An interferometer error calibration method and system based on multi-surface phase shift interference and gradient descent optimization
By using a multi-surface phase-shifting interferometry and gradient descent optimization method, combined with the gradient descent algorithm, high-precision decoupling and high-flexibility measurement of interferometer system errors are achieved. This solves the problems of complex detection process and limited accuracy in existing technologies, and improves the calibration accuracy and spatial resolution of the interferometer system.
Patent Information
- Application Number
- CN202610831169.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-06-10
- Publication Date
- 2026-07-10
AI Technical Summary
Existing interferometer system error calibration methods suffer from complex detection processes, numerous measurements, high dependence on the accuracy of rotational or translational mechanisms, multiple error propagation links, complex algorithm processing, and difficulty in completely separating rotational symmetry errors. This results in limited calibration accuracy and stability, making it difficult to balance ease of operation with the need for high-precision measurement.
By employing a multi-surface phase-shift interferometry and gradient descent optimization method, multi-surface phase-shift interferometry measurements are performed at different rotation angles using an auxiliary detection mirror. Combined with iterative optimization using the gradient descent algorithm, rotational symmetry components are removed, and the rotation angle is accurately extracted using the equivalent surface shape of optical thickness variation, thus achieving high-precision decoupling of interferometer system errors.
It effectively overcomes the inherent defects of rotational symmetry terms, improves the accuracy and spatial resolution of interferometer system error calibration, simplifies the operation process, enhances measurement flexibility and robustness, avoids the loss of high-frequency information, and significantly improves detection accuracy.
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Figure CN122360339A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the technical field of optical precision measurement, and in particular to an interferometer error calibration method and system based on multi-surface phase-shifting interferometry and gradient descent optimization. Background Technology
[0002] Interferometer-based surface shape detection is a relative measurement method based on the principle of interference. It typically obtains the topographic information of the measured surface by inverting the interference pattern formed by the measured light and the reference light. During this type of detection, the results are affected not only by the surface shape accuracy of the reference mirror itself, but also by factors such as interferometer optical path adjustment errors, optical component manufacturing errors, and system aberrations. These errors collectively constitute the interferometer's systematic error. To obtain high-precision surface shape detection results, it is usually necessary to calibrate the interferometer's systematic error before use and to compensate for or subtract errors in the subsequent data processing.
[0003] Existing systematic error calibration methods mainly include multi-face mutual inspection, rotation measurement, translational difference, and a combination of rotation and translation. While these methods can separate interferometer systematic errors or the absolute surface shape of the measured surface to a certain extent, they generally suffer from problems such as complex detection procedures, a large number of measurements, high dependence on the accuracy of rotation or translation mechanisms, multiple error propagation links, and complex algorithm processing. Some methods also have difficulties in completely separating rotational symmetry errors and are susceptible to the effects of rotation angle errors, eccentricity errors, or translational errors, thus limiting calibration accuracy and detection stability, making it difficult to balance ease of operation with high-precision measurement requirements. Summary of the Invention
[0004] To overcome the shortcomings of poor calibration accuracy described in the prior art, this invention provides an interferometer error calibration method and system based on multi-surface phase-shifting interferometry and gradient descent optimization.
[0005] To achieve the above-mentioned technical effects, the technical solution of the present invention is as follows: An interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization includes: An auxiliary inspection mirror is placed in the detection optical path of the interferometer system and its initial orientation is determined. The auxiliary inspection mirror is then subjected to multi-surface phase-shift interferometry measurements at different rotation angles along the central optical axis using the interferometer system. The mixed surface shape and the equivalent surface shape of optical thickness variation are obtained for each rotation angle. The mixed surface shape is the sum of the aberration surface shape of the interferometer system and the first surface shape of the auxiliary inspection mirror. The actual rotation angle of the auxiliary inspection mirror relative to its initial orientation is extracted based on the equivalent surface shape of optical thickness variation. Based on the mixed surface shape and its corresponding rotation angle, the predicted mixed surface shape under different rotation angles is calculated using the first surface shape estimate with a preset initial value and the aberration surface shape estimate of the interferometer system. A loss function is then constructed based on the predicted mixed surface shape. The loss function is iteratively optimized using a gradient descent algorithm. After each iteration, the estimated value of the first surface shape and the estimated value of the aberration surface shape of the interferometer system are updated, and the rotational symmetry component in the estimated value of the first surface shape is removed. When the preset convergence condition is met, the first estimated value of the aberration surface shape of the interferometer system containing the rotational symmetry component of the first surface is output. The auxiliary detection mirror is flipped 180 degrees along the central transverse axis in the initial posture, and the above-mentioned rotation, multi-surface phase-shift interferometry and iterative solution steps are repeated for the flipped auxiliary detection mirror to obtain a second estimate of the aberration surface shape of the interferometer system, which includes the rotational symmetry component of the first surface after flipping; the central transverse axis is parallel to the first surface and passes through the center of the first surface; The error of the interferometer system is calculated based on the first and second estimates.
