Method and device for determining full-aperture surface shape machining error of aspherical mirror

Abstract

The invention provides a method and a device for determining a full-aperture surface shape processing error of an aspherical mirror. The method comprises the following steps: acquiring a phase measurement value of each phase measurement point in each annular sub-aperture region of a to-be-detected aspherical mirror; constructing a global optimization function by taking the full-aperture circular Zernike polynomial coefficient and each sub-aperture annular Zernike polynomial coefficient as independent variables, and calculating an independent variable optimal solution of the global optimization function; and aberration terms corresponding to the phase measurement points when the optimal solutions of the independent variables are obtained, the difference values between the phase measurement values of the phase measurement points and the corresponding aberration terms are calculated, and the full-aperture surface shape machining error phase value of the to-be-detected aspherical mirror is obtained. According to the invention, decoupling of the surface shape processing error of the aspheric mirror is realized, the surface shape measurement precision of the aspheric optical element is improved, and the surface shape measurement accuracy and precision are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of optical interference measurement, and in particular to a method and device for determining full-aperture surface machining errors of an aspherical mirror. Background Art

[0002] Aspheric optical elements are of great value in various cutting-edge technologies and industrial manufacturing fields, and there is an increasingly urgent need for their surface shape detection technology. At present, surface shape detection technology usually uses interferometric measurement of annular sub-aperture splicing for detection. During the scanning measurement process, the workpiece stage of the measurement system drives the mirror to be measured to perform eccentricity, pitch / yaw adjustment and axial scanning measurement. In this process, mechanical adjustment errors will inevitably produce corresponding measurement errors in each annular sub-aperture.

[0003] In the existing stitching method, the measurement error is calculated by fitting the phase of the overlapping area of ​​the annular sub-aperture and then subtracted to eliminate the influence of the mechanical adjustment error. However, for the measurement of aspheric mirrors with large apertures and large asphericity, slight mechanical adjustment errors can also cause a large degree of measurement error in the sub-aperture measurement results, and manifest as various first-order and high-order aberrations such as coma, astigmatism, and spherical aberration, which are not effectively handled in the existing stitching method; in addition, the measurement errors generated that vary with the sub-aperture include various types of high-order aberrations, which may have common characteristics with the surface processing errors of the mirror to be measured and couple with the surface processing errors. The fitting calculation and aberration subtraction in the existing stitching method are difficult to eliminate the influence of the measurement error, resulting in a decrease in the accuracy and precision of the surface measurement. Summary of the invention

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

[0005] In order to achieve the above purpose, the technical solution adopted by the embodiment of the present invention is as follows:

[0006] In a first aspect, an embodiment of the present invention provides a method for determining a full-aperture surface shape processing error of an aspheric mirror, comprising:

[0007] Obtaining a phase measurement value of each phase measurement point within each annular sub-aperture region of the aspheric mirror to be detected;

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

[0009] The aberration term corresponding to each phase measurement point when the independent variable takes the optimal solution is obtained, and the difference between the phase measurement value of each phase measurement point and the corresponding aberration term is calculated to obtain the full-aperture surface processing error phase value of the aspheric mirror to be detected.

[0010] Further, an embodiment of the present invention provides a first possible implementation manner of the first aspect, wherein the global optimization function is constructed with the full-aperture circular Zernike polynomial coefficients and the sub-aperture annular Zernike polynomial coefficients as independent variables, including:

[0011] Establishing a loss function based on the full-aperture circular Zernike polynomial coefficients, the sub-aperture annular Zernike polynomial coefficients and the phase measurement value of each phase measurement point;

[0012] The sum of the loss function and the regularization term of the independent variable is calculated to obtain the global optimization function.

[0013] Further, an embodiment of the present invention provides a second possible implementation manner of the first aspect, wherein the loss function is established based on the full-aperture circular Zernike polynomial coefficients, the sub-aperture annular Zernike polynomial coefficients and the phase measurement value of each phase measurement point, including:

[0014] Based on the full-aperture circular Zernike polynomial coefficients and the sub-aperture annular Zernike polynomial coefficients, fitting results of the full-aperture and each sub-aperture Zernike polynomial are obtained;

[0015] The square error between the superposition value of the Zernike polynomial fitting results of the full aperture and each of the sub-apertures and the phase measurement values ​​of all the phase measurement points is used as the loss function.

[0016] Further, an embodiment of the present invention provides a third possible implementation manner 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 by taking the regularization term of the independent variable as a constraint to obtain the optimal solution of the full-aperture circular Zernike polynomial coefficients and the sub-aperture annular Zernike polynomial coefficients.

