Aberration estimation method, aberration estimation device, arithmetic unit, program, and storage medium

Abstract

To provide an aberration estimation method with which the aberration of an optical system to be tested can be estimated at high speed and with high accuracy despite using a light source having a wide wavelength width.SOLUTION: An aberration estimation method includes: a measurement step (S1) of picking up images of an object at a plurality of defocus positions different from each other through an optical system to be tested, thereby acquiring a plurality of first light intensity distributions corresponding to the plurality of defocus positions; a calculation step (S32) of calculating a plurality of second light intensity distributions corresponding to the plurality of defocus positions; and composition steps (S33, S37) of compositing the plurality of first light intensity distributions or the plurality of second light intensity distributions. The aberration of the optical system to be tested is estimated based on a result of the composition step.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to an aberration estimation method, an aberration estimation device, a calculation device, a program, and a storage medium. [Background technology]

[0002] Conventionally, there is known an aberration estimation method that uses a monochromatic light source such as a laser to measure the light intensity distribution at multiple defocus positions, and estimates the aberration that best reproduces the measurement results through optimization calculation. However, monochromatic light sources such as lasers are more expensive than other light sources and have high management costs. In addition, depending on the measurement conditions, there are cases where a monochromatic light source such as a laser cannot be used. For this reason, an aberration estimation method that uses a light source with a wavelength range, such as an LED or an incandescent lamp, instead of a monochromatic light source such as a laser, is desired.

[0003] In the aberration estimation method using optimization calculation, the light intensity distribution on the image plane is calculated from the estimated wavefront aberration, and it is determined whether it matches the measured light intensity distribution. Therefore, if the calculation conditions for calculating the light intensity distribution from the wavefront aberration differ from the measurement conditions, such as when a light source with a wavelength range is used, an error will occur in the estimation result.

[0004] Non-Patent Document 1 discloses a method for reproducing the same calculation conditions as the measurement conditions by calculating the light intensity distribution at each wavelength and adding up the light intensity distributions when calculating the light intensity distribution from the wavefront aberration. Non-Patent Document 2 discloses a method for bringing the calculation conditions closer to the measurement conditions by convolving a blur kernel in a two-dimensional plane with the light intensity distribution calculated in a single color. Patent Document 1 discloses a method for bringing the measured light intensity distribution closer to the calculation result in a single color by adding an image sharpening process using a blur kernel to the measured light intensity distribution. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] International Publication No. 2019 / 142313 [Non-patent literature]

[0006] [Non-Patent Document 1] James. R. Fienup, “Phase retrieval for undersampled broadband images” Journal of the Optical Society of America A Vol.16, pp.1831, July 1999, USA. [Non-Patent Document 2] Alden. S. Jurling and James. R. Fienup, “A Fast Approximation Method for Broadband Phase Retrieval” in Imaging and Applied Optics, OSA Technical Digest (CD) (Optical Society of America, July 2011), paper SMC3. Summary of the Invention [Problem to be solved by the invention]

[0007] In the method disclosed in Non-Patent Document 1, since it is necessary to calculate the light intensity distribution at multiple wavelengths according to the spread of the wavelength width, the calculation time increases. In the method disclosed in Non-Patent Document 2, high-speed calculation is possible, but since the change in the light intensity distribution caused by the spread of the wavelength width is different from the blur that simply spreads on a two-dimensional plane, the aberration cannot be estimated with high accuracy. In particular, since the axial chromatic aberration, whose focal position differs depending on the wavelength, cannot be reproduced by the blur in a two-dimensional plane, when the axial chromatic aberration exists in the test optical system, the aberration cannot be estimated with high accuracy. Similarly, in the method disclosed in Patent Document 1, since the influence of the axial chromatic aberration cannot be removed by the image sharpening process by the blur kernel, the aberration cannot be estimated with high accuracy.

[0008] SUMMARY OF THE PRESENT EMBODIMENTS Accordingly, an object of the present invention is to provide an aberration estimation method capable of estimating the aberration of an optical system to be measured quickly and with high accuracy even when a light source having a wide wavelength band is used. [Means for solving the problem]

[0009] An aberration estimation method as one aspect of the present invention includes a measurement step of acquiring a plurality of first light intensity distributions corresponding to a plurality of defocus positions by imaging an object via a test optical system at different defocus positions, a calculation step of calculating a plurality of second light intensity distributions corresponding to the plurality of defocus positions, and a synthesis step of synthesizing the plurality of first light intensity distributions or the plurality of second light intensity distributions, and estimates the aberration of the test optical system based on a result of the synthesis step.

