A method and device for determining the machining error of the full-aperture surface of an aspheric mirror

Abstract

This invention provides a method and apparatus for determining the full-aperture surface shape processing error of an aspherical mirror. The method includes: acquiring the phase measurement values ​​of each phase measurement point within each annular sub-aperture region of the aspherical mirror to be tested; constructing a global optimization function using the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables, and calculating the optimal solution of the independent variables of the global optimization function; obtaining the aberration terms corresponding to each phase measurement point when the independent variables take the optimal solution, and calculating the difference between the phase measurement value of each phase measurement point and the corresponding aberration term to obtain the phase value of the full-aperture surface shape processing error of the aspherical mirror to be tested. This invention achieves decoupling of the surface shape processing error of the aspherical mirror, improves the surface shape measurement accuracy of aspherical optical elements, and enhances the accuracy and precision of surface shape measurement.

Description

Technical Field

[0001] This invention relates to the field of optical interferometry technology, and in particular to a method and apparatus for determining the surface shape processing error of an aspherical mirror with full aperture. Background Technology

[0002] Aspherical optical components are of great value in various cutting-edge technologies and industrial manufacturing fields, and there is an increasingly urgent need for surface shape detection technology. Currently, surface shape detection technology usually adopts an interferometric measurement method with interlocking annular sub-apertures. During the scanning measurement process, the workpiece stage of the measurement system moves the mirror under test to perform eccentricity, pitch / yaw adjustment and axial scanning measurement. Inevitably, mechanical adjustment errors will produce corresponding measurement errors in each annular sub-aperture during this process.

[0003] Existing stitching methods eliminate the influence of mechanical adjustment errors by fitting and subtracting the phase measurement error of the overlapping region of the annular sub-apertures. However, for the measurement of large-aperture, high-asphericity aspherical mirrors, even slight mechanical adjustment errors can cause significant measurement errors in the sub-aperture measurement results, manifesting as various first-order and higher-order aberrations such as coma, astigmatism, and spherical aberration. Existing stitching methods lack effective solutions for handling these aberrations. Furthermore, the resulting measurement errors, varying with the sub-aperture, include various types of higher-order aberrations. These higher-order aberrations may share common characteristics with the surface machining errors of the mirror itself, coupling with these errors. The fitting calculations and aberration subtraction in existing stitching methods are insufficient to eliminate the influence of measurement errors, leading to a decrease in the accuracy and precision of surface measurement. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method and apparatus for determining the surface shape processing error of an aspherical mirror with full aperture, thereby decoupling the surface shape processing error of the aspherical mirror, improving the surface shape measurement accuracy of the aspherical optical element, and improving the accuracy and precision of surface shape measurement.

[0005] To achieve the above objectives, the technical solutions adopted in the embodiments of the present invention are as follows:

[0006] In a first aspect, embodiments of the present invention provide a method for determining the surface shape machining error of an aspherical mirror across its entire aperture, comprising:

[0007] Acquire the phase measurement values ​​of each phase measurement point within each annular sub-aperture region of the aspherical mirror to be tested;

[0008] A global optimization function is constructed using the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables, and the optimal solution of the independent variables of the global optimization function is calculated.

[0009] Obtain the aberration terms corresponding to each phase measurement point when the independent variable takes the optimal solution, calculate the difference between the phase measurement value of each phase measurement point and the corresponding aberration term, and obtain the phase value of the full aperture surface shape processing error of the aspherical mirror to be tested.

[0010] Furthermore, this embodiment of the invention provides a first possible implementation of the first aspect, wherein constructing a global optimization function using the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables includes:

[0011] A loss function is established based on the full-aperture circular Zernike polynomial coefficients, the sub-aperture annular Zernike polynomial coefficients, and the phase measurement values ​​of each phase measurement point;

[0012] The global optimization function is obtained by calculating the sum of the loss function and the regularization term of the independent variable.

[0013] Furthermore, this embodiment of the invention provides a second possible implementation of the first aspect, wherein establishing a loss function based on the full-aperture circular Zernike polynomial coefficients, the sub-aperture annular Zernike polynomial coefficients, and the phase measurement values ​​of each phase measurement point includes:

[0014] The Zernike polynomial fitting results for the full aperture and each of the sub-apertures are obtained by fitting the full aperture and each of the sub-apertures using the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients.

[0015] The loss function is the sum of the Zernike polynomial fitting results of the full aperture and each of the sub-apertures, and the squared error of the phase measurement values ​​of all the phase measurement points.

[0016] Furthermore, this embodiment of the invention provides a third possible implementation of the first aspect, wherein calculating the optimal solution of the independent variable of the global optimization function includes:

[0017] The global optimization function is minimized using the regularization term of the independent variable as a constraint to obtain the optimal solutions for the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each of the sub-apertures.

