A method for measuring the instrument transfer function of an interferometer based on a spatial light modulator

Abstract

The present invention discloses a method for measuring the instrument transfer function of an interferometer based on a spatial light modulator, which includes the following steps: compensating for the inherent phase difference of the spatial light modulator to generate a set of sine phases with different periods and the same amplitude, and using a wavefront interferometer and the spatial light modulator to measure the sine phase results under different sine phases; calculating the ITF value according to the obtained sine phase results under different sine phases, and plotting a fitting curve graph with the ITF value on the vertical coordinate and the frequency on the horizontal coordinate to obtain the transfer function curve of the wavefront interferometer to be measured. The purpose of the present invention is to realize a method for measuring the instrument transfer function of an interferometer that can meet the international standard definition and is not restricted by processing conditions, and improve the measurement accuracy, frequency coverage range and flexibility.

Description

Technical Field

[0001] The present invention relates to the technical fields of optical instruments and precision measurement, and particularly relates to a method for measuring the instrument transfer function of an interferometer based on a spatial light modulator. Background Art

[0002] An interferometer is an optical instrument that uses the principle of light wave interference for high-precision measurement, and is widely used in fields such as optical surface detection, wavefront analysis, quality control of optical components, and ultra-precision optical manufacturing. The interferometer analyzes the surface topography, wavefront aberration, or refractive index change of the object to be measured by measuring the interference fringes, and its measurement accuracy usually reaches the nanometer level or even higher. However, in actual measurement, the interferometer is affected by various factors such as the transfer characteristics of the optical system, environmental disturbances, and non-ideal optical components. These factors will introduce measurement errors, thereby affecting the accuracy and reliability of the measurement results. The Instrument Transfer Function (ITF) is a key parameter that describes the frequency response characteristics of the interferometer. The international standard ISO 25178-600 gives its definition - under ideal conditions, the ITF is the ratio of the measured height of a sinusoidal grating with a specified spatial frequency to the true height of the grating. The ITF characterizes the measurement sensitivity and transfer characteristics of the interferometer at different spatial frequencies, and reflects the response degree of the interferometer to different spatial frequency components on the surface of the object to be measured. The measurement accuracy of the ITF is directly related to the measurement accuracy and traceability of the interferometer.

[0003] Regarding the ITF measurement method, many domestic and foreign units have proposed their own unique measurement methods. In the 1990s, companies such as Zygo, Wyko in the United States and Peter Z T et al. proposed to manufacture a standard phase step plate, calculate the power spectral density by detecting its wavefront data, and then compare it with the ideal power spectral density to obtain its ITF. The French Atomic Energy Commission etched a planar test plate with sinusoidal phases of different periods to detect the interferometer transfer function. Domestically, Liu Qian et al. from the Institute of Mechanical Manufacturing Technology of the China Academy of Engineering Physics analyzed the ITF of a white light interferometer and its nonlinearity through a standard step test plate. Cai Mengxue et al. from the Changchun Institute of Optics and Fine Mechanics proposed a method for calibrating the ITF of sub-aperture stitching for detecting high-steepness mirrors based on a spherical step test plate. However, almost all of the above methods using the phase step plate method do not follow the most basic international standard definition, and there will be differences in the measurement results; the production of planar test plates with sinusoidal phases of different periods is restricted by processing accuracy and cost, and it is impossible to measure sinusoidal gratings with arbitrary periods. Therefore, how to realize a method for measuring the instrument transfer function of an interferometer that can meet the international standard definition and is not restricted by processing conditions has important significance and broad application prospects.

[0004] In recent years, with the development of optical modulation technology, the Spatial Light Modulator (SLM) has gradually become an important tool for precision optical measurement due to its high resolution, high-frequency response, programmability, and dynamic modulation capabilities. The SLM can dynamically adjust the amplitude and phase of light waves in the spatial domain, thereby generating arbitrary spatial frequency distributions and wavefront aberrations. Compared with traditional processing and manufacturing of single-frequency sinusoidal gratings, the SLM has a higher frequency coverage range, more precise phase control, and more flexible modulation methods. Summary of the Invention