[0006] As a preferred embodiment, the multi-surface phase-shift interferometry measurement includes: forming three interference cavities by the first surface of the reference mirror, the first surface of the auxiliary detection mirror, and the second surface of the auxiliary detection mirror in the interferometer system; adjusting the wavelength of the laser in the interferometer system to induce different phase shifts in the three interference cavities, thereby obtaining a series of interference patterns; and obtaining the hybrid surface and the equivalent surface shape of the optical thickness change based on the light intensity and phase shift of the interference patterns, respectively; the expressions are as follows:
[0007]
[0008]
[0009] in, I The acquired mixed interference signal, Background light intensity, To modulate light intensity, For the first i The initial phase of each interference cavity, For the first i The phase shift step size corresponding to each interference cavity; For the first i The optical path length of the interference cavity The center wavelength of the laser within the interferometer system. This represents the wavelength change at each step. The number of interferogram samples collected. For the first The light intensity of the second sample. This is the sampling window function.
[0010] As a preferred embodiment, the step of extracting the actual rotation angle of the auxiliary detection mirror relative to the initial posture based on the equivalent surface shape of the optical thickness change includes: obtaining the equivalent surface shape of the optical thickness change corresponding to any rotation angle and the equivalent surface shape of the optical thickness change under the initial posture, and solving the actual rotation angle through coordinate transformation and angle matching.
[0011] As a preferred embodiment, the initial values of the first surface shape estimate and the interferometer system aberration shape estimate are both zero matrices.
[0012] As a preferred embodiment, the loss function is calculated based on the sum of squares of the differences between the measured values and the estimated values of the mixed surface, and its expression is as follows:
[0013] in, For loss function, S For the aberration surface shape of the interferometer system, T This is the first surface shape; The preset effective area is defined as N, where N is the number of rotations. For observations of mixed surface shapes, For the angle is The rotation operator is given by (x,y), where (x,y) is the position coordinate of a point on the interference pattern.
[0014] As a preferred embodiment, the step of iteratively optimizing the loss function using the gradient descent algorithm includes: calculating the update amount corresponding to the estimated value of the aberration surface shape of the interferometer system and the update amount corresponding to the estimated value of the first surface shape based on the loss function, and updating the estimated values of the aberration surface shape of the interferometer system and the estimated values of the first surface shape according to a preset learning rate; the calculation formula for the update amount is as follows:
[0015]
[0016] in, This represents the update value corresponding to the aberration surface shape estimate of the interferometer system. This is the update amount corresponding to the estimated value of the first surface shape.
[0017] As a preferred embodiment, the rotational symmetry component is represented as follows:
[0018]
[0019] in, It is a rotationally symmetric component. Let Zernike basis functions contain only rotationally symmetric terms. This represents the rotational asymmetric component of the first surface in round t+1, i.e., the result after removing the rotational symmetric component from the estimated surface shape of the first surface. This is the estimated surface shape value for the first surface in round t+1.
[0020] As a preferred embodiment, the step of calculating the error of the interferometer system based on the first estimate and the second estimate includes calculating the average of the first estimate and the second estimate, the expression of which is as follows:
[0021] in, For the error of the interferometer system, and These are the first estimate and the second estimate, respectively.
[0022] As a preferred embodiment, if the first surface is a surface far from the interferometer system, then based on the refractive index of the auxiliary detection mirror, the intermediate surface shape obtained by multi-surface phase-shift interferometry is subjected to refractive index compensation processing to obtain the surface shape of the first surface.
