A hartmann wavefront measurement dynamic range expansion method based on quadratic phase control

Abstract

The present application relates to a kind of Hartmann wavefront measurement dynamic range extension method based on quadratic phase control, belong to wavefront measurement technical field.For the problem that the measurable slope interval is limited in the limited detection displacement range in traditional Hartmann wavefront measurement, at least the sub-aperture phase distribution containing reference focusing phase and quadratic phase term is constructed in super surface phase control, and the displacement of each sub-aperture corresponding light spot on the detection surface and the local average slope of the sub-aperture satisfy the preset monotone reversible nonlinear mapping relationship in design working interval by combining theoretical modeling, numerical optimization and / or experimental calibration.The present application can reconstruct the slope-displacement encoding rule of traditional Hartmann under the premise of keeping local average slope reversible and wavefront reconstructable, extend the encodable slope range in given displacement range, so as to improve the dynamic range of Hartmann wavefront measurement, especially suitable for the measurement scene of strong non-uniform, large dynamic range wavefront.

Description

Technical Field

[0001] This invention relates to a method for extending the dynamic range of Hartmann wavefront measurement based on secondary phase modulation, applicable to Hartmann wavefront sensors, and particularly suitable for Hartmann wavefront measurement scenarios using metasurfaces for phase modulation, belonging to the field of wavefront measurement technology. Background Technology

[0002] Hartmann wavefront sensors, especially Shak-Hartmann wavefront sensors, are widely used in adaptive optics, laser transmission, astronomical imaging, and precision optical detection due to their advantages such as good real-time performance, compact structure, no need for reference light, and wide applicability. Their basic principle is to divide the wavefront to be measured into multiple sub-apertures using a microlens array or equivalent beam-splitting focusing structure, and to reflect the local slope of the wavefront within the corresponding sub-aperture by the displacement of the focal spot of each sub-aperture on the detector.

[0003] In traditional Hartmann sensor readout methods, the wavefront to be measured is typically approximated as a local linear phase within each sub-aperture, thus establishing a linear correspondence between the spot displacement and the local average slope of the sub-aperture. This linear relationship is easy to solve and reconstruct under small slope conditions. However, when the wavefront to be measured has strong non-uniformity, a large dynamic range, or rapid time-varying characteristics, the local average slope may increase significantly. In this case, the displacement of the spot on the detection surface is easily limited by the effective sampling range of the detector, the spacing between adjacent sub-aperture spots, and the stability of the focal spot morphology of the sub-aperture, thereby limiting the measurable dynamic range.

[0004] Under conditions of strong phase gradients or complex wavefront distortions, traditional linear readout methods are prone to phenomena such as local spot stretching, distortion, energy dissipation, boundary crossing, and even aliasing with adjacent spots. This causes deviations in the slope values ​​obtained by position estimation methods based on the centroid method, thus affecting the accuracy of wavefront reconstruction. How to map a finite probe displacement range to a larger local average slope range while maintaining invertibility has become a key issue in improving the Hartmann dynamic range. In recent years, metasurfaces, with their high degree of freedom in phase manipulation and compact integration, have provided a new technical approach for spot manipulation in Hartmann wavefront measurement. However, most existing metasurface Hartmann wavefront measurement schemes still rely primarily on linear displacement encoding. Existing technologies include approaches that use binary phase modulation to alter the intensity distribution of the light spot and combine it with phase retrieval algorithms to reconstruct the wavefront, such as CN111998962A. This approach primarily focuses on wavefront reconstruction accuracy under conditions of low spatial sampling rates or weak beacons, and does not extend the range of coded slopes within a given displacement range based on the monotonic, reversible, nonlinear mapping relationship between the light spot displacement and the local average slope of the sub-aperture. Existing metasurface Hartmann wavefront measurement schemes still need to further utilize the phase modulation degrees of freedom of metasurfaces to reconstruct the traditional Hartmann slope-displacement readout relationship in order to achieve a systematic extension of the dynamic range. Summary of the Invention

[0005] To address the problem of limited measurable slope range within a finite detection displacement due to the approximately linear correspondence between spot displacement and local average slope of the sub-aperture in traditional Hartmann wavefront measurements, this invention proposes a dynamic range extension method for Hartmann wavefront measurements based on quadratic phase modulation. By designing a phase distribution in the metasurface phase modulation that includes at least a reference focusing phase and a quadratic phase term, the spot displacement relative to the local average slope of the sub-aperture satisfies a preset monotone reversible nonlinear mapping relationship. Under the premise of maintaining the invertibility of the local average slope and the reconstructibility of the wavefront, the slope and displacement encoding rules are reconstructed to improve the dynamic range and enhance the dynamic range of Hartmann wavefront measurements.