[0018] Furthermore, this embodiment of the invention provides a fourth possible implementation of the first aspect, wherein obtaining the phase measurement values ​​of each phase measurement point within each annular sub-aperture region of the aspherical mirror to be tested includes:

[0019] Interference patterns of each of the aforementioned annular sub-aperture mask regions are acquired, and wavefront phase values ​​of each of the aforementioned phase detection points are determined based on the interference patterns of each of the aforementioned annular sub-aperture mask regions.

[0020] The residual between the wavefront phase value of each phase detection point and the wavefront phase value under ideal conditions is calculated to obtain the phase measurement value of each phase measurement point within each annular sub-aperture region.

[0021] Furthermore, this embodiment of the invention provides a fifth possible implementation of the first aspect, wherein determining the wavefront phase value of each phase detection point based on the interferogram of each of the annular sub-aperture mask regions includes:

[0022] Phase adjustment is performed on the interferogram within each of the annular sub-aperture mask regions to determine the wrapping phase value of each of the phase detection points;

[0023] The wavefront phase value of each phase detection point is obtained based on the preset phase unwrapping algorithm and the unwrapping calculation of the wrapped phase value of each phase detection point.

[0024] Furthermore, this embodiment of the invention provides a sixth possible implementation of the first aspect, wherein acquiring the interferogram of each of the annular sub-aperture mask regions includes:

[0025] Obtain the axial scanning position corresponding to each annular sub-aperture of the aspherical mirror to be tested;

[0026] The aspherical mirror to be tested is moved to the corresponding axial scanning position, and the interferogram of the aspherical mirror to be tested at the axial scanning position corresponding to each of the annular sub-apertures is acquired based on the surface interferometer.

[0027] Furthermore, the present invention provides a seventh possible implementation of the first aspect, wherein each of the annular sub-apertures has no overlapping region.

[0028] Secondly, embodiments of the present invention also provide a device for determining the surface shape processing error of an aspherical mirror across its entire aperture, comprising:

[0029] The acquisition module is used to acquire the phase measurement values ​​of each phase measurement point within each annular sub-aperture region of the aspherical mirror to be tested;

[0030] The first calculation module is used to construct a global optimization function with the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables, and to calculate the optimal solution of the independent variables of the global optimization function.

[0031] The second calculation module is used to obtain the aberration terms corresponding to each phase measurement point when the independent variable takes the optimal solution, calculate the difference between the phase measurement value of each phase measurement point and the corresponding aberration term, and obtain the phase value of the full aperture surface shape processing error of the aspherical mirror to be tested.

[0032] Thirdly, embodiments of the present invention provide an aspherical surface shape measurement system, comprising: a measurement model and a surface shape measurement controller, wherein the measurement model includes a surface shape interferometer and a workpiece stage, and the surface shape measurement controller includes a processor and a storage device;

[0033] The storage device stores a computer program that, when executed by the processor, performs the method as described in any of the first aspects.

[0034] This invention provides a method and apparatus for determining the surface shape processing error of an aspherical mirror across its entire aperture. The method includes: acquiring phase measurement values ​​at each phase measurement point within each annular sub-aperture region of the aspherical mirror to be tested; constructing a global optimization function using the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables; calculating the optimal solution of the global optimization function for the independent variables; obtaining the aberration terms corresponding to each phase measurement point when the independent variables take the optimal solution; calculating the difference between the phase measurement value of each phase measurement point and the corresponding aberration term; and obtaining the phase value of the full-aperture surface shape processing error of the aspherical mirror to be tested. This invention, by constructing a global optimization function using the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables and calculating the optimal solution of the global optimization function, achieves decoupling of the surface shape processing error of the aspherical mirror, improves the surface shape measurement accuracy of aspherical optical elements, and enhances the accuracy and precision of surface shape measurement.

[0035] Other features and advantages of the embodiments of the present invention will be set forth in the following description, or some features and advantages may be inferred from the description or determined without doubt, or may be learned by practicing the techniques described above in the embodiments of the present invention.

[0036] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0037] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0038] Figure 1 A flowchart illustrating a method for determining the surface shape processing error of an aspherical mirror with full aperture, provided by an embodiment of the present invention, is shown.

[0039] Figure 2 This invention illustrates an aspherical surface shape measurement model based on annular sub-aperture splicing, provided by an embodiment of the present invention.

[0040] Figure 3 This invention provides an embodiment of an interferometer that captures interferograms of a mirror under test at various axial scanning positions.

[0041] Figure 4a This invention provides a graph showing the variation curve of the circular Zernike polynomial coefficients of the full-diameter surface machining error according to an embodiment of the invention.

[0042] Figure 4b This invention provides a graph showing the variation curves of the circumferential Zernike polynomial coefficients for the aberration terms of various circumferential sub-aperture measurement errors, as provided in an embodiment of the invention.