[0023] This application also proposes an interferometer error calibration system based on multi-surface phase-shifting interferometry and gradient descent optimization, applied to the interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization. The system includes: The multi-surface phase-shifting interferometry module is used to place the auxiliary detection mirror in the detection optical path of the interferometer system and determine the initial attitude. Based on the initial attitude, the interferometer system measures the auxiliary detection mirror at different rotation angles along the central optical axis to obtain the corresponding mixed surface shape and optical thickness change equivalent surface shape at each rotation angle. The measurement operation is repeated after flipping the auxiliary detection mirror. The parameter iterative solution module is used to calculate the actual rotation angle and construct the loss function. It uses the gradient descent method for iterative solution. After updating the estimated value in each iteration, the rotational symmetry component in the first surface shape estimate is removed, and the aberration surface shape estimate of the interferometer system is obtained by solving them respectively. The error calculation module is used to perform fusion calculations based on the aberration surface shape estimates of different interferometer systems and output the error calibration results of the interferometer.
[0024] Compared with the prior art, the beneficial effects of the present invention are as follows: This application effectively overcomes the inherent defect of conventional rotation detection methods in completely separating rotational symmetry terms by introducing flip detection and actively subtracting the rotational symmetry component of the auxiliary detection mirror during the iterative solution process, thus achieving high-precision decoupling of the absolute error of the interferometer system. At the same time, this scheme uses the equivalent surface shape of optical thickness change to accurately extract the actual rotation angle at each step, without the need to strictly fix or rely on high-precision rotation interval angles during the actual measurement process. In addition, the surface shape calculation process of this method is a pixel-level point-to-point restoration, which completely breaks through the order limitation brought about by the global fitting of traditional Zernike polynomials. When solving the surface shape error of the interferometer, it can effectively avoid the loss of high-frequency spatial information, thereby improving the spatial resolution and final accuracy of the interferometer error calibration. Attached Figure Description
[0025] Figure 1 This is a flowchart of the interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization in Example 1; Figure 2 This is a schematic diagram of the multi-surface phase-shift interferometry principle in Example 1; Figure 3 This is a graph showing the relationship between the interference signal and the phase shift step size in Example 1; Figure 4 This is a flowchart of Example 1; Figure 5 This is an architecture diagram of the interferometer error calibration system based on multi-surface phase-shifting interferometry and gradient descent optimization in Example 2; Figure 6 This is a structural diagram of the wavelength modulation Fizeau interferometer in Example 3; Figure 7 The measurement results of the aberration surface shape estimation values of the interferometer system in Example 3; Figure 8 This is a comparison diagram of the interferometer system error before and after correction in Example 3; Figure 9 This is a graph showing the measurement results of the comparative interferometer in Example 3. Detailed Implementation
[0026] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0027] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.
[0028] Example 1 This embodiment proposes an interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization, such as... Figure 1The diagram shown is a flowchart of the interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization in this embodiment.
[0029] An interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization includes: An auxiliary inspection mirror is placed in the detection optical path of the interferometer system and its initial orientation is determined. The auxiliary inspection mirror is then subjected to multi-surface phase-shift interferometry measurements at different rotation angles along the central optical axis using the interferometer system. The mixed surface shape and the equivalent surface shape of optical thickness variation are obtained for each rotation angle. The mixed surface shape is the sum of the aberration surface shape of the interferometer system and the first surface shape of the auxiliary inspection mirror. The actual rotation angle of the auxiliary inspection mirror relative to its initial orientation is extracted based on the equivalent surface shape of optical thickness variation. Based on the mixed surface shape and its corresponding rotation angle, the predicted mixed surface shape under different rotation angles is calculated using the first surface shape estimate with a preset initial value and the aberration surface shape estimate of the interferometer system. A loss function is then constructed based on the predicted mixed surface shape. The loss function is iteratively optimized using a gradient descent algorithm. After each iteration, the estimated value of the first surface shape and the estimated value of the aberration surface shape of the interferometer system are updated, and the rotational symmetry component in the estimated value of the first surface shape is removed. When the preset convergence condition is met, the first estimated value of the aberration surface shape of the interferometer system containing the rotational symmetry component of the first surface is output. The auxiliary detection mirror is flipped 180 degrees along the central transverse axis in the initial posture, and the above-mentioned rotation, multi-surface phase-shift interferometry and iterative solution steps are repeated for the flipped auxiliary detection mirror to obtain a second estimate of the aberration surface shape of the interferometer system, which includes the rotational symmetry component of the first surface after flipping; the central transverse axis is parallel to the first surface and passes through the center of the first surface; The error of the interferometer system is calculated based on the first and second estimates.