[0006] The present invention adopts the following technical solution:

[0007] A method for extending the dynamic range of Hartmann wavefront measurements based on secondary phase modulation includes the following steps:

[0008] S1, so that the beam to be measured is incident on the Hartmann wavefront measurement unit and the beam to be measured is divided into multiple sub-apertures;

[0009] S2, design a metasurface phase distribution for each sub-aperture, wherein the metasurface phase distribution includes at least a reference focusing phase and a secondary phase term;

[0010] S3 utilizes the metasurface phase distribution to control the emitted wavefront of each sub-aperture, so that the spot displacement of the corresponding light spot on the detector surface and the local average slope of the sub-aperture satisfy a preset monotonic reversible nonlinear mapping relationship.

[0011] S4, collect the spot displacement of each sub-aperture;

[0012] S5. Based on the inverse mapping of the monotone invertible nonlinear mapping relationship, the spot displacement of each sub-aperture is inverted to obtain the local average slope of each sub-aperture.

[0013] S6. The wavefront distribution of the beam to be measured is obtained by reconstructing the wavefront based on the local average slope of each sub-aperture.

[0014] Preferably, in step S2, the center coordinates of the m-th and n-th sub-apertures are ( , Metasurface phase distribution satisfy:

[0015] (6)

[0016] In the formula, As the reference focusing phase, It is a quadratic phase term;

[0017] The reference focusing phase is expressed as:

[0018] (7)

[0019] In the formula, =2π / λ, where λ is the wavelength of the incident light. For reference focal length;

[0020] The quadratic phase term is represented as:

[0021] (8)

[0022] In the formula, , and These are the design coefficients for the square term (first), the square term (second), and the cross term (third); depending on the target mapping relationship, choose to retain only the square term or introduce the cross term simultaneously.

[0023] Preferably, the metasurface phase distribution in step S2 further includes a corrected phase term, expressed as:

[0024] (9)

[0025] in, The phase correction term is used to compensate for the residual of the actual slope-displacement response formed by the reference focusing phase and the secondary phase term. The phase correction term is obtained through numerical optimization, diffraction simulation iteration or experimental calibration table lookup.

[0026] Preferably, the expression for the phase correction term is:

[0027] (10)

[0028] In the formula, These are higher-order correction coefficients. , are non-negative integers and + ≥3.

[0029] Preferably, in step S3, the relationship between the spot displacement and the local average slope of the sub-aperture satisfies:

[0030] (11)

[0031] (12)

[0032] in, , These represent the displacements of the light spots corresponding to the m-th and n-th sub-apertures along the u and v directions on the detection surface, respectively. , Let be the local average slopes of the m-th and n-th sub-apertures along the x and y directions, respectively. and The nonlinear mapping function is obtained by pre-setting the phase design and remains monotonic and invertible within the working interval.

[0033] Preferably, a phase design target is established according to the target dynamic range and the displacement range of the detection surface. The correspondence between the metasurface phase distribution and the nonlinear mapping function is determined through one or more methods, such as theoretical calculation, numerical optimization, experimental calibration, or calibration lookup table. That is, the corresponding nonlinear mapping function, so that the actual spot displacement and the local average slope response curve approximate the preset target mapping relationship within the design working range.

[0034] Preferably, in step S5, after obtaining the spot displacement of each sub-aperture... , Then, the corresponding local average slope is obtained through inverse mapping, and the expression is:

[0035] (13)

[0036] (14)

[0037] in, , These are nonlinear mapping functions. , The inverse mapping of .

[0038] Preferably, if the upper limits of the displacement of the detection surface in the u direction and the v direction are respectively denoted as... and The corresponding upper limits of measurable local average slopes are as follows:

[0039] (15)

[0040] (16)

[0041] When satisfied , This indicates that within the same available displacement range of the detection surface, the nonlinear mapping relationship can correspond to a larger local average slope range, thus achieving an improvement in dynamic range.