[0005] The technical problem to be solved by the present invention: Aiming at the above problems of the prior art, a method for measuring the interferometer instrument transfer function based on a spatial light modulator is provided. The present invention aims to realize a method for measuring the interferometer instrument transfer function that can meet the international standard definition and is not restricted by processing conditions, and improve the measurement accuracy, frequency coverage range, and flexibility.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0007] A method for measuring the interferometer instrument transfer function based on a spatial light modulator includes the following steps:

[0008] Compensate for the inherent phase difference of the spatial light modulator, generate a set of sine phases with different periods and the same amplitude, and use a wavefront measurement interferometer and the spatial light modulator to measure the sine phase results under different sine phases;

[0009] Calculate the ITF value based on the sine phase results obtained under different sine phases, and draw a fitting curve graph with the ITF value on the vertical axis and the frequency on the horizontal axis to obtain the transfer function curve of the wavefront measurement interferometer to be measured;

[0010] When generating a set of sine phases with different periods and the same amplitude, the function expression of the generated sine phase is:

[0011] ,

[0012] where, is the sine phase, is the amplitude of the sine phase, is the th required period of the sine phase, is the index of the current data row, is the phase of the sine phase, is the offset of the sine phase.

[0013] Optionally, compensating for the inherent phase difference of the spatial light modulator, generating a set of sine phases with different periods and the same amplitude, and measuring the sine phase results at different sine phases using a wavefront interferometer and a spatial light modulator includes:

[0014] S101: Place the spatial light modulator at the corresponding position of the interferometer to be measured, and adjust the light spot and fringe spacing;

[0015] S102: Measure the inherent surface shape data of the spatial light modulator;

[0016] S103: Compensate the inherent surface shape data of the spatial light modulator to generate first compensated surface shape data;

[0017] S104: Adjust the first-order diffracted light spot of the spatial light modulator to coincide with the light spot of the interferometer to be measured;

[0018] S105: Measure the compensated surface shape data of the spatial light modulator;

[0019] S106: Compensate the inherent surface shape data of the spatial light modulator again to generate compensated surface shape data again;

[0020] S107: Determine whether the compensated surface shape data generated again meets the accuracy requirements. If it does not meet the accuracy requirements, repeat steps S105 and S106 again until the compensated surface shape data generated again meets the accuracy requirements;

[0021] S108: Measure the final compensated surface shape data;

[0022] S109: Generate the th required period of the sine phase, and the amplitude of this sine phase is a fixed value;

[0023] S110: Measure the sine phase result corresponding to the th required period of the sine phase;

[0024] S111: Determine whether the sine phases of all required periods have been measured. If not, generate the rd compensated surface shape data, and repeat steps S105 and S110 again until the sine phases of all required periods are measured.

[0025] Optionally, compensating for the inherent surface shape data of the spatial light modulator includes: generating a grayscale image with a grayscale value of 0, and generating a new compensated phase grayscale image from the inherent surface shape data of the spatial light modulator and the grayscale image with a grayscale value of 0:

[0026] ,

[0027] ,

[0028] Among them, is the new compensated phase grayscale image, is the horizontal coordinate of the spatial light modulator, is the rounding operator, and are respectively the coefficients of the tilt carrier along the axis and axis of the spatial light modulator, is the phase, with the unit of radian; represents the conjugate phase of the inherent wavefront distortion after resampling to match the resolution of the spatial light modulator.

[0029] Optionally, calculating the ITF value according to the sine phase results under different obtained sine phases and plotting a fitting curve graph with the ITF value as the vertical coordinate and the frequency as the horizontal coordinate to obtain the transfer function curve of the wavefront interferometer to be measured includes:

[0030] S201: Obtain the amplitude corresponding to the sine phase according to the sine phase results under different obtained sine phases;

[0031] S202: Calculate the ratio of the amplitude under each sine phase to the standard amplitude value to obtain the ITF value;

[0032] S203: Plot a fitting curve graph with the ITF value as the vertical coordinate and the frequency as the horizontal coordinate for the ITF values under each sine phase to obtain the transfer function curve of the wavefront interferometer to be measured.