[0018] Further, the embodiment of the present invention provides a fourth possible implementation manner of the first aspect, wherein the obtaining of the phase measurement value of each phase measurement point within each annular sub-aperture region of the aspheric mirror to be detected includes:

[0019] Collecting interference patterns of each of the annular sub-aperture mask regions, and determining a wavefront phase value of each of the phase detection points based on the interference patterns of each of the annular sub-aperture mask regions;

[0020] The residual of the wavefront phase value of each phase detection point and the wavefront phase value in an ideal state is calculated to obtain the phase measurement value of each phase measurement point in each annular sub-aperture area.

[0021] Further, an embodiment of the present invention provides a fifth possible implementation of the first aspect, wherein the determining the wavefront phase value of each phase detection point based on the interference pattern of each annular sub-aperture mask area includes:

[0022] Performing phase adjustment on the interference pattern in each of the annular sub-aperture mask regions to determine a wrapping phase value of each of the phase detection points;

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

[0024] Further, the embodiment of the present invention provides a sixth possible implementation of the first aspect, wherein the collecting the interference pattern of each of the annular sub-aperture mask regions includes:

[0025] Acquire the axial scanning position corresponding to each annular sub-aperture of the aspheric mirror to be detected;

[0026] The aspheric mirror to be detected is moved to the corresponding axial scanning position, and the interference pattern of the aspheric mirror to be detected at the axial scanning position corresponding to each annular sub-aperture is collected based on the surface interferometer.

[0027] Furthermore, an embodiment of the present invention provides a seventh possible implementation of the first aspect, wherein the annular sub-apertures have no overlapping area.

[0028] In a second aspect, an embodiment of the present invention further provides a device for determining a full-aperture surface shape processing error of an aspherical mirror, comprising:

[0029] An acquisition module, used for acquiring a phase measurement value of each phase measurement point in each annular sub-aperture region of the aspheric mirror to be detected;

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

[0031] The second calculation module is used to obtain the aberration term 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 full-aperture surface processing error phase value of the aspheric mirror to be tested.

[0032] In a third aspect, an embodiment of the present invention provides a non-spherical surface shape measurement system, including: a measurement model and a surface shape measurement controller, 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, and when the computer program is executed by the processor, the method according to any one of the first aspects is executed.

[0034] The embodiment of the present invention provides a method and device for determining the full-aperture surface processing error of an aspheric mirror, the method comprising: obtaining the phase measurement value of each phase measurement point in each annular sub-aperture region of the aspheric mirror to be detected; constructing 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 calculating the independent variable optimal solution of the global optimization function; obtaining the aberration term corresponding to each phase measurement point when the independent variable takes the optimal solution, calculating the difference between the phase measurement value of each phase measurement point and the corresponding aberration term, and obtaining the full-aperture surface processing error phase value of the aspheric mirror to be detected. The present invention realizes the decoupling of the surface processing error of the aspheric mirror by constructing 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 calculating the optimal solution of the global optimization function, thereby improving the surface measurement accuracy of the aspheric optical element, and improving the accuracy and precision of the surface measurement.

[0035] Other features and advantages of the embodiments of the present invention will be described in the following description, or some features and advantages can be inferred or determined without doubt from the description, or can be learned by implementing the above-mentioned techniques of the embodiments of the present invention.

[0036] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0038] Figure 1 A flow chart of a method for determining a full-aperture surface shape processing error of an aspheric mirror provided by an embodiment of the present invention is shown;

[0039] Figure 2 An aspheric surface shape measurement model based on annular sub-aperture splicing provided by an embodiment of the present invention is shown;

[0040] Figure 3 The interference diagram when the mirror to be measured is located at various axial scanning positions is shown, which is collected by a surface interferometer provided by an embodiment of the present invention;

[0041] Figure 4a A curve diagram showing a change in coefficients of a circular Zernike polynomial of a full-aperture surface machining error provided by an embodiment of the present invention is shown;

[0042] Figure 4b A curve diagram showing a change in annular Zernike polynomial coefficients of each annular sub-aperture measurement error aberration term provided by an embodiment of the present invention is shown;

[0043] Figure 5 A schematic diagram showing the measurement results of the full-aperture surface machining error of a mirror to be measured provided by an embodiment of the present invention is shown;

[0044] Figure 6 A schematic structural diagram of a device for determining full-aperture surface shape processing error of an aspheric mirror provided by an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution of the present invention will be described below in conjunction with the drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments.

