JP2022044113A - Aberration estimation method, aberration estimation device, program and storage medium - Google Patents

Abstract

To provide an aberration estimation method, an aberration estimation device, a program, and a storage medium that, even when the relationship between the amount of instructions for means controlling defocus and a defocus amount is inaccurate or unknown, can estimate the aberration of an optical system under test with high accuracy.SOLUTION: An aberration estimation method has: a first acquisition step of acquiring the light intensity distribution of an optical image of a subject formed through an optical system under test; a second acquisition step of acquiring a defocus amount by using the amount of instructions for changing the amount of defocus of the optical system under test and the light intensity distribution; and an estimation step of estimating the aberration of the optical system under test by using the light intensity distribution and the defocus amount.SELECTED DRAWING: Figure 7

Description

The present invention relates to an aberration estimation method, an aberration estimation device, a program, and a storage medium for estimating aberrations of an optical system using a light intensity distribution.

In optical instruments such as cameras and telescopes, it is required to measure the aberration of the optical system in order to evaluate and guarantee the performance. In Patent Document 1 and Patent Document 2, aberrations are estimated by performing optimization operations on a plurality of light intensity distributions in an optical system.

Japanese Patent No. 441395 Japanese Unexamined Patent Publication No. 2020-060469 Japanese Unexamined Patent Publication No. 2000-294488

Kazuyoshi Okada, Kenji Amaya, Yuki Onishi, "Development of Aberration Analysis Method Using Low Resolution Spot Image", Optics 41 (12), pp. 627, December 10, 2012 Joseph Goodman, "Introduction to Futureer Optics", Roberts and Company Publics Simon C.I. Woods, Alan H. Green's way, "Wave-front sensing by use of a Green's function solution to the intensity continuity equation", J. Mol. Opt. Soc. Am. A Vol. 20, pp. 508, March 2003, USA Scott W. Paine and James R. Fienup, “Machine learning for impacted image-based wavefront sensing”, Optics letters Vol. 43, pp. 1235, March 2018, USA

In the method of estimating the aberration by performing the optimization calculation, the light intensity distribution acquired at one or more defocus positions is used. In this method, in order to search for an aberration in which the light intensity distribution obtained by the calculation and the actually measured light intensity distribution match, it is necessary that the conditions for performing the calculation exactly match the measurement conditions. Therefore, a drive device capable of controlling defocus with high accuracy is required, which complicates the device. Defocus may be controlled using the focus mechanism of the optical system under test in order to reduce the complexity of the device, but the relationship between the amount indicated to the focus mechanism and the amount of defocus generated is inaccurate or unknown. Therefore, the operation cannot be executed.

The present invention is an aberration estimation method and an aberration estimation device capable of estimating the aberration of the test optical system with high accuracy even when the relationship between the indicated amount and the defocus amount for the means for controlling the defocus is inaccurate or unknown. , Programs, and storage media.

In the aberration estimation method as one aspect of the present invention, the first acquisition step of acquiring the light intensity distribution of the optical image of the subject formed through the optical system under test and the defocus amount of the optical system under test are changed. It is characterized by having a second acquisition step of acquiring the defocus amount using the indicated amount and the light intensity distribution for the purpose, and an estimation step of estimating the aberration of the optical system under test using the light intensity distribution and the defocus amount. And.

Further, the aberration estimation device as another aspect of the present invention is an image pickup element that acquires a light intensity distribution of an optical image of a subject formed via an optical system under test, and changes the amount of defocus of the optical system under test. An aberration estimation device comprising a control unit for estimating an aberration of an optical system under test using an instruction amount for making the aberration and a defocus amount acquired based on a light intensity distribution.

According to the present invention, an aberration estimation method and aberration that can estimate the aberration of the test optical system with high accuracy even when the relationship between the indicated amount and the defocus amount for the means for controlling the defocus is inaccurate or unknown. An estimation device, a program, and a storage medium can be provided.

