KR102653060B1 - Method for tolerance analysis on optics figure error - Google Patents

Abstract

The present invention relates to a method for analyzing the shape error of an optical element, (a) the number of combinations (M) of the PV (Peak-to-Valley) shape error and the RMS (Root Mean Square) shape error of the optical element, the PV Shape error C _PV ^m , the RMS shape error C _RMS ^m , number of sets of ZFR coefficients (fringe Zernike coefficients) of the fringed Zernike (ZFR) polynomial (N), number of optical performance analyzes (L), required optical performance (O _required ), inputting the probability of satisfying the required optical performance (P _required ), (b) using the PV shape error C _PV ^m as input, generating a random number in the range of ±C _PV ^m , and the initial value of the ZFR coefficient A ZFR coefficient C ₁ ^{m optimized by the step of generating, (c) generating an optimal solution of the ZFR coefficient using the initial value of the ZFR coefficient as a variable, (d) generating an optimal solution of the ZFR coefficient,} Store ⁿ , C ₂ ^m,n , C ₃ ^m,n , ..., C ₁₃ ^m,n , repeat from n=1 to n=N, repeat from m=1 to m=M, and A step of storing N sets of ZFR coefficients per combination (M) of shape errors, (e) a ZFR coefficient application step of analyzing L optical performance by applying the set of ZFR coefficients to the optical surface (s) of the optical element to be analyzed and (f) calculating the probability P of satisfying the required optical performance (O _required ) by analyzing the probability distribution of the L optical performance analysis results, and the calculated probability P is the probability of satisfying the required optical performance (P According to the _present invention, it is possible to accurately analyze the effect of the shape error of the optical element on optical performance as a method of analyzing the shape error of an optical element that includes a shape error analysis step to determine whether the condition (required) is satisfied.

Description

Optical element shape error analysis method {METHOD FOR TOLERANCE ANALYSIS ON OPTICS FIGURE ERROR}

The present invention relates to a method for analyzing the effect of shape error of an optical element on optical performance.

During the manufacturing process of optical elements, errors occur between design specifications and actual specifications, and the allowable value of this error is defined as tolerance. Tolerances are determined through statistical analysis based on the required optical performance. Existing optical device tolerance analysis has been done by using the tolerance analysis function provided by commercial optical design programs such as Code V, or by creating a macro that creates a specific tolerance by the user.

At this time, the amount of deformation, or shape error, of each optical surface is randomly generated and applied within the tolerance range specified by the user. The shape error can be expressed as a fringe Zernike (ZFR) coefficient, and commercial optical design programs generate a random PV (Peak-to-Valley) shape error or RMS shape error near the shape error input value. In other words, it is difficult to simultaneously control the PV shape error and the RMS shape error.

Therefore, it is difficult to accurately analyze the effect of shape error of optical elements on optical performance, and especially in the case of optical elements with high shape error sensitivity, it is difficult to determine tolerances for PV shape error and RMS shape error in the drawing. .

The matters described in the above background technology are intended to aid understanding of the background of the invention, and may include matters that are not prior art already known to those skilled in the art in the field to which this technology belongs.

Korean Patent Publication No. 10-2009-0107419

The present invention was made to solve the above-mentioned problems, and the purpose of the present invention is to provide a method for analyzing the shape error of an optical element to accurately analyze the effect of the shape error of the optical element on optical performance.

The method for analyzing the shape error of an optical element according to one aspect of the present invention includes (a) the number of combinations of the PV shape error and the RMS (Root Mean Square) shape error of the optical element ( M), the PV shape error C _PV ^m , the RMS shape error C _RMS ^m , the number of sets of ZFR coefficients (fringe Zernike coefficients) of the fringe Zernike (ZFR) polynomial (N), the number of optical performance analyzes (L), required Inputting the optical performance (O _required ) and the probability of satisfying the required optical performance (P _required ), (b) using the PV shape error C _PV ^m as an input, generating a random number in the range ±C _PV ^m , and ZFR coefficient C ₁ optimized by the steps of generating an initial value of the ZFR coefficient, (c) generating an optimal solution of the ZFR coefficient using the ZFR coefficient as a variable, and (d) generating an optimal solution of the ZFR coefficient. Store ^m,n , C ₂ ^m,n , C ₃ ^m,n , ..., C ₁₃ ^m,n, repeat from n=1 to n=N, repeat from m=1 to m=M , storing N sets of ZFR coefficients per combination (M) of the shape errors, (e) ZFR coefficients analyzing L optical performance by applying the set of ZFR coefficients to the optical surface (s) of the optical element to be analyzed. Application step and (f) analyzing the probability distribution of the L optical performance analysis results to calculate the probability P of satisfying the required optical performance (O _required ), and the calculated probability P is the probability of satisfying the required optical performance It includes a shape error analysis step to determine whether (P _required ) is satisfied.

