A stitching diffraction system common phase error measurement method based on dual-wavelength interference

Abstract

The application provides a splicing diffraction system common phase error measurement method based on two-wavelength interference, and belongs to the technical field of optical wavefront detection. The method comprises the following steps: S1, generating a binary mask and an overall pupil mask for each sub-aperture according to the layout and effective radius of a plurality of sub-apertures; S2, acquiring an interference frame sequence of two laser wavelengths; S3, performing phase demodulation on the interference frame sequence of the two laser wavelengths, and multiplying the overall pupil mask to respectively calculate a single-wavelength effective phase; S4, calculating a synthesized wavefront optical path according to the single-wavelength effective phase; and S5, performing segmented Zernike polynomial fitting on the synthesized wavefront optical path according to the binary mask corresponding to each sub-aperture to obtain piston error and tilt error of each sub-aperture, so that the common phase error is obtained. The application only considers the measurement link and does not involve imaging evaluation, and has the advantages of simple implementation, large range, high precision and strong applicability.

Description

Technical Field

[0001] This invention belongs to the field of optical wavefront detection technology, and in particular, relates to a method for measuring the co-phase error of a spliced ​​diffraction system based on dual-wavelength interference. Background Technology

[0002] During assembly, adjustment, and operation, spliced ​​diffraction systems are prone to phase inconsistencies between sub-apertures. For example, piston errors can cause abrupt changes in optical path, and tilting errors can introduce phase gradients. Existing technologies typically employ Shack-Hartmann wavefront detectors or capacitive / inductive edge sensors for monitoring. However, the former has limited sensitivity in detecting minute piston errors across segments, while the latter is an indirect measurement method and is susceptible to environmental drift. Furthermore, while traditional single-wavelength interferometry, as a direct measurement method, possesses extremely high detection accuracy, its unambiguous measurement range is typically less than one wavelength due to phase entanglement caused by the periodicity of light waves, making it difficult to stably recover the true optical path difference over a large dynamic range. Therefore, a measurement scheme that combines a large range with high accuracy is urgently needed. Summary of the Invention

[0003] The purpose of this invention is to propose a method for measuring the co-phase error of a stitched diffraction system based on dual-wavelength interference, which can be used to solve the problem of high-precision measurement of piston error and tilt error in stitched diffraction imaging systems.

[0004] To achieve the above objectives, this invention provides a method for measuring the co-phase error of a spliced ​​diffraction system based on dual-wavelength interference, the method comprising:

[0005] Step S1: Based on the layout and effective radius of the multiple sub-apertures of the diffractive optical element, generate a binary mask for each sub-aperture and generate an overall pupil mask for the diffractive optical element.

[0006] Step S2: Obtain interference frame sequences for two laser wavelengths using a four-step phase-shifting sequence;

[0007] Step S3: The four-step phase-shifting algorithm is used to demodulate the phase of the interference frame sequences of the two laser wavelengths respectively, and multiply them by the overall pupil mask to calculate the single-wavelength effective phase of each laser wavelength in the two laser wavelengths respectively.

[0008] Step S4: Calculate the composite wavefront optical path of the diffractive optical element using the single-wavelength effective phase of the two laser wavelengths.

[0009] Step S5: Perform piecewise Zernike polynomial fitting on the synthesized wavefront optical path according to the binarized mask corresponding to each sub-aperture to obtain the piston error and tilt error of each sub-aperture, thereby obtaining the co-phase error.

[0010] The beneficial effects of this invention are as follows:

[0011] The technical solution of this invention achieves precise quantification of the sub-aperture adjustment error, including:

[0012] (1) No complex hardware modification required: It only relies on two laser wavelengths and four-step phase shift acquisition. The synthesized wavelength is directly calculated and the phase of the two channels is demodulated in the code to achieve large-range optical path recovery and is more robust to light intensity bias.

[0013] (2) Direct output of adjustment: By combining the pupil mask and piecewise Zernike polynomial fitting, the piston error and tilt error of each sub-aperture can be directly obtained, and the relative phase can be calculated to form a unified zero reference, which facilitates rapid on-site calibration and closed-loop iteration.

[0014] (3) It has strong engineering usability, can generate interference frames and error visualization of two wavelengths and the composite wavelength at the same time, and outputs measurement results for easy quality inspection and playback. The overall process is clear and the experiment is easy to reproduce. Attached Figure Description

[0015] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:

[0016] Figure 1 A flowchart of the method for measuring the co-phase error of a spliced ​​diffraction system based on dual-wavelength interference provided by the present invention;

[0017] Figure 2 The measurement diagram provided by the present invention uses a four-step phase-shifting method via dual-wavelength interferometry, wherein, Figure 2 In the diagram, (a) shows the interference fringe pattern at the composite wavelength with a phase shift of 0. Figure 2 (b) in the equation represents the phase shift. Interference fringe pattern of the synthesized wavelength. Figure 2 (c) in the equation represents the phase shift. Interference fringe pattern of the synthesized wavelength. Figure 2 In this context, (d) represents the phase shift. Interference fringe pattern of the synthesized wavelength;

[0018] Figure 3 A comparison chart of common phase error measurement results obtained through simulation, provided for embodiments of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this invention adopts the following technical solution.

[0020] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0021] Figure 1 The flowchart of the method for measuring the co-phase error of a spliced ​​diffraction system based on dual-wavelength interferometry provided by this invention is as follows: Figure 1 As shown, the method includes:

[0022] Step S1: Based on the layout and effective radius of the multiple sub-apertures of the diffractive optical element, generate a binary mask for each sub-aperture and generate the overall pupil mask of the diffractive optical element.