It is a schematic diagram of the aberration estimation apparatus which concerns on embodiment of this invention. It is a figure which shows the positive or negative of defocus. It is a schematic diagram of the aberration estimation apparatus which concerns on another Embodiment of this invention. It is a figure which shows the method of determining the sign of the defocus amount. It is a figure which shows another method of determining the sign of a defocus amount. It is a figure which shows the method of estimating the absolute value of the defocus amount. It is a flowchart which shows the aberration estimation method of this embodiment. It is a figure which shows the estimation result of the aberration of Example 1. FIG.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. In each figure, the same member is given the same reference number, and duplicate description is omitted.

FIG. 1 is a schematic view of an aberration estimation device 100 according to an embodiment of the present invention. The light emitted from the subject 101 is imaged on the image pickup surface of the image pickup device 103 via the optical system 102 to be inspected to form an optical image of the subject 101. The subject 101 is, for example, a minute light source such as a pinhole. The image pickup device 103 is installed on the drive device 104. The drive device 104 is controlled by a computer (control unit) 105, and moves the image pickup device 103 to a designated position along the optical axis 106. The image sensor 103 acquires the light intensity distribution of the optical image at each moved position, and stores the acquired light intensity distribution in the computer 105 or a data holding device (not shown). The computer 105 estimates the aberration of the optical system 102 under test by performing post-processing on the light intensity distribution. The post-processing may be executed by the computer 105 or another arithmetic unit. Further, an arithmetic unit existing on the cloud through the network may execute post-processing.

Measuring the light intensity distribution at different positions in the optical axis direction means acquiring the light intensity distribution of the optical image at a plurality of defocus positions. Here, the defocus means that the measurement position is different from the image formation position of the test optical system 102, and the defocus position is the position in the optical axis direction with respect to the image formation position of the test optical system 102. Point to. In the present embodiment, the defocus amount refers to the distance from the image formation position to the defocus position. In addition to expressing the defocus amount by the distance from the image formation position to the defocus position, a value obtained by standardizing the defocus position with the depth of focus of the optical system 102 under test can also be used, and the defocus is related. It can also be expressed by the amount of wave surface aberration. In the present embodiment, the image formation position refers to the position where the wavefront aberration of the light imaged on the optical axis is the smallest. The image formation position may be represented by a paraxial imaging position, a design imaging position, or the like of the optical system 102 under test. Further, in the present embodiment, as shown in FIG. 2, the defocus is positive when the image pickup position is in front of the image sensor 103, and the defocus is negative when the image pickup position is behind the image sensor 103. Is defined as. The present invention is not limited by these definitions. If other definitions are adopted, the present invention may be carried out as appropriate.

In the present embodiment, the drive device 104 moves the image pickup device 103 to change the defocus amount, but the present invention is not limited to this. FIG. 3 is a schematic view of an aberration estimation device according to another embodiment of the present invention. As in the aberration estimation device 300 of FIG. 3A, the test optical system 102 may have a focus control mechanism 1021. In this case, the defocus may be controlled by driving at least a part of the lenses constituting the optical system 102 to be examined by using the signal received from the computer 105 by the focus control mechanism 1021. Further, the optical system 102 to be inspected may be installed on the drive device 104 as in the aberration estimation device 400 of FIG. 3 (b). In this case, the defocus may be controlled by moving the optical system 102 under test in the optical axis direction using the signal received from the computer 105 by the drive device 104. Further, the subject 101 may be installed on the drive device 104 as in the aberration estimation device 500 of FIG. 3C. In this case, the defocus may be controlled by moving the subject 101 in the optical axis direction based on the signal received from the computer 105 by the drive device 104. Further, as in the aberration estimation device 600 of FIG. 3D, a phase modulation element 107 that modulates the phase of light may be installed in the optical path. In this case, the defocus may be controlled by giving a phase change corresponding to the defocus change to the light based on the signal received from the computer 105 by the phase modulation element 107. In either method, it suffices to have a means for changing the defocus and to control the defocus based on a signal from a control device such as a computer. Hereinafter, the means for changing the defocus is referred to as a defocus changing means, and the instruction amount given to the defocus changing means is referred to as a defocus changing instruction amount.