[0043] Figure 5 This diagram illustrates the measurement results of the full-aperture surface shape machining error of a mirror under test, provided by an embodiment of the present invention.

[0044] Figure 6 A schematic diagram of a device for determining the surface shape processing error of an aspherical mirror with full aperture provided in an embodiment of the present invention is shown. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0046] Currently, aspherical optical components are of great value in various cutting-edge technologies and industrial manufacturing fields, and there is an increasingly urgent need for surface shape detection technologies. Interferometry based on ring sub-aperture stitching, with its simple measurement structure, is widely used in the measurement of large-aperture, high-asphericity rotationally symmetric aspherical optical components.

[0047] During the scanning measurement process, the workpiece stage of the measurement system drives the mirror under test to perform eccentricity, pitch / yaw adjustments, and axial scanning measurements. Mechanical adjustment errors are unavoidable during this process and will generate corresponding measurement errors in each annular sub-aperture. This is reflected in the various aberration terms in the Zernike polynomial fitting results of the annular sub-aperture phase measurements. In traditional stitching methods, the influence of mechanical adjustment errors is eliminated by fitting and calculating the measurement error of the phase in the overlapping area of ​​the annular sub-apertures and then subtracting it. However, for the measurement of large-aperture, high-asphericity aspherical mirrors, even slight mechanical adjustment errors can cause significant measurement errors in the sub-aperture measurement results, manifesting as various first-order and higher-order aberrations such as coma, astigmatism, and spherical aberration. Traditional stitching methods lack effective solutions for handling these. Furthermore, the measurement errors, varying with the sub-aperture, include various types of higher-order aberrations. These aberrations may share common characteristics with the surface machining errors of the mirror itself, thus coupling with these errors. Traditional stitching methods struggle to eliminate the influence of measurement errors through fitting calculations and aberration subtraction, leading to a decrease in measurement accuracy and precision. This is the current challenge of aspherical surface shape measurement technology and annular sub-aperture stitching technology.

[0048] Existing aspherical sub-aperture stitching techniques, such as fitting and calculating the overlapping areas of each annular sub-aperture and only subtracting translational, tilting, and defocusing aberrations as treatment for mechanical adjustment errors; using the overlapping area for fitting and calculation, and only fitting and processing translational, tilting, and defocusing aberrations; and more accurate surface shape fitting methods based on annular Zernike polynomials, all fail to consider higher-order aberrations. Current aspherical sub-aperture stitching techniques have not solved the problems of higher-order aberrations caused by mechanical adjustment errors in the surface shape measurement of large-aperture, high-asphericity aspherical optical elements, nor the decrease in measurement accuracy and precision caused by the coupling of measurement errors and surface shape processing errors, thus hindering the development of aspherical surface shape inspection technology.

[0049] To address the aforementioned issues, this invention provides a method and apparatus for determining the surface shape processing error of an aspherical mirror across its entire aperture. The embodiments of this invention will be described in detail below.

[0050] This embodiment provides a method for determining the surface shape machining error of an aspherical mirror with a full aperture. See [link to relevant documentation]. Figure 1 The flowchart shown illustrates a method for determining the surface shape machining error of an aspherical mirror across its entire aperture. This method mainly includes the following steps:

[0051] Step S102: Obtain the phase measurement values ​​of each phase measurement point in each annular sub-aperture region of the aspherical mirror to be tested;

[0052] A non-spherical surface shape measurement system based on annular sub-aperture stitching is constructed. A measurement model is built according to the system, and the mask regions of each annular sub-aperture are defined. Interference patterns within each annular sub-aperture mask region are acquired through the system's information acquisition module. The phase measurement values ​​of each phase measurement point within each annular sub-aperture mask region are then determined based on the interferograms. In one embodiment, phase demodulation and unwrapping calculations can be performed on the interferograms to obtain the wavefront phase values ​​of each phase measurement point. The residuals are then calculated by comparing these residuals with the ideal wavefront phase values ​​to obtain the phase measurement values ​​of each phase measurement point within each annular sub-aperture region.

[0053] Step S104: Construct a global optimization function using the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables, and calculate the optimal solution of the independent variables of the global optimization function.

[0054] The loss function is determined by using the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables, and a global optimization function is constructed based on the loss function and the corresponding constraint terms.

[0055] Minimize the global optimization function to obtain the optimal solution for the independent variables, namely the optimal solution for the full-aperture circular Zernike polynomial coefficients and the optimal solution for the annular Zernike polynomial coefficients of each sub-aperture.

[0056] In one specific implementation, the global optimization function is minimized using the regularization term of the independent variable as a constraint to obtain the optimal solution for the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture.