[0042] Preferably, the relationship between the spot displacement and the local average slope of the sub-aperture satisfies:

[0043] (17)

[0044] (18)

[0045] in, To characterize the nonlinear intensity, the characteristic slope constant is adjusted... It can change the degree of compression of the mapping in the high-slope region; Indicates the reference focal length;

[0046] when (where the symbol "≪" means "much smaller than", that is, the absolute value of the local average slope of the sub-aperture is much smaller than the characteristic slope constant.) ),satisfy Maintaining the same sensitivity as traditional linear readout methods; when | When | significantly increased It tends to saturate, thus bearing a larger local average slope within a limited range of probe surface displacement;

[0047] The corresponding inverse mapping is:

[0048] (19)

[0049] (20)

[0050] Require , ;

[0051] exist Under the given conditions, substituting equation (19) into equation (15) yields:

[0052] (twenty one)

[0053] Right now , The condition is always true, and the dynamic range improvement factor compared to traditional linear readout is:

[0054] (twenty two)

[0055] And the increase multiplier varies It increases monotonically.

[0056] For any details not covered in this invention, please refer to the prior art.

[0057] The beneficial effects of this invention are as follows:

[0058] (1) This invention extends the relationship between the spot displacement and the local average slope of the sub-aperture from the traditional approximate linear relationship to a designable monotonic reversible nonlinear relationship, which in principle increases the measurable slope range corresponding to the finite detection displacement range, thereby achieving a systematic improvement in the dynamic range.

[0059] (2) This invention reconstructs the slope and displacement coding rules by using phase modulation with the second phase term as the main component, so that the system can still maintain the slope invertibility under large slope conditions, thereby expanding the range of measurable local average slope under the condition of a given upper limit of the displacement of the detection surface, and improving the applicability of Hartmann wavefront measurement in strongly non-uniform, large dynamic range wavefront measurement scenarios.

[0060] (3) The present invention still uses the local average slope of the sub-aperture as an intermediate variable for wavefront reconstruction, which is compatible with the existing Hartmann wavefront reconstruction framework and is easy to promote and apply in optical measurement and wavefront diagnosis scenarios. Attached Figure Description

[0061] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an undue limitation of this application.

[0062] Figure 1 This is a schematic diagram illustrating the principle of the Hartmann wavefront measurement dynamic range extension method based on secondary phase modulation of the present invention.

[0063] Figure 2 This is a schematic diagram of nonlinear spot displacement mapping according to a certain embodiment of the present invention;

[0064] Figure 3 This is a flowchart of the Hartmann wavefront measurement dynamic range extension method based on secondary phase modulation according to the present invention. Detailed Implementation

[0065] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. However, this is not the only description; all aspects not described in detail herein are based on conventional techniques in the art.

[0066] Example 1

[0067] A method for extending the dynamic range of Hartmann wavefront measurements based on secondary phase modulation, such as... Figure 1 , Figure 3 As shown, it includes the following steps:

[0068] S1, the beam to be measured is incident on the Hartmann wavefront measurement unit and the beam to be measured is divided into multiple sub-apertures. The Hartmann sub-aperture division structure can be a microlens array, a metasurface sub-aperture array or an equivalent aperture division structure. The multiple sub-apertures can be set according to a rectangular array, a hexagonal array or other preset arrangement. Each sub-aperture corresponds to a local phase adjustment unit and forms a reference spot area on the detection surface.

[0069] S2, design a metasurface phase distribution for each sub-aperture, wherein the metasurface phase distribution includes at least a reference focusing phase and a secondary phase term;

[0070] S3 utilizes the metasurface phase distribution to control the emitted wavefront of each sub-aperture, so that the spot displacement of the corresponding light spot on the detector surface and the local average slope of the sub-aperture satisfy a preset monotonic reversible nonlinear mapping relationship.

[0071] S4, collect the spot displacement of each sub-aperture;

[0072] S5. Based on the inverse mapping of the monotone invertible nonlinear mapping relationship, the spot displacement of each sub-aperture is inverted to obtain the local average slope of each sub-aperture.

