阅读说明：本技术 降低分光棱镜色差对相位差法波前探测精度影响的方法 (Method for reducing influence of chromatic aberration of beam splitter prism on wavefront detection precision of phase difference method ) 是由 鞠国浩 徐抒岩 白晓泉 许博谦 姜凤义 于 2021-09-29 设计创作，主要内容包括：降低分光棱镜色差对相位差法波前探测精度影响的方法,属于光学检测领域,包括明确分光棱镜色差所影响的像差类型；对特定光谱带宽且受分光棱镜色差影响的PSF图像与中心波长下的像差系数之间的成像模型进行修正；根据分光棱镜尺寸和材料、光谱带宽、中心波长确定分光棱镜色差所造成的像差系数改变量与波长之间的具体量化函数关系,得到PSF图像与中心波长下的像差系数之间的成像模型；采集两幅不同焦面位置处的PSF图像对；利用修正色差后的成像模型及PSF图像对,建立非线性方程组；建立目标函数利用数值最优化算法求解非线性方程组。本发明提高了基于相位差原理的波前探测方法在应用分光棱镜且非单色光成像时的波前探测精度。(A method for reducing the influence of the chromatic aberration of a beam splitter prism on the wavefront detection precision of a phase difference method belongs to the field of optical detection, and comprises the steps of determining the type of the aberration influenced by the chromatic aberration of the beam splitter prism; correcting an imaging model between a PSF image with a specific spectral bandwidth and affected by chromatic aberration of a spectroscope and aberration coefficients under a central wavelength; determining a specific quantitative function relationship between aberration coefficient change quantity caused by chromatic aberration of the beam splitter prism and wavelength according to the size and material of the beam splitter prism, spectral bandwidth and central wavelength to obtain an imaging model between a PSF image and the aberration coefficient under the central wavelength; collecting two PSF image pairs at different focal plane positions; establishing a nonlinear equation set by using the imaging model and the PSF image pair after the color difference correction; and establishing an objective function and solving a nonlinear equation set by using a numerical optimization algorithm. The invention improves the wavefront detection precision of the wavefront detection method based on the phase difference principle when a beam splitter prism is applied and non-monochromatic light is imaged.)

1. The method for reducing the influence of the chromatic aberration of the beam splitter prism on the wavefront detection precision of the phase difference method is characterized by comprising the following steps of:

the method comprises the steps of firstly, determining a main aberration type influenced by chromatic aberration of a beam splitter prism, and analyzing the relation between aberration coefficient change quantity and wavelength caused by chromatic aberration of the beam splitter prism;

correcting an imaging model between a point spread function image with a specific spectral bandwidth and affected by chromatic aberration of the dispersion prism and an aberration coefficient under a central wavelength;

determining a specific quantitative function relation between aberration coefficient change quantity caused by chromatic aberration of the beam splitter prism and wavelength according to the size and material of the beam splitter prism, spectral bandwidth and central wavelength, and obtaining a final imaging model between a point spread function image and aberration coefficients under the central wavelength;

step four, adopting a light splitting prism to split light in a prism light splitting mode, and collecting two point spread function image pairs at different focal plane positions;

fifthly, establishing a nonlinear equation set for solving aberration coefficients by using the imaging model after correcting the aberration and the collected two point spread function image pairs at different focal plane positions;

and step six, establishing an objective function and solving a nonlinear equation set by using a numerical optimization algorithm to obtain an aberration coefficient.