[0046] At present, aspheric optical components have important value in various cutting-edge science and technology and industrial manufacturing fields, and there is an increasingly urgent need for the detection technology of their surface shape. The interferometric measurement technology based on annular subaperture splicing is widely used in the measurement of large-diameter, large-asphericity rotationally symmetric aspheric optical components due to its simple measurement structure.

[0047] During the scanning measurement process, the workpiece stage of the measurement system drives the mirror to be measured to perform eccentricity, pitch / yaw adjustment and axial scanning measurement. During this process, mechanical adjustment errors are inevitable and will produce corresponding measurement errors in each annular sub-aperture, which is reflected in the various aberration terms in the Zernike polynomial fitting results of the annular sub-aperture phase measurement value. In the traditional stitching method, the measurement error is fitted and calculated for the phase of the overlapping area of ​​the annular sub-aperture and then subtracted to eliminate the influence of mechanical adjustment errors. However, for the measurement of large-aperture and large-asphericity aspheric mirrors, slight mechanical adjustment errors can also cause large measurement errors in the sub-aperture measurement results, and manifest as various first-order and higher-order aberrations such as coma, astigmatism, and spherical aberration, which have no effective solution in the traditional stitching method; in addition, the measurement errors generated with different sub-apertures include various types of high-order aberrations, which may have common characteristics with the surface processing errors of the mirror to be measured and thus couple with the surface processing errors. It is difficult for traditional stitching methods to eliminate the influence of measurement errors through fitting calculations and aberration subtraction, resulting in a decrease in measurement accuracy and precision. This is the difficulty of current aspheric surface measurement technology and annular sub-aperture stitching technology.

[0048] Existing aspheric sub-aperture stitching technologies, such as fitting and calculating the overlapping areas of the annular sub-apertures one by one, and only deducting translation, tilt, and defocus aberrations as processing for mechanical adjustment errors; using the overlapping areas for fitting calculations, and only fitting and processing translation, tilt, and defocus aberrations; a more accurate surface shape fitting method based on annular Zernike polynomials; all do not consider high-order aberrations. The current aspheric sub-aperture stitching technology does not solve the influence of high-order aberrations caused by mechanical adjustment errors in the surface shape measurement of aspheric optical elements with large apertures and large asphericities, as well as the problem of reduced measurement accuracy and precision caused by the coupling of measurement errors and surface shape processing errors, which restricts the development of aspheric surface shape detection technology.

[0049] In order to improve the above problems, an embodiment of the present invention provides a method and device for determining the full-aperture surface shape processing error of an aspheric mirror. The embodiment of the present invention is introduced in detail below.

[0050] This embodiment provides a method for determining the full-aperture surface shape processing error of an aspherical mirror, see Figure 1 The flowchart of the method for determining the full-aperture surface shape processing error of the aspheric mirror shown in the figure mainly includes the following steps:

[0051] Step S102, obtaining the phase measurement value of each phase measurement point in each annular sub-aperture region of the aspheric mirror to be tested;

[0052] A non-spherical surface shape measurement system based on annular sub-aperture splicing is built, a measurement model is constructed according to the measurement system, each annular sub-aperture mask area is divided and determined, the interference pattern in each annular sub-aperture mask area is collected by the information acquisition module of the measurement system, and the phase measurement value of each phase measurement point in each annular sub-aperture mask area is determined according to the interference pattern. In one embodiment, the interference pattern can be phase demodulated and unwrapped to obtain the wavefront phase value of each phase measurement point, and the residual is calculated with the wavefront phase value under the ideal state to obtain the phase measurement value of each phase measurement point in each annular sub-aperture area.

[0053] Step S104, constructing a global optimization function with full-aperture circular Zernike polynomial coefficients and each sub-aperture annular Zernike polynomial coefficient as independent variables, and calculating the optimal solution of the independent variables of the global optimization function;

[0054] The loss function is determined with the full-aperture circular Zernike polynomial coefficients and the sub-aperture annular Zernike polynomial coefficients as independent variables, and a global optimization function is constructed based on the loss function and the corresponding constraints.

[0055] The global optimization function is minimized to obtain the optimal solution of the independent variable, that is, the optimal solution of the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture.

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

[0057] Step S106, obtaining the aberration term corresponding to each phase measurement point when the independent variable takes the optimal solution, calculating the difference between the phase measurement value of each phase measurement point and the corresponding aberration term, and obtaining the full-aperture surface processing error phase value of the aspheric mirror to be tested.