[0033] Optionally, step S201 includes:

[0034] S301: Load the sine phase results under different sine phases, including X, Y coordinates and Z values;

[0035] S302: Use the surface shape compensation algorithm to remove the measurement error from the sine phase results under different sine phases; among them, using the surface shape compensation algorithm to remove the measurement error means subtracting the final compensated surface shape data obtained above from the sine phase results under each sine phase, and the measurement error can be removed to obtain the sine phase results after removing the measurement error;

[0036] S303: Divide the sine phase results after removing the measurement error into data blocks;

[0037] S304: Perform sine function fitting on each data block and extract the amplitude of the sine function obtained by fitting;

[0038] S305: Average the amplitudes of each data block under the same sine phase as the amplitude under this sine phase.

[0039] Optionally, when dividing the sine phase result after removing measurement errors into data blocks in step S303, the sizes of the data blocks of sine phases with different periods are different from each other.

[0040] Optionally, after extracting the amplitude of the sine function obtained by fitting in step S304, it further includes constructing an amplitude matrix based on the amplitudes of each data block and optimizing the result of the amplitude matrix to ensure that the fitting result is consistent with the measurement data, including:

[0041] S304.1: Conduct initial parameter estimation for the amplitude matrix, including: for each row of data in the amplitude matrix , where and are respectively the positions of the -th pixel in a single row of the amplitude matrix, the amplitude measurement value of the -th pixel, is the total number of pixels in a single row, and initialize the parameters based on the data characteristics:

[0042] ,

[0043] where, is the initial peak-to-peak value, is the initial mean value, is the initial phase offset;

[0044] S304.2: Conduct non-linear least squares optimization, including: aiming at minimizing the sum of squared residuals, solve for the optimal parameters:

[0045] ,

[0046] where, is the peak-to-peak value, is the -th frequency to be measured, is the mean value,

[0047] S304.3: Adopt the Levenberg-Marquardt algorithm and iteratively update the parameters until convergence:

[0048] ,

[0049] where, and are respectively the parameter vectors composed of the parameters at the -th and -th iterations , and there is , is the Jacobian matrix of the residuals with respect to the parameters, is the residual vector, is the damping factor, and the superscript represents the transpose operation.

[0050] Optionally, after calculating the ITF value according to the sine phase results under different sine phases and plotting a fitting curve graph with the ITF value on the vertical axis and the frequency on the horizontal axis to obtain the transfer function curve of the wavefront interferometer to be measured, it further includes generating a result chart of the transfer function curve of the wavefront interferometer to be measured and saving it to a specified file.

[0051] Optionally, when generating a result chart of the transfer function curve of the wavefront interferometer to be measured and saving it to a specified file, it further includes writing the amplitude, phase, and offset of the sine function fitting under each sine phase into the result chart and saving it to a specified file.

[0052] Optionally, the spatial light modulator is a reflective spatial light modulator.

[0053] Compared with the prior art, the present invention can mainly achieve the following beneficial effects: (1) The method for measuring the instrument transfer function of the interferometer based on the spatial light modulator in the present invention solves the problem that the current measurement of the instrument transfer function is restricted by the basic definition and processing conditions, and improves the flexibility of measuring the instrument transfer function. (2) The method for measuring the instrument transfer function of the interferometer based on the spatial light modulator in the present invention can effectively eliminate the surface shape distortion and measurement error of the spatial light modulator and the interferometer itself through multiple rounds of iterative compensation and sine phase generation, significantly improving the measurement accuracy and reliability of the instrument transfer function and ensuring the high accuracy of the measurement results. (3) The method for measuring the instrument transfer function of the interferometer based on the spatial light modulator in the present invention has high flexibility, can adjust the amplitude and period of the sine phase according to different experimental requirements, is applicable to the measurement of the transfer function of various wavefront interferometers, and this method can be widely applied to fields such as optical element quality control and surface detection, and has broad application prospects. Description of the Drawings

[0054] In order to more clearly illustrate the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art.

[0055] Figure 1 is the basic flowchart of the method of the embodiment of the present invention.

[0056] Figure 2 is the detailed flowchart of the method of the embodiment of the present invention.

[0057] Figure 3 is the schematic diagram of the optical path structure in the embodiment of the present invention, where 1 is the wavefront interferometer, 2 is the spatial light modulator; 3 is the spatial light modulator control module, and 4 is the instrument transfer function processing module.

[0058] Figure 4 This is the inherent surface shape diagram of the spatial light modulator in the embodiment of the present invention.

[0059] Figure 5 This is the first compensation surface shape diagram in the embodiment of the present invention.