2. The method for reducing the influence of chromatic aberration of the beam splitter prism on the wavefront detection precision of the phase difference method according to claim 1, wherein the specific process of the first step is as follows:

for the refraction of the beam splitter prism, the refractive indexes of light with different wavelengths are different, after passing through the beam splitter prism, the positions of the light convergence focuses with different wavelengths are different, after two beams of light with different wavelengths pass through the beam splitter prism, the difference of the focus positions is as follows:

wherein n is₁And n₂The light with two different wavelengths respectively passes through the refractive index of the beam splitter prism, and L is the thickness of the beam splitter prism;

for light of a specific spectral bandwidth, the refractive index corresponding to the center wavelength of the spectrum is assumed to be n₀Then the axial deviation between the focal position of the light beam at a certain wavelength λ and the focal position of the central wavelength λ 0 within the spectral bandwidth is:

wherein, Δ d_λDenotes the difference between the focal position of the light beam with the wavelength λ and the focal position of the light beam with the center wavelength λ 0, n_λAnd n_λ0Refractive indexes of a light beam with the wavelength of lambda and a light beam with the central wavelength of lambda 0 when passing through the prism respectively;

from the aspect of aberration, the different axial positions of the focal points at different wavelengths represent that defocusing aberration exists between different wavelengths; the difference in defocus aberration between an imaging beam at a certain wavelength λ and the central wavelength λ 0 is:

wherein, is_defocusPV value representing defocus aberration, D is the aperture of the optical system, and f is the focal length of the optical system.

3. The method for reducing the influence of chromatic aberration of the beam splitter prism on the wavefront detection precision of the phase difference method according to claim 2, wherein the specific process of the second step is as follows:

in the presence of chromatic aberration, the point spread function image of the optical system at a certain wavelength λ is represented as:

wherein s represents a two-dimensional PSF image matrix,denotes an image plane coordinate vector, λ 0 denotes a center wavelength, x denotes an aberration coefficient vector corresponding to the center wavelength λ 0, and FT^-1Representing the inverse fourier transform, P the pupil plane aperture function matrix,expressing a pupil plane coordinate vector, i is an imaginary unit, W represents a pupil plane wave aberration matrix under a central wavelength lambda 0, and Δ V represents the difference of defocusing aberration between imaging light beams with two different wavelengths of the wavelength lambda and the central wavelength lambda 0; in the formula, the wave aberration at the wavelength λ is divided into two parts, one part is the wave aberration corresponding to the central wavelength λ 0, and the other part is the difference between the wave aberration corresponding to the wavelength λ and the wave aberration corresponding to the central wavelength λ 0;

for a point spread function image at a particular spectral bandwidth, it is represented as a superposition of a plurality of monochromatic wavelength images within the spectral bandwidth:

wherein the content of the first and second substances,represents a spectral width of λ_LAnd a non-monochromatic spot spread function image with x as the aberration coefficient vector at the central wavelength of λ 0, round represents rounding, λ 0_jAnd the wavelength corresponding to the jth single-wavelength image is represented, and the delta lambda represents the wavelength interval adopted when the single-wavelength images are used for describing the specific bandwidth image in an overlapping mode.

4. The method for reducing the influence of chromatic aberration of the beam splitter prism on the wavefront detection precision of the phase difference method according to claim 3, wherein the concrete process of the fifth step is as follows:

the relationship between the acquired pairs of point spread function images at two different focal plane positions and the aberration coefficients is represented as:

wherein S is₁And S₂Two point spread function image data matrixes with specific bandwidth, which are actually acquired at two different focal plane positions, are respectively represented, and deltax is the known aberration difference between the two focal planes.

5. The method for reducing the influence of chromatic aberration of the beam splitter prism on the wavefront detection precision of the phase difference method according to claim 4, wherein the specific process of the step six is as follows:

subtracting the left side and the right side of each equation in the equation set and taking the square, then integrating the whole image data area, namely, subtracting the left side and the right side of all equations and taking the square result to add, and establishing the following objective function related to the aberration coefficient vector x to be solved:

and solving the minimum value of the objective function E (x) by using a correlation numerical optimization algorithm, wherein the corresponding aberration coefficient vector x is the solved aberration coefficient.

6. The method for reducing the influence of chromatic aberration of a beam splitter prism on the accuracy of wavefront measurement by a phase difference method according to claim 5, wherein the correlation value optimization algorithm adopts a gradient method, a Newton method or a particle swarm optimization algorithm.