[0073] S6. The wavefront distribution of the beam to be measured is obtained by reconstructing the wavefront based on the local average slope of each sub-aperture.

[0074] Example 2

[0075] A method for extending the dynamic range of Hartmann wavefront measurement based on secondary phase modulation, as described in Example 1, differs in that the center coordinates of the m-th and n-th sub-apertures are set as ( , Within this sub-aperture, the wavefront to be measured... It can be approximated as

[0076] (1)

[0077] in, and Let represent the local average slopes of the m-th and n-th sub-apertures along the x and y directions, respectively.

[0078] For traditional focal length The Hartmann linear readout relation holds that the displacement of the m-th, n-th sub-aperture spot on the detector surface satisfies:

[0079] (2)

[0080] (3)

[0081] in, and These represent the displacements of the light spot relative to the reference position along the u and v directions of the detector surface, respectively. In this embodiment, the x and y directions are two orthogonal coordinate directions within the phase control surface where the sub-aperture is located, corresponding to the row and column directions of the sub-aperture array, respectively. The u and v directions are two orthogonal coordinate directions within the detector surface, corresponding to the displacement readout directions in the x and y directions, respectively. If the upper limits of the usable displacement of the detector surface in the two directions are respectively... and Then the measurable range of the local average slope corresponding to the traditional linear readout method satisfies:

[0082] (4)

[0083] (5)

[0084] As can be seen from the above formula, under the traditional linear model, the displacement range of the probe surface directly determines the dynamic range of the local average slope. When the local average slope of the wavefront to be measured exceeds the above range, it is easy for the spot to cross the boundary, aliasing, or slope inversion distortion to occur.

[0085] To modify the aforementioned linear constraint relationship, this embodiment designs a metasurface phase distribution within the m-th and n-th sub-apertures. satisfy:

[0086] (6)

[0087] In the formula, As the reference focusing phase, It is a quadratic phase term;

[0088] The reference focusing phase is expressed as:

[0089] (7)

[0090] In the formula, =2π / λ, where λ is the wavelength of the incident light. For reference focal length;

[0091] The quadratic phase term is represented as:

[0092] (8)

[0093] In the formula, , and The design coefficients are 1 for the square term, 2 for the square term, and 3 for the cross term, respectively. Based on the target mapping relationship, only the square term is retained, that is, the first two square terms after the equal sign in formula (8), or the cross term is introduced at the same time, that is, the last term after the equal sign in formula (8).

[0094] In this embodiment, design coefficients one and two of the squared term are used to set the equivalent convergence capability of the sub-aperture along the x and y directions and the readout sensitivity in the low-slope region; design coefficient three of the cross term is used to set the coupling degree between the x and y directions; when using a two-dimensional separable design, design coefficient three of the cross term is taken. For symmetrical designs with similar response characteristics along the x and y directions, take = Each coefficient can be considered relative to the quadratic coefficient of the reference focusing phase. Select proportionally, for example, take Among them, the scaling factor For example, take a positive number that is greater than 0 and less than 1. =0.1~0.5. With an incident light wavelength λ=0.633μm and a reference focal length... Taking a hole diameter of 5mm and a sub-aperture width D of 0.15mm as an example, at this time... =2π / λ≈9.93rad / μm, ≈9.9×10⁻ 4 rad / μm 2 Correspondingly Approximately 1×10⁻ 4 ~5×10⁻ 4 rad / μm 2 , Set to 0. When different compression characteristics need to be introduced in the x and y directions, or when compensating for non-orthogonal aberrations, a value of 0 can be used. And introduce nonzero For example, take for The specific values ​​of the above coefficients are determined by numerical optimization or experimental calibration to ensure that the actual slope-displacement response curve approximates the target mapping relationship within the design working range.

[0095] Example 3

[0096] A method for extending the dynamic range of Hartmann wavefront measurements based on quadratic phase modulation, as described in Example 2, differs in that a modified phase term is introduced in this embodiment, resulting in the metasurface phase distribution expression as follows:

[0097] (9)

[0098] in, The phase correction term is used to compensate for the residual of the actual slope-displacement response formed by the reference focusing phase and the secondary phase term, so that the actual response curve between the spot displacement of the detection surface and the local average slope of the sub-aperture further approximates the nonlinear mapping relationship of the target. The phase correction term is obtained through numerical optimization, diffraction simulation iteration or experimental calibration table lookup.