Hereinafter, the calculated aberration will be described as the wavefront aberration of the optical system 102 under test, but the aberration that can be measured by the present invention is not limited to this. Once the wavefront aberration is obtained, the amount of lateral aberration and the amount of longitudinal aberration can be calculated by a simple calculation. Chromatic aberration can also be measured by measuring at a plurality of wavelengths. Further, by developing the wavefront aberration with a Zernike polynomial, it is possible to convert it into Seidel aberration such as coma aberration and spherical aberration.

As a method of post-processing performed by the computer 105, for example, there is optimization. Optimization is a calculation method for estimating an aberration by sequentially changing the aberration so that the value of the objective function becomes the smallest. The objective function is the degree to which the estimated aberration in each iteration step of optimization reproduces the measurement result. For example, the sum of squared differences between the light intensity distribution obtained by calculation from the estimated aberration and the light intensity distribution obtained by measurement, There is a difference squared sum of amplitude distributions. The objective function may be appropriately selected according to the problem. As a method for calculating the light intensity distribution by calculation, for example, a method disclosed in Non-Patent Document 1 or Non-Patent Document 2 can be used.

There are various optimization methods, such as the steepest descent method, the conjugate gradient method, the quasi-Newton method, the Gauss-Newton method, and the Levenberg-Marquardt method. The method to be used may be appropriately selected according to the problem.

In order to reduce the computational load of optimization, it is also possible to expand the aberration with an appropriate function and use the coefficient as an optimization variable. As a function that develops aberrations, for example, there is a Zernike polynomial. Since the Zernike polynomial corresponds to the basis function and the type of aberration, it is suitable as a function for developing the aberration.

By the method described above, the aberration of the optical system 102 under test can be estimated from the measured light intensity distribution. In order to estimate the aberration by the above-mentioned method, it is necessary that the actual measurement conditions and the calculation conditions for executing the calculation are exactly the same. Therefore, it is necessary to accurately know the defocus amount z given by the defocus changing means. However, in order to know the defocus amount z accurately, it is necessary to take measures such as using a drive stage that can be driven with high accuracy or adding a measuring device for measuring the actual drive amount with high accuracy. , The cost of the entire device will increase. In order to avoid an increase in cost, it is conceivable to use an inexpensive and low-precision drive device 104, but since an error occurs between the drive amount specified by the computer 105 and the actual drive amount, the calculation conditions and the actual state There is a discrepancy with the measurement conditions of, and the estimation accuracy of aberration is reduced. In order to avoid an increase in cost, the focus control mechanism 1021 included in the optical system 102 under test may be used as shown in FIG. 3A. However, since the measurer usually does not know the relationship between the instruction amount sent to the focus control mechanism 1021 and the generated defocus amount z, it is not possible to execute the aberration estimation calculation.

The present invention enables highly accurate aberration estimation even when the defocus amount z given by the defocus changing means is inaccurate or unknown. Specifically, the defocus amount z actually generated is acquired by using the defocus change instruction amount given to the defocus changing means and the measured light intensity distribution, and afterwards based on the obtained defocus amount Zoom. Execute the process.

Since there are two defocus amounts z, a sign and an absolute value | z |, it is necessary to determine each of them. First, a method of calculating the sign of the defocus amount will be described. In this embodiment, a method of using a plurality of bright spots as a method of calculating the sign of the defocus amount is exemplified. FIG. 4 is a diagram showing a method of determining the sign of the defocus amount. First, as shown in FIG. 4A, two bright spots having different heights are imaged. In the state shown in FIG. 4 (b) in which a negative defocus amount is generated when a positive indicated amount is given to the defocus changing means, the distance between the two point images is smaller than that in FIG. 4 (a). .. That is, the intervals between the two point images are compared before and after the indicated amount is given, and it can be seen that a negative defocus amount is given when the interval is narrowed, and a positive defocus amount is given when the interval is widened.