Technical Field

The invention belongs to the technical field of optical detection, and particularly relates to a method for reducing the influence of chromatic aberration of a beam splitter prism on wavefront detection precision of a phase difference method.

Background

The large-caliber astronomical telescope has important strategic significance on scientific and technological progress and social development in China. The device is not only a key device for researching a series of important frontier scientific problems of the universe evolution, the life origin, the dark matter, the dark energy essence and the like, but also can provide an important driving force for the original innovation of the photoelectric field and draw the rapid development of a plurality of frontier technologies and industries.

The increase of the mirror surface aperture of the large-aperture astronomical telescope presents a serious challenge to the maintenance of the imaging quality of the system. The quality of each mirror and the distance between the mirrors are increased, so that each mirror is more susceptible to the influence of factors such as vibration, gravity, temperature change and the like to cause maladjustment and surface shape change, and additional wavefront aberration is introduced to cause image quality degradation. The active optical technology is an effective means for solving the problem, and continuously maintains the imaging quality of the large-caliber astronomical telescope by detecting and correcting wave aberration caused by the position maladjustment of the mirror surface and the change of the surface shape in real time.

Wherein, high-precision wavefront detection is a precondition for effectively correcting wavefront aberration. Compared with a Hartmann sensor, a rectangular pyramid wave-front sensor and the like, the phase difference method utilizes different focal plane images (the defocusing distance is known) collected by an image sensor to calculate the wave-front phase, and does not need an additional precision device and a complex calibration process (the calibration process has errors as well). Meanwhile, with the development of computer technology, the problem of low wavefront detection efficiency of the phase difference method has been gradually solved.

The beam splitting prism is a common optical device for wave front detection by using a phase difference technology. Compared with the method of acquiring two different focal plane images in a time-sharing manner by means of focusing, the method of utilizing the prism to split light can acquire two different focal plane images at the same time, thereby omitting a focusing process (so that a movable part is not needed), improving the wave-front detection efficiency and reducing the risk; compared with a mode of splitting light by using a light splitting piece, the light splitting prism is easy to support and fix, and two paths of light splitting equal optical distances are convenient to apply and can ensure the wavefront detection precision. However, the chromatic aberration of the beam splitter prism affects the accuracy of wave front detection by the phase difference technique. In practice, it is often necessary to limit the exposure time of the detector (reduce the influence of factors such as micro-vibration and visual axis drift on the acquired image) while ensuring the signal-to-noise ratio of the acquired out-of-focus image, which means that the spectrum participating in imaging needs to reserve a certain bandwidth to ensure the signal-to-noise ratio. The beam splitter prism is a transmission optical device, the optical refractive indexes of light with different wavelengths are different, and introduced wave aberration is different (namely chromatic aberration exists), so that an acquired Point Spread Function (PSF) image is blurred, and the accuracy of wavefront detection is reduced.

How to improve the wavefront detection accuracy of a wavefront detection method based on a Phase Diversity (Phase Diversity) principle when a beam splitter prism is applied and non-monochromatic light is used for imaging has become one of the problems to be solved in the art.

Disclosure of Invention

The invention aims to provide a method for reducing the influence of chromatic aberration of a beam splitter prism on wavefront detection precision of a Phase difference method, so as to improve the wavefront detection precision of the wavefront detection method based on a Phase difference (Phase Diversity) principle when the beam splitter prism is applied and non-monochromatic light is imaged.