[0010] Other objects and features of the present invention will be described in the following embodiments. Effect of the Invention

[0011] According to the present invention, it is possible to provide an aberration estimation method capable of estimating the aberration of an optical system to be measured quickly and with high accuracy even when a light source having a wide wavelength band is used. [Brief description of the drawings]

[0012] [Figure 1] FIG. 2 is a schematic diagram of an aberration measuring device in each embodiment. [Diagram 2] 10 is a flowchart showing an aberration estimation method in each embodiment. [Diagram 3] 4 is a flowchart illustrating an aberration estimation method in the first embodiment. [Figure 4] FIG. 13 is a diagram showing an estimation result in the first embodiment. [Diagram 5] 10 is a flowchart illustrating an aberration estimation method in the second embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0013] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, an embodiment of the present invention will be described in detail with reference to the drawings. In each drawing, the same reference numerals are used to refer to the same components, and duplicated explanations will be omitted.

[0014] First, an aberration estimation device 100 in this embodiment will be described with reference to FIG. 1. FIG. 1 is a schematic diagram of the aberration estimation device 100. Light emitted from a light source 101 illuminates an object 102. The light passing through the object 102 is focused on an image sensor 104 by a test optical system 103 to form an optical image. The image sensor 104 is installed on a driving device (motorized stage) 105. The driving device 105 is controlled by a computer (control unit) 106, and moves the image sensor 104 to a specified position in a direction along the optical axis indicated by an arrow (optical axis direction). The image sensor 104 acquires a light intensity distribution of an optical image at the moved position, and stores the acquired light intensity distribution in the computer 106 or a data storage device (not shown). The computer 106 estimates the aberration of the test optical system 103 by performing post-processing on the acquired light intensity distribution. At this time, the computer 106 functions as a calculation device having an acquisition unit, a calculation unit, a synthesis unit, and an estimation unit, which will be described later. The post-processing may be executed by the computer 106 or by another computing device. Alternatively, the post-processing may be executed by a computing device present on a cloud via a network. The display unit 107 displays the estimated aberration.

[0015] The light source 101 is, for example, a light source having a width (wavelength width) in the emission spectrum (having a wide wavelength width). Light sources having a wide wavelength width are, for example, LEDs, fluorescent lamps, or incandescent lamps, but are not limited to these. A heat source may be prepared, and infrared light emitted from the heat source may be used as the illumination light. The light source 101 may also include an element for limiting the wavelength, such as a bandpass filter. For example, by using a halogen lamp equipped with a bandpass filter as the light source 101, light having a desired wavelength width can be used as the illumination light. Fluorescence emitted from a fluorescent dye used in biological observation, etc. may also be used.

[0016] The subject 102 is a member having a minute opening, for example, a pinhole, but is not limited thereto. Also, the same effect can be obtained by setting the end of an optical fiber as the subject 102 and illuminating the opposite end with the light source 101. The subject 102 is not limited to a member that spatially limits light by a transmission part such as a pinhole, but may be a member that limits the light generation area by a scattering part or a light emitting part. For example, a minute white circle or minute luminous paint drawn on a flat base of a black body may be used as the subject 102. Anything that has a minute transmission area, minute scattering area, or minute light emitting area functions as the subject 102. Also, the light source 101 may double as the subject 102. For example, when a magnifying optical system such as a microscope is used as the test optical system 103, light from a minute fluorescent dye may be imaged on the image sensor 104. In this case, the minute fluorescent dye becomes the light source 101 and doubles as the subject 102.

[0017] The test optical system 103 may be an optical system to be measured (a single optical system), or a combination of the optical system to be measured and another optical system. For example, when the measurement target is a camera lens or a telescope, the test optical system 103 is the camera lens or the telescope itself. When the measurement target is an objective lens of a microscope, the test optical system 103 may be a combination of a microscope objective lens and an imaging lens. Any optical system that includes the optical system to be measured and can form an optical image of the subject 102 can be used as the test optical system 103. In addition, in adaptive optics used in astronomical telescopes, microscopes, etc., aberrations caused by the atmosphere or a biological sample are measured. Since these aberrations can also be measured by this embodiment, the test optical system 103 may include the atmosphere or a biological sample that generates these aberrations.

[0018] The imaging element 104 is an imaging sensor such as a CCD sensor or a CMOS sensor, and is a device in which photoelectric conversion elements (pixels) are arranged in an array. The driving device 105 may be a device that can be driven in one-dimensional directions, such as an electric stage. The object moved by the driving device 105 is not limited to the imaging element 104. The driving device 105 may drive the test optical system 103 or the object 102. If the test optical system 103 has a focus adjustment mechanism, the focus adjustment mechanism may be driven using a control unit that can communicate with the focus adjustment mechanism. Either method may have a mechanism that changes the defocus given to the optical image. In this embodiment, the description will be given assuming that the driving device 105 changes the defocus amount by moving the imaging element 104. For this reason, the position in the optical axis direction and the defocus position are synonymous. The image formation position of the object 102 formed by the test optical system 103 is set as the origin, and the position where the imaging element 104 is placed is determined based on the origin.