There are various methods for installing a plurality of bright spots, and the height and distance may be changed. FIG. 5 is a diagram showing another method of determining the sign of the defocus amount. For example, as shown in FIG. 5A, the bright spot outside the optical axis may be installed at a position farther from the lens under test than the bright spot on the optical axis. In this case, the light is focused on about one point at the image formation position on the optical axis, but a blurred point image is measured outside the optical axis. When a positive indicated amount is given to the defocus changing means and a negative defocus amount occurs in the state of FIG. 5B, the point image on the optical axis is blurred and the point image outside the optical axis is collected. It will be in a illuminated state. That is, it can be seen that when the point image off the optical axis changes so as to be focused before and after giving an instruction to the defocus changing means, a negative defocus amount occurs.

It is not limited to installing multiple bright spots as a subject. A subject with breadth or a subject with depth may be used. Regardless of the subject used, the method of determining the positive or negative of the defocus amount results in the above-mentioned two methods. For example, if the subject has a wide area, the enlargement / reduction of the image when the instruction is given to the defocus changing means may be seen, and if the three-dimensional chart is tilted in the optical axis direction, the instruction is given to the defocus changing means. You can see the change in the focus position at the time.

Subsequently, a method of calculating the absolute value | z | of the defocus amount will be described. The absolute value | z | of the defocus amount can be calculated from, for example, the blur amount of the point image acquired when an instruction is given to the defocus changing means and the numerical aperture number NA on the image side of the optical system under test. FIG. 6 is a diagram showing a method of estimating the absolute value | z | of the defocus amount. When the measurement position changes from the dotted line in FIG. 6 (a) to the thick line by giving an instruction to the defocus changing means, the spread diameter D of the point image is the absolute defocus amount shown in FIG. 6 (b). It is expressed by the following equation (1) using the value | z | and the angle θ of the outermost angle of the light collection.
D = 2 | z | tanθ (1)
The numerical aperture NA on the image side of the optical system to be inspected is expressed by the following equation (2).
NA = sinθ (2)
To know the absolute value | z | of the defocus amount by calculating the spread diameter D of the point image from the acquired image when the defocus changing means is instructed using the equations (1) and (2). Can be done.

Alternatively, two bright spots may be used as another method. When an instruction is given to the defocus changing means, the distance between the two point images changes with the defocus amount z, so the absolute value of the defocus amount from the amount of change in the distance and the angle of the main ray with respect to the point image | z | Can also be estimated. However, when the defocus amount z is small, the spread of the point image and the change in the interval between the point images are small, so that it is difficult to apply this method as it is. Therefore, a conversion formula between the defocus change instruction amount p and the defocus amount z is determined. When the conversion coefficient is α, the defocus change instruction amount p and the defocus amount z usually have a linear relationship, so the conversion formula is expressed by the following formula (3).
z = αp (3)
Since this method works well when the absolute value | z | of the defocus amount is large, the sign of the conversion coefficient α is obtained from the defocus amount z obtained in a state where a large defocus change instruction amount p is given. The absolute value may be calculated. This makes it possible to estimate the defocus amount z even when a small defocus change instruction amount p is given.

The relationship between the defocus amount z and the defocus change instruction amount p may deviate from the linearity. In that case, the conversion formula is represented by the following formula (4).

By obtaining N conversion coefficients α _k (k = 1 to N), it is possible to know the defocus amount z with higher accuracy. When there are multiple conversion coefficients, it is desirable to use multiple images. For the sake of simplicity, the relationship between the defocus change instruction amount p and the defocus amount z is a linear relationship unless otherwise specified, and the conversion coefficient α is a scalar.

Although the defocus amount z or the conversion coefficient α can be calculated by using the method described above, since the acquired point image contains blur and sensor noise, an error occurs in the spread diameter D and the interval between the point images. .. Therefore, the defocus amount z and the conversion coefficient α calculated by the above method are approximate values including an error.

Therefore, in the present embodiment, further calculations are performed in order to improve the estimation accuracy of the defocus amount. The wavefront aberration amount W _def generated when the defocus amount is z is expressed by the following equation (5).