The technical scheme adopted by the invention for solving the technical problem is as follows:

the invention discloses a method for reducing the influence of chromatic aberration of a beam splitter prism on wavefront detection precision of a phase difference method, which comprises the following steps of:

the method comprises the steps of firstly, determining a main aberration type influenced by chromatic aberration of a beam splitter prism, and analyzing the relation between aberration coefficient change quantity and wavelength caused by chromatic aberration of the beam splitter prism;

correcting an imaging model between a point spread function image with a specific spectral bandwidth and affected by chromatic aberration of the dispersion prism and an aberration coefficient under a central wavelength;

determining a specific quantitative function relation between aberration coefficient change quantity caused by chromatic aberration of the beam splitter prism and wavelength according to the size and material of the beam splitter prism, spectral bandwidth and central wavelength, and obtaining a final imaging model between a point spread function image and aberration coefficients under the central wavelength;

step four, adopting a light splitting prism to split light in a prism light splitting mode, and collecting two point spread function image pairs at different focal plane positions;

fifthly, establishing a nonlinear equation set for solving aberration coefficients by using the imaging model after correcting the aberration and the collected two point spread function image pairs at different focal plane positions;

and step six, establishing an objective function and solving a nonlinear equation set by using a numerical optimization algorithm to obtain an aberration coefficient.

Further, the specific process of the step one is as follows:

for the refraction of the beam splitter prism, the refractive indexes of light with different wavelengths are different, after passing through the beam splitter prism, the positions of the light convergence focuses with different wavelengths are different, after two beams of light with different wavelengths pass through the beam splitter prism, the difference of the focus positions is as follows:

wherein n is₁And n₂The light with two different wavelengths respectively passes through the refractive index of the beam splitter prism, and L is the thickness of the beam splitter prism;

for light of a specific spectral bandwidth, the refractive index corresponding to the center wavelength of the spectrum is assumed to be n₀Then the axial deviation between the focal position of the light beam at a certain wavelength λ and the focal position of the central wavelength λ 0 within the spectral bandwidth is:

wherein, Δ d_λDenotes the difference between the focal position of the light beam with the wavelength λ and the focal position of the light beam with the center wavelength λ 0, n_λAnd n_λ0Refractive indexes of a light beam with the wavelength of lambda and a light beam with the central wavelength of lambda 0 when passing through the prism respectively;

from the aspect of aberration, the different axial positions of the focal points at different wavelengths represent that defocusing aberration exists between different wavelengths; the difference in defocus aberration between an imaging beam at a certain wavelength λ and the central wavelength λ 0 is:

wherein, is_defocusPV value representing defocus aberration, D is the aperture of the optical system, and f is the focal length of the optical system.

Further, the specific process of the second step is as follows:

in the presence of chromatic aberration, the point spread function image of the optical system at a certain wavelength λ is represented as:

wherein s represents a two-dimensional PSF image matrix,denotes an image plane coordinate vector, λ 0 denotes a center wavelength, x denotes an aberration coefficient vector corresponding to the center wavelength λ 0, and FT^-1Representing the inverse fourier transform, P the pupil plane aperture function matrix,expressing a pupil plane coordinate vector, i is an imaginary unit, W represents a pupil plane wave aberration matrix under a central wavelength lambda 0, and Δ V represents the difference of defocusing aberration between imaging light beams with two different wavelengths of the wavelength lambda and the central wavelength lambda 0; in the formula, the wave aberration at the wavelength λ is divided into two parts, one part is the wave aberration corresponding to the central wavelength λ 0, and the other part is the difference between the wave aberration corresponding to the wavelength λ and the wave aberration corresponding to the central wavelength λ 0;

for a point spread function image at a particular spectral bandwidth, it is represented as a superposition of a plurality of monochromatic wavelength images within the spectral bandwidth:

wherein the content of the first and second substances,represents a spectral width of λ_LAnd a non-monochromatic spot spread function image with x as the aberration coefficient vector at the central wavelength of λ 0, round represents rounding, λ 0_jAnd the wavelength corresponding to the jth single-wavelength image is represented, and the delta lambda represents the wavelength interval adopted when the single-wavelength images are used for describing the specific bandwidth image in an overlapping mode.

Further, the specific process of the step five is as follows:

the relationship between the acquired pairs of point spread function images at two different focal plane positions and the aberration coefficients is represented as:

wherein S is₁And S₂Two point spread function image data matrixes with specific bandwidth, which are actually acquired at two different focal plane positions, are respectively represented, and deltax is the known aberration difference between the two focal planes.