[0058] Based on the optimal solution of the independent variable, the annular Zernike polynomial corresponding to each measuring point in the annular subaperture is determined to obtain the aberration term corresponding to each phase measurement point. When the independent variable takes the optimal solution, the terms of the annular Zernike polynomial corresponding to each measuring point in the annular subaperture are obtained, and the aberration term belonging to the measurement error is obtained from the fitting result of the polynomial.

[0059] The aberration terms belonging to the measurement error in the annular Zernike polynomial corresponding to the phase measurement value of each phase measurement point and the position of each measurement point in the annular sub-aperture are calculated to obtain the measurement result of the full-aperture surface processing error phase value of the aspheric mirror to be measured.

[0060] By correspondingly deducting the aberration terms belonging to the measurement error in the fitting results of the annular Zernike polynomials of each sub-aperture during the process of scanning and measuring the phase measurement values ​​of all phase measurement points, the measurement results of the full-aperture surface processing error phase values ​​of the aspheric mirror to be measured are obtained.

[0061] The method for determining the full-aperture surface shape processing error of the above-mentioned aspheric mirror provided in this embodiment constructs a global optimization function by taking the full-aperture circular Zernike polynomial coefficients and the sub-aperture annular Zernike polynomial coefficients as independent variables, calculates the optimal solution of the global optimization function, and calculates the full-aperture surface shape processing error phase value of the aspheric mirror to be tested, thereby realizing the decoupling of the surface shape processing error of the aspheric mirror, improving the surface shape measurement accuracy of the aspheric optical element, and improving the accuracy and precision of the surface shape measurement.

[0062] In one embodiment, this embodiment provides an implementation method for constructing a global optimization function using full-aperture circular Zernike polynomial coefficients and each sub-aperture annular Zernike polynomial coefficient as independent variables, which can be specifically performed with reference to the following steps:

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

[0064] In a specific implementation, the Zernike polynomial fitting results of the full aperture and each sub-aperture are obtained based on the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture; the superposition value of the Zernike polynomial fitting results of 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 annular Zernike polynomial of each sub-aperture are taken as independent variables, and the square error of the superposition value of the fitting results of the full-aperture and each sub-aperture Zernike polynomial and the phase measurement values ​​of all phase measurement points in all sub-aperture areas is taken 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 calculation formula of the global optimization function f(X) can be:

[0068] Among them, 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 measurement values ​​of all phase measurement points, and A satisfies:

[0069]

[0070] Each element in the first column of A0k satisfy:

[0071]

[0072] Among them, each element A 0kij It is the various terms of the circular Zernike polynomial corresponding to the position of each measuring point within the full aperture range. When calculating the normalized radius, the full aperture radius of the aspheric mirror to be measured is taken as the maximum radius. 0kij is the i-th circular Zernike term corresponding to the j-th measurement point of the k-th annular subaperture; there are K annular subapertures in the measurement process, among which the k-th annular subaperture has J measurement points, and a total of I Zernike terms are fitted in the fitting process.

[0073] Each element A that appears starting from the second column in A k satisfy:

[0074]

[0075] Among them, each element A kij A is the terms of the annular Zernike polynomial corresponding to the positions of the measurement points in the annular subaperture. When calculating the aperture ratio, the inner and outer radius values ​​are taken as the inner and outer radius of the annular subaperture; kij is the i-th annular Zernike term corresponding to the j-th measurement point within the l-th annular subaperture; there are K annular subapertures in the measurement process, among which, there are J measurement points in the k-th annular subaperture, and I Zernike terms are fitted in the fitting process;

[0076] X in f(X) satisfies:

[0077]

[0078] Each element X in X k satisfy:

[0079]

[0080] Among them, each element X ki When k = 0, X ki is the i-th circular Zernike term coefficient within the full aperture range; when k = 1,…,K, X ki is the coefficient of the i-th annular Zernike term of the k-th annular subaperture, and a total of I Zernike terms are fitted in the fitting process.

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

[0082]

[0083] Each element l in l k satisfy:

[0084]

[0085] Among them, each element l kj is the phase measurement value of the jth measurement point within the kth annular subaperture; there are K annular subapertures in the measurement process, and there are J measurement points in the kth annular subaperture.

