Wavefront phase inversion method and apparatus

Abstract

The application discloses a wave front phase inversion method and device, and relates to the technical field of optical measurement and wave front recovery. The method is used for solving the problem that the existing single-frame phase inversion method converges to a false solution due to phase symbol symmetry. The method uses a bifocal lens to perform common-path coherent modulation on an incident wave front, establishes a forward transmission model from the wave front phase to a modulated light spot, and uses a Gauss-Newton algorithm for single inversion to realize high-precision reconstruction of the wave front phase. The application can complete detection only by using a single frame of image, and the interference coding mechanism breaks the symbol symmetry of phase recovery from the physical layer, thereby providing a new technical approach for high-precision single-frame wave front measurement.

Description

Technical Field

[0001] This invention relates to the field of optical detection technology, and more specifically to a wavefront phase inversion method and apparatus. Background Technology

[0002] Wavefront measurement is a key technology in fields such as optical detection and adaptive optics, and its accuracy and efficiency directly affect the performance of optical systems. Traditional wavefront sensing methods, such as interferometers, Shak-Hartmann wavefront sensors, or curvature sensors, suffer from problems such as system complexity, insufficient environmental adaptability, limited dynamic range, or the need for multiple sampling, making it difficult to meet the requirements of dynamic and compact measurements.

[0003] Phase inversion techniques based on single-frame focal plane images have attracted widespread attention due to their simple optical path and fast data acquisition. However, existing single-frame methods, such as the Gauss-Newton iterative algorithm based on a single-lens modulation spot and its improved versions, generally suffer from bottlenecks such as easy convergence to spurious solutions, strong dependence on initial values, and limited inversion accuracy. From the perspective of Fourier optics, the intensity response generated by the phase function and its conjugate term on a single focal plane has high even symmetry, leading to a large number of local minima traps in the energy surface of the objective function, which limits its practical application in precision detection. The phase difference method can effectively solve the multi-solution problem by introducing defocus image information, but it requires simultaneous acquisition of focal plane and defocus plane images, inevitably increasing the complexity of the optical system and the amount of data acquisition.

[0004] Therefore, how to achieve high-precision, deterministic wavefront inversion while maintaining the simplicity of single-frame imaging remains a pressing technical problem in the field of optics. Summary of the Invention

[0005] This invention provides a wavefront phase inversion method and apparatus to solve the problems of convergence to pseudo-solution caused by phase symbol symmetry in existing single-frame phase inversion methods, as well as the problems of limited inversion accuracy and sensitivity to system noise.

[0006] This invention provides a wavefront phase inversion method, comprising:

[0007] By loading a zero-phase plane wave onto the spatial light modulator included in the wavefront detection system of the bifocal lens, a calibration interference intensity map containing system error is obtained. Based on the calibration-specific forward model, the inherent phase error of the system and the partition modulation parameters of the bifocal lens are obtained.

[0008] The phase of the wavefront to be measured is loaded onto the spatial light modulator, so that the incident laser is modulated and outputs a distorted wavefront carrying a preset phase distortion. After the distorted light wave is modulated and interfered by the beam splitter and the bifocal lens, a measured interference light intensity map containing wavefront phase information is obtained.

[0009] The total phase distribution of the optical path is obtained by superimposing the inherent phase error of the system and the phase of the wavefront to be measured. A complete forward transmission model is constructed based on the Fresnel diffraction transmission law, the forward integral model of light intensity, the inherent phase error of the system, and the partitioned modulation parameters.

[0010] An initial iterative value is assigned to the wavefront phase to be measured. The total iterative phase distribution is obtained based on the superposition of the inherent phase error of the system. The total iterative phase distribution, the partitioned modulation parameters, and the complete forward transmission model are used to obtain a theoretical simulation light intensity map through Fresnel diffraction integral calculation. A light intensity residual function is constructed based on the theoretical simulation light intensity map and the measured interference light intensity map at the same pixel position.

[0011] In each iteration, the normalized residual sum of squares is determined based on the light intensity residual function. When the normalized residual sum of squares meets the preset convergence threshold, the optimal Zernike coefficient is output. Finally, the high-precision phase distribution of the wavefront to be measured is reconstructed based on the optimal Zernike coefficient.

[0012] This invention provides a wavefront phase inversion device, comprising:

[0013] The first obtaining unit is used to obtain a calibration interference intensity map containing system error by loading a zero-phase plane wave onto the spatial light modulator included in the wavefront detection system of the bifocal lens and loading a zero-phase plane wave onto the spatial light modulator. Based on the calibration-specific forward model, the inherent phase error of the system and the partition modulation parameters of the bifocal lens are obtained.

[0014] The second obtaining unit is used to load the wavefront phase to be measured onto the spatial light modulator, so that the incident laser outputs a distorted wavefront carrying a preset phase distortion after modulation. After the distorted light wave is modulated and interfered by the beam splitter and the dual-focal lens, a measured interference light intensity map containing wavefront phase information is obtained.

[0015] A construction unit is used to superimpose the inherent phase error of the system and the phase of the wavefront to be measured to obtain the total phase distribution of the optical path, and to construct a complete forward transmission model based on the Fresnel diffraction transmission law, the forward integration model of light intensity, the inherent phase error of the system and the partitioned modulation parameters;

[0016] An iterative unit is used to assign an initial iterative value to the wavefront phase to be measured, and to obtain the iterative total phase distribution based on the superposition of the inherent phase error of the system. The iterative total phase distribution, the partitioned modulation parameters, and the complete forward transmission model are used to obtain a theoretical simulation light intensity map through Fresnel diffraction integral calculation. A light intensity residual function is constructed based on the theoretical simulation light intensity map and the measured interference light intensity map at the same pixel position.

[0017] The output unit is used to determine the normalized residual sum of squares based on the light intensity residual function in each iteration. When the normalized residual sum of squares meets the preset convergence threshold, the optimal Zernike coefficient is output. Finally, the high-precision phase distribution of the wavefront to be measured is reconstructed based on the optimal Zernike coefficient.

[0018] This invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform any of the wavefront phase inversion methods described above.

[0019] This invention provides a computer device, which includes a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs any of the wavefront phase inversion methods described above.