[0060] Figure 6 This is the second compensation surface shape diagram in the embodiment of the present invention.

[0061] Figure 7 This is the result of the sine phase with a frequency of 0.5 mm -1 and an amplitude of 10 nm measured in the embodiment of the present invention.

[0062] Figure 8 This is the result of the sine phase with a frequency of 1 mm -1 and an amplitude of 10 nm measured in the embodiment of the present invention.

[0063] Figure 9 This is the result of the sine phase with a frequency of 2 mm -1 and an amplitude of 10 nm measured in the embodiment of the present invention.

[0064] Figure 10 This is the calibration result diagram of the instrument transfer function finally generated in the embodiment of the present invention. Detailed implementation manners

[0065] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention will be further described in detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0066] As Figure 1 shown, the method for measuring the instrument transfer function of the interferometer based on the spatial light modulator in this embodiment includes the following steps: compensating the inherent phase difference of the spatial light modulator, generating a set of sine phases with different periods and the same amplitude, and using a wavefront interferometer and the spatial light modulator to measure the sine phase results under different sine phases; calculating the ITF value according to the obtained sine phase results under different sine phases, and plotting a fitting curve graph with the ITF value on the vertical axis and the frequency on the horizontal axis to obtain the transfer function curve of the wavefront interferometer to be measured. The method for measuring the instrument transfer function of the interferometer based on the spatial light modulator in this embodiment meets the international standard definition and is not restricted by processing conditions. The present invention significantly improves the accuracy and flexibility of measuring the instrument transfer function of the interferometer through high-precision spatial light modulation and multiple rounds of iterative compensation, not only effectively improving the accuracy and frequency coverage range of measuring the instrument transfer function of the interferometer, but also realizing high flexibility in the measurement process.

[0067] The function expression of the sine phase generated in this embodiment is:

[0068] ,

[0069] wherein, is the sine phase, is the amplitude of the sine phase, is the th required period of the sine phase, is the index of the current data row, is the phase of the sine phase, is the offset of the sine phase. The amplitude and period can be modified as needed to generate the required sine phase; where i = 1, 2,.... In this embodiment, when generating a set of sine phases with different periods and the same amplitude, a sine phase with a frequency of mm -1 and an amplitude of nm can be generated and measured first. Then, when generating another set of sine phases with different periods and the same amplitude, a sine phase with a frequency of mm -1 and an amplitude of nm can be generated and measured, and so on, until the generation and measurement of this set of sine phases are completed.

[0070] Figure 3Schematic diagram of the optical path structure in this embodiment. The optical path structure includes a wavefront interferometer 1, a spatial light modulator 2, a spatial light modulator control module 3, and an instrument transfer function processing module 4. In this embodiment, the spatial light modulator 2 is a reflective spatial light modulator. Additionally, other types of spatial light modulators can also be used according to requirements. The spatial light modulator control program module 3 includes an inherent surface shape display program module, a surface shape compensation program module, and a sine phase generation program module. Among them, the inherent surface shape display module is used to generate a grayscale image with a grayscale value of 0; the surface shape compensation module can generate a new grayscale image for compensation based on the inherent surface shape data and the previous compensation surface shape data; the sine phase generation module is used to generate sine phases with different amplitudes and periods. The process by which the surface shape compensation module can generate a new grayscale image for compensation based on the inherent surface shape data and the previous compensation surface shape data includes: using the inherent surface shape data measured by the interferometer under test or the previous compensation surface shape data to generate a new compensation phase grayscale image. After iterative compensation or single compensation through the above process, the influence of the inherent surface shape of the spatial light modulator is eliminated. The instrument transfer function processing module 4 is used to calculate the ITF value based on the sine phase results under different sine phases and draw a fitting curve graph with the ITF value on the vertical axis and the frequency on the horizontal axis to obtain the transfer function curve of the interferometer under test. The instrument transfer function processing program module 4 includes a data preprocessing program module, a phase fitting and optimization program module, an instrument transfer function calculation program module, and a result storage and output program module. Among them, the data preprocessing module is responsible for reading, cropping, and compensating data; the phase fitting and optimization module fits the processed data, optimizes the data through a sine function model, and extracts amplitude information; the instrument transfer function calculation module calculates the instrument transfer function of the interferometer under test based on the fitting results; the result storage and output module stores the final calculation results and outputs them in a format suitable for further use. The process by which the data preprocessing module is responsible for reading, cropping, and compensating data includes: loading interference data files with different frequencies, including X, Y coordinates, and Z values; cropping the data according to the row and column differences of the data to ensure that the sizes of all data sets are consistent; using a surface shape compensation algorithm to remove measurement errors to ensure the accuracy and consistency of the data and provide high-quality data for the fitting module. The process by which the phase fitting and optimization module fits the processed data, optimizes the data through a sine function model, and extracts amplitude information includes: dividing the data into small blocks, and the size of each small block is determined according to the period of the spatial frequency; performing sine function fitting on each row of data in each data block, optimizing the amplitude, phase, and offset parameters; extracting the amplitude information of each row to generate an amplitude matrix and optimizing the results to ensure that the fitting results are consistent with the measurement data.The instrument transfer function calculation module calculates the instrument transfer function of the interferometer to be tested based on the fitting results, including: averaging the amplitude of the data block of each frequency to obtain the average amplitude value at the frequency; calculating the ratio of the average amplitude of each frequency to the standard amplitude value to obtain the instrument transfer function. The result storage and output module stores the final calculation results and outputs them in a format suitable for further use, including: saving the fitted data and transfer function to a specified file, generating and saving the result chart for subsequent analysis.