[0019] The principle on which this embodiment works and an aberration estimation method based on this principle will be described below in order. First, the principle on which this embodiment works will be described. Hereinafter, the calculated aberration will be described as the aberration (wavefront aberration) W(ξ, η) of the test optical system 103. (ξ, η) are Cartesian coordinates in the pupil space normalized by the pupil radius. The aberration that can be measured by this embodiment is not limited to this. Once the wavefront aberration W(ξ, η) is obtained, the amount of lateral aberration and the amount of longitudinal aberration can be calculated by simple calculation. The aberration W(ξ, η) can be converted to Seidel aberration by expanding it in Zernike polynomials.

[0020] An example of a method for estimating the aberration W(ξ, η) of the test optical system 103 by the computer 106 from the measured light intensity distribution is optimization. In the optimization, W(ξ, η) that minimizes the objective function F(W) expressed by the following formula (1) is searched for by iterative calculation.

[0021]

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[0022] Here, I s (x,y,z;W) is the light intensity distribution calculated from the aberration W(ξ,η), I m (x,y,z) is the measured light intensity distribution, x and y are two-dimensional Cartesian coordinates on a plane perpendicular to the optical axis, z is the coordinate in the optical axis direction, j is the z position number where the measurement was performed, and J is the total number of measurements. There are various forms of the objective function. I s and I m In addition to the sum of squared differences of the amplitude distribution (the square root of the light intensity distribution), the sum of squared differences of the amplitude distribution can also be used. The objective function F(W) can be appropriately selected depending on the problem.

[0023] There are various methods for minimizing the objective function F(W), including the steepest descent method, the conjugate gradient method, the quasi-Newton method, etc. Optimization can also be achieved by repeating the Fourier transform as in the method described in Patent Document 1, without explicitly calculating the objective function. In this embodiment, for ease of explanation, optimization using the objective function F(W) is shown.

[0024] To calculate the objective function F(W) expressed by equation (1), the light intensity distribution I s (x, y, z; W) must be calculated. The method for calculating the light intensity distribution I'(x, y, z; W) from the aberration W(ξ, η) for monochromatic light with a wavelength λ is given by Equation 2.

[0025]

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[0026] FT is an operator representing the Fourier transform. T(ξ, η) is a function representing the transmittance distribution of the pupil, which is a circular aperture in a normal optical system. NA is the image-side numerical aperture of the test optical system 103. In general, the left and right sides of equation (2) are proportional to each other, but to simplify the explanation, the proportionality coefficient is omitted and the equation is expressed by an equal sign.

[0027] Since equation (2) is a calculation formula for a single color, when the light source 101 has a wavelength range, I s When formula (2) is used to calculate Im As shown in equation (1), the optimization calculation uses I s and I m Therefore, in order to estimate the aberration with high accuracy, it is necessary to find the W that reduces the difference value of s In the process of calculating, a process for correcting the influence of the wavelength width is required. One of the major causes of the mismatch caused by the wavelength width of the light source 101 is the chromatic aberration of the test optical system 103. In particular, since wavefront aberration is often measured on the axis, axial chromatic aberration is the main cause of the mismatch. Therefore, in this embodiment, a process for quickly and accurately adding or removing the influence of axial chromatic aberration is added, thereby realizing high-speed and high-precision estimation of aberration even when a light source with a wavelength width is used.

[0028] According to imaging theory, the light intensity distribution I(x, y, z; W) formed by the light source 101 having a wavelength range is the sum of monochromatic light intensity distributions I'(x, y, z; W; λ) and is expressed by the following equation (3).

[0029]

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[0030] Here, S(λ) is determined by the emission spectrum of the light source 101 and the sensitivity characteristics of the image sensor 104. In some cases, the transmittance spectrum of the test optical system 103 is also taken into consideration. λ1 and λ2 are the lower and upper ends of λ where S(λ) has a value. Although the light intensity distribution I when the light source 101 with a wavelength range is used can be calculated using equation (3), integration by wavelength imposes a high computational load. Therefore, equation (3) is approximated with high accuracy.

[0031] Axial chromatic aberration is an aberration in which the focal position differs depending on the wavelength. The effect of this aberration is focused only on the difference in focal position, and other effects are ignored. In other words, the light intensity distribution I'(x,y,z;W;λ) at wavelength λ is regarded as the light intensity distribution in which the wavelength λ remains constant at λ0 and only the focal position is changed, and is expressed by the following formula (4).

[0032]

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[0033] Moreover, the difference in the focal position due to the difference in wavelength is expressed by the following formula (5).

[0034]

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[0035] Here, z' is the amount of shift in the focal position due to chromatic aberration, and α is the proportionality coefficient between the amount of shift in the focal position and the wavelength. Substituting equation (4) into equation (3), we obtain the following equation (6).