[0030] In this embodiment, the back surface morphology, which cannot be solved by conventional surface shape detection, was successfully obtained by multi-surface phase-shift interferometry. This allows the results of two rounds of rotational detection to be averaged, effectively eliminating the rotational symmetry component error of the detection mirror itself. At the same time, the optical thickness variation surface shape is calculated using the multi-surface phase-shift interferometry algorithm, achieving accurate angle recognition. Furthermore, the absolute measurement value of the surface shape is calculated by combining the gradient descent algorithm, breaking the angle limitations of traditional testing. This enables the system to accurately solve the surface shape at any rotation angle, significantly improving the overall flexibility, robustness, and detection accuracy of the absolute measurement.
[0031] In an optional embodiment, the multi-surface phase-shift interferometry measurement includes: forming three interference cavities from the first surface of the reference mirror, the first surface of the auxiliary detection mirror, and the second surface of the auxiliary detection mirror in the interferometer system; adjusting the wavelength of the laser in the interferometer system to generate different phase shifts in the three interference cavities to obtain a series of interference patterns; and obtaining the hybrid surface and the equivalent surface shape of the optical thickness change based on the light intensity and phase shift of the interference patterns; the expressions are as follows:
[0032]
[0033]
[0034] in, I The acquired mixed interference signal, Background light intensity, To modulate light intensity, For the first i The initial phase of each interference cavity, For the first i The phase shift step size corresponding to each interference cavity; For the first i The optical path length of the interference cavity The center wavelength of the laser within the interferometer system. This represents the wavelength change at each step. The number of interferogram samples collected. For the first The light intensity of the second sample. This is the sampling window function.
[0035] More specifically, the initial phase is It is an unknown quantity to be measured, and For phase shift, it is a known quantity. It is the total phase, that is, by introducing This produces the overall phase change.
[0036] like Figure 2 The diagram shown illustrates the principle of multi-surface phase-shift interferometry. The interferometer is located at... Figure 2 Above, it will generate three main reflected beams, each originating from the reference plane. R Test mirror surface and surface The three reflected beams interfere with each other in pairs, forming a multi-surface interference signal at the camera.
[0037] like Figure 3 The figure shows the relationship between the interference signal and the phase shift step size. For example... Figure 2 For the three interference cavities shown, the relationship between the acquired interference signal and the phase shift step size is as follows: Figure 3 As shown. Here, it is assumed that the air segment interference cavity... Greater than the optical thickness of the auxiliary inspection mirror Signal I represents the self-interference signal of the two surfaces of the auxiliary test mirror; signal II represents the interference signal between the reflected light from the auxiliary test mirror surface closer to the reference mirror and the reflected light from the reference mirror; and signal III represents the interference signal between the reflected light from the auxiliary test mirror surface farther from the reference mirror and the reflected light from the reference mirror. During phase-shift interferometry measurement, the phase shift corresponding to each signal is... They are all different.
[0038] In this embodiment, the first surface of the parallel plate lens can be determined simultaneously through a single detection. Second surface and optical thickness variation .
[0039] In an optional embodiment, the step of extracting the actual rotation angle of the auxiliary detection mirror relative to the initial posture based on the equivalent surface shape of the optical thickness change includes: obtaining the equivalent surface shape of the optical thickness change corresponding to any rotation angle and the equivalent surface shape of the optical thickness change in the initial posture, and solving the actual rotation angle through coordinate transformation and angle matching.
[0040] Furthermore, the false first i The rotation angle is A total of N -1 rotation will yield the result N A mixed surface With different rotation angles Its expression is as follows:
[0041] in, For the angle is The rotation operator, due to Given a quantity, the actual rotation angle can be expressed in various ways. Find out, and then obtain each rotation operator. In this embodiment, the rotation angle is obtained by coordinate transformation and angle matching.
[0042] In an optional embodiment, the initial values of the first surface shape estimate and the interferometer system aberration shape estimate are both zero matrices.
[0043] Furthermore, the loss function is calculated based on the sum of squares of the differences between the measured values and the estimated values of the mixed surface, and its expression is as follows:
[0044] in, For loss function, S For the aberration surface shape of the interferometer system, T This is the first surface shape; For the preset effective area, For the number of rotations, For observations of mixed surface shapes, For the angle is Rotation operator.
[0045] As an example, In simulations and experiments, it is usually set as a circular area.
[0046] In this embodiment, a strictly convex and differentiable optimization objective is constructed by accumulating the sum of the squares of the differences between the predicted and measured values within the effective region, such that... and The joint estimation can converge to the global optimum.