[0020] This invention provides a wavefront phase inversion method and apparatus. The method, through a system calibration step, pre-calculates and solidifies the inherent phase error of the system and the partitioned modulation parameters of the bifocal lens. This accurately eliminates fixed system errors introduced by optical component processing and optical path assembly, avoiding the mixing and superposition of system errors and the distortion information of the wavefront under test. This completely solves the problems of error accumulation and baseline offset in traditional uncalibrated detection methods, providing a clean and reliable modeling foundation for subsequent high-precision wavefront inversion. Secondly, by acquiring the interference light intensity under test in a single frame, single-image sampling is achieved based on the partitioned interference characteristics of the bifocal lens. This eliminates the need for multi-frame phase iteration scanning and multiple exposure operations required by traditional techniques, greatly simplifying the detection process and shortening the detection time. Simultaneously, it avoids frame-by-frame errors caused by environmental vibrations, airflow, and light source fluctuations during multi-frame acquisition, effectively improving detection real-time performance and environmental anti-interference capabilities. Thirdly, by constructing a full-path forward transmission model that includes the wavefront under test and system errors, the true light field transmission process of near-field diffraction and partitioned interference is fully reproduced, overcoming the limitations of traditional models that simplify the optical path and ignore partitioned modulation differences. To address the shortcomings of traditional methods, this approach achieves a high-precision mathematical mapping from wavefront phase to interference intensity, ensuring a high degree of matching between simulation and measured data. This improves the accuracy and reliability of iterative calculations at the model level. Then, iterative initialization is completed by superimposing systematic errors to construct the total iterative phase. The iterative process is optimized using multiple constraints, including pixel-level residuals, global residuals, and normalized residuals. This ensures that the iterative parameters are initialized to match the actual optical path state, effectively avoiding problems such as iterative divergence and getting trapped in local optima. Simultaneously, it adapts to the characteristics of optical imaging noise, accurately quantifies fitting deviations, and ensures accurate Zernike coefficient iterative correction direction and stable convergence. Finally, through Gaussian-Newton second-order optimization iteration combined with normalized threshold convergence judgment and wavefront reconstruction, it achieves faster convergence speed and higher solution accuracy compared to traditional first-order iterative algorithms. This effectively avoids under-iteration and over-iteration problems. Relying on the orthogonality of Zernike polynomials, it achieves accurate reconstruction of complex multi-order optical aberrations. The overall solution features a simple hardware structure, strong algorithm robustness, and balances detection accuracy, computational efficiency, and engineering applicability, making it widely applicable to various high-precision optical inspection and system assembly scenarios. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of a wavefront phase inversion method provided in an embodiment of the present invention;

[0023] Figure 2A schematic diagram of the optical path structure of a wavefront detection system based on a bifocal lens provided in an embodiment of the present invention;

[0024] Figure 3 This is a schematic diagram of the bifocal lens structure and parameters provided in an embodiment of the present invention;

[0025] Figure 4 This is a schematic diagram of bifocal lens interference provided in an embodiment of the present invention;

[0026] Figure 5A This is a schematic diagram of the measurement results of a single-order aberration interferometer provided in an embodiment of the present invention;

[0027] Figure 5B This is a schematic diagram of the experimental results of a single-order aberration provided in an embodiment of the present invention;

[0028] Figure 6A This is a schematic diagram of a combined aberration interferometer measurement provided in an embodiment of the present invention;

[0029] Figure 6B This is a schematic diagram of the combined aberration experimental results provided in an embodiment of the present invention;

[0030] Figure 7 This is a schematic diagram of a wavefront phase inversion device provided in an embodiment of the present invention. Detailed Implementation

[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] Figure 1 This is a schematic diagram of a wavefront phase inversion method provided in an embodiment of the present invention; Figure 2 A schematic diagram of the optical path structure of a wavefront detection system based on a bifocal lens provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the bifocal lens structure and parameters provided in an embodiment of the present invention; the following is in conjunction with... Figure 1 Figure - illustrates in detail an embodiment of the wavefront phase inversion method provided by the present invention. For example... Figure 1 As shown, the method includes the following steps:

[0033] Step 101: By loading a zero-phase plane wave onto the spatial light modulator included in the wavefront detection system of the bifocal lens, a calibration interference intensity map containing system error is obtained. Based on the calibration-specific forward model, the inherent phase error of the system and the partition modulation parameters of the bifocal lens are obtained.

[0034] Step 102: Load the wavefront phase to be measured onto the spatial light modulator so that the incident laser outputs a distorted wavefront carrying a preset phase distortion after modulation. After the distorted light wave is modulated and interfered by the beam splitter and the bifocal lens, a measured interference light intensity diagram containing wavefront phase information is obtained.

[0035] Step 103: Superimpose the inherent phase error of the system and the phase of the wavefront to be measured to obtain the total phase distribution of the optical path. Construct a complete forward transmission model based on the Fresnel diffraction transmission law, the forward integration model of light intensity, the inherent phase error of the system, and the partitioned modulation parameters.

[0036] Step 104: Assign an initial iterative value to the wavefront phase to be measured, obtain the iterative total phase distribution based on the superposition of the inherent phase error of the system, and obtain the theoretical simulated light intensity map by the iterative total phase distribution, the partitioned modulation parameters, and the complete forward transmission model through Fresnel diffraction integral calculation; construct the light intensity residual function based on the theoretical simulated light intensity map and the measured interference light intensity map at the same pixel position.

[0037] Step 105: In each iteration, the normalized residual sum of squares is determined based on the light intensity residual function. When the normalized residual sum of squares meets the preset convergence threshold, the optimal Zernike coefficient is output. Finally, the high-precision phase distribution of the wavefront to be measured is reconstructed based on the optimal Zernike coefficient.

[0038] Before introducing the wavefront phase inversion method provided in the embodiments of the present invention, let's first... Figure 2 This paper introduces the wavefront detection system provided in the embodiments of the present invention, such as... Figure 2 As shown, the system includes: a light source module using a He-Ne laser, a beam expander collimating lens, an aperture, a neutral density filter, a linear polarizer, a beam splitter prism, a spatial light modulator (SLM), a bifocal lens, a detector, and a data processing module.

[0039] Specifically, the laser beam is converted into a parallel wide beam by a beam-expanding and collimating module with a 10x beam-expansion ratio. It passes through the central uniform portion of the aperture cutoff, then undergoes intensity attenuation by a neutral density filter. The attenuated beam is then converted into purely linearly polarized light by a linear polarizer, with its transmission axis parallel to the working axis of the liquid crystal molecules in the spatial light modulator, ensuring the system is in pure phase modulation mode. After passing through a non-polarizing beam splitter, the polarized light is incident perpendicularly on the spatial light modulator. The spatial light modulator applies target phase modulation to the wavefront under test according to the loaded grayscale image. The modulated beam is reflected back to the non-polarizing beam splitter along its original path and partially reflected and redirected by the non-polarizing beam splitter, then incident perpendicularly on a bifocal lens. The beam modulated by the bifocal lens is finally focused onto the detector. The data processing module is connected to the detector and the spatial light modulator to execute the wavefront inversion algorithm.

[0040] In practical applications, the components of the aforementioned wavefront detection system can be selected with the following parameters: a He-Ne laser with a working wavelength of 632.8 nm and an output power of 2 mW; an aperture cutoff diameter of 6.3 mm; neutral density filters with OD values ​​of 0.5, 1, and 2; a non-polarizing beam splitter with a transmittance-to-reflectance ratio of 50:50; and a spatial light modulator with a resolution of 1920×1200 and 8 pixels. The bifocal lens is made of PMMA with a refractive index of 1.49 and a thickness of 4 mm. The aperture of the bifocal lens is divided into a central region and an outer ring region; the diameter of the central region is [missing information]. =3.15mm, corresponding to a focal length of =18mm; its outer ring diameter is =6.3mm, corresponding to a focal length of =20mm, focal length difference is =2mm. The aperture ratio of the two regions is : The ratio of 2:1 ensures that the intensity of the two outgoing beams is balanced when they overlap on the detector surface, resulting in high-contrast interference fringes; the detector pixel size is 3.75. m×3.75 m, resolution 1280×960; the detector is positioned behind the focal point of the bifocal lens. 2mm behind.

[0041] The method provided in the embodiments of the present invention is to Figure 2 The wavefront detection system shown in the figure is executed by a controller, which is electrically connected to at least a spatial light modulator and a data processing module.