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

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

[0088] In one implementation, this embodiment provides an implementation for obtaining the phase measurement value of each phase measurement point in each annular sub-aperture region of the aspheric mirror to be detected, which can be specifically performed with reference to the following steps:

[0089] Step 1): collecting interference patterns of each annular sub-aperture mask area, and determining the wavefront phase value of each phase detection point based on the interference patterns of each annular sub-aperture mask area;

[0090] In a specific implementation, the axial scanning position corresponding to each annular sub-aperture of the aspheric mirror to be detected is obtained; the aspheric mirror to be detected is moved to the corresponding axial scanning position, and the interference pattern of the aspheric mirror to be detected at the axial scanning position corresponding to each annular sub-aperture is collected based on the surface interferometer. The axial scanning position corresponding to each annular sub-aperture can be the position information received from the user, or can be set according to the model parameters. After the model is determined, the fringe density in 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 the sub-aperture is joined.

[0091] Build as Figure 2 The aspheric surface shape measurement model based on annular sub-aperture splicing is shown, which 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 interference measurement of spherical optical elements and aspheric optical elements; the workpiece stage is used to load the mirror to be measured and drive the mirror to be measured to achieve axial movement and scanning measurement, the length measuring interferometer can achieve high-precision positioning of the workpiece stage, and the precise motion control of the mirror to be measured can be achieved through the workpiece stage and the length measuring interferometer.

[0092] A measurement model is constructed according to the measurement system, the axial scanning position corresponding to each sub-aperture is calculated, the mask area of ​​each annular sub-aperture is divided and determined, wherein the divided annular sub-apertures have no overlapping areas, and the lateral coordinates on the mirror to be measured corresponding to each measurement point in each annular sub-aperture mask area are calculated.

[0093] The workpiece stage of the control measurement system drives the mirror to be tested to move to each calculated axial scanning position, and the corresponding interference pattern is collected by the information collection module of the measurement system. Based on the workpiece stage driving the aspheric mirror to be tested to move until the focus of the standard spherical wave just falls on the vertex of the aspheric mirror to be tested, and zero-position interference fringes are observed in the image collected by the surface interferometer, the aspheric mirror to be tested is moved to the cat's eye position, and the axial position of the cat's eye position is used as the reference position; the cat's eye position is used as the reference position, according to the calculated sub-aperture axial scanning position, the precise movement of the aspheric mirror to be tested is controlled by the movement control of the workpiece stage and the precise axial positioning of the length measuring interferometer, and the aspheric mirror to be tested is moved to the corresponding axial scanning position; the interference pattern of the aspheric mirror to be tested at the corresponding axial scanning position is collected by the surface interferometer.

[0094] In a specific implementation, the interference pattern is phase-adjusted in each annular sub-aperture mask area to determine the wrapped phase value of each phase detection point; the wavefront phase value of each phase detection point is obtained by unwrapping calculation based on a preset phase unwrapping algorithm and the wrapped phase value of each phase detection point.

[0095] In each annular sub-aperture mask area, the interference pattern is phase demodulated accordingly, and the wrapped phase value of each phase measurement point is calculated based on the multi-step phase shifting interference pattern and the multi-step phase shifting algorithm; in each annular sub-aperture mask area, the wavefront phase value of each phase measurement point is calculated based on the wrapped 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 the ideal state, and obtain the phase measurement value of each phase measurement point in each annular sub-aperture area.

[0097] In each annular sub-aperture mask area, the residual is calculated between the wavefront phase value of each phase measurement point and the wavefront phase value in the ideal state (which can be calculated based on the design parameters of the aspheric mirror to be tested) to obtain the phase measurement value of each phase measurement point in each annular sub-aperture area.

[0098] In a specific implementation, the annular sub-apertures provided in this embodiment have no overlapping regions. By setting the annular sub-apertures to have no overlapping regions, there is no need for sub-aperture overlap, which can reduce the number of scans and reduce the dependence on the sub-aperture overlap region, thereby improving measurement efficiency.

[0099] The method for determining the full-aperture surface shape processing error of the above-mentioned aspheric mirror provided in this embodiment is aimed at the problem that the mechanical adjustment error introduces high-order aberrations in the measurement results during the surface shape measurement of large-aperture and large-asphericity aspheric optical elements. The measurement error is fitted and calculated using Zernike polynomials containing high-order terms; for the coupling problem of surface shape processing error and measurement error, full-aperture circular Zernike polynomials and circular Zernike polynomials of each annular sub-aperture are used for global fitting calculation, and the fitting results of surface shape processing error and each sub-aperture measurement error are obtained at the same time, so as to achieve the decoupling of the two; in addition, for the problem that it is difficult to obtain the optimal solution for the underdetermined problem in global splicing, the L1 regularization term constraint is used to achieve the calculation of the optimal result. The technical solution improves the surface shape measurement accuracy of aspheric optical elements by realizing the measurement of high-order aberrations and the decoupling of errors; at the same time, the technical solution does not require sub-aperture overlap, which can reduce the number of scans and improve the measurement efficiency.