And, the step of generating the optimal solution of the ZFR coefficient is the fringe Zernike polynomial W(R,θ) (Equation 1) as follows, an equation for calculating C _PV ′, which is the PV value of W(R,θ) (mathematics Equation 2), an equation for calculating C _RMS ', which is the W(R, θ) rms value (Equation 3), an equation in which C _PV ' and the C _PV have the same value (Equation 4), the C _RMS ' and the It is characterized by generating an optimal solution of the optimized ZFR coefficient that satisfies all equations (Equation 5) in which C _RMS has the same value.

(수학식 1)

(Equation 1)

(수학식 2)

(Equation 2)

(수학식 3)

(Equation 3)

(수학식 4)

(Equation 4)

(수학식 5)

(Equation 5)

(Here, R and θ are the radius and angle of the spherical coordinate system, C ₁ , C ₂ to C ₁₃ are ZFR coefficients, and Z ₁ , Z ₂ , to Z ₁₃ are ZFR polynomials.)

In addition, the step of determining the effectiveness of the optimal solution of the ZFR coefficient generated by the step of generating the optimal solution of the ZFR coefficient may be further included.

In addition, the ZFR coefficient application step includes selecting a shape error combination m to be applied, selecting a random set from among the N sets of ZFR coefficients for the shape error combination m, and selecting the selected ZFR coefficient set. The step of applying to the interference pattern data of the optical surface (s) and the step of applying to the interference pattern data are repeatedly performed from the optical surface s = 1 until s = S (total number of optical surfaces) to improve optical performance. Includes an analysis step.

Furthermore, if the probability P calculated by the shape error analysis step does not satisfy the required optical performance satisfaction probability (P _required ), the PV shape error C _PV ^m in the input step, and the RMS shape error C It is characterized by correcting and inputting _RMS ^m .

In addition, the step of generating the optimal solution of the ZFR coefficients involves setting all of the ZFR coefficients C ₁ , C ₂ , to C ₁₃ as variables, or setting only some terms of the ZFR coefficients C ₁ , C ₂ , to C ₁₃ as variables. It is characterized by

According to the present invention, the shape error of an optical element can be accurately simulated for PV shape error and RMS shape error at the same time, and the optical performance and probability distribution of optical performance for the defined PV shape error and RMS shape error can be analyzed. , the PV shape error and RMS shape error that satisfy the required optical performance can be determined through a trade-off process.

In particular, in the case of optical devices whose optical performance is sensitive to shape errors, the effects of PV shape errors and RMS shape errors can be analyzed simultaneously and the manufacturing shape can be managed by setting tolerances.

1 is a flowchart of the optical element shape error analysis method of the present invention.
FIG. 2 is a flowchart illustrating the ZFR coefficient application steps of FIG. 1 in detail.
Figure 3 shows an example of the result of determining the effectiveness of the solution in the ZFR coefficient optimal solution generation step of Figure 1 as a shape error image.
Figure 4 is an example of a *.int file applied to the interference pattern data of the optical surface in the ZFR coefficient application step of Figure 1.
Figure 5 is an example showing the analysis results of optical performance in the shape error analysis step of Figure 1 as a probability distribution.

In order to fully understand the present invention, its operational advantages, and the objectives achieved by practicing the present invention, reference should be made to the accompanying drawings illustrating preferred embodiments of the present invention and the contents described in the accompanying drawings.

In describing preferred embodiments of the present invention, known techniques or repetitive descriptions that may unnecessarily obscure the gist of the present invention will be reduced or omitted.

FIG. 1 is a flowchart of the method for analyzing shape errors in optical elements of the present invention, and FIG. 2 is a flowchart illustrating in detail the ZFR coefficient application steps of FIG. 1.

Hereinafter, a method for analyzing the shape error of an optical element according to an embodiment of the present invention will be described with reference to FIGS. 1 and 2.

The purpose of the present invention is to accurately simulate the PV shape error and RMS shape error of optical elements at the same time, analyze statistical optical performance by shape error of optical elements, and determine shape error that satisfies the required optical performance through a trade-off process. It provides a method for determining tolerances.