[0036]

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[0037] Here, z1 = α(λ1-λ0) and z2 = α(λ2-λ0). Although the light intensity distribution when there is a wavelength width is converted into a calculation for a single color by formula (6), it is necessary to calculate all I'(x,y,z;W;λ0) in the integral domain in order to perform integration in the z direction, which takes time. Therefore, instead of calculating I'(x,y,z;W;λ0) for all z in the integral domain, it is possible to calculate I'(x,y,z;W;λ0) for a small number of positions z. j I'(x,y,z j It is assumed that I'(x,y,z;W;λ0) at other positions is calculated and I'(x,y,z;W;λ0) at other positions is substituted by an interpolation calculation. To simplify the explanation, calculations are first performed at two positions, z1 and z2, and I'(x,y,z;W;λ0) at other z positions is substituted by an interpolation calculation. If the simplest linear interpolation is performed, I'(x,y,z;W;λ0) is expressed by the following equation (7).

[0038]

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[0039] Since I'(x,y,z;W;λ0) in equation (7) is a linear function of z in the z direction, the integral of equation 6 is simply an integral of z. This can be performed analytically, allowing for high-speed processing.

[0040] We generalize this operation by dividing the n discrete positions z n (n=1,2,...N) is the light intensity distribution I'(x,y,z n ;W;λ0) is known, and the position z (z1≦z≦z N ) is expressed by the following equation (8) through an interpolation calculation.

[0041]

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[0042] where f n (z) is an appropriate basis function, a n (x, y; W; λ0) is I'(x, y, z n ;W;λ0) is determined by linear transformation to (x, y). f n For (z), we can use a polynomial of z or a basis function of a Fourier series. n If we take a polynomial of z as (z) and set N=2, then equation (8) reduces to equation (7). Also, let f be the basis function of the Fourier series. n If we take it as (z), then a n (x, y; W; λ0) is I'(x, y, z j ;W;λ0) are inverse Fourier transformed in the z direction at each x and y coordinate, resulting in the Fourier coefficients.

[0043] Here, let us consider the behavior of the light intensity distribution I'(x, y, z; W; λ0) in the z direction at each x, y coordinate. Since I'(x, y, z; W; λ0) is the light intensity distribution on the image plane formed by the optical system 103 to be tested, the behavior in the z direction is expressed as the focal depth λ0 / NA 2In other words, since the light intensity distribution I'(x, y, z; W; λ0) is a function that is band-limited in the frequency space in the z direction, Equation (8) can be expressed as Equation (9) below.

[0044]

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[0045] Here, Δz is z n By substituting equation (9) into equation (6), we obtain the following equations (10) and (11).

[0046]

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[0047]

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[0048] In the aberration estimation of this embodiment, the position z where the measurement is performed is of interest as I(x, y, z; W). j Therefore, z=z j Then, equation (10) can be expressed as the following equation (12).

[0049]

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[0050] In the actual calculation, a series of measurement positions z j (j=1,2,,,J) and z n Since it is not necessary to set (n=1,2,,,N) to different values, z j and z n It is acceptable to assume that have the same value. Then, if equation (12) is rewritten in matrix form, it is expressed as the following equations (13) and (14).

[0051]

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[0052]

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[0053] From equations (13) and (14), the light intensity distribution I(x, y, z) obtained by using a light source 101 with a wavelength range is j ) is a monochromatic light intensity distribution I'(x, y, z j ;W;λ0), that is, the weighted sum of I(x, y, z j ) is a set of multiple light intensity distributions I'(x, y, z j The light intensity distribution I calculated in this way can be calculated by the synthesis process using the I s By using the light source 101 as the light source 102, the calculation conditions and the measurement conditions can be matched even when a light source 101 with a wavelength width is used, and highly accurate aberration estimation is possible.

[0054] In particular, as can be seen from formula (6) or formula (12), the change in light intensity distribution caused by axial chromatic aberration can be considered as the superposition of light intensity distribution in the optical axis direction, not the blur spread of the light intensity distribution in a two-dimensional plane. For this reason, it is more effective for highly accurate aberration estimation to add the weighted sum of the light intensity distribution I' calculated at different positions in the optical axis direction shown in formula (13) of this embodiment as a correction process, rather than the convolution process using the blur kernel in a two-dimensional plane. In addition, since the conversion by formula (13) is a calculation by a matrix of at most N×N, high-speed processing is possible. In addition, β and B can be obtained by a simple one-dimensional integral calculation that does not depend on W, once they are calculated, there is no need to recalculate them during the optimization calculation.

[0055] Next, an aberration estimation method based on the above principle will be described with reference to Fig. 2. Fig. 2 is a flowchart showing the aberration estimation method.

[0056] First, in step S1, the aberration estimation apparatus 100 calculates the light intensity distribution I m (x,y,z j ) (measurement step, first acquisition step). That is, the aberration estimation apparatus 100 captures an image of an object via the test optical system 103 at a plurality of mutually different defocus positions (images of the object via the test optical system while positioning (moving) the imaging surface of the imaging element at the defocus position). Then, a calculation device (acquisition unit) such as a computer 106 acquires a plurality of first light intensity distributions corresponding to the plurality of defocus positions. This measurement is performed by repeating driving by the driving device 105 and acquisition of light intensity distributions by the imaging element 104 under the control of the computer 106. The acquired light intensity distribution I m (x,y,z j ) is stored in a data storage device or in a temporary memory (storage unit) of the computer 106. Then, in step S2, the computer 106 converts the acquired light intensity distribution I m (x,y,z j ) is read. In step S1, the light intensity distribution I m (x,y,z j ) is stored in the temporary memory of computer 106, this step can be skipped.