[0042] It should be noted that the method provided in this embodiment of the invention aims to solve the problem of convergence to a spurious solution caused by the phase sign symmetry of existing single-frame phase inversion methods. Before actually measuring the wave to be measured, it is necessary to calibrate the inherent phase error of the system. Because the system has its own inherent phase error, even if a perfect plane wave to be measured is input, the image will still have distorted interference fringes.

[0043] In step 101, under the control of the controller, a zero-grayscale phase image, i.e., a zero-phase plane wave, is loaded onto the hardware panel of the wavefront detection system of the bifocal lens, including the spatial light modulator. After the zero-phase plane wave is loaded onto the spatial light modulator, the zero-phase plane wave can prevent any phase modulation of each pixel of the spatial light modulator. The incident light from the laser is modulated by the spatial light modulator and outputs an ideal plane wave, thereby completing the standard incident light source configuration for the optical system calibration. Further, the ideal plane wave is acquired by the CCD camera after interference by the beam splitter prism and the bifocal lens. At this time, the calibration interference intensity image acquired by the CCD camera, which contains systematic errors, is determined only by the theoretical modulation phase of the bifocal lens and the inherent phase error of the system. The calibration interference intensity image containing systematic errors is inverted through the calibration-specific forward model to fit the inherent phase error of the system and the partition modulation parameters of the bifocal lens.

[0044] It should be noted that the zonal modulation parameters of the bifocal lens include the inherent phase modulation parameters of the outer ring region and the inherent phase modulation parameters of the central region of the bifocal lens. In this embodiment of the invention, the bifocal lens includes a central region and an outer ring region. The central region and the outer ring region have different radii of curvature, which correspond to different focal lengths. The aperture ratio of the bifocal lens is configured as 2:1, so that the two-channel outgoing beams form interference on the detection surface.

[0045] like Figure 3 As shown in the figure, the black-marked area represents the interference region produced by the bifocal lens. The light field within this region is formed by the superposition of light beams from two regions with different radii of curvature passing through the bifocal lens, and its interference characteristics are influenced by multiple system parameters. Among these, the aperture parameter... and The effective apertures, corresponding to two different curvature regions of the bifocal lens, directly affect the proportion of light energy distribution transmitted through each region, thus determining the degree of intensity matching between the two interference beams.

[0046] like Figure 4 The bifocal lens interferogram shown in this embodiment of the invention uses Zernike polynomials to simulate the incident wave aberration in order to clearly demonstrate the modulation effect of different wave aberrations on the interference fringes.

[0047] In the above method, the CCD detector is located behind the focal point of the bifocal lens. The specific position is determined according to the focal length difference of the bifocal lens so that the interference image meets the detector sampling conditions. The CCD does not acquire a clean plane wave, but a calibrated interference intensity map containing system errors after passing through the bifocal lens and system assembly and adjustment errors. That is, the method provided in this embodiment of the invention requires calibration because the system has inherent errors. Even if a perfect plane wave is input, there will still be distorted interference fringes in the image.

[0048] Specifically, the forward model is as follows:

[0049] (1)

[0050] in, The coordinates of the probe surface are: The calibration interference light intensity at the location containing systematic errors is the standard light intensity signal collected during the system calibration stage; This indicates a calibration-specific forward model operator that takes the system's inherent phase error and the dual-focal lens zonal modulation parameters as inputs and outputs the calibration light intensity. This indicates the inherent phase error of the optical system, which is caused by deviations in component manufacturing and optical path assembly and adjustment, and remains constant throughout the entire process. This represents the inherent phase modulation parameters of the central region of the bifocal lens; This represents the inherent phase modulation parameters of the outer ring region of the bifocal lens. It should be noted that since the phase diagram loaded onto the spatial light modulator is a zero-grayscale phase diagram, the incident light outputs a distortion-free ideal plane wave after passing through the spatial light modulator, and its true wavefront phase satisfies: .

[0051] In step 102, the phase diagram of the wavefront to be measured is loaded on the hardware panel of the spatial light modulator by the controller. The incident light from the laser is modulated by the spatial light modulator and outputs a distorted wavefront carrying a preset phase distortion. The distorted wavefront is interfered by a beam splitter and a dual-focal lens and then collected by a CCD detector. At this time, the measured interference light intensity diagram containing wavefront phase information is collected by the CCD detector.

[0052] In this embodiment of the invention, the phase of the wavefront to be measured can be parameterized using Zernike polynomials, as follows:

[0053] (2)

[0054] in, Represents the rectangular coordinates of the pupil plane The phase of the wavefront to be measured corresponding to the position. This indicates the highest fitting order of the Zernike polynomial. The coefficients represent the fitting coefficients of the nth-order Zernike polynomial. Represents the pupil plane coordinates The corresponding nth-order Zernike basis function.

[0055] Furthermore, the distorted wavefront, after passing through a beam splitter prism, is incident on a bifocal lens and split into two beams: a central region and an outer ring region. These two beams are propagated by Fresnel diffraction, forming a total complex amplitude optical field on the detector surface, as shown below:

[0056] (3)

[0057] in, Indicates the distance of propagation Below, the coordinates of the probe surface The complex amplitude of the light field emitted from the central region of the bifocal lens. Indicates the distance of propagation Below, the coordinates of the probe surface The complex amplitude of the light field emitted from the outer ring region of the bifocal lens. This represents the fixed propagation distance from the pupil surface to the detector surface. Represents the phase factor of free propagation of the light field. Represents the imaginary unit. This represents the effective integration area of ​​the pupil plane of a bifocal lens. Represents the light wave number. , Indicates the center wavelength of the incident coherent laser. Represents the two-dimensional coordinate vector of the pupil plane. Represents the pupil plane coordinates The light field amplitude distribution in the central region of the lens, Represents the pupil plane coordinates The optical field amplitude distribution in the outer ring region of the lens. Represents the pupil plane coordinates Phase distribution of the incident wavefront in the central region of the lens Represents the pupil plane coordinates Phase distribution of the incident wavefront in the outer ring region of the lens Represents the spatial aperture function of the central region of the lens. This represents the spatial aperture function of the outer ring region of the lens. Represents the pupil plane coordinates The inherent phase modulation amount in the central region of the lens. This represents the squared difference between the coordinates of the probe surface and the coordinates of the pupil surface. This represents a two-dimensional, minute area element of the pupil surface, used for integrating the global light field contribution. The complex amplitude of the light field represents the position of the light field emitted from the pupil surface at the detector surface after near-field diffraction at a distance of z. The complex light field distribution at that location.

[0058] Furthermore, the two beams self-interfere in the near-field region behind the lens, forming interference fringes containing phase information. The CCD detector acquires one frame of the interference intensity map in a single exposure, i.e.

[0059] The measured interferometric intensity diagram containing wavefront phase information is shown below:

[0060] (4)

[0061] in, The distance the light field travels is 1. The coordinates of the detection surface are The measured interference light intensity at the location, express Indicates the distance of propagation Below, the coordinates of the probe surface The complex amplitude of the light field emitted from the central region of the bifocal lens. This represents the actual light intensity value corresponding to the complex amplitude in the outer ring region. This indicates taking the real part of the result of a complex number operation. express The complex conjugate, This represents the fixed propagation distance from the pupil surface to the detector surface.

[0062] It should be noted that the phase map loaded on the spatial light modulator in this step contains the wavefront information to be measured, that is, a preset phase distortion is applied to the spatial light modulator, so the incident light carries the preset phase distortion after passing through the spatial light modulator; while in step 101, the phase map loaded on the spatial light modulator is a zero grayscale phase map, and no phase distortion is applied to the spatial light modulator, so the incident light outputs an ideal plane wave without distortion after passing through the spatial light modulator.