[0047] In an optional embodiment, the step of iteratively optimizing the loss function using the gradient descent algorithm includes: calculating the update amount corresponding to the estimated value of the aberration surface shape of the interferometer system and the update amount corresponding to the estimated value of the first surface shape based on the loss function, and updating the estimated values of the aberration surface shape of the interferometer system and the estimated values of the first surface shape according to a preset learning rate; the calculation formula for the update amount is as follows:
[0048]
[0049] in, This represents the update value corresponding to the aberration surface shape estimate of the interferometer system. This is the update amount corresponding to the estimated value of the first surface shape.
[0050] Alternatively, the gradient descent method can be used to update the estimates of both as follows:
[0051]
[0052] in, For the number of iterations, This is the learning rate.
[0053] In an optional embodiment, the rotational symmetry component is represented as:
[0054] in, It is a rotationally symmetric component. is a Zernike basis function that contains only rotationally symmetric terms.
[0055] More specifically, the parallel plates to be tested are divided into rotationally symmetric components. With rotational asymmetric components After removing the rotationally symmetric components, the remaining components are the rotationally asymmetric components, whose expressions are:
[0056] in, This represents the rotational asymmetric component of the first surface in round t+1, i.e., the result after removing the rotational symmetric component from the estimated surface shape of the first surface. This is the estimated surface shape value for the first surface in round t+1.
[0057] like Figure 4 The diagram shown is a flowchart. The y-axis is the central horizontal axis. The blue area represents the first surface.
[0058] As an example, the preset convergence condition is that the tolerance is less than If the difference between two adjacent iterations is used, or if the number of iterations exceeds 1000, and the maximum radial order is selected as 20, then high-frequency rotational symmetry information will be included.
[0059] In an optional embodiment, the step of calculating the error of the interferometer system based on the first estimate and the second estimate includes calculating the average of the first estimate and the second estimate, the expression of which is as follows:
[0060] in, For the error of the interferometer system, and These are the first estimate and the second estimate, respectively.
[0061] In an optional embodiment, if the first surface is a surface far from the interferometer system, then based on the refractive index of the auxiliary detection mirror, the intermediate surface shape obtained by multi-surface phase-shift interferometry is subjected to refractive index compensation processing to obtain the surface shape of the first surface.
[0062] More specifically, assuming a given material refractive index The three surface shapes were obtained through interferometry. , and , usually As a result of the detection near the reference mirror, As optical thickness change ,Will or As a measurement result of the surface far from the reference mirror.
[0063] In this embodiment, by compensating for the refractive index of the auxiliary detection mirror, the true surface shape of the surface far from the reference mirror can be directly calculated from the intermediate surface shape result obtained by multi-surface phase-shift interferometry. This eliminates the optical path coupling and surface aliasing introduced by the refraction of the flat plate. The absolute separation of the front and rear surface morphologies can be achieved without flipping or re-clamping the test piece, avoiding alignment errors caused by multiple clamping, and significantly improving the accuracy and efficiency of the measurement.
[0064] Example 2 This embodiment proposes an interferometer error calibration system based on multi-surface phase-shifting interferometry and gradient descent optimization, which is applied to the interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization proposed in Embodiment 1. Figure 5 The diagram shown is an architecture diagram of the interferometer error calibration system based on multi-surface phase-shifting interferometry and gradient descent optimization in this embodiment.
[0065] An interferometer error calibration system based on multi-surface phase-shifting interferometry and gradient descent optimization, the system comprising: The multi-surface phase-shifting interferometry module is used to place the auxiliary detection mirror in the detection optical path of the interferometer system and determine the initial attitude. Based on the initial attitude, the interferometer system measures the auxiliary detection mirror at different rotation angles along the central optical axis to obtain the corresponding mixed surface shape and optical thickness change equivalent surface shape at each rotation angle. The measurement operation is repeated after flipping the auxiliary detection mirror. The parameter iterative solution module is used to calculate the actual rotation angle and construct the loss function. It uses the gradient descent method for iterative solution. After updating the estimated value in each iteration, the rotational symmetry component in the first surface shape estimate is removed, and the aberration surface shape estimate of the interferometer system is obtained by solving them respectively. The error calculation module is used to perform fusion calculations based on the aberration surface shape estimates of different interferometer systems and output the error calibration results of the interferometer.
[0066] Example 3 This embodiment applies in detail the interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization proposed in Embodiment 1.