[0057] Next, in step S3, the computer 106 calculates the light intensity distribution I m (x,y,z j ) to estimate the aberration of the test optical system 103. The estimated aberration is sent to the display unit 107 and displayed. Here, the aberration estimation method executed by the computer 106 in step S3 will be described with reference to Fig. 3. Fig. 3 is a flowchart showing the aberration estimation method.

[0058] First, in step S31, the computer 106 calculates a weighting factor β based on formula (11). In formula (11), Δz may be the interval between the defocus positions measured in step S1. S(z) may be a function obtained by variable-transforming the product of the emission spectrum of the light source 101 and the wavelength dependency of the sensitivity of the image sensor 104 using formula (5). Moreover, the integration in formula (11) may be performed within a range determined by the chromatic aberration of the test optical system 103.

[0059] Next, in step S32, the computer (calculation unit) 106 calculates the position z where the measurement was performed from the aberration (estimated aberration) W. j Monochromatic light intensity distribution I'(x, y, z j ;W;λ0) is calculated (calculation step, second acquisition step). That is, the computer 106 calculates a plurality of second light intensity distributions corresponding to a plurality of defocus positions. At the start of the repeated calculation, an initial value is set as W. The initial value may be set to be free of aberration, or an aberration approximately obtained by another calculation means may be used. In addition, an aberration estimated from a design value or the like may be used. A light intensity distribution I'(x, y, z) is calculated from the aberration W and the central wavelength λ0. j ;W;λ0) can be calculated using equation (2). It is also possible to add a calculation that takes into account the effect of discretizing the light intensity distribution due to the pixels of the image sensor 104.

[0060] Next, in step S33, the computer (combining unit) 106 combines the weight β calculated in step S31 and the light intensity distribution I'(x, y, z j ;W;λ0), a synthesis process is performed based on equation (13) or equation (14). That is, the computer 106 synthesizes a plurality of second light intensity distributions using the weight β (synthesizing step). As a result, a light intensity distribution I(x, y, z) in which the influence of chromatic aberration is taken into account is obtained. j ;W) can be calculated.

[0061] Next, in step S34, the computer 106 calculates I(x, y, zj ;W) to I s (x, y, z j ;W) to calculate the objective function F(W) of equation (1). Then, in step S35, the computer 106 compares the calculated objective function F(W) with a predetermined value. If the computer 106 determines that the objective function F(W) is equal to or smaller than the predetermined value, it ends the calculation and outputs the aberration W. On the other hand, if the computer 106 determines that the objective function F(W) is greater than the predetermined value, it proceeds to step S36.

[0062] In step S36, the computer 106 updates the aberration W. There are various methods for updating at this time, but a gradient method may be used in which the update is performed based on an equation obtained by differentiating the objective function F(W) with respect to the aberration W. The computer (estimation unit) 106 repeatedly executes steps S32 to S36 until the objective function F(W) falls below a predetermined value or a predetermined number of repetitions have been performed. Through the above flow, the aberration W of the test optical system 103 is estimated.

[0063] The present embodiment can be mathematically modeled and therefore can be implemented as a software function of a computer system. Here, the software function of the computer system includes programming (programs) including executable code. The software code is executable on a general-purpose computer. During the operation of the software code, the code, or associated data records, are stored in a general-purpose computer platform. However, in other cases, the software is stored elsewhere or loaded into a suitable general-purpose computer system. Thus, the software code can be held in at least one machine-readable medium (storage medium) as one or more modules.

[0064] A preferred embodiment of this invention will now be described in detail. EXAMPLES

[0065] First, the aberration estimation method in the first embodiment will be described using the analysis results by simulation. This embodiment is realized by the aberration estimation device 100 of FIG. 1. The light source 101 has a white illumination unit and a bandpass filter. The bandpass filter transmits light of 500 nm to 550 nm. The subject 102 is a pinhole with a hole of 3 μm in diameter. The test optical system 103 is a lens with a 1:1 magnification and NA of 0.179. The lens has wavefront aberration, and has an aberration amount of 10 nm in the fifth term, 50 nm in the eighth term, and 80 nm in the ninth term in coefficients when expanded by Fringe Zernike polynomials. In addition, the lens has axial chromatic aberration, and the focal position changes by 662 nm in the optical axis direction when the wavelength differs by 1 nm. The driving device 105 moves to a position z in the optical axis direction instructed by the computer 106, and the light intensity distribution is acquired by the image sensor 104.