[0057] Step S106: Obtain the aberration terms corresponding to each phase measurement point when the independent variable takes the optimal solution, calculate the difference between the phase measurement value of each phase measurement point and the corresponding aberration term, and obtain the phase value of the full aperture surface shape processing error of the aspherical mirror to be tested.

[0058] Based on the optimal solution of the independent variable, the circumferential Zernike polynomial corresponding to the position of each measurement point within the circumferential sub-aperture is determined, and the aberration terms corresponding to each phase measurement point are obtained. Each term of the circumferential Zernike polynomial corresponding to the position of each measurement point within the circumferential sub-aperture when the independent variable takes the optimal solution is obtained, and the aberration terms belonging to the measurement error are extracted from the fitting result of this polynomial.

[0059] The phase measurement value of each phase measurement point is calculated, and the aberration term belonging to the measurement error in the annular Zernike polynomial corresponding to the position of each measurement point within the annular sub-aperture is obtained, thus obtaining the measurement result of the phase value of the full aperture surface shape processing error of the aspherical mirror under test.

[0060] By subtracting the aberration terms belonging to the measurement error in the annular Zernike polynomial fitting results of each sub-aperture during the scanning measurement of the phase measurement values ​​of all phase measurement points, the measurement results of the phase value of the full aperture surface shape processing error of the aspherical mirror under test are obtained.

[0061] The method for determining the full-aperture surface shape processing error of the aspherical mirror provided in this embodiment constructs a global optimization function using the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables, calculates the optimal solution of the global optimization function, and calculates the phase value of the full-aperture surface shape processing error of the aspherical mirror to be tested. This decouples the surface shape processing error of the aspherical mirror, improves the surface shape measurement accuracy of the aspherical optical element, and enhances the accuracy and precision of surface shape measurement.

[0062] In one embodiment, this embodiment provides an implementation method for constructing a global optimization function using the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables. The specific steps are as follows:

[0063] Step (1): Establish a loss function based on the full-aperture circular Zernike polynomial coefficients, the annular Zernike polynomial coefficients of each sub-aperture, and the phase measurement values ​​of each phase measurement point;

[0064] In one specific implementation, the Zernikal polynomial fitting results for the full aperture and each sub-aperture are obtained by fitting the full-aperture circular Zernikal polynomial coefficients and the annular Zernikal polynomial coefficients of each sub-aperture; the sum of the Zernikal polynomial fitting results for the full aperture and each sub-aperture and the square error of the phase measurement values ​​of all phase measurement points are used as the loss function.

[0065] The coefficients of the full-aperture circular Zernike polynomial and the coefficients of the annular Zernike polynomials of each sub-aperture are used as independent variables, and the square error between the superposition of the fitting results of the full-aperture and each sub-aperture Zernike polynomials and the phase measurement values ​​of all phase measurement points in all sub-aperture regions is used as the loss function.

[0066] Step (2): Calculate the sum of the loss function and the regularization term of the independent variable to obtain the global optimization function.

[0067] The formula for calculating the global optimization function f(X) can be:

[0068] Where X is the independent variable, including the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture, L includes the phase measurements of all phase measurement points, and A satisfies:

[0069]

[0070] The elements of the first column A in A0k satisfy:

[0071]

[0072] Among them, each element A 0kij These are the terms of the circular Zernike polynomials corresponding to the positions of each measurement point across the entire aperture range. When calculating the normalized radius, the radius of the entire aperture of the aspherical mirror under test is taken as the maximum radius. A 0kij Let i be the i-th circular Zernike term corresponding to the j-th measurement point of the k-th annular sub-aperture; the measurement process involves a total of K annular sub-apertures, of which the k-th annular sub-aperture has a total of J measurement points, and the fitting process fits a total of I Zernike terms.

[0073] The elements A starting from the second column in column A k satisfy:

[0074]

[0075] Among them, each element A kij These are the terms of the annular Zernike polynomials corresponding to the positions of each measurement point within the annular sub-aperture. When calculating the aperture ratio, the inner and outer radius values ​​are taken from the inner and outer radii of the annular sub-aperture; A kij Within the range of the l-th annular sub-aperture, the i-th annular Zernike term corresponding to the j-th measurement point; the measurement process involves a total of K annular sub-apertures, of which the k-th annular sub-aperture has a total of J measurement points, and the fitting process fits a total of I Zernike terms;

[0076] X in f(X) satisfies:

[0077]

[0078] Each element X in X k satisfy:

[0079]

[0080] Among them, each element X ki For: when k = 0, X ki It is the coefficient of the i-th circular Zernike term across the entire caliber range; when k = 1,…,K, X ki It is the coefficient of the i-th annular Zernike term of the k-th annular sub-aperture. The fitting process fits a total of I Zernike terms.