The optical elements that make up the optical system generally consist of several lenses or mirrors. The front and back surfaces of the lens and the reflective surface of the mirror are all referred to as optical surfaces (s), and the total number of optical surfaces can be referred to as S. (For example, in the case of an optical system consisting of two single lenses and one mirror, there are 2x2+1=5 optical surfaces.)

Optical surface: s = 1, 2, 3, ..., S

Optical elements have different tolerances for PV shape error and RMS shape error depending on design specifications such as wavelength band, refractive or reflective surface, and aspheric surface. Depending on the type of optical element, shape error tolerance can be assigned as shown in the examples in Table 1, but the actual shape error tolerance is different for each optical system.

Shape error combination (m) optical element PV shape error (C _pv ^m ) RMS shape error (C _RMS ^m ) One Aspherical reflector 0.075um 0.015um 2 flat reflector 0.050um 0.010um 3 Visible wavelength band lens 0.053um 0.015um 4 Infrared wavelength band lens 0.105um 0.030um

The shape error of the optical element can be expressed by a fringe Zernike (ZFR) polynomial. The equation is as follows, and terms 1 to 13 are used in the present invention.

Here, W(R,θ) is the wavefront error, and R and θ are the radius and angle of the spherical coordinate system. C ₁ , C ₂ , C ₃ , ..., C ₁₃ are ZFR coefficients. Z ₁ , Z ₂ , Z ₃ , ..., Z ₁₃ are ZFR polynomials, and each polynomial is as follows. Each polynomial represents optical aberrations such as distortion, tilt, astigmatism, and coma, and depending on the characteristics of the optical system, all terms 1 to 13 can be effectively used, or only some terms can be effectively used and the rest can be set to 0. there is.

The present invention is implemented by a computer program, and the basic configuration is as shown in Figure 1. A combination of M PV shape errors and RMS shape errors is defined and input according to the type of optical element, and the ZFR coefficient is calculated based on the PV shape error. Generating an initial value, generating a ZFR coefficient that satisfies the PV shape error and RMS shape error, storing each N set of ZFR numbers for each M shape error combination, applying the ZFR coefficient to all optical surfaces. It includes the step of analyzing optical performance by shape error of the optical surface. The detailed structure of each step is as follows.

In the shape error input step (S110), the number of combinations of PV shape error and RMS shape error M, PV shape error C _PV ^m , RMS shape error C _RMS ^m , number of ZFR coefficient sets N, number of optical performance analysis L, and required optical performance Enter O _required and the probability of satisfying the required optical performance, P _required . Here m is an integer from 1 to M. According to the examples in Tables 1 and 2, M=4, C _PV ¹ =0.075um, C _RMS ¹ =0.015um, C _PV ² =0.050um, C _RMS ² =0.010um, C _PV ³ =0.053um, C It can be said that _RMS ³ =0.015um, C _PV ⁴ =0.105um, C _RMS ⁴ =0.030um, N=100, L=1000, S=20, O _required =0.83, P _required =0.9.

Entry Mark value Number of combinations of PV shape error and RMS shape error M 4 Number of ZFR coefficient sets N 100 Number of shape error analyzes L 1000 Number of optical surfaces S 20 Required optical performance O _required 0.83 Probability of satisfying required optical performance P _required 0.9

In the ZFR coefficient initial value generation step (S120), the PV shape error C _PV ^m is received as input, and random numbers are generated in the range of ±C _PV ^m to generate the ZFR coefficient initial values C _1,0 , C _2,0 , C _3,0 , ..., save as C _13,0 .

...

In the above equation, rand is a function that generates a random number between 0 and 1, and rand(1) returns one random number between 0 and 1. Therefore, the initial value of each ZFR coefficient has a random value between -CPV and +CPV. The initial value of the ZFR coefficient is used as the initial value to start searching for the optimal solution of the ZFR coefficient in the next step.

In the ZFR coefficient optimal solution generation step (S130), the ZFR coefficient initial values C _1,0 , C _2,0 , C _3,0 , ..., C _13,0 and PV shape error C _PV ^m , RMS shape error C _RMS It takes ^m as input. The shape error can use the ZFR equation W(R, θ), and the PV shape error and RMS shape error can be obtained through the PV and rms values of W(R, θ).