[0071] like Figure 2 As shown, the inherent phase difference compensation of the spatial light modulator in this embodiment is performed to generate a set of sinusoidal phases with different periods and the same amplitude, and the sinusoidal phase results under different sinusoidal phases are measured by using a wavefront interferometer and a spatial light modulator, including:

[0072] S101: Place the spatial light modulator at the corresponding position of the interferometer to be tested, and adjust the interval between the light spot and the fringe; the corresponding position means that the spatial light modulator can be placed at different positions such as the top, bottom, left, and right of the interferometer lens to be tested as needed; the core of adjusting the light spot of the wavefront interferometer is to optimize the optical path alignment and interference conditions, ensure that the reference light and the test light overlap accurately to improve the fringe contrast and eliminate system errors; adjust the fringe interval by controlling the angle between the two light beams, balancing the measurement sensitivity and dynamic range, so that the fringe density adapts to the observation requirements, algorithm processing and environmental anti-disturbance capabilities, so as to accurately analyze the surface morphology or wavefront characteristics of the component under test;

[0073] S102: Measure and obtain the intrinsic surface data of the spatial light modulator. The result is as follows: Figure 4 As shown; in step S102 of this embodiment, measuring the intrinsic surface data of the spatial light modulator includes the following specific steps: using the interferometer's own software to mask the effective display area of ​​the spatial light modulator, running the intrinsic surface display module in the spatial light modulator control module 3, and after the operation is completed, performing continuous measurements with an average number of times of not less than 100, until the two data values ​​before and after are stable, and taking the last measurement data as the intrinsic surface data.

[0074] S103: compensating the intrinsic surface shape data of the spatial light modulator to generate first compensated surface shape data; in step S103 of this embodiment, generating the first compensated surface shape data includes the following specific steps: inputting the obtained intrinsic surface shape data into the spatial light modulator control module 3, running the surface shape compensation module, and generating a new compensated phase map on the spatial light modulator;

[0075] S104: adjusting the first-order diffracted light spot of the spatial light modulator to coincide with the light spot of the interferometer to be measured;

[0076] S105: Measure the compensation surface shape data of the spatial light modulator, and the obtained result is as Figure 5 shown;

[0077] S106: Compensate the inherent surface shape data of the spatial light modulator and generate the compensation surface shape data again;

[0078] S107: Determine whether the compensation surface shape data generated again meets the accuracy requirements. If it does not meet the accuracy requirements, repeat steps S105 and S106 again until the compensation surface shape data generated again meets the accuracy requirements;

[0079] S108: Measure the final compensation surface shape data, and the obtained result is as Figure 6 shown;

[0080] S109: Generate the sine phase of the th required period , and the amplitude of this sine phase is a fixed value; in step S109, generating the required sine phase includes the following specific steps: modify the amplitude or period parameter of the sine phase generation module in the spatial light modulator control module 3, and run the sine phase generation module;

[0081] S110: Measure the sine phase result corresponding to the sine phase of the th required period ; for example, in this embodiment, the sine phase results of the sine phase with a frequency of 0.5 mm -1 and an amplitude of 10 nm are as Figure 7 shown, the sine phase results of the sine phase with a frequency of 1 mm -1 and an amplitude of 10 nm are as Figure 8 shown, and the sine phase results of the sine phase with a frequency of 2 mm -1 and an amplitude of 10 nm are as Figure 9 shown;

[0082] S111: Determine whether the sine phases of all required periods have been measured. If not, generate the th compensation surface shape data, and repeat steps S105 and S110 again until the sine phases of all required periods are measured.