[0081] In f(X), L satisfies:

[0082]

[0083] Each element in l k satisfy:

[0084]

[0085] Among them, each element l kj It is the phase measurement value of the j-th measurement point within the range of the k-th annular sub-aperture; the measurement process involves a total of K annular sub-apertures, and the k-th annular sub-aperture has a total of J measurement points.

[0086] In f(X): Let λ be the loss function, which is the squared error of AX and L, λ‖X‖1 be the regularization term of the independent variable, ‖X‖1 be the L1 norm of X, and λ be the coefficient.

[0087] In one implementation, the phase measurement value at each phase measurement point is calculated and fitted to the corresponding sub-aperture annular Zernike polynomial result A. kij The difference in aberration terms belonging to measurement error can be used to obtain the phase value of the full-aperture surface shape processing error of the aspherical mirror.

[0088] In one embodiment, this embodiment provides an implementation method for obtaining phase measurement values ​​at each phase measurement point within each annular sub-aperture region of the aspherical mirror to be tested, which can be specifically performed according to the following steps:

[0089] Step 1): Acquire the interferogram of each annular sub-aperture mask region, and determine the wavefront phase value of each phase detection point based on the interferogram of each annular sub-aperture mask region;

[0090] In one specific implementation, the axial scanning positions corresponding to each annular sub-aperture of the aspherical mirror to be tested are obtained; the aspherical mirror to be tested is moved to the corresponding axial scanning position, and an interferogram of the aspherical mirror to be tested at each annular sub-aperture corresponding to the axial scanning position is acquired based on a surface interferometer. The axial scanning positions corresponding to each annular sub-aperture can be position information received from user input, or they can be set according to model parameters. After determining the model, the fringe density within the sub-aperture corresponding to each axial scanning position is calculated, the fringe density level within the sub-aperture boundary is set, and the scanning position is selected to ensure that the fringe density does not exceed the set value and that the sub-apertures are joined.

[0091] Building such Figure 2 The aspherical surface shape measurement model shown is based on annular sub-aperture splicing. This aspherical surface shape measurement model includes a surface shape interferometer, a length measuring interferometer, a transmission spherical mirror, and a workpiece stage. The surface shape interferometer, combined with the transmission spherical mirror, can realize the interferometric measurement of spherical and aspherical optical elements. The workpiece stage is used to load the mirror under test and drive the mirror under test to realize axial movement and scanning measurement. The length measuring interferometer can realize high-precision positioning of the workpiece stage. Through the workpiece stage and the length measuring interferometer, the precise motion control of the mirror under test can be realized.

[0092] Based on the measurement system, a measurement model is constructed, the axial scanning position corresponding to each sub-aperture is calculated, and the mask region of each annular sub-aperture is defined, ensuring that the divided annular sub-apertures have no overlapping areas. The lateral coordinates of each measurement point within the mask region of each annular sub-aperture on the mirror under test are calculated.

[0093] The workpiece stage of the control measurement system moves the mirror under test to the calculated scanning positions along each axis, and the corresponding interferograms are acquired through the information acquisition module of the measurement system. Based on the workpiece stage moving the aspherical mirror under test until the focal point of the standard spherical wave falls precisely on the vertex of the aspherical mirror, and zero-position interference fringes are observed in the image acquired by the surface shape interferometer, the aspherical mirror under test is moved to the cat's eye position, with the axial position of the cat's eye position used as the reference position. Using the cat's eye position as the reference position, according to the calculated sub-aperture axial scanning position, the precise movement of the aspherical mirror under test is controlled by the movement control of the workpiece stage and the precise axial positioning of the length measuring interferometer, moving the aspherical mirror to the corresponding axial scanning position. The interferogram of the aspherical mirror under test at the corresponding axial scanning position is acquired through the surface shape interferometer.

[0094] In one specific implementation, phase adjustment is performed on the interferogram within each annular sub-aperture mask region to determine the wrapped phase value of each phase detection point; the wavefront phase value of each phase detection point is obtained by unwrapping based on a preset phase unwrapping algorithm and the wrapped phase value of each phase detection point.

[0095] Within each annular sub-aperture mask region, the interferogram is demodulated accordingly. Based on the multi-step phase-shifting interferogram, the wrapping phase value of each phase measurement point is calculated using a multi-step phase-shifting algorithm. Within each annular sub-aperture mask region, the wavefront phase value of each phase measurement point is calculated based on the wrapping phase value and the unwrapping algorithm.

[0096] Step 2): Calculate the residual between the wavefront phase value of each phase detection point and the wavefront phase value under ideal conditions to obtain the phase measurement value of each phase measurement point in each annular sub-aperture region.

[0097] Within each annular sub-aperture mask region, the residual between the wavefront phase value of each phase measurement point and the wavefront phase value under ideal conditions (which can be calculated based on the design parameters of the aspherical mirror to be tested) is calculated to obtain the phase measurement value of each phase measurement point within each annular sub-aperture region.