Further, the specific process of the step six is as follows:

subtracting the left side and the right side of each equation in the equation set and taking the square, then integrating the whole image data area, namely, subtracting the left side and the right side of all equations and taking the square result to add, and establishing the following objective function related to the aberration coefficient vector x to be solved:

and solving the minimum value of the objective function E (x) by using a correlation numerical optimization algorithm, wherein the corresponding aberration coefficient vector x is the solved aberration coefficient.

Further, the correlation value optimization algorithm adopts a gradient method, a Newton method or a particle swarm optimization algorithm.

The invention has the beneficial effects that:

the invention discloses a method for reducing the influence of chromatic aberration of a beam splitter prism on wavefront detection precision of a phase difference method, which comprises the steps of determining the main aberration type influenced by the chromatic aberration of the beam splitter prism, and analyzing the relation between aberration coefficient change quantity and wavelength caused by the chromatic aberration of the beam splitter prism; correcting an imaging model between a point spread function image with a specific spectral bandwidth and affected by chromatic aberration of a beam splitter prism and aberration coefficients under a central wavelength; determining a specific quantitative function relation between aberration coefficient change quantity caused by chromatic aberration of the beam splitter prism and wavelength according to the size and material of the beam splitter prism, spectral bandwidth and central wavelength, and obtaining a final imaging model between a point spread function image and an aberration coefficient under the central wavelength; splitting light by adopting a light splitting prism in a prism light splitting mode, and collecting two point spread function image pairs at different focal plane positions; establishing a nonlinear equation set for solving aberration coefficients by using the imaging model after correcting the aberration and the acquired point spread function image pairs at two different focal plane positions; and establishing an objective function and solving a nonlinear equation set by using a numerical optimization algorithm to obtain an aberration coefficient.

The method for reducing the influence of the chromatic aberration of the beam splitter prism on the wavefront detection precision of the Phase difference method improves the wavefront detection precision of the wavefront detection method based on the Phase Diversity principle when the beam splitter prism is applied and non-monochromatic light is imaged. The method has certain reference value for popularization and practical application of the phase difference wavefront detection technology.

Drawings

FIG. 1 is a schematic diagram of the detection of the wave aberration of an optical system using a phase-difference wavefront-sensing technique.

Fig. 2 shows the difference of the focal positions of the converging lights with different wavelengths after passing through the beam splitter prism.

FIG. 3 is a flowchart of a method for reducing the influence of chromatic aberration of a beam splitter prism on wavefront measurement accuracy by a phase difference method according to the present invention.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings.

As shown in fig. 3, a method for reducing the influence of chromatic aberration of a beam splitter prism on wavefront detection precision by a phase difference method of the present invention mainly includes the following steps:

the method comprises the steps of firstly, determining a main aberration type influenced by chromatic aberration of the beam splitter prism, and analyzing the relation between aberration coefficient change quantity and wavelength caused by chromatic aberration of the beam splitter prism.

The application of the beam splitter prism in the phase difference wavefront detection technology comprises the following steps: the phase difference wavefront detection technology is a wavefront detection method based on an image information optical system, and generally utilizes a focal plane image and an out-of-focus plane image to solve wavefront phase distribution according to a certain processing algorithm. The beam splitter prism is a commonly used optical device in the phase difference wavefront detection technology and is used for simultaneously obtaining two images with known defocusing aberration.

As shown in fig. 1, which is a schematic diagram of detecting the wave aberration of an optical system by using the phase-difference wavefront sensing technology, in fig. 1, 1 is an optical system, 2 is a distorted wavefront, 3 is a beam splitter prism, 4 is a beam splitting surface, 5 is a focal plane, 6 is a focal plane image, 7 is a wavefront phase distribution, 8 is an out-of-focus surface, and 9 is an out-of-focus image. Parallel light emitted by the point light source at infinity passes through the optical system 1, and then the wavefront (equiphase surface) is distorted (namely, wave aberration exists). The beam splitting prism 3 is located in an imaging light path of the optical system 1, and divides a condensed light beam into two paths, each path of light beam has detectors (the two detectors are located at different focal plane positions, but the defocusing amount is known), and receives the image energy distribution of a Point Spread Function (PSF) for solving the wavefront phase distribution.

