when a variable change is large.

FIG. 5 is a graph illustrating that the performance of an optical system decreases with a manufacturing error, but the performance is allowed to be reduced to a reference value, and the error is used as a tolerance.

FIG. 6 shows an evaluation function E ₀ giving no error according to a conventional method.
FIG. 4 is a diagram for explaining that a tolerance is reduced when an optical parameter is determined in FIG.

FIG. 7 shows an example in which some parameters are given errors according to the concept of the present invention, and parameters are selected so that an evaluation function in a state including an error and an integrated evaluation function added to an evaluation function containing no error are minimized. FIG. 7 is a diagram for explaining that tolerances are widened in the case and manufacturing becomes easy.

FIG. 8 is a view for explaining a procedure of a conventional method for obtaining an optical parameter by minimizing an evaluation function E _{0 in a} state where no error is given.

FIG. 9 shows an integrated evaluation function obtained by adding the evaluation functions E ₁ and E ₂ in a state where a decenter error of ± δ is given to an evaluation function E ₀ in a state where no error is given, and minimizing the integrated function to set parameters. The figure explaining the procedure of this invention to determine.

FIG. 10 explains that according to the conventional method of determining a parameter by minimizing an evaluation function in a state where no error is given, even if a manufacturing error is slight, an aberration increases significantly and a wide tolerance cannot be obtained. Graph. The abscissa represents the manufacturing error, which expresses the errors of various parameters collectively.

FIG. 11 shows a method according to the present invention for determining a parameter by minimizing an integrated evaluation function obtained by adding an evaluation function in an error-given state and an evaluation function in an error-free state; Is a graph for explaining that the increase in aberration is slight and the tolerance can be widened. The abscissa represents the manufacturing error, which expresses the errors of various parameters collectively. The vertical axis indicates the aberration, which indicates an aberration related to the performance in general, and an appropriate aberration such as a positional deviation or a wavefront aberration in ray tracing can be selected.

FIG. 12 is a view for explaining the flow of the design method of the present invention using an evaluation function for a state where an error is given.

FIG. 13 is a diagram showing a state where axes of two lenses are shifted. This is the decenter error.

FIG. 14A is a diagram illustrating a state in which the optical axis of one of two lenses is inclined. This is the tilt error. (2)
FIG. 4 is a diagram showing a state in which the thickness of the lens is not uniform and changes in a wedge shape. This is the wedge.

FIG. 15 is a graph showing distortion of a cylindrical surface. A solid line indicates an ideal lens curved surface, and a broken line indicates an actual lens curved surface. Since it is a curved surface, it has a two-dimensional spread. Here, an xz section and a yz section are shown. This indicates that the surface is the same as the ideal curved surface in the y direction, but deviates from the ideal curved surface in the x direction.

FIG. 16 shows interference fringes by a He-Ne laser (wavelength λ = 0.633 μm) of a lens having a curved surface shifted in the x direction as shown in FIG.

FIG. 17 is a diagram showing that parallel light is converged at one point in an aspheric lens having a first surface that is convex (aspheric surface) and a second surface that is concave (spherical).

FIG. 18 is a diagram showing a state in which light incident on the lens at angles of incidence of 0 °, 8 °, and 16 ° in the f-θ lens is converged to different positions on the image plane.

FIG. 19 shows an example of an f-θ lens in the entrance pupil.
The figure which shows the example which takes eight light rays.

FIG. 20 shows a state S _{0 in} which no error is given according to the conventional method.
Of the f-θ lens determined by the optical parameters obtained by minimizing the evaluation function E ₀ of
When a decenter error of μm is given, 0 °, 8 °, 1 °
The figure which shows the intensity distribution of the condensed spot on an image plane for each incident angle of 6 degrees by a contour line.

According FIG. 21 the present invention, to the evaluation function E _1, E ₂ of the error state gave decenter error, minimizes the integrated evaluation function E was added to the evaluation function E ₀ state S ₀ which does not give error When a decenter error of 160 μm is added to the f-θ lens determined by the optical parameters determined by the above, the intensity distribution of the condensed spot on the image plane is obtained for each of the incident angles of 0 °, 8 °, and 16 °. The figure shown by a contour line.

──────────────────────────────────────────────────の Continued on the front page (58) Field surveyed (Int. Cl. ⁷ , DB name) G02B 13/00 G06F 17/50 JICST file (JOIS) [Lens * design * evaluation function * tolerance]

Claims (1)

(57) [Claims] And 1. A rating function E ₀ for the parameter sets of states S ₀ no error For all optical parameters determining the optical system, an error ± at least one optical parameter
The evaluation function E for the states S ₁ , S ₂ ...
An evaluation function E = w obtained by adding ₁ , E ₂ .
_{0 E 0 + w 1 E 1} + w 2 E 2 ... = make? W _k E _k, lenses and the design method of the optical system and obtaining a set of optical parameters such as this to a minimum.