[0066] In this embodiment, the estimation of the aberration is performed according to the flowcharts shown in Figures 2 and 3. In step S1, the computer 106 controls the driving device 105 and the image sensor 104 to obtain a light intensity distribution I m (x,y,z j ) is acquired at different defocus positions. j The seven locations are -49.4μm, -32.9μm, -16.5μm, 0μm, 16.5μm, 32.9μm, and 49.4μm. The light intensity distribution I m (x,y,z j ) is stored in the hard disk of the computer 106. In step S2, the computer 106 stores the stored light intensity distribution I m (x,y,z j ) to load the

[0067] Next, in step S2, the computer 106 reads the light intensity distribution I m (x,y,z j ) is read out and temporarily stored in a memory. Then, in step S3, the computer 106 estimates the aberration of the test optical system 103 by calculation. In this embodiment, in order to simplify the calculation, the following calculation formula is used in step S3.

[0068] z j are set at equal intervals (z j =(j-1)Δz+z0), and from the characteristics of the sinc function, zz j When β(zz j ) is negligibly small, so equation (14) can be regarded as the following equation (15).

[0069]

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[0070]

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[0071] That is, the position z to be calculated j The defocus position before and after (z j -Δz and z j By simply multiplying the light intensity distribution calculated with β(Δz) by weights (β(Δz) and β(-Δz)) and adding them together, it is possible to calculate the light intensity distribution I that takes into account the effects of chromatic aberration. Step S3 is carried out based on this formula.

[0072] First, in step S31, the computer 106 calculates the weighting factor β based on the formulas (16a) to (16c). In this embodiment, the computer 106 executes the integral calculation with z1=-16.5 μm, z2=16.5 μm, and Δz=16.5 μm. Then, in step S32, the computer 106 calculates the weighting factor β based on the formulas (16a) to (16c). j Monochromatic light intensity distribution I'(x,y,z j ;W;λ0) was calculated with a central wavelength of λ0 = 525 nm. The initial value of W is stigmatic.

[0073] Next, in step S33, the computer 106 calculates β and I′(x, y, z j ;W;λ0) to the target position z j Position before and after (z j -Δz and zj +Δz) are multiplied by weights (β(Δz) and β(-Δz)) and added together. This gives I(x,y,z j ;W) can be obtained.

[0074] Next, in step S34, the computer 106 calculates the light intensity distribution I(x, y, z) taking into account the chromatic aberration. j ;W) to I s (x,y,z j ;W) and calculates an objective function F(W) based on equation (1). Then, in step S35, the computer 106 evaluates the objective function F(W). Then, in step S36, the computer 106 updates W by the gradient method.

[0075] FIG. 4 is an explanatory diagram of the aberration W estimated by the above processing of this embodiment, and shows a comparison between the true value, the conventional example, and this embodiment. The aberration W is shown as a coefficient expanded by the Fringe Zernike polynomial. In FIG. 4, the horizontal axis shows the Zernike term, and the vertical axis shows the coefficient. The dashed line, which is the estimation result of this embodiment, is closer to the solid line of the true value than the dotted line of the conventional example. That is, this embodiment enables highly accurate estimation. EXAMPLES

[0076] Next, an aberration estimation method in the second embodiment will be described. Unlike the first embodiment, the second embodiment estimates the aberration of a plurality of measured I m By applying a correction process to the light intensity distribution of the light beam, high-speed and high-precision aberration estimation is realized. The principle of this embodiment will be described below, followed by a method of estimating aberration based on the principle.

[0077] As mentioned above, in the aberration estimation using the optimization calculation, I s The calculation condition for calculating I m In the first embodiment, the measurement conditions must be the same as those for measuring I s In the calculation of I, the discrepancy was resolved by converting I' to I based on equation (13). Another method to resolve the discrepancy is to convert the measured light intensity distribution Im By adding a correction process to the light intensity distribution I m ' is calculated.

[0078] By multiplying both sides of equation (13) by the inverse matrix of matrix B from the left, we obtain the following equation (17).

[0079]

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[0080] The light intensity distribution I obtained by the light source 101 with a wavelength range is converted to a monochromatic light intensity distribution I' by linear transformation, i.e., weighted sum. Therefore, in equation (17), I is converted to I m , I' to I m ' and I in Eq. (1) m I m ', I s This eliminates the discrepancy between the wavefront aberration and the reflection wavefront aberration, making it possible to estimate the wavefront aberration with high accuracy.

[0081] With reference to FIG. 5, an aberration estimation method executed by the computer 106 based on this principle will be described. FIG. 5 is a flowchart showing the aberration estimation method in this embodiment. Note that step S31 is the same as in the first embodiment. In this embodiment, step S37 is executed after step S31. In step S37, the computer (combining unit) 106 combines the measured multiple light intensity distributions I m The synthesis process is performed based on equation (17) to obtain the monochromatic light intensity distribution I m That is, the computer 106 synthesizes a plurality of first light intensity distributions. -1 is calculated from β and B determined from equations (11) and (14).