[0083] In this embodiment, the compensation for the inherent surface shape data of the spatial light modulator includes: generating a grayscale image with a grayscale value of 0, and generating a new compensation phase grayscale image from the inherent surface shape data of the spatial light modulator and the grayscale image with a grayscale value of 0:

[0084] ,

[0085] ,

[0086] Among them, is the new compensated phase grayscale image, is the horizontal coordinate of the spatial light modulator, is the rounding operator, and are respectively the coefficients of the tilt carrier along the axis and axis of the spatial light modulator, is the phase, with the unit of radian; represents the conjugate phase of the IWD (Inherent wavefront distortion) resampled to match the resolution of the spatial light modulator.

[0087] In this embodiment, calculating the ITF value according to the sine phase results under different sine phases and drawing a fitting curve graph with the ITF value as the ordinate and the frequency as the abscissa to obtain the transfer function curve of the wavefront interferometer to be measured includes:

[0088] S201: Obtain the amplitude corresponding to the sine phase according to the sine phase results under different sine phases;

[0089] S202: Calculate the ratio of the amplitude under each sine phase to the standard amplitude value to obtain the ITF value;

[0090] S203: Draw a fitting curve graph with the ITF value as the ordinate and the frequency as the abscissa for the ITF values under each sine phase to obtain the transfer function curve of the wavefront interferometer to be measured, as Figure 10 shown.

[0091] In this embodiment, step S201 includes:

[0092] S301: Load the sine phase results under different sine phases, including X, Y coordinates and Z values; the data can be cropped according to the row and column differences of the data to ensure that the sizes of all data sets are consistent;

[0093] S302: Use the surface shape compensation algorithm to remove the measurement error from the sine phase results under different sine phases. By using the surface shape compensation algorithm to remove the measurement error, the accuracy and consistency of the data are ensured, providing high-quality data for the fitting module; among them, using the surface shape compensation algorithm to remove the measurement error means subtracting the final compensated surface shape data obtained above from the sine phase results under each sine phase, and then the measurement error can be removed and the sine phase results after removing the measurement error can be obtained;

[0094] S303: Divide the sine phase results after removing the measurement error into data blocks;

[0095] S304: Fit a sine function to each data block and extract the amplitude of the sine function obtained from the fitting; As an optional implementation, this embodiment further includes extracting the amplitudes of the data blocks to generate an amplitude matrix, and optimizing the results of the amplitude matrix to ensure that the fitting results are consistent with the measurement data, including:

[0096] S304.1: Perform initial parameter estimation on the amplitude matrix, including: for each row of data in the amplitude matrix , where 、 are respectively the positions of the th pixel in a single row of the amplitude matrix, the amplitude measurement value of the th pixel, is the total number of pixels in a single row, and initialize the parameters based on the data characteristics:

[0097] ,

[0098] where, is the initial peak-to-peak value, is the initial mean value, is the initial phase offset;

[0099] S304.2: Perform non-linear least squares optimization, including: aiming at minimizing the sum of squared residuals, solve for the optimal parameters:

[0100] ,

[0101] where, is the peak-to-peak value, is the th frequency to be measured, is the mean value,

[0102] S304.3: Adopt the Levenberg-Marquardt algorithm to iteratively update the parameters until convergence:

[0103] ,

[0104] where, and are respectively the parameter vectors and formed by the parameters of the th and th iterations, and there is , is the Jacobian matrix of the residuals with respect to the parameters, is the residual vector, is the damping factor, and the superscript

[0105] S305: Average the amplitudes of each data block under the same sine phase as the amplitude under that sine phase.