The difference of defocusing aberration of the convergent light beams with different wavelengths after passing through the beam splitter prism is as follows:

for prism refraction, the refractive indexes of light with different wavelengths are different, and after passing through the beam splitter prism, the positions of the light convergence focuses with different wavelengths are different, as shown in fig. 2, 10 is a light beam formed by mixing two light beams with different wavelengths a and B in fig. 2, 11 is a light beam with wavelength a, 12 is the beam splitter prism, 13 is a light beam focus position with wavelength a, 14 is a light beam focus position with wavelength B, 15 is a light beam with wavelength B. After two beams of light with different wavelengths pass through the light splitting prism, the difference of the focal positions is about:

wherein n is₁And n₂The light with two different wavelengths respectively passes through the refractive index of the beam splitter prism, and L is the thickness of the beam splitter prism.

For light of a specific spectral bandwidth, the refractive index corresponding to the center wavelength of the spectrum is assumed to be n₀Then, the axial offset between the focal position of a certain wavelength λ beam and the focal position of the central wavelength λ 0 within the spectral bandwidth is:

wherein, Δ d_λDenotes the difference between the focal position of the light beam with the wavelength λ and the focal position of the light beam with the center wavelength λ 0, n_λAnd n_λ0Refractive indexes of a light beam with the wavelength of lambda and a light beam with the central wavelength of lambda 0 when passing through the prism respectively;

from the aspect of aberration, the different axial positions of the focal points at different wavelengths represent that defocusing aberration exists between different wavelengths; the difference in defocus aberration between an imaging beam at a certain wavelength λ and the central wavelength λ 0 is approximately:

wherein, is_defocusPV value representing defocus aberration, D is the aperture of the optical system, and f is the focal length of the optical system.

Therefore, it can be known that the chromatic aberration introduced by the beam splitter prism has a certain regularity in the aberration type. Specifically, when the optical axis is incident perpendicularly to the surface of the beam splitter prism, the beam splitter prism does not generate non-axisymmetric aberrations (such as astigmatism, coma, trefoil, and the like), and only generates axisymmetric aberrations (mainly defocus).

In addition, by studying the relationship between the aberration coefficient change amount and the wavelength caused by the chromatic aberration of the beam splitter prism, the relationship between the magnitude of the defocusing aberration introduced by the beam splitter prism and the wavelength can be established in an analytic mode, specifically, the analytic function relationship between the defocusing aberration generated by the beam splitter prism and the parameters of the beam splitter prism, such as the size, the material, the spectral bandwidth and the central wavelength, is relatively clear, and the method can be obtained through a mathematical modeling mode on the basis of proper approximation.

Step two, correcting the imaging model

And on the basis of the first step, correcting an imaging model between a Point Spread Function (PSF) image with a specific spectral bandwidth and affected by chromatic aberration of the spectroscope and aberration coefficients at the central wavelength.

The specific correction process is as follows:

within a specific spectral band range, the spectral intensity changes smoothly with the wavelength, and the method can be simplified properly. Although the stellar spectrum generally used for wavefront sensing is unknown, when the wavelength band is relatively narrow (100n m-200 nm), the spectral intensity distribution can be approximately considered to be uniform. Thus, in the presence of chromatic aberration, an optical system Point Spread Function (PSF) image at a certain wavelength λ can be represented as:

wherein s represents a two-dimensional PSF image matrix,denotes an image plane coordinate vector, λ 0 denotes a center wavelength, x denotes an aberration coefficient vector corresponding to the center wavelength λ 0, and FT^-1Representing the inverse fourier transform, P the pupil plane aperture function matrix (1 in the aperture, 0 outside the aperture),denotes a pupil plane coordinate vector, i is an imaginary unit, W denotes a pupil plane wave aberration matrix at a central wavelength λ 0, and Δ V denotes a difference (mainly, distance) in defocus aberration between an image beam at two different wavelengths between the wavelength λ and the central wavelength λ 0Focal aberration). In this formula, the wave aberration at the wavelength λ is divided into two parts, one part is the wave aberration corresponding to the central wavelength λ 0, and the other part is the difference between the wave aberration corresponding to the wavelength λ and the wave aberration corresponding to the central wavelength λ 0.