[0098] In one specific implementation, the annular sub-apertures provided in this embodiment have no overlapping regions. By setting each annular sub-aperture to have no overlapping regions, the number of scans can be reduced, and the dependence on overlapping sub-aperture regions can be decreased, thereby improving measurement efficiency.

[0099] The method for determining the surface shape processing error of the aspherical mirror provided in this embodiment addresses the problem of mechanical adjustment errors introducing higher-order aberrations into the measurement results during the surface shape measurement of large-aperture, high-asphericity aspherical optical elements. It uses Zernike polynomials containing higher-order terms to fit and calculate the measurement error. To address the coupling problem between surface shape processing error and measurement error, it uses a global fitting calculation with a circular Zernike polynomial for the entire aperture and the circular Zernike polynomials for each annular sub-aperture, simultaneously obtaining the fitting results for both the surface shape processing error and the measurement error of each sub-aperture, thus decoupling them. Furthermore, to address the difficulty in obtaining the optimal solution for the underdetermined problem in global stitching, L1 regularization constraints are used to calculate the optimal result. This technical solution improves the surface shape measurement accuracy of aspherical optical elements by achieving the measurement of higher-order aberrations and the decoupling of errors. Simultaneously, this technical solution eliminates the need for sub-aperture overlap, reducing the number of scans and improving measurement efficiency.

[0100] For example, suppose the laser source wavelength of the surface interferometer in the measurement system is λ = 633 nm; the aspherical mirror to be tested is a concave mirror with a diameter of 92 mm, a vertex radius of curvature of 350 mm, and a conic constant of -2.5. Based on the measurement system, a measurement model is constructed, the axial scanning position corresponding to each sub-aperture is calculated, and the mask regions for each annular sub-aperture are defined, ensuring that the defined annular sub-apertures have no overlapping areas. During the interferometric measurement process, the optical path difference between the zero position at the center of the annular sub-aperture and the edge of the sub-aperture is set to be < 0.5λ. According to the calculation, there are a total of 6 axial scanning positions and annular sub-apertures; the 1st to 6th axial scanning positions are 350.0000mm, 350.7474mm, 352.2262mm, 353.7106mm, 355.1918mm, 356.6751mm and 357.5088mm respectively; the normalized radii of the inner and outer edges of the 1st to 6th annular sub-apertures are [0.0000, 0.3245], [0.3245, 0.4310], [0.4310, 0.6298], [0.6298, 0.7701], [0.7701, 0.8896], [0.8896, 0.9952] and [0.9952, 1.0000]. Calculate the lateral coordinates of the positions on the mirror under test corresponding to each measurement point within each annular sub-aperture mask area.

[0101] The mirror under test is moved to the cat's eye position using the workpiece stage as a reference position, and the axial position of the cat's eye position is defined as 0mm. Based on the reference position, the mirror under test is moved to the corresponding axial scanning positions, and the corresponding interferograms are acquired and compared with those obtained from other data. Figure 3 The image shows the interferograms acquired by the surface interferometer when the mirror under test is located at various axial scanning positions.

[0102] Based on the acquired interferograms and the calculated annular sub-aperture mask region, phase demodulation and unwrapping calculations are performed on the interferograms within the mask region. The residuals are then calculated by comparing these residuals with the wavefront phase values ​​under ideal conditions, yielding the phase measurements at each phase measurement point within the annular sub-aperture region. A global optimization function is constructed, and based on the calculated lateral coordinates and phase measurements of the measurement points, a global optimization fitting calculation is performed to obtain the calculated results of the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients for each sub-aperture. See [reference needed]. Figure 4a The graph showing the variation curve of the circular Zernike polynomial coefficients of the full-diameter surface machining error and Figure 4b The graph shows the variation curves of the annular Zernike polynomial coefficients for the aberration terms of the measurement error of each annular sub-aperture. The calculation results for the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients for each sub-aperture in this example are as follows: Figure 4a and Figure 4b As shown.

[0103] See also Figure 5 The diagram shown illustrates the measurement results of the full-aperture surface shape processing error of the mirror under test. During the scanning measurement process, the annular Zernike aberration term corresponding to the measurement error is subtracted from the phase measurement values ​​of all measurement points to complete the stitching and obtain the measurement results of the phase value of the full-aperture surface shape processing error of the mirror under test.

[0104] Based on the foregoing embodiments, this embodiment provides an example of using the aforementioned method for determining the full-aperture surface shape processing error of aspherical mirrors to perform scanning measurement of aspherical surface shape. The specific steps are as follows:

[0105] Step 201: Construct an aspherical surface shape measurement system based on annular sub-aperture splicing;

[0106] Step 202: Construct a measurement model based on the measurement system, calculate the axial scanning position corresponding to each sub-aperture, divide and determine the mask area of ​​each annular sub-aperture, so that the divided annular sub-apertures have no overlapping areas; calculate the lateral coordinates on the mirror to be tested (i.e. the aspherical mirror to be tested) corresponding to each measurement point in each annular sub-aperture mask area.