[0100] For example, assume that the wavelength of the laser light source of the surface interferometer in the measurement system is λ=633nm; the aspheric mirror to be detected is a concave mirror with a diameter of 92mm, a vertex curvature radius of 350mm, and a cone constant of -2.5. Construct a measurement model based on the measurement system, calculate the axial scanning position corresponding to each sub-aperture, and divide and determine the mask area of ​​each annular sub-aperture so that there is no overlapping area between the divided annular sub-apertures. Set the optical path difference between the zero position of the center of the annular sub-aperture and the edge of the sub-aperture to be less than 0.5λ during the interferometric measurement process. According to the calculation, there are 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] respectively. Calculate the lateral coordinates of the position on the mirror to be measured corresponding to each measuring point in each annular sub-aperture mask area.

[0101] Move the mirror to be tested to the cat's eye position as the reference position through the workpiece stage, and define the axial position of the cat's eye position as 0mm. According to the reference position, move the mirror to be tested to each corresponding axial scanning position and collect the corresponding interference pattern. Figure 3 The interference pattern collected by the surface interferometer when the mirror to be tested is located at various axial scanning positions.

[0102] Based on the collected interference pattern and the calculated annular sub-aperture mask area, the interference pattern in the mask area is phase demodulated and unwrapped, and the residual is calculated with the wavefront phase value under the ideal state to obtain the phase measurement value of each phase measurement point in the annular sub-aperture area. A global optimization function is constructed, and a global optimization fitting calculation is performed based on the calculated lateral coordinates and phase measurement values ​​of the measurement points to obtain the calculation results of the full-aperture circular Zernike polynomial coefficients and the annular Zernike polynomial coefficients of each sub-aperture. See, for example Figure 4a The circular Zernike polynomial coefficient variation curve of the full-aperture surface machining error and Figure 4b The annular Zernike polynomial coefficient variation curve of each annular sub-aperture measurement error aberration term is shown in FIG. 1 . The calculation results of the full-aperture circular Zernike polynomial coefficient and the annular Zernike polynomial coefficient of each sub-aperture in this example are shown in FIG. Figure 4a and Figure 4b shown.

[0103] See Figure 5 The schematic diagram of the measurement results of the full-aperture surface processing error of the mirror to be tested is shown. In the phase measurement values ​​of all measurement points during the scanning measurement process, the annular Zernike aberration term corresponding to the measurement error is deducted, and the splicing is completed and the measurement results of the phase value of the full-aperture surface processing error of the mirror to be tested are obtained.

[0104] On the basis of the above-mentioned embodiment, this embodiment provides an example of applying the above-mentioned method for determining the full-aperture surface shape processing error of an aspheric mirror to implement scanning measurement of an aspheric surface shape, which can be specifically performed with reference to the following steps:

[0105] Step 201, building an aspheric surface shape measurement system based on annular sub-aperture splicing;

[0106] Step 202, constructing a measurement model according to the measurement system, calculating the axial scanning position corresponding to each sub-aperture, dividing and determining each annular sub-aperture mask area so that the divided annular sub-apertures have no overlapping area; calculating the lateral coordinates on the mirror to be measured (i.e., the aspherical mirror to be tested) corresponding to each measurement point in each annular sub-aperture mask area;

[0107] Step 203, control the workpiece stage of the measurement system to drive the mirror to be measured to move to each calculated axial scanning position, and collect the corresponding interference pattern through the information acquisition module of the measurement system; in each annular sub-aperture mask area, perform corresponding phase demodulation and unwrapping calculation on the interference pattern to obtain the wavefront phase value of each phase measurement point, calculate the residual of the wavefront phase value of each phase measurement point and the wavefront phase value in the ideal state, and obtain the phase measurement value of each phase measurement point in each annular sub-aperture area;

[0108] Sub-step 301, driving the mirror to be tested to move by the workpiece stage until the focus of the standard spherical wave just falls on the vertex of the mirror to be tested and zero-position interference fringes are observed in the image collected by the surface interferometer, that is, moving the mirror to be tested to the cat's eye position, and taking 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, according to the calculated sub-aperture axial scanning position, the precise movement of the mirror to be measured is controlled by the movement control of the workpiece stage and the precise axial positioning of the length measuring interferometer, and the mirror to be measured is moved to the corresponding axial scanning position;