[0099] When the reference focusing phase and the secondary phase term can already meet the approximation accuracy requirements of the target mapping relationship, a correction phase term can be omitted, i.e., let .

[0100] Example 4

[0101] A method for extending the dynamic range of Hartmann wavefront measurements based on quadratic phase modulation, as described in Example 3, differs in that the expression for the modified phase term is as follows:

[0102] (10)

[0103] In the formula, These are higher-order correction coefficients. , are non-negative integers and + ≥3.

[0104] In this embodiment, the higher-order correction coefficients The magnitude of this is usually much smaller than the design coefficient of the quadratic phase term, and can be taken as 0.1% to 10% of the quadratic term coefficient. Taking the incident light wavelength λ = 0.633 μm and the reference focal length... Taking a 5mm diameter and a sub-aperture width D=0.15mm as an example: When using a two-dimensional separable design, the main introduction is a fourth-order term along the x-direction and a fourth-order term along the y-direction, i.e., taking p=4, q=0 and p=0, q=4 respectively, with corresponding correction coefficients. , Approximately 1×10⁻ 9 ~1×10⁻ 7 rad / μm 4 When further refined compensation is needed, a sixth-order term along the x-direction or y-direction can be introduced, i.e., p=6, q=0 or p=0, q=6, with corresponding correction coefficients. , Approximately 1×10 can be taken. -13 ~1×10 -11 rad / μm 4 For cases requiring coupling compensation in the x and y directions, hybrid higher-order terms can be introduced, for example, taking p=2 and q=2, with corresponding coefficients... Take a value of the same order as the pure directional term. The specific values ​​of the above higher-order correction coefficients are determined by minimizing the residual between the actual response curve and the target mapping relationship (Equation (17) and Equation (18)) after numerical optimization or experimental calibration.

[0105] Example 5

[0106] A method for extending the dynamic range of Hartmann wavefront measurement based on secondary phase modulation, as described in Example 4, differs in that, in step S3, when the local incident wavefront (the local incident wavefront refers to the portion of the wavefront to be measured that is incident within the range of the m-th or n-th sub-aperture after the beam to be measured is divided by the Hartmann sub-aperture, i.e., the local part of the global wavefront to be measured within that sub-aperture, which can be approximately characterized as the local linear phase component within that sub-aperture) has an average slope within that sub-aperture. , At this time, the corresponding local phase tilt, together with the metasurface phase distribution, determines the location of the principal energy accumulation on the probe surface. By constructing a phase distribution containing at least a quadratic phase term, and combining theoretical modeling, numerical optimization, and experimental calibration, the response of the principal energy location on the probe surface to the local average slope can be made to approximate a preset monotone invertible nonlinear mapping relationship within the design working range, such as... Figure 2 As shown, in this embodiment, the relationship between the spot displacement and the local average slope of the sub-aperture satisfies:

[0107] (11)

[0108] (12)

[0109] in, , These represent the displacements of the light spots corresponding to the m-th and n-th sub-apertures along the u and v directions on the detection surface, respectively. , Let be the local average slopes of the m-th and n-th sub-apertures along the x and y directions, respectively. and The nonlinear mapping function is obtained by pre-setting the phase design and remains monotonic and invertible within the working interval.

[0110] Example 6

[0111] A method for extending the dynamic range of Hartmann wavefront measurement based on secondary phase modulation, as described in Example 5, differs in that, in step S5, after obtaining the spot displacement of each sub-aperture... , Then, the corresponding local average slope is obtained through inverse mapping, and the expression is:

[0112] (13)

[0113] (14)

[0114] in, , These are nonlinear mapping functions. , The inverse mapping of .

[0115] Example 7

[0116] A method for extending the dynamic range of Hartmann wavefront measurement based on quadratic phase modulation, as described in Example 6, differs in that the upper limits of the displacement of the probe surface in the u and v directions are respectively denoted as... and The corresponding upper limits of measurable local average slopes are as follows:

[0117] (15)

[0118] (16)

[0119] Comparing equations (15) and (16) with equations (4) and (5) of the traditional linear model, when the following conditions are met... , This indicates that within the same available displacement range of the detection surface, the nonlinear mapping relationship can correspond to a larger local average slope range, thus achieving an improvement in dynamic range.