In the above equation, W(R,θ) is a function expressing the wavefront error in the spherical coordinate system as a ZFR polynomial. R and θ are the radius and angle of the spherical coordinate system, where R ranges from 0 to 1 and θ ranges from 0 to 2π. C ₁ , C ₂ , C ₃ , ..., C ₁₃ are ZFR coefficients and variables. Z ₁ , Z ₂ , Z ₃ , ..., Z ₁₃ are polynomials and functions of R and θ.

max is a function that returns the maximum value, and min is a function that returns the minimum value. max(W(R,θ)) returns the maximum value of the wavefront error, and min(W(R,θ)) returns the minimum value of the wavefront error. The difference between the maximum and minimum values of the wavefront error means the PV error and is stored as C _PV ′. rms is the root mean sqaure function, and rms(W(R,θ)) means the rms value of the wavefront error, and is stored as C _RMS ′. C _PV ′ and C _RMS ′ calculated in this way should be the same as C _PV ^m and C _RMS ^m , respectively.

ZFR coefficients C ₁ , C ₂ , C ₃ , ..., C ₁₃ are used as variables, and Equation 1, Equation 2, Equation 3, Equation 4, and Equation 5 are simultaneous equations, and the Calculate the optimal solution.

Here, the fsolve function is a library function supported by Mathlab ^TM , a well-known mathematical program, function f is a simultaneous equation of functions f1 and f2, and the variables C ₁ , C ₂ , C for which functions f1 and f2 are both 0. Calculate ₃ , ..., C ₁₃ . At this time, C _1,0 , C _2,0 , C _3,0 , ..., C _13,0 are used as initial values to start finding the optimal solution for the variable. For the process of finding solutions to simultaneous equations with multiple variables in fsolve, many different optimization algorithms are available, but the trust-region-dogleg algorithm, which is the default algorithm of fsolve, is the optimal optimization algorithm for these equations. It can be used as Here, x is the matrix calculating the optimal solution of C ₁ , C ₂ , C ₃ , ..., C ₁₃ .

The ZFR coefficient generated in this way is checked for validity as in the following equations. Return the x matrix to the ZFR coefficient, calculate the wave front error W(R, θ), calculate the PV value C _PV ′ and the rms value C _RMS ′ of the wave front error, and satisfy C _PV ′-C _PV = 0 At the same time, check whether C _RMS ′-C _RMS = 0 is satisfied (S140).

...

If C _PV ′-C _PV =0 and C _RMS ′-C _RMS =0 are not satisfied at the same time, return to the ZFR coefficient initial value generation step and repeat each step. If C _pv ′-C _PV =0 and C _RMS ′-CRMS=0 are simultaneously satisfied, output the x matrix and proceed to the next step. Figure 3 shows an example of the results of determining the validity of the ZFR coefficient. The left image shows W(R,θ) when generating a ZFR coefficient that simultaneously satisfies CPV'-CPV=0 and CRMS'-CRMS=0, and the right image shows CPV'-CPV=0 and CRMS'- This is an image showing W(R,θ) when generating ZFR coefficients that do not simultaneously satisfy CRMS=0.

Next, in the ZFR coefficient set storage step (S150), the x matrix, which is the result of generating the optimal solution, is received as input, and C ₁ ^m,n , C ₂ ^m,n , C ₃ ^m,n , ..., C ₁₃ ^m,n, respectively. Save it as

...

Shape error combination: m = 1, 2, 3, ..., M

ZFR coefficient set: n = 1, 2, 3, ..., N

The ZFR coefficient that simultaneously satisfies the PV shape error C _PV ^m and the RMS shape error C _RMS ^m has several solutions depending on the initial value of the ZFR coefficient, so N sets of ZFR coefficients are required for statistical analysis. According to the example in Table 2, N = 100, and each step is repeated by returning to the ZFR coefficient initial value creation step from n = 1 to n = 100. (S161) When n = 100, the output is the mth It is a set of N ZFR coefficients in shape error combination. According to the example in Table 2, since the number of shape error combinations is M = 4, return to the step of generating the initial ZFR coefficient and repeat each step until m = 1 to m = 4. (S162)

The final output is a set of N ZFR coefficients for each of the M shape error combinations. In other words, there are a total of MㅧN sets of ZFR coefficients. The ZFR coefficient set is divided by shape error combination and stored in the storage medium.

Here, m is an integer from 1 to M, and M is the number of combinations of PV shape error and RMS shape error. n is an integer from 1 to N, and N is the number of ZFR coefficient sets.

In the ZFR coefficient application step (S170), the ZFR coefficient is applied to the interference pattern data of all optical surfaces, and L optical performance data are output. The detailed steps are as shown in Figure 2, and are sequentially as follows.