[0110] Sub-step 303, collecting the interference pattern of the mirror to be measured at the corresponding axial scanning position by using a surface interferometer;

[0111] Sub-step 304, performing phase demodulation and unwrapping calculation on the collected interference pattern and the annular sub-aperture mask area determined by calculation, and calculating the residual with the wavefront phase value under the ideal state to obtain the phase measurement value of each phase measurement point in the annular sub-aperture area;

[0112] Sub-step 305, repeatedly executing the above sub-steps 302 to 304 until the phase measurement values ​​of all measurement points in the annular sub-aperture at all axial scanning positions are obtained;

[0113] Step 204, constructing a global optimization function: taking the full-aperture circular Zernike polynomial coefficients and the sub-aperture annular Zernike polynomial coefficients as independent variables; taking the superposition value of the full-aperture and sub-aperture Zernike polynomial fitting results and the square error of the phase measurement values ​​of all phase measurement points in all sub-aperture regions as the loss function; taking the L1 regularization term of the independent variable as a constraint; and adding the loss function and the L1 regularization term as the constructed global optimization function;

[0114] Step 205, minimizing the global optimization function to obtain the calculation results of the full-aperture circular Zernike polynomial coefficients and the sub-aperture annular Zernike polynomial coefficients. By deducting the aberration terms belonging to the measurement error in the fitting results of the annular Zernike polynomials of each sub-aperture from the phase measurement values ​​of all phase measurement points during the scanning measurement process, the measurement result of the full-aperture surface processing error phase value of the aspheric mirror to be measured is obtained.

[0115] Corresponding to the method for determining the full-aperture surface shape processing error of the aspheric mirror provided in the above embodiment, the embodiment of the present invention provides a device for determining the full-aperture surface shape processing error of the aspheric mirror, see Figure 6 The structure diagram of a device for determining the full-aperture surface shape processing error of an aspherical mirror is shown in FIG. 1 , and the device includes the following modules:

[0116] An acquisition module 61 is used to acquire the phase measurement value of each phase measurement point in each annular sub-aperture region of the aspheric mirror to be detected;

[0117] A first calculation module 62 is used to construct a global optimization function using the full-aperture circular Zernike polynomial coefficients and the sub-aperture annular Zernike polynomial coefficients as independent variables, and 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 term 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 full-aperture surface processing error phase value of the aspheric mirror to be tested.

[0119] The device for determining the full-aperture surface shape processing error of the above-mentioned aspheric mirror provided in this embodiment constructs a global optimization function by taking the full-aperture circular Zernike polynomial coefficients and the sub-aperture annular Zernike polynomial coefficients as independent variables, calculates the optimal solution of the global optimization function, and calculates the full-aperture surface shape processing error phase value of the aspheric mirror to be tested, thereby realizing the decoupling of the surface shape processing error of the aspheric mirror, improving the surface shape measurement accuracy of the aspheric optical element, and improving the accuracy and precision of the surface shape measurement.

[0120] The implementation principle and technical effects of the device provided in this embodiment are the same as those of the aforementioned embodiments. For the sake of brief description, for matters not mentioned in the device embodiment, reference may be made to the corresponding contents in the aforementioned method embodiment.

[0121] Corresponding to the method and device provided in the above-mentioned embodiment, the embodiment of the present invention further provides a non-spherical surface shape measurement system, the system comprising: a measurement model and a surface shape measurement controller, the measurement model comprising 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, and when the computer program is run by the processor, the method provided in the above embodiment is executed.

[0123] An embodiment of the present invention provides a computer-readable medium, wherein the computer-readable medium stores computer-executable instructions. When the computer-executable instructions are called and executed by a processor, the computer-executable instructions prompt the processor to implement the method described in the above embodiment.

[0124] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the system described above can refer to the corresponding process in the aforementioned embodiment, and will not be repeated here.

[0125] In addition, in the description of the embodiments of the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0126] If the functions are implemented in the form of 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 the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program codes.

[0127] In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance.