[0107] Step 203: The workpiece stage of the control measurement system moves the mirror under test to the calculated scanning positions of each axis. The corresponding interferogram is acquired through the information acquisition module of the measurement system. In each annular sub-aperture mask area, the interferogram is demodulated and unwrapped to obtain the wavefront phase value of each phase measurement point. The residual between the wavefront phase value of each phase measurement point and the wavefront phase value under ideal conditions is calculated to obtain the phase measurement value of each phase measurement point in each annular sub-aperture area.

[0108] Sub-step 301: Move the mirror under test by the workpiece stage until the focal point of the standard spherical wave falls exactly on the vertex of the mirror under test and observe the zero-position interference fringes in the image acquired by the surface interferometer. That is, move the mirror under test to the cat's eye position and use the axial position of the cat's eye position as the reference position.

[0109] Sub-step 302: Using the cat's eye position as the reference position, and based on the calculated sub-aperture axial scanning position, the precise movement of the mirror under test is controlled by the movement control of the workpiece stage and the precise axial positioning of the length measuring interferometer, so as to move the mirror under test to the corresponding axial scanning position.

[0110] Sub-step 303: Acquire the interferogram of the mirror under test at the corresponding axial scanning position using a surface interferometer;

[0111] Sub-step 304: For the acquired interferogram and the calculated annular sub-aperture mask region, perform phase demodulation and unwrapping calculations on the interferogram within the mask region, and calculate the residual with the wavefront phase value under ideal conditions to obtain the phase measurement value of each phase measurement point within the annular sub-aperture region.

[0112] Sub-step 305: Repeat sub-steps 302 to 304 until the phase measurement values ​​of all measurement points in the annular sub-aperture under all axial scanning positions are obtained.

[0113] Step 204: Construct a global optimization function: using the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables; using the sum of the fitting results of the full-aperture and each sub-aperture Zernike polynomials and the squared error of the phase measurement values ​​of all phase measurement points in all sub-aperture regions as the loss function; using the L1 regularization term of the independent variables as a constraint; and adding the loss function and the L1 regularization term to construct the global optimization function.

[0114] Step 205 involves minimizing the global optimization function to obtain the calculated coefficients of the full-aperture circular Zernike polynomial and the coefficients of the annular Zernike polynomials for each sub-aperture. By subtracting the aberration terms belonging to the measurement error from the phase measurement values ​​at all phase measurement points during the scanning measurement process, the measurement results of the phase values ​​of the full-aperture surface shape processing error of the aspherical mirror under test are obtained.

[0115] Corresponding to the method for determining the full-aperture surface shape machining error of aspherical mirrors provided in the above embodiments, this invention provides a device for determining the full-aperture surface shape machining error of aspherical mirrors. (See attached image) Figure 6 The diagram shows a device for determining the surface shape machining error of an aspherical mirror across its entire aperture. The device includes the following modules:

[0116] The acquisition module 61 is used to acquire the phase measurement values ​​of each phase measurement point within each annular sub-aperture region of the aspherical mirror to be tested;

[0117] The first calculation module 62 is used to construct a global optimization function with the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables, and to calculate the optimal solution of the independent variables of the global optimization function.

[0118] The second calculation module 63 is used to obtain the aberration terms corresponding to each phase measurement point when the independent variable takes the optimal solution, calculate the difference between the phase measurement value of each phase measurement point and the corresponding aberration term, and obtain the phase value of the full aperture surface shape processing error of the aspherical mirror to be tested.

[0119] The device for determining the surface shape processing error of the aspherical mirror provided in this embodiment constructs a global optimization function using the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables, calculates the optimal solution of the global optimization function, and calculates the phase value of the full-aperture surface shape processing error of the aspherical mirror to be tested. This decouples the surface shape processing error of the aspherical mirror, improves the surface shape measurement accuracy of the aspherical optical element, and enhances the accuracy and precision of surface shape measurement.

[0120] The device provided in this embodiment has the same implementation principle and technical effect as the aforementioned embodiments. For the sake of brevity, any parts not mentioned in the device embodiment can be referred to the corresponding content in the aforementioned method embodiment.

[0121] Corresponding to the methods and apparatus provided in the foregoing embodiments, this invention also provides an aspherical surface shape measurement system, which includes: a measurement model and a surface shape measurement controller. The measurement model includes a surface shape interferometer and a workpiece stage, such as... Figure 2 As shown, the measurement model also includes a length measuring interferometer and a transmission spherical mirror.