Here, ξ and η are the pupil coordinates in the horizontal and vertical directions with the pupil end as 1, and λ is the wavelength of light used for measurement. When the relationship between the defocus amount z and the defocus change instruction amount p is a linear relationship, the wavefront aberration amount W _def is expressed by the following equation (6).

The conversion coefficient α when the light intensity distribution obtained by calculation from the wavefront aberration amount W _def calculated by using the equation (6) for each defocus change instruction amount p and the measured light intensity distribution most match. By searching, it is possible to calculate the conversion coefficient α with higher accuracy. That is, the conversion coefficient α may be used as the optimization variable, and the optimization may be executed so that the difference between the light intensity distribution obtained by the calculation and the measured light intensity distribution becomes small. When the light intensity distribution obtained by calculation from the wavefront aberration W _def calculated using the equation (6) is _Iest and the measured light intensity distribution is I _mes , the objective function F is the following equation (7). expressed.

The conversion coefficient α that minimizes the objective function F is expressed by the following equation (8).

When performing the optimization, the approximate value of the conversion coefficient α obtained above may be used as the initial value. In this method, the conversion coefficient α having the best consistency is calculated from a plurality of light intensity distributions, so that the obtained conversion coefficient α has high accuracy in which the influence of blurring and noise of the image is suppressed. By calculating the defocus amount z from the obtained conversion coefficient α and estimating the aberration, it is possible to estimate the aberration with higher accuracy.

In the present embodiment, the case where the relationship between the defocus amount z and the focus change instruction amount p is assumed to be a linear relationship is illustrated, but as shown in the equation (4), the defocus amount z is a conversion coefficient α. It is a function of _k and the defocus change instruction amount p. That is, the gist of the present invention is to determine the conversion coefficient α _k or the conversion formula based on the defocus change instruction amount p and the measured light intensity distribution, and to estimate the aberration based on these. In a broader sense, it is an object of the present invention to estimate the aberration by using the defocus amount z estimated from the defocus change instruction amount p and at least a part of the measured light intensity distribution.

When calculating the conversion coefficient α by optimization, it is desirable to use the approximate aberration of the optical system. Since the light intensity distribution changes not only with the defocus wavefront aberration but also with the aberration of the optical system under test, the light intensity distribution and conversion coefficient α calculated without considering the aberration of the optical system at the time of calculation are inaccurate. Become. However, since the aberration of the optical system under test is unknown at the stage of calculating the conversion coefficient α, it is necessary to obtain both from the state where both the conversion coefficient α and the aberration of the optical system are unknown. Therefore, it is effective to use the approximate aberration of the optical system to be inspected. As a method for acquiring approximate aberration, there are a method of solving the intensity transport equation of Non-Patent Document 3, a Fourier iterative method of Patent Document 3, a method of using machine learning of Non-Patent Document 4, and the like. Some of these methods require a defocus amount for the operation. In that case, the approximate value of the absolute value z of the defocus amount described above may be used. That is, the processing may proceed in the order of calculation of the approximate value of the defocus amount z, calculation of the approximate aberration, correction of the absolute value of the defocus amount, and estimation of the aberration. By repeating these processes as necessary, more accurate estimation can be performed, and some processes can be omitted by giving priority to the speed of the processes.

Hereinafter, the aberration estimation method of the present embodiment will be described with reference to FIG. 7. FIG. 7 is a flowchart showing the aberration estimation method of the present embodiment.

In step S1, the computer 105 transmits the defocus change instruction amount to the defocus change means.

In step S2 (first acquisition step), the computer 105 acquires the light intensity distribution of the optical image imaged by the optical system 102 to be imaged on the image sensor 103.

In step S3, the computer 105 determines whether or not the number of executions of the processes of step S1 and step S2 has reached a predetermined number of times. If the predetermined number of times is reached, the process proceeds to step S4, and if not, the process returns to step S1.