Point Spread Function (PSF) images in the presence of chromatic aberration may be iteratively approximated by a plurality of single-wavelength Point Spread Function (PSF) images. Thus, for a Point Spread Function (PSF) image at a particular spectral bandwidth, it can be approximated as a superposition of a plurality of monochromatic wavelength images within the spectral bandwidth:

wherein the content of the first and second substances,represents a spectral width of λ_LNon-monochromatic spot spread function (PSF) image with aberration coefficient vector x at center wavelength λ 0, round denotes rounding, λ 0_jAnd the wavelength corresponding to the jth single-wavelength image is represented, the delta lambda represents the wavelength interval adopted when the single-wavelength images are used for describing the image with the specific bandwidth in an overlapping mode, and the delta lambda can be 10 nm.

Step three, determining model parameters

According to the parameters such as the specific size and material of the adopted light splitting prism, the spectral bandwidth, the central wavelength and the like, the specific quantitative function relation between the aberration coefficient change quantity caused by the chromatic aberration of the light splitting prism and the wavelength is determined, and a final imaging model between a Point Spread Function (PSF) image and the aberration coefficient under the central wavelength is obtained.

The actual detector imaging is a process of continuous integration of spectra of different wavelengths, but when mathematical modeling is performed, the continuous spectral imaging can be simulated with the superposition of a small number of single-wavelength images using cumulative and alternative integration.

The specific model parameter determination process is as follows:

according to parameters such as specific size and material of the adopted light splitting prism, spectral bandwidth and central wavelength, specific numerical values of Δ V (wave aberration difference between two different wavelengths of the wavelength λ and the central wavelength λ 0) in formula 5 are determined.

Step four, acquiring focal plane image pairs

The light is split by a prism light splitting mode through a light splitting prism (with chromatic aberration), and two Point Spread Function (PSF) image pairs at different (off) focal plane positions are collected. Wherein the focal plane position interval is known, i.e. the defocus distance is known.

Step five, establishing a nonlinear equation

And establishing a nonlinear equation system for solving aberration coefficients by using the imaging model (with the prism chromatic aberration influence reduced) after correcting the chromatic aberration and the acquired Point Spread Function (PSF) image pairs at two different (off) focal plane positions.

The relationship between the acquired pairs of Point Spread Function (PSF) images at two different (out of) focal plane positions and the aberration coefficients can be expressed as:

wherein S is₁And S₂Two specific bandwidth Point Spread Function (PSF) image data matrices actually acquired at two different focal plane positions are respectively represented, and Δ x is a known aberration difference (mainly a defocus difference) between the two focal planes.

Sixthly, establishing an objective function and solving an equation set

The solution of the nonlinear equation set is converted into a numerical optimization problem by establishing an objective function, and then the aberration coefficient is solved by using a numerical optimization algorithm.

The specific aberration coefficient solving process is as follows:

according to the above equation set, the left side and the right side of each equation in the equation set are subtracted and squared, and then the left side and the right side of each equation in the equation set are integrated in the whole image data area (i.e. the left side and the right side of all equations are subtracted and the squared results are added), and the following objective function related to the aberration coefficient vector x to be solved is established:

then, the minimum value of the objective function e (x) can be solved by using a correlation numerical optimization algorithm (such as a gradient method, a newton method, a particle swarm optimization algorithm, etc.), and the corresponding aberration coefficient vector x is the solved aberration coefficient.

The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.