① Determining the type of optical element and determining the shape error combination m to be applied to the optical surface s, (S210)

② Step of calling one random set among N sets of ZFR coefficients for shape error combination m, (S220)

③ Step of applying the called ZFR coefficient to the interference pattern data of optical surface s, (S230)

④ Repeat steps ① to ③ from optical surface s=1 until s=S, (S240)

⑤ Step of analyzing and storing optical performance, (S250)

⑥ This is the step of repeating ①~⑤ L times (S260).

According to the examples in Tables 1 and 2, if the sth optical element is determined to be a plane reflector in step S210, m = 2, C _PV ² = 0.050 um, and C _RMS ² = 0.010 um.

In step S220, the ZFR coefficient set with shape errors C _PV ² and C _RMS ² [C ₁ ^2,1 , C ₂ ^2,1 , C ₃ ^2,1 , ..., C ₁₃ ^2,1 ], [C ₁ ^2,2 , C ₂ ^2,2 , C ₃ ^2,2 , ..., C ₁₃ ^2,2 ], ..., [C ₁ ^2,100 , C ₂ ^2,100 , C ₃ ^2,100 , ..., C ₁₃ ^2,100 ], call one random set [C ₁ ^2,n , C ₂ ^2,n , C ₃ ^2,n , ..., C ₁₃ ^2,n ].

In step S230, the called ZFR coefficients are applied to the interference pattern data of the optical surface. In the case of Code V, a commercial optical design program, each coefficient can be applied in *.int file format, and Figure 4 shows the *.int file format. An example is shown. Referring to Figure 4, line 1 represents a description of the corresponding *.int file. In the second row, 'ZFR 13' means that the ZFR coefficient is used up to 13 terms, 'SUR' means the shape error of the optical surface, and 'WVL 1' means that the wavelength when measured with an interferometer is 1 um. means, and 'SSZ 1' means 1x scale. Previously, the ZFR coefficient was analyzed using the wavefront error equation W(R, θ), but by setting the application condition of the ZFR coefficient to 'SUR WVL 1' as shown in Figure 3, the wavefront error of the optical surface can be applied as a shape error as is. . The embodiment of Figure 4 is an example of analyzing and applying the optimal solution of terms 4, 5, 6, and 13 by setting only terms 4, 5, 6, and 13 among ZFR coefficient terms 1 to 13 as variables, and setting the remaining terms as constants 0. The method of applying this ZFR coefficient is not limited to the method described above, and includes a method in which the user uses commands in a commercial optical design program and a method in which a macro program is used. In addition, the variable setting of the ZFR coefficient is not limited to setting all items 1 to 13. As in the example of Figure 4, only significant coefficients in the optical system designed by the user are set as variables, and the rest are set to the constant 0. Includes.

In step S240, steps S210 to S230 are repeated until s=1 to s=S for all optical surfaces of the optical system. According to the example in Table 2, steps S210 to S230 are repeated until the optical surface s becomes S (=20).

In step S250, the optical performance of the optical system is analyzed and stored with shape errors applied to all optical surfaces. Here, optical performance is explained using the modulation transfer function (MTF) as an example, but optical performance also includes aberration, Strehl ratio, and point spread function (PSF). It also includes separately defined optical performance that the user wishes to analyze.

In step S260, steps S210 to S250 are repeated L times to statistically analyze optical performance due to shape error. According to the example in Table 2, steps S210 to S250 are repeated 1000 times. After completing step S260, the output is the L optical performance analysis results.

After this ZFR coefficient application step (S170), in the shape error analysis step (S180), L optical performance analysis results are received as input, and the probability distribution of optical performance is analyzed. Figure 5 is an example of the results of modulation transfer function probability analysis in terms of optical performance. As a result of analysis of 1000 modulation transfer functions (MTF), the X-direction modulation transfer function and Y-direction modulation transfer function at a specific spatial frequency of 0.7 field are shown as a histogram. In Figure 5, the dotted line indicates the required optical performance O _required according to the example in Table 2. Calculate the probability P of satisfying the _required optical performance O required from the L optical performance analysis results, and determine whether the probability P of satisfying O _required satisfies the required optical performance satisfaction probability P _required (S190). If P < P _required , go back to the shape error input step (S110), correct and input the PV shape error C _PV ^m and RMS shape error C _RMS ^m , and repeat each step. If P≥P _required , the shape error analysis step is terminated.

Through these steps, the tolerances of PV shape error and RMS shape error can be simultaneously assigned to each optical element, and the impact of each shape error on optical performance can be analyzed.