[0063] In step 103, the inherent phase error of the system and the phase of the wavefront under test are superimposed to obtain the total phase distribution of the optical path transmission, as shown below:

[0064] (5)

[0065] in, Indicates the position of the pupil The total phase distribution of the optical path at that location, Indicates the position of the pupil The phase distribution of the wavefront to be measured at the location, Indicates the position of the pupil The inherent phase error of the system at that location.

[0066] Furthermore, based on the Fresnel diffraction transmission law, the forward integration model of light intensity, the inherent phase error of the system, and the partitioned modulation parameters, a complete forward transmission model is constructed, as shown below:

[0067] (6)

[0069] in, Indicates the distance of propagation Detection surface coordinates Theoretical simulated light intensity at the location, Represents the complete forward transport model operator. This represents the inherent phase modulation parameter of the central region of the bifocal lens. This represents the inherent phase modulation parameter of the outer ring region of the bifocal lens. This indicates the inherent phase error of the system. This represents the true phase distribution of the wavefront to be measured, where i represents the imaginary unit. This represents the effective integration area of ​​the pupil plane of a bifocal lens. Represents the light wave number. , Indicates the center wavelength of the incident coherent laser. Represents the two-dimensional coordinate vector of the pupil plane. Represents dummy variables. Represents the pupil plane coordinates The total amplitude distribution at the location includes the central region and the outer ring region; The spatial aperture function representing the central region of a bifocal lens. This represents the spatial aperture function of the outer ring region of a bifocal lens. Represents the pupil plane coordinates Phase distribution of the incident wavefront in the central region of the lens Represents the pupil plane coordinates Phase distribution of the incident wavefront in the outer ring region of the lens Represents the pupil plane coordinates The total phase distribution of the optical path at that location.

[0070] It should be noted that in the above formula, the operator For the forward propagation model constructed based on Fresnel diffraction and partitioned interference effects, the above quadruple integral expression is the mathematical expansion of this operator. This represents the total phase distribution, which includes the wavefront under test and the system error.

[0071] Since the true phase distribution of the wavefront to be measured has been obtained, a complete forward propagation model has been established including the system's inherent phase error, the fitting order N of the Zernike polynomial has been determined, and initial vectors have been assigned to the Zernike coefficients, the preceding steps complete the three preparatory works for the iteration, providing a complete foundation for subsequent iterations.

[0072] In step 104, the actual phase distribution before wave measurement is acquired is used as input, and the Gauss-Newton iterative algorithm is used to solve the forward propagation model inversely. Specifically, this includes the following steps:

[0073] 104-1, Initialize iterative wavefront estimation:

[0074] Assign initial iteration values ​​to the wavefront phase under test, and let the initial Zernike coefficients be 1. The initial iterative phase of the wavefront to be measured is reconstructed using Zernike polynomials, as shown below:

[0075] (7)

[0076] in, Represents the rectangular coordinates of the pupil plane The initial iterative wavefront phase to be measured at the location, Denotes the initial iteration coefficients of the nth Zernike polynomial. This indicates the highest fitting order of the Zernike polynomial. Represents the pupil plane coordinates The corresponding nth-order Zernike basis function.

[0077] The initial iteration of the wavefront phase to be measured is the first estimate of the actual wavefront to be measured during the iteration process, and all subsequent simulations are based on this estimate.

[0078] Furthermore, by superimposing the initial iterative wavefront phase to be measured with the system's inherent phase error, the following iterative total phase distribution is obtained:

[0079] (8)

[0080] in, Represents the pupil plane coordinates The total phase distribution at the iteration point, Represents the pupil plane coordinates The initial iterative phase value of the wavefront to be measured at the location, Represents the pupil plane coordinates The initial iterative phase value of the wavefront to be measured at the location.

[0081] 104-2, Forward simulation to generate theoretical light intensity

[0082] The Zernike coefficient vector for the current iteration round (Corresponding to the total phase of the current iteration) Input the established forward model, combine it with the fixed system error, and generate the theoretical simulation light intensity map of the k-th iteration through Fresnel diffraction integral operation:

[0083] (9)

[0084] in, This represents the coordinates of the probe surface in the k-th iteration. Theoretical simulation of light intensity at the location. This indicates the current iteration of the operation. Indicates the first The Zernike coefficient vector corresponding to each iteration. Represents the complete forward transmission model. This represents the inherent phase error of the optical system.

[0085] 104-3, Construct the light intensity residual vector

[0086] Using theoretical simulation of light intensity diagrams Based on the deviation between the theoretically simulated light intensity map and the measured interference light intensity map at the same pixel position, the single-pixel light intensity residual is determined using the following formula:

[0087] (10)

[0088] in, Indicates the first In the round of iteration, the probe surface is the first The light intensity residual value corresponding to each pixel. Indicates the detection surface number 1 Two-dimensional coordinates of pixels, Indicates the first Round iteration pixels The square root value of the simulated light intensity. Represents pixels The square root of the measured light intensity.

[0089] Furthermore, based on the light intensity residual function at the same pixel location, all pixel residuals are arranged in order to construct a residual vector:

[0090] (11)

[0091] In this embodiment of the invention, the residual vector directly quantifies the deviation between the theoretically simulated light intensity map and the measured interference light intensity map, and is the core basis for subsequent iterative optimization.

[0092] After calculating the single-pixel residual and constructing the residual vector, in order to quantify the overall deviation between the theoretical simulated light intensity and the measured interference light intensity in the current iteration, a global total error function needs to be defined. This function obtains the total error index characterizing the consistency between the current wavefront estimation and the actual wavefront to be measured by summing the squares of the residuals of all effective pixels. This provides the core basis for subsequent iterative optimization and convergence determination. The global total error function is determined by the following formula:

[0093] (12)

[0094] in, Indicates the first The round of iterations is based on the global total residual sum of squares with the current Zernike coefficients. This represents the total number of effective pixels involved in the calculation on the probe surface. Indicates the first Round iteration pixels The square root value of the simulated light intensity. Represents pixels The square root of the measured light intensity.

[0095] 104-4, Calculate the Jacobian matrix

[0096] To quantify the sensitivity of the residuals to the Zernike coefficients, the partial derivatives of the residuals with respect to the Zernike coefficients of each order are calculated, yielding the elements of the Jacobian matrix:

[0097] (13)

[0098] in, Indicates the first The rate of change of the intensity residual of each pixel with respect to the nth-order Zernike coefficient. This matrix reflects the degree of influence of coefficient adjustment on the residual and is key information for Gauss-Newton iteration.

[0099] 104-5, Updating Zernike coefficients using Gauss-Newton normal equations

[0100] Based on the residual vector and the Jacobian matrix, the Gauss-Newton normal equation is solved to obtain the coefficient correction for the current round:

[0101] (14)

[0102] The current Zernike coefficients are then corrected to obtain the coefficient vector for the next iteration:

[0103] (15)

[0104] After completing the above steps, use the updated coefficient vector Starting from a new point, the forward simulation, residual calculation, Jacobian matrix calculation and coefficient update process are repeated to enter the next iteration until the normalized sum of squared residuals meets the preset convergence threshold.

[0105] It should be noted that during the iterative inversion process, after each theoretical simulation of light intensity generation, residual calculation, and Zernike coefficient update is completed, the convergence determination phase begins.