[0106] In this embodiment, when dividing the sine phase result after removing measurement errors into data blocks in step S303, the sizes of the data blocks of sine phases with different periods are different.

[0107] In this embodiment, after calculating the ITF value according to the sine phase results under different sine phases obtained, and drawing a fitting curve graph with the ITF value as the ordinate and the frequency as the abscissa to obtain the transfer function curve of the wavefront interferometer to be measured, it further includes generating a result chart of the transfer function curve of the wavefront interferometer to be measured and saving it to a specified file.

[0108] In this embodiment, when generating a result chart of the transfer function curve of the wavefront interferometer to be measured and saving it to a specified file, it further includes writing the amplitude, phase, and offset of the sine function fitting under each sine phase into the result chart and saving it to a specified file.

[0109] In summary, the method of this embodiment accurately obtains the instrument transfer function of the interferometer by measuring the nano-precision and reconfigurable different-period sine phases generated by the spatial light modulator, and solves the problems of poor flexibility and insufficient precision in traditional measurement methods. The method of this embodiment can improve the precision and flexibility of the measurement of the instrument transfer function of the interferometer, and is particularly suitable for the calibration and detection of wavefront interferometers. Compared with traditional methods, the method of this embodiment not only avoids the difficulty of processing ITF sine phase plates with millimeter, sub-millimeter, or even nano-amplitude by traditional processing methods, but also can provide more accurate measurement results starting from the definition of the instrument transfer function, and has important theoretical value and application prospects.

[0110] The above are only the preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the idea of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for measuring the transfer function of an interferometer instrument based on a spatial light modulator, characterized in that: The steps include: Compensate the inherent phase difference of the spatial light modulator to generate a set of sinusoidal phases with different periods and the same amplitude, and use a wavefront interferometer and a spatial light modulator to measure the sinusoidal phase results under different sinusoidal phases; The ITF value is calculated according to the obtained sinusoidal phase results under different sinusoidal phases, and a fitting curve is drawn with the ordinate being the ITF value and the abscissa being the frequency to obtain the transfer function curve of the wavefront interferometer to be tested; When a group of sinusoidal phases with different periods and the same amplitude are generated, the function expression of the generated sinusoidal phases is: ， in, is the sinusoidal phase, is the amplitude of the sinusoidal phase, The sinusoidal phase The required cycle, is the index of the current data row, is the phase of the sine phase, is the sinusoidal phase offset.

2. The interferometer instrument transfer function measurement method based on spatial light modulator according to claim 1, characterized in that: The method of compensating the inherent phase difference of the spatial light modulator to generate a set of sinusoidal phases with different periods and the same amplitude and measuring the sinusoidal phase results under different sinusoidal phases by using a wavefront interferometer and a spatial light modulator comprises: S101: placing the spatial light modulator at the corresponding position of the interferometer to be measured, and adjusting the interval between the light spot and the fringe; S102: Measure and obtain intrinsic surface shape data of the spatial light modulator; S103: compensating the inherent surface shape data of the spatial light modulator to generate first compensated surface shape data; S104: adjusting the first-order diffracted light spot of the spatial light modulator to coincide with the light spot of the interferometer to be measured; S105: Measure and obtain compensation surface shape data of the spatial light modulator; S106: compensating the inherent surface shape data of the spatial light modulator to generate compensated surface shape data again; S107: judging whether the compensated surface shape data generated again meets the accuracy requirement, and if it does not meet the accuracy requirement, repeating steps S105 and S106 until the compensated surface shape data generated again meets the accuracy requirement; S108: Measure and obtain final compensated surface shape data; S109: Generate Required cycles The sine phase of the sine phase has a fixed amplitude; S110: Measure the Required cycles The sinusoidal phase result corresponding to the sinusoidal phase of ; S111: Determine whether all the required periodic sinusoidal phases have been measured. If not, generate the first The surface shape data is compensated again, and steps S105 and S110 are repeated again until all the sinusoidal phases of the required periods are measured.

3. The interferometer instrument transfer function measurement method based on spatial light modulator according to claim 2, characterized in that: The compensating the intrinsic surface shape data of the spatial light modulator includes: generating a grayscale image with a grayscale value of 0, and generating a new compensated phase grayscale image by using the intrinsic surface shape data of the spatial light modulator and the grayscale image with a grayscale value of 0: ， ， in, is the new compensated phase grayscale image, is the lateral coordinate of the spatial light modulator, is the rounding operator, and are along the spatial light modulator Axis and The coefficient of the tilt of the axis of the carrier, is the phase, the unit is radian; Represents the conjugate phase of the inherent wavefront distortion resampled to match the resolution of the spatial light modulator.