Although the present invention as described above has been described with reference to the illustrative drawings, it is not limited to the described embodiments, and it is common knowledge in the field of this technology that various modifications and changes can be made without departing from the spirit and scope of the present invention. It is self-evident to those who have it. Accordingly, such modifications or variations should be considered to fall within the scope of the patent claims of the present invention, and the scope of rights of the present invention should be interpreted based on the appended claims.

S110: Shape error input step
S120: ZFR coefficient initial value generation step
S130: ZFR coefficient optimal solution generation step
S140: Judgment of simultaneous satisfaction of PV value and RMS value
S150: ZFR coefficient set storage step
S161: Determine whether n reaches N
S162: Determine whether m reaches M
S170: ZFR coefficient application step
S180: Shape error analysis step
S190: Judgment of probability of satisfaction of required optical performance

Claims (6)

In a method of analyzing shape errors of optical elements,
(a) Implemented by a computer program, the number (M) of the combination (m) of the PV (Peak-to-Valley) shape error and the RMS (Root Mean Square) shape error of the optical element, the PV shape error C _PV ^m , the RMS shape error C _RMS ^m , the number of sets of ZFR coefficients (fringe Zernike coefficients) of the fringed Zernike (ZFR) polynomial (N), the number of optical performance analyzes (L), the required optical performance (O _required ), the required Inputting the optical performance satisfaction probability (P _required ) into the program;
(b) using the PV shape error C _PV ^m as input, generating a random number in the range of ±C _PV ^m , and generating an initial value of the ZFR coefficient;
(c) generating an optimal solution of the ZFR coefficient using the ZFR coefficient as a variable;
(d) storing the optimized ZFR coefficients C ₁ ^m,n , C ₂ ^m,n , C ₃ ^m,n , ..., C ₁₃ ^m,n by the step of generating the optimal solution of the ZFR coefficient, and n repeating from =1 to n=N, repeating from m=1 to m=M, and storing N sets of ZFR coefficients per combination (m) of the shape errors;
(e) a ZFR coefficient application step of analyzing L optical performance by applying the set of ZFR coefficients to the optical surface (s) of the optical element to be analyzed; and
(f) Analyzing the probability distribution of the L optical performance analysis results, calculate the probability P of satisfying the required optical performance (O _required ), and the calculated probability P is the probability of satisfying the required optical performance (P _required) . ), including a shape error analysis step to determine whether it satisfies
Optical element shape error analysis method. In claim 1,
The step of generating the optimal solution of the ZFR coefficient is,
The fringe Zernike polynomial W(R,θ) (Equation 1) as follows, the equation for calculating C _PV ′, which is the PV value of W(R,θ) (Equation 2), and C, which is the rms value of W(R,θ) An equation for calculating _RMS ' (Equation 3), an equation in which C _PV ' and C _PV have the same value (Equation 4), and an equation in which C _RMS ' and C _RMS have the same value (Equation 5) Characterized in generating an optimal solution of the optimized ZFR coefficient that satisfies all,
Optical element shape error analysis method.

(Equation 1)

(Equation 2)

(Equation 3)

(Equation 4)

(Equation 5)
(Here, R and θ are the radius and angle of the spherical coordinate system, C ₁ , C ₂ to C ₁₃ are ZFR coefficients, and Z ₁ , Z ₂ , to Z ₁₃ are ZFR polynomials.) In claim 2,
Further comprising the step of determining validity of the optimal solution of the ZFR coefficient generated by the step of generating the optimal solution of the ZFR coefficient,
Optical element shape error analysis method. In claim 1,
The ZFR coefficient application step is,
Selecting a shape error combination m to be applied;
selecting a random set from among the N sets of ZFR coefficients for the shape error combination m;
applying the selected set of ZFR coefficients to the interference pattern data of the optical surface (s);
Comprising the step of analyzing optical performance by repeatedly performing the step of applying to the interference pattern data from the optical surface s = 1 until s = S (total number of optical surfaces),
Optical element shape error analysis method. In claim 4,
If the probability P calculated by the shape error analysis step does not satisfy the required optical performance satisfaction probability (P _required ), the PV shape error C _PV ^m and the RMS shape error C _RMS ^m in the input step Characterized by modifying and entering,
Optical element shape error analysis method. In claim 2,
The step of generating the optimal solution of the ZFR coefficient is characterized by setting all of the ZFR coefficients C ₁ , C ₂ , to C ₁₃ as variables, or setting only some terms of the ZFR coefficients C ₁ , C ₂ , to C ₁₃ as variables. to,
Optical element shape error analysis method.

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