By executing the processes from step S1 to step S3, the light intensity distribution for a plurality of defocus amounts can be acquired. If the aberration is estimated from only one light intensity distribution, it is not necessary to repeat the processes of steps S1 and S2.

In step S4 (second acquisition step), the computer 105 acquires the defocus amount. The defocus amount may be obtained by determining the conversion coefficient α in the equation (3) or the conversion equation in the equation (4). In step S401, the computer 105 acquires the sign of the defocus amount. In step S402, the computer 105 acquires an approximate value of the defocus amount. In step S403, the computer 105 acquires the approximate aberration. In step S404, the computer 105 acquires a modified value of the estimated defocus amount.

In step S5 (estimation step), the computer 105 estimates the aberration of the optical system under test.

It should be noted that it may be determined whether or not to execute the sub-step processing in step S4 according to the conditions for carrying out the present invention. That is, it is not necessary to execute all the processes from step S401 to step S404. For example, if it is known in advance whether positive or negative defocus will occur in response to the instruction to the defocus changing means from the design value of the optical system to be inspected and the specifications of the stage to be used, the process of step S401 is unnecessary. be. Further, if the approximate value of the defocus amount for the instruction to the defocus changing means is known from the design value or the specification, the process of step S402 is unnecessary. Further, the processing from step S401 to step S403 may be executed with priority given to the processing speed, and the processing in step S404 may be omitted.

Further, the process of step S404 and the process of step S5 may be combined and executed. For example, it is also possible to optimize the conversion coefficient together with the aberration as an optimization variable. However, in this case, since the optimization variables increase, problems such as generation of local solutions and non-convergence may occur. In order to avoid this problem, it is desirable that the conversion factor and the aberration are optimized separately. For example, the process of step S403 and the process of step S5 may be repeated alternately.

Since this embodiment can be mathematically modeled, it can be implemented as a software function of a computer system. Here, the software function of a computer system includes programming (program) including executable code. The software code can be executed on a general purpose computer. During software code operation, the code, or associated data record, is stored within the general purpose computer platform. However, in other cases, the software is stored elsewhere or loaded into a suitable general purpose computer system. Therefore, the software code can be held on at least one machine-readable medium (storage medium) as one or more modules.

Hereinafter, preferred embodiments of the present invention will be described in detail.

Hereinafter, the aberration estimation method of this embodiment will be described by analysis using simulation. This embodiment is realized by the aberration estimation device 100 of FIG. The F value of the optical system 102 to be inspected is 1.2, the measurement wavelength λ is 524 nm, and the pixel size of the image sensor 103 is 6.4 μm. The image pickup device 103 is installed on the drive device 104 and moves along the optical axis according to the drive instruction pulse instructed by the computer 105. In this embodiment, a positive defocus amount of 1 μm is generated for each drive instruction pulse received. That is, the conversion coefficient α in the equation (3) is 1 μm / pulse. The optical system 102 under test has aberrations, and the expansion coefficient of the Fringe Zernike polynomial is −0.75λ for the fifth term, 1.5λ for the seventh term, and 1λ for the ninth term.

Aberration estimation in this embodiment is performed according to the flowchart of FIG.

In step S1, the computer 105 transmits a drive instruction pulse (defocus change instruction amount) to the drive device 104.

In step S2, the computer 105 acquires the light intensity distribution on the image sensor 103.

In this embodiment, the processes of steps S1 and S2 are repeated eight times, and eight light intensity distributions are acquired. The drive instruction pulse transmitted from the computer 105 in step S1 is −450, −160, −120, −80, 80, 120, 160, 450 pulse. Transmitting a negative pulse signal means driving the drive device 104 in the opposite direction.

In step S401, the computer 105 acquires the code of the conversion coefficient α. In this embodiment, in addition to the point light source on the optical axis, an off-axis point light source that forms a point image at an image height of 5 mm at the image formation position is used. Since the distance between the two points increases when the drive instruction pulse is 450 pulses, the conversion coefficient α is determined to be positive.