[0082] The subsequent step S32 is the same as in the first embodiment. In step S34, the computer 106 converts I′ calculated in step S32 into I in the formula (1). s In step S37, I m' in Eq. (1) m The objective function F(W) is calculated by using the above formula (1). Note that steps S35 and S36 are the same as those in the first embodiment.

[0083] Although the inverse matrix of B is used in equation (17), the present invention is not limited to this. A pseudo-inverse matrix of B may be used, or a matrix in the form of a Wiener filter used in image processing may be used. Whichever matrix is ​​used, the measurement conditions can be made to match the calculation conditions of equation (2) by performing synthesis processing on at least two or more of the multiple measured light intensity distributions. Then, by matching the conditions, highly accurate aberration estimation can be realized.

[0084] In the above-mentioned embodiments, the discussion was conducted in the vicinity of the optical axis for ease of explanation, but it also works for light that forms an image off the optical axis. Because the chief ray is inclined off the optical axis, the image shifts sideways when the measurement position z changes. Therefore, before performing the calculations of equation (13) or equation (17), it is necessary to add an image shift that matches the inclination of the chief ray.

[0085] In each embodiment, the range (z1 and z2) for performing the integral calculation of equation (11) or equation (16) is determined based on the chromatic aberration of the test optical system 103. However, there are cases where the chromatic aberration of the test optical system 103 cannot be known in advance. In such cases, it is sufficient to determine the integral range to be a little wider than the expected chromatic aberration. Alternatively, each embodiment will function if the integral range is set to a range of about 1 to 3 times Δz based on the interval Δz at which the light intensity distribution is acquired. Also, as mentioned above, I' is λ0 / NA in the z direction. 2 Since the change is only of a small magnitude, Δz~λ0 / NA 2 It is fine to leave it as it is.

[0086] In each embodiment, z in formula (12) j and z n The calculation in step S32 is performed assuming that z j and z nEach embodiment works as long as I is calculated based on light intensity distributions I' calculated at two or more different positions z.

[0087] In each embodiment, in the calculation of I′ in step S32, all z j In each embodiment, the same λ0 is used for I' in f n We have explained how to derive the linear transformation in equation (13) and the weighting factor β in equation (11) by using a sinc function as (z). More generally, we obtain equations (18) and (19) by substituting equation (8) into equation (6).

[0088]

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[0089]

number

[0090] a n (x,y;W;λ0) is I'(x,y,z j ;W;λ0), I and I' are converted into each other by linear transformation, i.e., weighted sum. In each embodiment, for at least one of the calculated light intensity distribution and the measured light intensity distribution, the light intensity distributions at at least two or more defocus positions are converted by a weighted sum based on the chromatic aberration of the test optical system 103. This allows the calculation conditions to match the measurement conditions. Since the conditions are matched, highly accurate aberration estimation is realized. In a broader sense, each embodiment relates to an aberration estimation method having a synthesis process for the light intensity distributions at at least two defocus positions.

[0091] In each embodiment, the optimization calculation is exemplified as an example of the aberration estimation calculation, but the present invention is not limited to this. There are also other calculation methods for estimating the aberration from the light intensity distribution, such as a method of solving the transport of intensity equation or a method using machine learning. Since most of the methods assume a monochromatic calculation, the I shown in the second embodiment is not used. m By adding a synthesis process to the above, it is also effective for other calculation methods.

[0092] (Other Examples) The present invention can also be realized by a process in which a program for implementing one or more of the functions of the above-mentioned embodiments is supplied to a system or device via a network or a storage medium, and one or more processors in a computer of the system or device read and execute the program. It can also be realized by a circuit (e.g., ASIC) that implements one or more of the functions.

[0093] According to each embodiment, it is possible to provide an aberration estimation method, an aberration estimation device, a calculation device, a program, and a storage medium that are capable of estimating the aberration of a test optical system quickly and accurately even when a light source having a wide wavelength range is used.

[0094] The disclosure of each embodiment includes the following configurations and methods.