4. The interferometer instrument transfer function measurement method based on spatial light modulator according to claim 1, characterized in that: The method of calculating the ITF value according to the obtained sinusoidal phase results under different sinusoidal phases and drawing a fitting curve graph with the ordinate being the ITF value and the abscissa being the frequency to obtain the transfer function curve of the wavefront interferometer to be measured includes: S201: Obtaining the amplitude at the corresponding sinusoidal phase according to the obtained sinusoidal phase results at different sinusoidal phases; S202: Calculate the ratio of the amplitude at each sinusoidal phase to the standard amplitude value to obtain an ITF value; S203: Plotting the ITF values ​​at each sinusoidal phase into a fitting curve graph with the ordinate being the ITF value and the abscissa being the frequency to obtain a transfer function curve of the wavefront interferometer to be tested.

5. The interferometer instrument transfer function measurement method based on spatial light modulator according to claim 4, characterized in that: Step S201 includes: S301: Load the sine phase results under different sine phases, including X, Y coordinates and Z value; S302: using a surface shape compensation algorithm to remove measurement errors from the sinusoidal phase results at different sinusoidal phases; wherein using the surface shape compensation algorithm to remove measurement errors means subtracting the sinusoidal phase results at each sinusoidal phase from the final compensated surface shape data obtained above, thereby removing the measurement errors and obtaining sinusoidal phase results after the measurement errors are removed; S303: Divide the sinusoidal phase result after removing the measurement error into data blocks; S304: performing sinusoidal function fitting on each data block, and extracting the amplitude of the fitted sinusoidal function; S305: average the amplitudes of the data blocks under the same sinusoidal phase as the amplitude under the sinusoidal phase.

6. The interferometer instrument transfer function measurement method based on spatial light modulator according to claim 5, characterized in that: When the sinusoidal phase result after the measurement error is removed is divided into data blocks in step S303, the sizes of the data blocks of sinusoidal phases with different periods are different.

7. The interferometer instrument transfer function measurement method based on spatial light modulator according to claim 5, characterized in that: After extracting the amplitude of the fitted sine function in step S304, the process further includes constructing an amplitude matrix according to the amplitudes of each data block, and optimizing the amplitude matrix to ensure that the fitting result is consistent with the measured data, including: S304.1: Perform initial parameter estimation on the amplitude matrix, including: ,in , They are the single row in the amplitude matrix The pixel position, The amplitude measurement of pixels, The total number of pixels in a single row, initialized based on the data characteristics: ， in, is the initial peak-to-peak value, is the initial mean value, is the initial phase offset; S304.2: Perform nonlinear least squares optimization, including: solving the optimal parameters with the goal of minimizing the sum of squared residuals: ， in, is the peak-to-peak value, is the frequency to be measured for the ith frequency, is the mean, is the phase offset; S304.3: Use the Levenberg-Marquardt algorithm to iteratively update parameters until convergence: ， in, and Respectively and The parameter vector consisting of the parameters of the iteration , and there is , is the Jacobian matrix of the residual to parameters, is the residual vector, is the damping factor, the superscript is the transpose operation.

8. The interferometer instrument transfer function measurement method based on spatial light modulator according to claim 7, characterized in that: After calculating the ITF value according to the obtained sinusoidal phase results under different sinusoidal phases, and drawing a fitting curve graph with the ordinate as the ITF value and the abscissa as the frequency to obtain the transfer function curve of the wavefront interferometer to be measured, it also includes generating a result chart from the transfer function curve of the wavefront interferometer to be measured and saving it to a designated file; when generating the result chart from the transfer function curve of the wavefront interferometer to be measured and saving it to the designated file, it also includes writing the amplitude, phase and offset of the sinusoidal function fitting under each sinusoidal phase into the result chart and saving it to the designated file.

9. The interferometer instrument transfer function measurement method based on spatial light modulator according to claim 1, characterized in that: The spatial light modulator is a reflective spatial light modulator.

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