[0128] Finally, it should be noted that the above-described embodiments are only specific implementations of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The protection scope of the present invention is not limited thereto. Although the present invention is described in detail with reference to the above-described embodiments, ordinary technicians in the field should understand that any technician familiar with the technical field can still modify the technical solutions recorded in the above-described embodiments within the technical scope disclosed by the present invention, or can easily think of changes, or make equivalent replacements for some of the technical features therein; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for determining the full-aperture surface shape processing error of an aspheric mirror, characterized in that: include: Obtaining a phase measurement value of each phase measurement point within each annular sub-aperture region of the aspheric mirror to be detected; A global optimization function is constructed using the full-aperture circular Zernike polynomial coefficients and the sub-aperture annular Zernike polynomial coefficients as independent variables, and an optimal solution of the independent variables of the global optimization function is calculated; The aberration term corresponding to each phase measurement point when the independent variable takes the optimal solution is obtained, and the difference between the phase measurement value of each phase measurement point and the corresponding aberration term is calculated to obtain the full-aperture surface processing error phase value of the aspheric mirror to be detected.

2. The method according to claim 1, characterized in that: The global optimization function is constructed by taking the full-aperture circular Zernike polynomial coefficients and the sub-aperture annular Zernike polynomial coefficients as independent variables, including: Establishing a loss function based on the full-aperture circular Zernike polynomial coefficients, the sub-aperture annular Zernike polynomial coefficients and the phase measurement value of each phase measurement point; The sum of the loss function and the regularization term of the independent variable is calculated to obtain the global optimization function.

3. The method according to claim 2, characterized in that The loss function is established based on the full-aperture circular Zernike polynomial coefficients, the sub-aperture annular Zernike polynomial coefficients and the phase measurement value of each phase measurement point, including: Based on the full-aperture circular Zernike polynomial coefficients and the sub-aperture annular Zernike polynomial coefficients, fitting results of the full-aperture and each sub-aperture Zernike polynomial are obtained; The square error between the superposition value of the Zernike polynomial fitting results of the full aperture and each of the sub-apertures and the phase measurement values ​​of all the phase measurement points is used as the loss function.

4. The method according to claim 3, characterized in that: The calculating the optimal solution of the independent variable of the global optimization function comprises: The global optimization function is minimized by taking the regularization term of the independent variable as a constraint to obtain the optimal solution of the full-aperture circular Zernike polynomial coefficients and the sub-aperture annular Zernike polynomial coefficients.

5. The method according to claim 1, characterized in that The step of obtaining the phase measurement value of each phase measurement point within each annular sub-aperture region of the aspheric mirror to be detected comprises: Collecting interference patterns of each of the annular sub-aperture mask regions, and determining a wavefront phase value of each of the phase detection points based on the interference patterns of each of the annular sub-aperture mask regions; The residual of the wavefront phase value of each phase detection point and the wavefront phase value in an ideal state is calculated to obtain the phase measurement value of each phase measurement point in each annular sub-aperture area.

6. The method according to claim 5, characterized in that The step of determining the wavefront phase value of each phase detection point based on the interference pattern of each annular sub-aperture mask area comprises: Performing phase adjustment on the interference pattern in each of the annular sub-aperture mask regions to determine a wrapping phase value of each of the phase detection points; The wavefront phase value of each phase detection point is obtained based on a preset phase unwrapping algorithm and an unwrapping calculation of the wrapped phase value of each phase detection point.

7. The method according to claim 5, characterized in that The collecting of interference patterns of the annular sub-aperture mask regions comprises: Acquire the axial scanning position corresponding to each annular sub-aperture of the aspheric mirror to be detected; The aspheric mirror to be detected is moved to the corresponding axial scanning position, and the interference pattern of the aspheric mirror to be detected at the axial scanning position corresponding to each annular sub-aperture is collected based on the surface interferometer.

8. The method according to any one of claims 1 to 7, characterized in that: The annular sub-apertures have no overlapping area.

9. A device for determining the full-aperture surface shape processing error of an aspherical mirror, characterized in that: include: An acquisition module, used for acquiring a phase measurement value of each phase measurement point in each annular sub-aperture region of the aspheric mirror to be detected; A first calculation module is used to construct a global optimization function with full-aperture circular Zernike polynomial coefficients and each sub-aperture annular Zernike polynomial coefficient as independent variables, and calculate the independent variable optimal solution of the global optimization function; The second calculation module is used to obtain the aberration term 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 full-aperture surface processing error phase value of the aspheric mirror to be tested.

10. An aspheric surface shape measurement system, characterized in that: include: A measurement model and a surface measurement controller, wherein the measurement model includes a surface interferometer and a workpiece table, and the surface measurement controller includes a processor and a storage device; The storage device stores a computer program, which, when executed by the processor, performs the method according to any one of claims 1 to 8.

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