[0095] (Method 1) a measuring step of acquiring a plurality of first light intensity distributions corresponding to a plurality of defocus positions different from each other by capturing images of the object via the test optical system; a calculation step of calculating a plurality of second light intensity distributions corresponding to the plurality of defocus positions; a combining step of combining the plurality of first light intensity distributions or the plurality of second light intensity distributions, An aberration estimation method, comprising estimating an aberration of the test optical system based on a result of the combining step. (Method 2) The aberration estimation method according to Method 1, wherein the synthesis step calculates a weighted sum of the plurality of light intensity distributions for the plurality of second light intensity distributions or the plurality of first light intensity distributions. (Method 3) 3. The aberration estimation method according to Method 1 or 2, wherein the synthesis step is performed based on chromatic aberration of the test optical system. (Method 4) 4. The aberration estimation method according to any one of Methods 1 to 3, wherein the combining step uses a weighting coefficient calculated based on the chromatic aberration of the test optical system. (Method 5) 5. The aberration estimation method according to any one of Methods 1 to 4, wherein in the measurement step, the plurality of first light intensity distributions are measured by moving an image sensor along the optical axis direction of the test optical system. (Configuration 1) A light source; an image pickup element that photoelectrically converts an optical image formed by the test optical system and outputs image data; a control unit that estimates an aberration of the test optical system based on the image data, The control unit is capturing images of an object via a test optical system at a plurality of defocus positions different from one another to obtain a plurality of first light intensity distributions corresponding to the plurality of defocus positions; calculating a plurality of second light intensity distributions corresponding to the plurality of defocus positions; an aberration estimation device that estimates an aberration of the test optical system by combining the plurality of first light intensity distributions or the plurality of second light intensity distributions. (Configuration 2) 7. The aberration estimation device according to configuration 6, wherein the light source is an LED, a fluorescent lamp, or an incandescent lamp. (Configuration 3) an acquisition unit that acquires a plurality of first light intensity distributions corresponding to a plurality of defocus positions different from each other by capturing images of an object via a test optical system; a calculation unit that calculates a plurality of second light intensity distributions corresponding to the plurality of defocus positions; a combining unit that combines the plurality of first light intensity distributions or the plurality of second light intensity distributions; an estimation unit that estimates an aberration of the test optical system based on a result of the synthesis unit. (Configuration 4) 6. A program for causing a computer to execute the aberration estimation method according to any one of Methods 1 to 5. (Configuration 5) A computer-readable storage medium storing the program according to configuration 4.

[0096] 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 changes are possible within the scope of the gist of the present invention. [Explanation of symbols]

[0097] 100 Aberration Estimation Device 101 Light source 103 Test Optical System 104 Image sensor 106 Computer (control unit)

Claims

1. An estimation method for estimating a second aberration of a test optical system by optimization calculation, comprising: a measuring step of capturing images of an object through the test optical system at a plurality of defocus positions different from each other to obtain a plurality of first light intensity distributions corresponding to the plurality of defocus positions; a calculation step of calculating a plurality of second light intensity distributions corresponding to the plurality of defocus positions based on the first aberration in the optimization calculation; a combining step of combining one of the plurality of first light intensity distributions and the plurality of second light intensity distributions to generate a third light intensity distribution, calculating an objective function based on the third light intensity distribution and the other of the plurality of first light intensity distributions and the plurality of second light intensity distributions; an estimation method comprising: estimating the second aberration by optimizing the first aberration using the objective function;

2. 2. The estimation method according to claim 1, wherein in the combining step, the third light intensity distribution is combined by calculating a weighted sum of either the plurality of second light intensity distributions or the plurality of first light intensity distributions.

3. 2. The estimation method according to claim 1, wherein in the combining step, the third light intensity distribution is combined based on chromatic aberration of the optical system to be measured.

4. 2. The estimation method according to claim 1, wherein in the combining step, the third light intensity distribution is combined using a weighting coefficient calculated based on chromatic aberration of the optical system to be measured.

5. 2. The estimation method according to claim 1, wherein in the measuring step, an image pickup element is moved along the optical axis direction of the optical system to be measured, thereby capturing images of the object at the plurality of defocus positions.

6. A light source and an imaging element that photoelectrically converts an optical image formed by the optical system to output image data; a control unit that estimates a second aberration of the test optical system by performing an optimization calculation based on the image data, The control unit capturing images of an object via the test optical system at a plurality of defocus positions different from one another to obtain a plurality of first light intensity distributions corresponding to the plurality of defocus positions; calculating a plurality of second light intensity distributions corresponding to the plurality of defocus positions based on the first aberration in the optimization calculation; an estimation device comprising: a first light intensity distribution and a second light intensity distribution; a third light intensity distribution; an objective function; and an optimization device for optimizing the first aberration by calculating an objective function based on the third light intensity distribution and the other of the first light intensity distribution and the second light intensity distribution.

7. The estimation device according to claim 6 , wherein the light source is an LED, a fluorescent lamp, or an incandescent lamp.

8. A calculation device that estimates a second aberration of a test optical system by optimization calculation, comprising: an acquisition unit that acquires a plurality of first light intensity distributions corresponding to a plurality of defocus positions different from each other by capturing images of an object via the test optical system at the plurality of defocus positions; a calculation unit that calculates a plurality of second light intensity distributions corresponding to the plurality of defocus positions based on the first aberration in the optimization calculation; a combining unit that combines one of the plurality of first light intensity distributions and the plurality of second light intensity distributions to generate a third light intensity distribution; an estimation unit that calculates an objective function based on the third light intensity distribution and the other of the plurality of first light intensity distributions and the plurality of second light intensity distributions, and estimates the second aberration by optimizing the first aberration using the objective function.

9. A program causing a computer to execute the estimation method according to any one of claims 1 to 5.

10. A computer-readable storage medium storing the program according to claim 9.

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