In step S402, the computer 105 acquires an approximate value of the conversion coefficient α. In this embodiment, the approximate value of the conversion coefficient α is determined using each of the light intensity distributions acquired when the defocus change instruction amount is −450 pulse and 450 pulse. It was calculated that the spread of the point image was 428.8 μm from the image when the drive instruction pulse was −450 pulse, and 377.6 μm from the image when the drive instruction pulse was 450 pulse. The conversion coefficients α are acquired as 1.143 μm / pulse and 1.007 μm / pulse, respectively. By taking the average value of these, the conversion coefficient α is acquired as 1.075 μm / pulse. The amount of defocus calculated using this conversion coefficient α is 483.8 μm, -172.0 μm, -129.0 μm, -86.0 μm, 86.0 μm, 129.0 μm, for each drive instruction pulse. It will be 172.0 μm and 484.0 μm.

In step S403, the computer 105 acquires the approximate aberration. In this embodiment, the approximate aberration is calculated by solving the intensity transport equation.

In step S404, the computer 105 acquires the corrected conversion coefficient α. The conversion coefficient α is corrected by executing an optimization calculation so that the difference between the light intensity distribution _Iest obtained by the imaging calculation and the measured light intensity distribution _Image is small. In this embodiment, the modified conversion coefficient α is 1.001 μm / pulse. The defocus amount calculated using this conversion coefficient α is −450.5 μm, -160.2 μm, -120.1 μm, -80.1 μm, 80.1 μm, 120.1 μm for each drive instruction pulse. It is 160.2 μm and 450.5 μm.

In step S5, the computer 105 estimates the aberration of the optical system under test by using the defocus amount acquired in step S4. Aberration estimation is performed using an optimization operation. The optimization variable is each coefficient from the second term to the 36th term when the aberration is expanded by the Fringe Zernike polynomial.

FIG. 8 is a diagram showing the estimation result of the aberration of this embodiment. FIG. 8 (a) shows the coefficients of the estimated Zernike polynomial. FIG. 8A shows the results of estimating the aberrations using the respective conversion coefficients α acquired in steps S402 and S404. In both cases, the value is close to the true value. That is, the aberration can be estimated even when the conversion coefficient α and the defocus amount are unknown. Further, when the high-precision conversion coefficient α is acquired in step S404, the aberration closer to the true value can be estimated. In order to clearly show this difference, FIG. 8B shows the difference between the true value and the estimated value. When the aberration is estimated using the conversion coefficient α acquired in step S402, the error is about 330 mλ in the seventh term, but when the aberration is estimated using the conversion coefficient α acquired in step S404, the error is 35 mλ. It is suppressed to the extent.

Further, in order to evaluate the entire aberration, the residual RMS of the estimated aberration and the true aberration is calculated. The residual RMS is represented by the following equation (9).

Here, _West is the estimated aberration, W ₀ is the true aberration,

Is the number of data points within the aperture region of the pupil. The sum is done within the open area of the pupil. The smaller the residual RMS, the more accurate the estimation result. In this embodiment, the RMS _res is 182 mλ and 22 mλ, respectively, when the conversion coefficients acquired in steps S402 and S404 are used. That is, it is possible to perform aberration estimation with higher accuracy by obtaining the conversion coefficient α acquired in step S404 more accurately.

The method for calculating the conversion coefficient is not limited to the method shown in this embodiment. For example, the defocus amount or the conversion coefficient may be calculated using the light intensity distribution acquired by using machine learning represented by a neural network. When calculating the defocus amount or conversion coefficient using machine learning, a value is randomly set as learning data within the range of the assumed defocus amount or conversion coefficient and the aberration amount of the optical system under test. , Prepare a large amount of obtained light intensity distribution. Since the light intensity distribution depends on the amount of defocus and the aberration, it is necessary to prepare the data in which both are shaken when preparing the data for learning. At this time, if the approximate value of the conversion coefficient is known as prior information, a random number may be assigned around that value. Even if the approximate value is unknown, the learning accuracy can be improved by allocating a random number with the conversion coefficient in a general optical system as the center value.