[0120] From a physical perspective, Equations (15) and (16) show that the present invention does not simply increase the size of the detector, but rather reconstructs the displacement coding law to enable a greater range of slope changes within a finite displacement interval, thereby achieving a larger range of measurable local slopes without increasing the upper limit of the displacement of the detection surface.

[0121] Example 8

[0122] A method for extending the dynamic range of Hartmann wavefront measurement based on quadratic phase modulation is described in Example 7. The difference is that the inverse mapping can be achieved through analytical expressions, numerical inversion, piecewise fitting, or lookup table interpolation. After obtaining the local average slopes of all sub-apertures, the wavefront to be measured can be recovered using the gradient integration method or the modal fitting method. Since this invention still uses the local average slopes of the sub-apertures as the reconstruction input, it is compatible with existing Hartmann wavefront reconstruction procedures.

[0123] In this embodiment, the nonlinear mapping relationship between the spot displacement and the local average slope of the sub-aperture satisfies:

[0124] (17)

[0125] (18)

[0126] in, To characterize the nonlinear intensity, the characteristic slope constant is adjusted... It can change the degree of compression of the mapping in the high-slope region; Indicates the reference focal length;

[0127] when (where the symbol "≪" means "much smaller than", that is, the absolute value of the local average slope of the sub-aperture is much smaller than the characteristic slope constant.) ),satisfy Maintaining the same sensitivity as traditional linear readout methods; when | When | significantly increased It tends to saturate, thus bearing a larger local average slope within a limited range of probe surface displacement;

[0128] The corresponding inverse mapping is:

[0129] (19)

[0130] (20)

[0131] Require , ;

[0132] exist Under the given conditions, substituting equation (19) into equation (15) yields:

[0133] (twenty one)

[0134] Right now , The condition is always true, and the dynamic range improvement factor compared to traditional linear readout is:

[0135] (twenty two)

[0136] And the increase multiplier varies It increases monotonically.

[0137] During the design process, appropriate options can be selected. The value controls the magnitude of the increase, among which the characteristic slope constant The selection can be based on the target dynamic range enhancement factor, the upper limit of the available displacement of the detection surface, and the spot separation conditions; taking the u direction as an example, the enhancement factor of the dynamic range relative to the traditional linear readout method is denoted as... ,but When the expected improvement factor is approximately 1.5, it can be taken as... When the expected improvement factor is approximately 2, it is acceptable. In actual design, a safety margin should be set in combination with the detection noise, the stability of the spot morphology and the separation conditions of adjacent sub-aperture spots, in order to avoid the operating point getting too close to the mapping saturation region.

[0138] The metasurface phase distributions in equations (7) to (10) are numerically optimized to approximate the target mapping relationship: focusing the phase with a reference. As the initial term, with the second phase term The primary modulation term is used, and a correction phase term is selectively introduced based on the approximation accuracy requirements of the target mapping relationship. This is to ensure that the actual response curve between the probe surface spot displacement and the local average slope of the sub-aperture fully approximates the relationship between equations (17) and (18) within the designed working range. Equations (17) to (20) are only one specific implementation form. Those skilled in the art can select other nonlinear mapping functions that satisfy the monotonic reversibility condition according to actual measurement needs.

[0139] This invention addresses the problem of limited dynamic range in Hartmann wavefront measurements by introducing metasurface phase modulation, containing at least a quadratic phase term, into each sub-aperture. This causes the displacement of the corresponding light spot on the detector surface to no longer be simply proportional to the local average slope of the sub-aperture, but rather to satisfy a preset monotonically reversible nonlinear mapping relationship. Since this nonlinear mapping relationship can correspond to a larger range of local average slopes within a limited detection displacement range, the dynamic range of the system can be improved without violating the slope inversion condition.