[0106] In step 105, during each iteration, the initial conditions for that round are the theoretically simulated light intensity generated in real time during the iteration process. Pre-collected and fixed measured interference light intensity The theoretical simulated light intensity is determined by the total phase of the current iteration through the forward model, while the measured interference light intensity is the reference data that is fixed throughout the iteration.

[0107] During execution, the normalized sum of squared residuals is first determined based on the theoretically simulated light intensity and the measured interference light intensity of the current cycle using the following formula:

[0108] (16)

[0109] in, Indicates the first The normalized sum of squared residuals from each iteration. Indicates the effective integration region of the detection surface. This represents the coordinates of the probe surface in the k-th iteration. Theoretical simulation of light intensity at the location. The distance the light field travels is 1. The coordinates of the detection surface are The measured interference light intensity at the location.

[0110] By integrating the entire detection surface, the square integral of the difference between the square root of the theoretically simulated light intensity and the square root of the measured interference light intensity is first solved as the numerator, and then the global integral of the measured interference light intensity is used as the denominator to obtain the normalized residual that eliminates the influence of the light intensity baseline. This index is used to quantify the overall deviation between the current wavefront estimate and the real wave.

[0111] Then, the calculated Compare with the preset convergence threshold, or simultaneously determine whether the number of iterations has reached the set upper limit.

[0112] If the normalized residual sum of squares If the coefficients are less than a preset threshold, or the number of iterations reaches the upper limit, the iteration is considered converged and the loop is terminated; at this point, the optimal Zernike coefficient vector obtained from the final update during the iteration process is output. Finally, by substituting the optimal Zernike coefficient vector into the Zernike polynomial, a high-precision phase distribution of the wavefront under test is reconstructed:

[0113] (17)

[0114] in, This represents the pupil plane coordinates after iterative convergence. The high-precision phase distribution of the wavefront under test obtained by reconstruction. The first term obtained after iterative convergence is represented as... The optimal Zernike coefficients.

[0115] To verify the actual performance, inversion accuracy, and reliability of the bifocal lens coherent modulation and Gauss-Newton iterative single-frame wavefront phase inversion scheme provided in this embodiment of the invention, a complete wavefront detection experimental system was built. Experimental tests were conducted on two typical wavefronts to be tested: single-order optical aberrations and combined optical aberrations. The measurement results of a high-precision ZYGO interferometer were used as the true value reference for comparative analysis.

[0116] 1) Simulate a single type of wavefront distortion by loading single-order astigmatism using a spatial light modulator. First, a ZYGO interferometer is used to acquire standard wavefront data (corresponding to...). Figure 5A The peak and trough values ​​of the wavefront to be measured were obtained. , ;

[0117] Subsequently, the wavefront phase inversion system provided in this embodiment of the invention was used for testing: the incident laser was modulated by a spatial light modulator to generate a distorted wavefront containing single-order astigmatism, and then partitioned and subjected to common-path interference by a beam splitter and a bifocal lens. A single-frame interference intensity image was acquired by a detector; this single-frame image was input into the algorithm flow of this invention, and system error compensation, forward propagation model calculation, and Gauss-Newton iterative solution were executed sequentially to finally reconstruct the inverted wavefront (corresponding to...). Figure 5B The inversion result of this method is: , .

[0118] Data comparison shows that the relative error of wavefront PV value restoration is 17.4%, while the relative error of RMS value restoration is only 6.7%. Experiments demonstrate that this invention, relying on the technical approach of breaking phase sign symmetry through bifocal lens interferometric coding and combining calibration to eliminate inherent system errors, can effectively complete single-order aberration wavefront phase inversion using a single frame image, and the inversion results are in good agreement with the measurement results of the standard interferometer.

[0119] 2) Further complex operating condition tests were conducted by loading multiple types of superimposed combined optical aberrations into the spatial light modulator to simulate complex wavefront distortion scenarios in actual optical systems. The standard wavefront (corresponding to...) was measured using a ZYGO interferometer. Figure 6A ), its parameters are , .

[0120] Following the complete detection and inversion process of this invention: after acquiring a single-frame interference intensity map, based on the pre-calibrated system phase error and bifocal lens partition modulation parameters, the complete Fresnel diffraction forward propagation model is invoked, and iterative optimization is performed using the Gauss-Newton algorithm (maximum number of iterations set to 50). After iterative convergence, the combined aberration wavefront (corresponding to...) is reconstructed. Figure 6B The inversion result is , .

[0121] The experiments verified the adaptability of the proposed scheme to complex higher-order aberrations. Even when faced with complex wavefronts with multiple aberrations superimposed, the modeling logic and iterative algorithm of the proposed scheme can still converge stably and achieve effective reconstruction.

[0122] The small measurement errors in the two sets of experiments mentioned above mainly come from the hardware and optical path levels: first, the inherent process errors caused by the phase modulation of the spatial light modulator and the processing of optical components; second, the residual deviations caused by the assembly and adjustment of the experimental optical path and the alignment of components. The above errors are not defects in the phase inversion algorithm of the present invention, and further illustrate the key role of the early system calibration stage in suppressing fixed system errors and improving the overall inversion accuracy.

[0123] The combined experimental results of the two sets show that the wavefront phase inversion method and supporting device proposed in this embodiment of the invention solves the problems of traditional single-frame phase inversion being prone to spurious solutions and insufficient accuracy. It can achieve high-precision wavefront reconstruction of single-order and combined optical aberrations by relying only on a single frame interferometric image. The optical path structure is simple and has strong anti-environment interference capability, which fully meets the engineering application requirements of optical detection, optical system assembly and adjustment, etc.

[0124] To more clearly illustrate the wavefront phase inversion method provided in this embodiment of the invention, the method will be explained below with reference to a specific embodiment.

[0125] A bifocal lens interferometric wavefront detection system adapted to this invention was constructed, and the core parameters of each hardware device were determined to provide hardware support for subsequent wavefront acquisition, model building, and iterative inversion. The specific configurations of each device in this embodiment are as follows:

[0126] Light source: He-Ne laser, wavelength It provides a stable and highly coherent incident light source;

[0127] Spatial Light Modulator (SLM): Pure phase type, resolution It is used to load a preset wavefront phase to simulate various optical distortion wavefronts;

[0128] Bifocal lens: aperture focal length in the central area Focal length of the outer ring area It can realize optical field partitioning modulation and near-field interference, and is the core beam-splitting interference element of this invention;

[0129] CCD detector: Pixels, pixel size It is used for high-precision acquisition of interference light intensity images;

[0130] Propagation distance: the distance from the lens to the CCD. Fixed near-field diffraction propagation distance ensures the accuracy of forward model simulation;

[0131] Iteration parameter: Zernike polynomial order It can cover conventional low-order and high-order optical aberrations, and has a convergence threshold. Maximum number of iterations This approach balances iterative accuracy with computational efficiency.

[0132] Before formally conducting wavefront inversion iterations, the system calibration operation is first completed to eliminate fixed errors caused by optical path assembly and component processing. The inherent phase error of the system is then calculated through calibration experiments. Lens zonal modulation parameters , Based on the above calibration parameters and the Fresnel diffraction interference principle, a complete forward propagation model including systematic errors is established. This provides a precise theoretical basis for subsequent iterative simulations and error calculations.