[0067] like Figure 6 The diagram shown is a structural diagram of a wavelength-modulated Fizeau interferometer.
[0068] This embodiment performs systematic error detection on a wavelength modulation Fizeau interferometer. The auxiliary detection mirror is a 4-inch parallel flat crystal. Tables 1 and 2 show the rotation angles identified by the two-wheel rotation detection method.
[0069] Table 1 Actual rotation angles calculated for the first rotation
[0070] Table 2 Actual rotation angles calculated for the second rotation
[0071] like Figure 7 The figure shows the measurement results of the aberration surface shape estimation of the interferometer system.
[0072] in, Figure 7 a) Shows the first estimate of the aberration surface shape of the interferometer system obtained by the method of this application. , Figure 7 b) Shows the second estimate of the aberration surface shape of the interferometer system obtained by the method of this application. , Figure 7 c) is the final corrected absolute aberration surface shape of the interferometer system.
[0073] like Figure 8 The figure shown is a comparison of the interferometer system error before and after correction.
[0074] System aberrations were subtracted from the two surfaces of the 4-inch parallel optical flat. Figure 8 a) and b) show the detection results before and after aberration subtraction for the surface of the parallel optical plane that is closer to the reference mirror. Figure 8 d) and e) show the detection results before and after aberration subtraction for the surface of the parallel optical plane that is farther from the reference mirror. For ease of comparison, Figure 8 c) Figure 8 f) are respectively Figure 8 b) Figure 8 e) The result of fitting the first 36 terms of the Zernike polynomial can remove high-frequency components.
[0075] To verify the experimental results, a commercial interferometer was used for comparison. All commercial interferometers have had their system aberrations corrected at the factory.
[0076] like Figure 9 The image shown is a comparison of the measurement results obtained using an interferometer.
[0077] like Figure 9 As shown. The detection results for the two surfaces of the auxiliary detection mirror are as follows. Figure 9 a), Figure 9 As shown in c); Figure 9 b) Figure 9 d) respectively Figure 9 a), Figure 9 c) Results after fitting using the first 36 terms of the Zernike polynomial. Since the reflected light from the back surface cannot be completely eliminated, mid-to-high frequency error components are generated. The comparison results show that commercial interferometers and the error-calibrated interferometer of this application can obtain similar detection results.
[0078] The terminology used in the accompanying drawings is for illustrative purposes only.
[0079] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.
Claims
1. An interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization, characterized in that, include: An auxiliary inspection mirror is placed in the detection optical path of the interferometer system and its initial orientation is determined. The auxiliary inspection mirror is then subjected to multi-surface phase-shift interferometry measurements at different rotation angles along the central optical axis using the interferometer system. The mixed surface shape and the equivalent surface shape of optical thickness variation are obtained for each rotation angle. The mixed surface shape is the sum of the aberration surface shape of the interferometer system and the first surface shape of the auxiliary inspection mirror. The actual rotation angle of the auxiliary inspection mirror relative to its initial orientation is extracted based on the equivalent surface shape of optical thickness variation. Based on the mixed surface shape and its corresponding rotation angle, the predicted mixed surface shape under different rotation angles is calculated using the first surface shape estimate with a preset initial value and the aberration surface shape estimate of the interferometer system. A loss function is then constructed based on the predicted mixed surface shape. The loss function is iteratively optimized using a gradient descent algorithm. After each iteration, the estimated value of the first surface shape and the estimated value of the aberration surface shape of the interferometer system are updated, and the rotational symmetry component in the estimated value of the first surface shape is removed. When the preset convergence condition is met, the first estimated value of the aberration surface shape of the interferometer system containing the rotational symmetry component of the first surface is output. The auxiliary detection mirror is flipped 180 degrees along the central transverse axis in the initial posture, and the above-mentioned rotation, multi-surface phase-shift interferometry and iterative solution steps are repeated for the flipped auxiliary detection mirror to obtain a second estimate of the aberration surface shape of the interferometer system, which includes the rotational symmetry component of the first surface after flipping; the central transverse axis is parallel to the first surface and passes through the center of the first surface; The error of the interferometer system is calculated based on the first and second estimates.