Further, in this embodiment, the pinhole is used as the subject 101 for estimating the aberration, but if the optical system 102 to be inspected forms an image in which the light intensity distribution is concentrated in a minute region of the image plane, the present invention is used. The invention is not limited to this. For example, a general illuminating light source in a distant place, an astronomical object observed by a telescope or the like may be used as a subject. A parallel plane wave emitted from a laser or the like may be incident on the optical system 102 to be inspected. Even when a pinhole is used, the size of the opening may be finite.

Further, in this embodiment, the discussion was conducted in the vicinity of the optical axis for the sake of simplicity, but the same function applies to the light formed outside the optical axis. The present invention does not depend on the image height to be measured.

Hereinafter, the aberration estimation method of this embodiment will be described. In this embodiment, as shown in FIG. 3A, the defocus is changed by using the focus control mechanism 1021 included in the optical system 102 under test. Specifically, when the focus control mechanism 1021 receives a drive instruction pulse from the computer 105, the focus control mechanism 1021 moves the focus drive lens inside the optical system 102 under test. It is assumed that the defocus amount and the drive instruction pulse that change with the movement of the lens have a linear relationship shown in (3). As a result, the acquisition of the conversion coefficient α and the estimation of the aberration can proceed in the same manner as in the first embodiment. In this embodiment, the true value of the conversion coefficient α is 11.25 μm / pulse, and the drive instruction pulse is -40,-14,-11, -7,7,11,14,40 pulses for measuring the light intensity distribution. It is carried out under eight conditions. Other conditions are the same as in Example 1. In step S402, the conversion coefficient α is acquired as 12.095 μm / pulse. In step S404, the conversion coefficient α is acquired as 11.27 μm / pulse. By executing the aberration estimation using the acquired conversion coefficient α, it is possible to estimate the aberration of 102 of the optical system under test.
[Other Examples]
The present invention supplies a program that realizes one or more functions of the above-described embodiment to a system or device via a network or storage medium, and one or more processors in the computer of the system or device reads and executes the program. It can also be realized by the processing to be performed. It can also be realized by a circuit (for example, ASIC) that realizes one or more functions.

Although the preferred embodiments of the present invention have been described above, the present invention is not limited to these embodiments, and various modifications and modifications can be made within the scope of the gist thereof.

101 Subject 102 Optical system to be inspected

Claims (11)

The first acquisition step of acquiring the light intensity distribution of the optical image of the subject formed through the optical system under test, and
A second acquisition step of acquiring the defocus amount using the indicated amount for changing the defocus amount of the optical system to be inspected and the light intensity distribution, and
An aberration estimation method comprising an estimation step of estimating an aberration of the test optical system using the light intensity distribution and the defocus amount. The aberration estimation method according to claim 1, wherein in the second acquisition step, a coefficient for converting the indicated amount into the defocus amount is acquired. The aberration estimation method according to claim 2, wherein the coefficient is calculated by an optimization operation. The aberration estimation method according to claim 2, wherein the coefficient is calculated by machine learning. The aberration estimation method according to any one of claims 1 to 4, wherein the indicated amount is an indicated amount for a changing means for changing the defocus amount. The aberration estimation method according to claim 5, wherein the changing means changes a position for measuring the light intensity distribution using the indicated amount. The aberration estimation method according to claim 5, wherein the changing means changes the distance between the subject and the optical system to be inspected by using the indicated amount. The aberration estimation method according to claim 5, wherein the changing means uses the indicated amount to move at least a part of the lens constituting the test optical system. An image sensor that acquires the light intensity distribution of the optical image of the subject formed through the optical system under test, and
Having a control unit for estimating an aberration of the optical system under test using an indicated amount for changing the defocus amount of the optical system under test and a defocus amount acquired based on the light intensity distribution. Aberration estimation device as a feature. A program for causing a computer to execute the aberration estimation method according to any one of claims 1 to 8. A storage medium in which the program according to claim 10 can be read by a computer.

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