[0140] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for extending the dynamic range of Hartmann wavefront measurements based on secondary phase modulation, characterized in that, Includes the following steps: S1, so that the beam to be measured is incident on the Hartmann wavefront measurement unit and the beam to be measured is divided into multiple sub-apertures; S2, design a metasurface phase distribution for each sub-aperture, wherein the metasurface phase distribution includes at least a reference focusing phase and a secondary phase term; S3 utilizes the metasurface phase distribution to control the emitted wavefront of each sub-aperture, so that the spot displacement of the corresponding light spot on the detector surface and the local average slope of the sub-aperture satisfy a preset monotonic reversible nonlinear mapping relationship. S4, collect the spot displacement of each sub-aperture; S5. Based on the inverse mapping of the monotone invertible nonlinear mapping relationship, the spot displacement of each sub-aperture is inverted to obtain the local average slope of each sub-aperture. S6. The wavefront distribution of the beam to be measured is reconstructed based on the local average slope of each sub-aperture. In step S2, let the center coordinates of the m-th and n-th sub-apertures be ( , Metasurface phase distribution satisfy: （6） In the formula, As the reference focusing phase, It is a quadratic phase term; The reference focusing phase is expressed as: （7） In the formula, =2π / λ, where λ is the wavelength of the incident light. For reference focal length; The quadratic phase term is represented as: （8） In the formula, , and These are the design coefficients for the square term (first), the square term (second), and the cross term (third); depending on the target mapping relationship, choose to retain only the square term or introduce the cross term simultaneously.

2. The method for extending the dynamic range of Hartmann wavefront measurement based on secondary phase modulation according to claim 1, characterized in that, The metasurface phase distribution in step S2 also includes a corrected phase term, expressed as: （9） in, The phase correction term is used to compensate for the residual of the actual slope-displacement response formed by the reference focusing phase and the secondary phase term. The phase correction term is obtained through numerical optimization, diffraction simulation iteration or experimental calibration table lookup.

3. The method for extending the dynamic range of Hartmann wavefront measurement based on secondary phase modulation according to claim 2, characterized in that, The expression for the phase correction term is: （10） In the formula, These are higher-order correction coefficients. , are non-negative integers and + ≥3.

4. The method for extending the dynamic range of Hartmann wavefront measurement based on secondary phase modulation according to claim 3, characterized in that, In step S3, the relationship between the spot displacement and the local average slope of the sub-aperture satisfies: （11） （12） in, , These represent the displacements of the light spots corresponding to the m-th and n-th sub-apertures along the u and v directions on the detection surface, respectively. , Let be the local average slopes of the m-th and n-th sub-apertures along the x and y directions, respectively. and The nonlinear mapping function is obtained by pre-setting the phase design and remains monotonic and invertible within the working interval.

5. The method for extending the dynamic range of Hartmann wavefront measurement based on secondary phase modulation according to claim 4, characterized in that, Establish phase design targets based on the target dynamic range and the displacement range of the detection surface, and determine the correspondence between the metasurface phase distribution and the nonlinear mapping function, i.e. the corresponding nonlinear mapping function, through one or more methods such as theoretical calculation, numerical optimization, experimental calibration, or calibration lookup table, so that the actual spot displacement and the local average slope response curve approximate the preset target mapping relationship within the design working range.

6. The method for extending the dynamic range of Hartmann wavefront measurement based on secondary phase modulation according to claim 5, characterized in that, In step S5, after obtaining the spot displacement of each sub-aperture... , Then, the corresponding local average slope is obtained through inverse mapping, and the expression is: （13） （14） in, , These are nonlinear mapping functions. , The inverse mapping of .

7. The method for extending the dynamic range of Hartmann wavefront measurement based on secondary phase modulation according to claim 6, characterized in that, If the upper limits of the displacement of the probe surface in the u and v directions are respectively denoted as... and The corresponding upper limits of measurable local average slopes are as follows: （15） （16） When satisfied , This indicates that within the same available displacement range of the detection surface, the nonlinear mapping relationship can correspond to a larger local average slope range, thus achieving an improvement in dynamic range.

8. The method for extending the dynamic range of Hartmann wavefront measurement based on secondary phase modulation according to claim 7, characterized in that, The relationship between the spot displacement and the local average slope of the sub-aperture satisfies: （17） （18） in, The characteristic slope constant characterizing the nonlinear intensity; Indicates the reference focal length; The corresponding inverse mapping is: （19） （20） Require , ; exist Under the given conditions, substituting equation (19) into equation (15) yields: （21） Right now , The condition is always true, and the dynamic range improvement factor compared to traditional linear readout is: （22） And the increase multiplier varies It increases monotonically.

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