2. The interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization according to claim 1, characterized in that, The multi-surface phase-shift interferometry measurement includes: forming three interference cavities in the interferometer system with a reference mirror, a first surface of an auxiliary detection mirror, and a second surface of an auxiliary detection mirror; adjusting the wavelength of the laser in the interferometer system to induce different phase shifts in the three interference cavities, obtaining a series of interference patterns; and obtaining the hybrid surface and the equivalent surface shape of the optical thickness change based on the light intensity and phase shift of the interference patterns, respectively; their expressions are as follows: in, I The acquired mixed interference signal, Background light intensity, To modulate light intensity, For the first i The initial phase of each interference cavity, For the first i The phase shift step size corresponding to each interference cavity; For the first i The optical path length of the interference cavity The center wavelength of the laser within the interferometer system. This represents the wavelength change at each step. The number of interferogram samples collected. For the first The light intensity of the second sample. This is the sampling window function.
3. The interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization according to claim 1, characterized in that, The step of extracting the actual rotation angle of the auxiliary detection mirror relative to the initial posture based on the equivalent surface shape of the optical thickness change includes: obtaining the equivalent surface shape of the optical thickness change corresponding to any rotation angle and the equivalent surface shape of the optical thickness change under the initial posture, and solving the actual rotation angle through coordinate transformation and angle matching.
4. The interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization according to claim 1, characterized in that, The initial values of the first surface shape estimate and the interferometer system aberration surface shape estimate are both zero matrices.
5. The interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization according to claim 4, characterized in that, The loss function is calculated based on the sum of squares of the differences between the measured values and the estimated values of the mixed surface, and its expression is as follows: in, For loss function, S For the aberration surface shape of the interferometer system, T This is the first surface shape; For the preset effective area, N For the number of rotations, For observations of mixed surface shapes, For the angle is The rotation operator, ( x,y ) represents the position coordinates of a point on the interferogram.
6. The interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization according to claim 5, characterized in that, The step of iteratively optimizing the loss function using the gradient descent algorithm includes: calculating the update amount corresponding to the estimated value of the aberration surface shape of the interferometer system and the update amount corresponding to the estimated value of the first surface shape based on the loss function, and updating the estimated values of the aberration surface shape of the interferometer system and the estimated value of the first surface shape according to a preset learning rate; the calculation formula for the update amount is as follows: in, This represents the update value corresponding to the aberration surface shape estimate of the interferometer system. This is the update amount corresponding to the estimated value of the first surface shape.
7. The interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization according to claim 6, characterized in that, The rotationally symmetric component is represented as: in, It is a rotationally symmetric component. Let Zernike basis functions contain only rotationally symmetric terms. This represents the rotational asymmetric component of the first surface in round t+1, i.e., the result after removing the rotational symmetric component from the estimated surface shape of the first surface. This is the estimated surface shape value for the first surface in round t+1. The first rotational symmetric term of the Zernike polynomial The coefficient of the term, This represents the number of fitted terms.
8. The interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization according to any one of claims 1 to 7, characterized in that, The step of calculating the error of the interferometer system based on the first and second estimates includes calculating the average of the first and second estimates, as expressed below: in, For the error of the interferometer system, and These are the first estimate and the second estimate, respectively.
9. The interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization according to any one of claims 1 to 7, characterized in that, If the first surface is a surface far from the interferometer system, then based on the refractive index of the auxiliary detection mirror, the intermediate surface shape obtained by multi-surface phase-shift interferometry is subjected to refractive index compensation processing to obtain the surface shape of the first surface.
10. An interferometer error calibration system based on multi-surface phase-shifting interferometry and gradient descent optimization, applied to the interferometer error calibration method based on multi-surface phase-shifting interferometry and gradient descent optimization as described in any one of claims 1 to 7, characterized in that, The system includes: The multi-surface phase-shifting interferometry module is used to place the auxiliary detection mirror in the detection optical path of the interferometer system and determine the initial attitude. Based on the initial attitude, the interferometer system measures the auxiliary detection mirror at different rotation angles along the central optical axis to obtain the corresponding mixed surface shape and optical thickness change equivalent surface shape at each rotation angle. The measurement operation is repeated after flipping the auxiliary detection mirror. The parameter iterative solution module is used to calculate the actual rotation angle and construct the loss function. It uses the gradient descent method for iterative solution. After updating the estimated value in each iteration, the rotational symmetry component in the first surface shape estimate is removed, and the aberration surface shape estimate of the interferometer system is obtained by solving them respectively. The error calculation module is used to perform fusion calculations based on the aberration surface shape estimates of different interferometer systems and output the error calibration results of the interferometer.