[0133] Step 201: Load the wavefront to be measured and collect the measured light intensity

[0134] After system calibration and model building are completed, the wavefront detection phase begins. A spatial light modulator simulates the distorted wavefront in a real-world scene. Specifically, a preset wavefront phase is loaded using an SLM. The wavefront is characterized by Zernike polynomials, expressed as:

[0135]

[0136] in, The Zernike coefficients to be inverted are also the core solution parameters for subsequent iterative optimization. The Zernike basis function is used. After the laser is modulated by the SLM, the loaded phase information modulates to form a distorted wavefront carrying optical distortion. The distorted wavefront is incident on a bifocal lens through a beam splitter. Near-field interference is generated by the partitioned modulation of the central and outer ring regions of the bifocal lens. Finally, the measured interference intensity map containing the distortion information of the wavefront under test is acquired by a CCD detector. The measured light intensity will serve as the true benchmark data for the entire iterative calculation, providing a basis for subsequent simulation light intensity comparison and residual calculation.

[0137] Step 202: Iterative Initialization

[0138] After obtaining the measured reference light intensity, the Gauss-Newton iterative inversion process is initiated. First, the iterative parameters are initialized to provide the initial computational starting point for the first round of iterations. In this embodiment of the invention, the Zernike coefficients are initially set to an all-zero vector. Based on the initial coefficient vector, the iterative initial wavefront estimate is obtained through Zernike polynomial fitting, expressed as:

[0139]

[0140] Since the actual optical path has fixed system errors, the initial fitted wavefront alone cannot match the actual optical path transmission state. Therefore, it is necessary to superimpose the initial wavefront with the pre-calibrated inherent phase error of the system to obtain the iterative total phase distribution. The total phase of this iteration is the core input for each round of forward simulation, ensuring that the simulated light field is consistent with the transmission state of the real light field.

[0141] Step 203, Forward simulation and error calculation (including total error function)

[0142] After completing iterative initialization and determining the total iterative phase, the process enters the core iterative calculation stage. The theoretical light intensity is obtained through forward model simulation and then compared with the measured light intensity. The pixel residual and global total residual are calculated step by step to quantify the degree of deviation of the current wavefront estimation and provide an optimization basis for subsequent coefficient updates.

[0143] (1) Forward simulation

[0144] The Zernike coefficients in the current iteration round Using the input parameters and combining the complete forward transmission model of the solidification system error, the theoretical simulated light intensity of the current round is calculated, as shown in formula (9).

[0145] (2) Single pixel residual

[0146] To accurately quantify local light intensity deviation, error calculations were performed on all effective pixels of the detection surface one by one. The simulated light intensity and the measured light intensity at the same pixel position were compared. The single-pixel residual was constructed by the square root difference of the light intensity, which accurately reflects the single-point wavefront fitting deviation. The single-pixel residual is shown in formula (10).

[0147] (3) Global total error function

[0148] After calculating the individual pixel residuals, the local deviations of all pixels are integrated to construct a complete residual vector. Simultaneously, the global total residual sum of squares is calculated to achieve a quantitative evaluation of the overall wavefront fitting accuracy. First, all pixel residuals are arranged in order to construct the residual vector. Then, the global total residual sum of squares is calculated based on all individual pixel residuals.

[0149] This global error function can comprehensively quantify the overall deviation between the simulated wavefront light intensity distribution and the actual measured light intensity in the current iteration, intuitively reflecting the accuracy of the current Zernike coefficient fitting. It is the core judgment basis and calculation foundation for subsequent Jacobian matrix solving and iterative coefficient optimization and updating.

[0150] Step 204, Jacobian matrix and coefficient update

[0151] After obtaining the global residual and residual vector, in order to achieve adaptive optimization and correction of the Zernike coefficients, the optimal correction amount of the coefficients needs to be solved by the Gauss-Newton algorithm, so as to gradually reduce the deviation between the simulated light intensity and the measured light intensity, and make the fitted wavefront continuously approach the real wavefront to be measured.

[0152] (1) Calculate the Jacobian matrix

[0153] To quantify the sensitivity of the influence of Zernike coefficients of each order on the light intensity residual and accurately locate the direction of coefficient optimization, the partial derivatives of the light intensity residual with respect to Zernike coefficients of each order are calculated, and the Jacobian matrix is ​​constructed.

[0154] (2) Gauss-Newton update

[0155] Based on the obtained Jacobian matrix and residual vector, the Gauss-Newton normal equation is substituted to solve for the optimal correction amount of the Zernike coefficients in the current round. The obtained coefficient correction amount is superimposed on the current iteration coefficient to complete the coefficient update of this round and obtain a new Zernike coefficient vector adapted to the next round of iteration. The iterative update formula is shown in (15). After the coefficient update is completed, the single round of complete iteration calculation is completed. Subsequently, based on the updated coefficients, the forward simulation, residual calculation and coefficient update process will be repeatedly executed to continuously iterate and optimize.

[0156] Step 205, Convergence Determination and Wavefront Output

[0157] After each round of coefficient update iteration, a convergence determination is required to determine whether the current fitted wavefront meets the accuracy requirements. If it does, the iteration is terminated and the result is output; otherwise, the iteration continues. This invention eliminates light intensity baseline interference by normalizing the sum of squared residuals, thus achieving accurate convergence determination. The specific calculation method is shown in formula (16), where the normalized sum of squared residuals obtained from each iteration is used to calculate the sum of squared residuals. With preset convergence threshold The comparison is performed, and it is determined whether the current iteration count has reached the maximum iteration count of 50. If the number of iterations reaches the upper limit, the iteration is considered converged, the iteration loop is stopped immediately, and the optimal Zernike coefficient vector obtained by the iterative optimization is output. .

[0158] Finally, the optimal Zernike coefficients are substituted into the Zernike polynomial to reconstruct the phase distribution of the wavefront under test with high precision. The high precision phase distribution of the wavefront under test is obtained through formula (17).

[0159] In this embodiment of the invention, through the complete iterative inversion process described above, the normalized residual meets the convergence threshold requirement at the 32nd iteration, and the iteration automatically terminates. Comparison with the measurement results from a standard interferometer shows that the RMS error of the reconstructed wavefront obtained in this embodiment is less than [a certain value]. High-precision wavefront inversion can be completed using only a single frame of interference light intensity. It has fast iterative convergence speed and high measurement accuracy, effectively avoiding the shortcomings of traditional multi-frame detection methods, such as low efficiency and susceptibility to environmental disturbances. This fully verifies the feasibility and superiority of the technical solution provided by the embodiments of the present invention.