[0122] The surface shape measurement controller includes a processor and a storage device; the storage device stores a computer program that executes the methods provided in the above embodiments when run by the processor.

[0123] This invention provides a computer-readable medium storing computer-executable instructions. When these computer-executable instructions are invoked and executed by a processor, they cause the processor to implement the methods described in the above embodiments.

[0124] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the system described above can be referred to the corresponding process in the foregoing embodiments, and will not be repeated here.

[0125] Furthermore, in the description of the embodiments of the present invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention based on the specific circumstances.

[0126] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0127] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0128] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for determining the surface shape machining error of an aspherical mirror with full aperture, characterized in that, include: Acquire the phase measurement values ​​of each phase measurement point within each annular sub-aperture region of the aspherical mirror to be tested; A global optimization function is constructed using the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables, and the optimal solution of the independent variables of the global optimization function is calculated. Obtain the aberration terms corresponding to each phase measurement point when the independent variable takes the optimal solution, calculate the difference between the phase measurement value of each phase measurement point and the corresponding aberration term, and obtain the phase value of the full aperture surface shape processing error of the aspherical mirror to be tested; The construction of a global optimization function using the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables includes: The Zernike polynomial fitting results for the full aperture and each of the sub-apertures are obtained by fitting the full aperture and each of the sub-apertures using the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients. The loss function is the sum of the Zernike polynomial fitting results of the full aperture and each of the sub-apertures and the square error of the phase measurement values ​​of all the phase measurement points. The global optimization function is obtained by calculating the sum of the loss function and the regularization term of the independent variable.

2. The method according to claim 1, characterized in that, The calculation of the optimal solution of the independent variable of the global optimization function includes: The global optimization function is minimized using the regularization term of the independent variable as a constraint to obtain the optimal solutions for the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each of the sub-apertures.

3. The method according to claim 1, characterized in that, The acquisition of phase measurement values ​​at each phase measurement point within each annular sub-aperture region of the aspherical mirror to be tested includes: Interference patterns of each of the aforementioned annular sub-aperture mask regions are acquired, and wavefront phase values ​​of each of the aforementioned phase measurement points are determined based on the interferograms of each of the aforementioned annular sub-aperture mask regions. The residual between the wavefront phase value of each phase measurement point and the wavefront phase value under ideal conditions is calculated to obtain the phase measurement value of each phase measurement point within each annular sub-aperture region.

4. The method according to claim 3, characterized in that, The determination of the wavefront phase value of each phase measurement point based on the interferogram of each of the annular sub-aperture mask regions includes: Phase adjustment is performed on the interferogram within each of the annular sub-aperture mask regions to determine the wrap-around phase value of each of the phase measurement points; The wavefront phase value of each phase measurement point is obtained based on the preset phase unwrapping algorithm and the unwrapping calculation of the wrapped phase value of each phase measurement point.

5. The method according to claim 3, characterized in that, The acquisition of interferograms of each of the annular sub-aperture mask regions includes: Obtain the axial scanning position corresponding to each annular sub-aperture of the aspherical mirror to be tested; The aspherical mirror to be tested is moved to the corresponding axial scanning position, and the interferogram of the aspherical mirror to be tested at the axial scanning position corresponding to each of the annular sub-apertures is acquired based on the surface interferometer.

6. The method according to any one of claims 1-5, characterized in that, Each of the described annular sub-apertures has no overlapping area.

7. A device for determining the surface shape machining error of an aspherical mirror with full aperture, characterized in that, include: The acquisition module is used to acquire the phase measurement values ​​of each phase measurement point within each annular sub-aperture region of the aspherical mirror to be tested; The first calculation module is used to construct a global optimization function with the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture as independent variables, and to calculate the optimal solution of the independent variables of the global optimization function. The second calculation module is used to obtain the aberration terms corresponding to each phase measurement point when the independent variable takes the optimal solution, calculate the difference between the phase measurement value of each phase measurement point and the corresponding aberration term, and obtain the phase value of the full aperture surface shape processing error of the aspherical mirror to be tested. The first calculation module is further configured to obtain the Zernikal fitting results of the full aperture and each of the sub-apertures based on the full-aperture circular Zernikal polynomial coefficients and the annular Zernikal polynomial coefficients of each of the sub-apertures; use the superposition value of the Zernikal polynomial fitting results of the full aperture and each of the sub-apertures and the square error of the phase measurement values ​​of all the phase measurement points as a loss function; calculate the sum of the loss function and the regularization term of the independent variable to obtain the global optimization function.

8. A non-spherical surface shape measurement system, characterized in that, include: A measurement model and a surface shape measurement controller, wherein the measurement model includes a surface shape interferometer and a workpiece stage, and the surface shape measurement controller includes a processor and a storage device; The storage device stores a computer program that, when executed by the processor, performs the method as described in any one of claims 1 to 6.

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