[0160] In summary, the method provided by this invention offers multiple advantages over traditional wavefront phase detection techniques, including high detection accuracy, good operational stability, fast detection efficiency, and strong engineering applicability. This method, through pre-system calibration, accurately calculates and solidifies the inherent phase error of the optical path and the modulation parameters of the bifocal lens, eliminating fixed errors from system assembly and component processing at the source. This avoids confusion between errors and the distortion information of the wavefront under test, effectively solving the problems of error accumulation and large detection deviation in traditional techniques, thus laying a solid foundation for high-precision inversion. Simultaneously, this method relies on the bifocal lens's partitioned interference characteristics to achieve single-frame light intensity acquisition, eliminating the need for multi-frame scanning exposure, significantly simplifying the detection process, improving real-time detection, and effectively avoiding environmental disturbance errors caused by multi-frame acquisition, thus significantly enhancing system stability. Furthermore, This method constructs a full-path forward transmission model that integrates the wavefront distortion and systematic errors, fully reproducing the real optical field transmission and interference process. It overcomes the shortcomings of simplified optical paths in traditional models, achieving precise mapping between phase and intensity, and ensuring the accuracy of iterative simulation. During iteration, an iterative total phase initialization operation incorporating systematic errors is constructed to closely match the real optical path state, effectively avoiding problems such as iteration divergence and local optima, thus improving iteration stability. Multiple constraints, including the square root residual of intensity, global residual, and normalized residual, are combined to accurately quantify fitting deviations and ensure the accurate direction of coefficient iteration correction, closely matching optical noise characteristics. Based on the Gaussian-Newton second-order optimization algorithm, and with the Jacobian matrix, adaptive coefficient updates are achieved. Compared to traditional first-order algorithms, this method offers faster convergence speed and higher solution accuracy. The addition of a normalized threshold convergence criterion avoids under-iteration and over-iteration problems. Furthermore, relying on the orthogonal properties of Zernike polynomials, this invention can be adapted to multi-order optical aberration reconstruction. It features a simple hardware structure, robust algorithm, and balances detection accuracy, efficiency, and practicality, making it widely applicable to high-precision application scenarios such as precision optical inspection and system assembly.

[0161] Based on the same inventive concept, this invention provides a wavefront phase inversion device. Since the principle of this device in solving the technical problem is similar to that of a wavefront phase inversion method, the implementation of this device can refer to the implementation of the method, and the repeated parts will not be described again.

[0162] like Figure 7 As shown, the device includes a first obtaining unit 701, a second obtaining unit 702, a construction unit 703, an iteration unit 704, and an output unit 705.

[0163] The first obtaining unit 701 is used to obtain a calibration interference intensity map containing system error by loading a zero-phase plane wave onto the spatial light modulator included in the wavefront detection system of the bifocal lens and loading a zero-phase plane wave onto the spatial light modulator. Based on the calibration-specific forward model, the inherent phase error of the system and the partition modulation parameters of the bifocal lens are obtained.

[0164] The second unit 702 is used to load the wavefront phase to be measured onto the spatial light modulator, so that the incident laser outputs a distorted wavefront carrying a preset phase distortion after modulation. After the distorted light wave is modulated and interfered by the beam splitter and the dual-focal lens, a measured interference light intensity map containing wavefront phase information is obtained.

[0165] The construction unit 703 is used to superimpose the inherent phase error of the system and the phase of the wavefront to be measured to obtain the total phase distribution of the optical path, and to construct a complete forward transmission model based on the Fresnel diffraction transmission law, the forward integral model of light intensity, the inherent phase error of the system and the partitioned modulation parameters;

[0166] Iteration unit 704 is used to assign an initial iteration value to the wavefront phase to be measured, obtain the iterative total phase distribution based on the superposition of the inherent phase error of the system, and obtain the theoretical simulation light intensity map by the iterative total phase distribution, the partitioned modulation parameters and the complete forward transmission model through Fresnel diffraction integral operation; construct the light intensity residual function according to the theoretical simulation light intensity map and the measured interference light intensity map at the same pixel position;

[0167] The output unit 705 is used to determine the normalized residual sum of squares based on the light intensity residual function in each iteration. When the normalized residual sum of squares meets the preset convergence threshold, the optimal Zernike coefficient is output. Finally, the high-precision phase distribution of the wavefront to be measured is reconstructed based on the optimal Zernike coefficient.

[0168] It should be understood that the units included in the above-described wavefront phase inversion device are only a logical division based on the functions implemented by the device. In practical applications, the above units can be superimposed or split. Furthermore, the functions implemented by the wavefront phase inversion device provided in this embodiment correspond one-to-one with the wavefront phase inversion method provided in the above-described embodiment. The more detailed processing flow implemented by this device has been described in detail in the first embodiment of the method described above, and will not be described in detail here.

[0169] Another embodiment of the present invention provides a computer device, the computer device including: a processor and a scene database; the scene database is used to store computer program code, the computer program code including computer instructions; when the processor executes the computer instructions, the electronic device executes each step of the wavefront phase inversion method shown in the above method embodiment.

[0170] Another embodiment of the present invention provides a computer-readable storage medium storing computer instructions that, when executed on a computer device, cause the computer device to perform the various steps of the wavefront phase inversion method shown in the above-described method embodiment.

[0171] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A wavefront phase inversion method, characterized in that, include: By loading a zero-phase plane wave onto the spatial light modulator included in the wavefront detection system of the bifocal lens, a calibration interference intensity map containing system error is obtained. Based on the calibration-specific forward model, the inherent phase error of the system and the partition modulation parameters of the bifocal lens are obtained. The phase of the wavefront to be measured is loaded onto the spatial light modulator, so that the incident laser is modulated and outputs a distorted wavefront carrying a preset phase distortion. After the distorted light wave is modulated and interfered by the beam splitter and the bifocal lens, a measured interference light intensity map containing wavefront phase information is obtained. The total phase distribution of the optical path is obtained by superimposing the inherent phase error of the system and the phase of the wavefront to be measured. A complete forward transmission model is constructed based on the Fresnel diffraction transmission law, the forward integral model of light intensity, the inherent phase error of the system, and the partitioned modulation parameters. An initial iterative value is assigned to the wavefront phase to be measured. The total iterative phase distribution is obtained based on the superposition of the inherent phase error of the system. The total iterative phase distribution, the partitioned modulation parameters, and the complete forward transmission model are used to obtain a theoretical simulation light intensity map through Fresnel diffraction integral calculation. A light intensity residual function is constructed based on the theoretical simulation light intensity map and the measured interference light intensity map at the same pixel position. In each iteration, the normalized residual sum of squares is determined based on the light intensity residual function. When the normalized residual sum of squares meets the preset convergence threshold, the optimal Zernike coefficient is output. Finally, the high-precision phase distribution of the wavefront to be measured is reconstructed based on the optimal Zernike coefficient.

2. The method as described in claim 1, characterized in that, The calibrated interferometric intensity diagram containing systematic errors is represented by the following formula: The phase of the wavefront to be measured is expressed by the following formula: in, The coordinates of the probe surface are: The calibration interference light intensity at the location containing systematic errors. This indicates the calibration-specific forward model operator. This represents the inherent phase error of the optical system. This represents the inherent phase modulation parameters of the central region of the bifocal lens; This represents the inherent phase modulation parameter of the outer ring region of the bifocal lens. Represents the rectangular coordinates of the pupil plane The phase of the wavefront to be measured corresponding to the position. This indicates the highest fitting order of the Zernike polynomial. The coefficients represent the fitting coefficients of the nth-order Zernike polynomial. Represents the pupil plane coordinates The corresponding nth-order Zernike basis function.

3. The method as described in claim 1, characterized in that, The measured interferometric intensity map containing wavefront phase information is represented by the following formula: The complete forward transport model is expressed by the following formula: in, The distance the light field travels is 1. The coordinates of the detection surface are The measured interference light intensity at the location, Indicates the distance of propagation Below, the coordinates of the probe surface The complex amplitude of the light field emitted from the central region of the bifocal lens. express Indicates the distance of propagation Below, the coordinates of the probe surface The complex amplitude of the light field emitted from the central region of the bifocal lens. Indicates the distance of propagation Below, the coordinates of the probe surface The complex amplitude of the light field emitted from the outer ring region of the bifocal lens. This represents the actual light intensity value corresponding to the complex amplitude in the outer ring region. This indicates taking the real part of the result of a complex number operation. express The complex conjugate, This represents the fixed propagation distance from the pupil surface to the detector surface. This represents the phase factor for free propagation of the light field, where i represents the imaginary unit. This represents the effective integration area of ​​the pupil plane of a bifocal lens. Represents the light wave number. , Indicates the center wavelength of the incident coherent laser. Represents the two-dimensional coordinate vector of the pupil plane. Represents the pupil plane coordinates The light field amplitude distribution in the central region of the lens, Represents the pupil plane coordinates The optical field amplitude distribution in the outer ring region of the lens. Represents the pupil plane coordinates Phase distribution of the incident wavefront in the central region of the lens Represents the pupil plane coordinates Phase distribution of the incident wavefront in the outer ring region of the lens Represents the spatial aperture function of the central region of the lens. This represents the spatial aperture function of the outer ring region of the lens. Represents the pupil plane coordinates The inherent phase modulation amount in the central region of the lens. This represents the squared difference between the coordinates of the probe surface and the coordinates of the pupil surface. This represents a two-dimensional, minute area element of the pupil surface, used for integrating the global light field contribution. Indicates the distance of propagation Detection surface coordinates Theoretical simulated light intensity at the location, Represents the complete forward transport model operator. This represents the inherent phase modulation parameter of the central region of the bifocal lens. This represents the inherent phase modulation parameters of the outer ring region of the bifocal lens; This indicates the inherent phase error of the system. This represents the true phase distribution of the wavefront to be measured.

4. The method as described in claim 1, characterized in that, The total phase distribution of the optical path is expressed by the following formula: The total phase distribution of the iteration is expressed by the following formula: in, Indicates the position of the pupil The total phase distribution of the optical path at that location, Indicates the position of the pupil The phase distribution of the wavefront to be measured at the location, Indicates the position of the pupil The system's inherent phase error at that point, Represents the pupil plane coordinates The total phase distribution at the iteration point, Represents the pupil plane coordinates The initial iterative phase value of the wavefront to be measured at the location, Represents the pupil plane coordinates The initial iterative phase value of the wavefront to be measured at the location.

5. The method as described in claim 1, characterized in that, The initial iterative value is assigned to the wavefront phase to be measured, resulting in the following initial iterative wavefront phase to be measured: The theoretically simulated light intensity diagram is represented by the following formula: The light intensity residual function is expressed by the following formula. Total error function: in, Represents the rectangular coordinates of the pupil plane The initial iterative wavefront phase to be measured at the location, Denotes the initial iteration coefficients of the nth Zernike polynomial. This indicates the highest fitting order of the Zernike polynomial. Represents the pupil plane coordinates The corresponding nth-order Zernike basis function, This represents the coordinates of the probe surface in the k-th iteration. Theoretical simulation of light intensity at the location. This indicates the current iteration of the operation. This represents the Zernike coefficient vector corresponding to the k-th iteration. Represents the complete forward transmission model. This represents the inherent phase error of the optical system. Indicates the first In the round of iteration, the probe surface is the first The light intensity residual value corresponding to each pixel. Indicates the detection surface number 1 Two-dimensional coordinates of pixels, Indicates the first Round iteration pixels The square root value of the simulated light intensity. Represents pixels The square root of the measured light intensity. Indicates the first The round of iterations is based on the global total residual sum of squares with the current Zernike coefficients. This represents the total number of valid pixels involved in the calculation on the detection surface.

6. The method as described in claim 1, characterized in that, In each iteration, if the normalized sum of squared residuals determined based on the light intensity residual function does not meet the preset convergence threshold, the process further includes: Based on the Jacobian matrix of the light intensity residual function with respect to the Zernike coefficients, the wavefront phase correction is determined according to the Gauss-Newton iterative formula. The Zernike coefficients corresponding to the wavefront phase to be measured are updated according to the wavefront phase correction to obtain the updated wavefront phase to be measured. The Jacobian matrix is ​​expressed by the following formula: The Zernike coefficient is updated using the following formula: in, Indicates the first The Jacobian matrix of the first iteration Line 1 Column elements, This represents the partial differential operator. Indicates the first Pixel simulated light intensity square root value for the first Partial derivatives of the Zernike iteration coefficients of order Zernike ... Indicates the first The Zernike coefficient correction amount in the round of iteration, Indicates the first The transpose of the Jacobian matrix. Indicates the first Wheel residual vector, Indicates the first The Zernike coefficient vector updated after rounds of iterations. Indicates the first The original Zernike coefficient vector of the round of iterations, Indicates the first The coefficient correction amount obtained from the round calculation.

7. The method as described in claim 1, characterized in that, The normalized sum of squared residuals is expressed by the following formula: The high-precision wavefront phase distribution to be measured is expressed by the following formula: in, Indicates the first The normalized sum of squared residuals from each iteration. Indicates the effective integration region of the detection surface. This represents the coordinates of the probe surface in the k-th iteration. Theoretical simulation of light intensity at the location. The distance the light field travels is 1. The coordinates of the detection surface are The measured interference light intensity at the location, This represents the pupil plane coordinates after iterative convergence. The high-precision phase distribution of the wavefront under test obtained by reconstruction. The first term obtained after iterative convergence is represented as... The optimal Zernike coefficients.

8. A wavefront phase inversion device, characterized in that, include: The first obtaining unit is used to obtain a calibration interference intensity map containing system error by loading a zero-phase plane wave onto the spatial light modulator included in the wavefront detection system of the bifocal lens and loading a zero-phase plane wave onto the spatial light modulator. Based on the calibration-specific forward model, the inherent phase error of the system and the partition modulation parameters of the bifocal lens are obtained. The second obtaining unit is used to load the wavefront phase to be measured onto the spatial light modulator, so that the incident laser outputs a distorted wavefront carrying a preset phase distortion after modulation. After the distorted light wave is modulated and interfered by the beam splitter and the dual-focal lens, a measured interference light intensity map containing wavefront phase information is obtained. A construction unit is used to superimpose the inherent phase error of the system and the phase of the wavefront to be measured to obtain the total phase distribution of the optical path, and to construct a complete forward transmission model based on the Fresnel diffraction transmission law, the forward integration model of light intensity, the inherent phase error of the system and the partitioned modulation parameters; An iterative unit is used to assign an initial iterative value to the wavefront phase to be measured, and to obtain the iterative total phase distribution based on the superposition of the inherent phase error of the system. The iterative total phase distribution, the partitioned modulation parameters, and the complete forward transmission model are used to obtain a theoretical simulation light intensity map through Fresnel diffraction integral calculation. A light intensity residual function is constructed based on the theoretical simulation light intensity map and the measured interference light intensity map at the same pixel position. The output unit is used to determine the normalized residual sum of squares based on the light intensity residual function in each iteration. When the normalized residual sum of squares meets the preset convergence threshold, the optimal Zernike coefficient is output. Finally, the high-precision phase distribution of the wavefront to be measured is reconstructed based on the optimal Zernike coefficient.

9. A computer-readable storage medium, characterized in that, The device contains a computer program that, when executed by a processor, causes the processor to perform a wavefront phase inversion method as described in any one of claims 1-7.

10. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, causes the processor to perform a wavefront phase inversion method as described in any one of claims 1-7.

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