[0023] Step S2 involves obtaining interference frame sequences for two laser wavelengths using a four-step phase-shifting sequence. The four-step phase-shifting sequence is, for example... .

[0024] Step S3: The four-step phase-shifting algorithm is used to demodulate the phase of the interference frame sequences of the two laser wavelengths respectively, and multiply them by the overall pupil mask to calculate the single-wavelength effective phase of each laser wavelength.

[0025] Step S4: Calculate the composite wavefront optical path of the diffractive optical element using the single-wavelength effective phase of the two laser wavelengths.

[0026] Step S5: Perform piecewise Zernike polynomial fitting on the synthesized wavefront optical path according to the binarized mask corresponding to each sub-aperture to obtain the piston error and tilt error of each sub-aperture, thereby obtaining the co-phase error.

[0027] In the embodiments provided by the present invention, the two laser wavelengths are respectively the first laser wavelength. Second laser wavelength Therefore, the combined wavelength formed by combining the two laser wavelengths can be calculated:

[0028] ;

[0029] in, The composite wavelength is formed by combining two laser wavelengths.

[0030] In step S4, the optical path length of the synthesized wavefront is calculated as follows:

[0031] ;

[0032] in, To synthesize the wavefront optical path, The composite wavelength is formed by combining two laser wavelengths. , The first laser wavelength, The second laser wavelength is included in the two laser wavelengths, which are the first laser wavelength. Second laser wavelength , This indicates the argument operation, which extracts the phase angle of a complex number. The argument range is typically 10 ... , This represents an exponential function with base e. The imaginary unit, For the first laser wavelength The first single-wavelength effective phase is obtained by phase demodulation after multiplying a four-step phase-shift sequence with a pupil mask. To the second laser wavelength The second single-wavelength effective phase is obtained by phase demodulation after multiplying a four-step phase-shift sequence with a pupil mask.

[0033] First single-wavelength effective phase Second single-wavelength effective phase The phase demodulation of the interference frame sequence was performed using a four-step phase shift algorithm.

[0034] Among them, the first single-wavelength effective phase Second single-wavelength effective phase The first single-wavelength effective phase is obtained by phase demodulating the interferometric frame sequence using a four-step phase-shifting algorithm. Second single-wavelength effective phase The calculation is as follows:

[0035] ;

[0036] ;

[0037] in, Represents the arctangent function in the four quadrants, with a range of . , , , , These correspond to the first laser wavelength. The light intensity distribution of four interferograms obtained from the interferometric frame sequence is shown below. , , , These correspond to the second laser wavelength. The light intensity distribution of four interferograms obtained by the interferometric frame sequence is shown below.

[0038] Generating a binarized mask for each sub-aperture includes: determining the geometric center coordinates and effective radius of each sub-aperture based on the layout of multiple sub-apertures of the diffractive optical element; calculating the Euclidean distance from each pixel in the sub-aperture to the center of the corresponding sub-aperture for each sub-aperture to generate a binarized mask for each sub-aperture; and the binarized masks of all sub-apertures constitute a set of binarized masks.

[0039] Generating the overall pupil mask of the diffractive optical element includes: performing a logical OR operation on the binary mask corresponding to each sub-aperture in the binary mask set to generate a pupil mask covering all sub-apertures, so as to form the overall pupil mask of the diffractive optical element.

[0040] For each sub-aperture, calculate the Euclidean distance from each pixel in the sub-aperture to the center of the corresponding sub-aperture to generate a binary mask for each sub-aperture. This includes: assigning the corresponding pixel a value of 1 if the Euclidean distance is less than or equal to the effective radius of the corresponding sub-aperture, and otherwise assigning a value of 0.

[0041] Among them, at the interferometric acquisition end, according to Generate a four-step interferometric frame sequence for two laser wavelengths. For the first laser wavelength... Second laser wavelength The corresponding light intensity formulas for the four interferogram frames are as follows:

[0042] ;

[0043] ;

[0044] in, For the first laser wavelength The intensity distribution of the interferogram at the k-th phase shift. For the second laser wavelength The intensity distribution of the interferogram at the k-th phase shift, where k takes the values ​​1, 2, 3, and 4; For the reference light intensity, To test the light intensity, The first laser wavelength The phase difference distribution between the reference beam and the test beam, including piston error and tilt error. The second laser wavelength The phase difference distribution between the lower reference beam and the test beam includes piston error and tilt error; The phase shift introduced at the k-th phase shift has the following value sequence: .

[0045] Figure 2 The measurement diagram provided by the present invention uses a four-step phase-shifting method via dual-wavelength interferometry, wherein, Figure 2 In the diagram, (a) shows the interference fringe pattern at the composite wavelength with a phase shift of 0. Figure 2 (b) in the equation represents the phase shift. Interference fringe pattern of the synthesized wavelength. Figure 2 (c) in the equation represents the phase shift. Interference fringe pattern of the synthesized wavelength. Figure 2 In this context, (d) represents the phase shift. Interference fringe patterns of the synthesized wavelengths, such as Figure 2 As shown, through Figure 2 The interference fringe pattern shown allows for a direct observation of the fringe misalignment caused by co-phase error.

[0046] A binary mask set and a global pupil mask are generated based on the geometric data of the sub-apertures (including the effective diameter, focal length, and center coordinates of the sub-apertures). First, the local coordinates of each pixel relative to the geometric center of its respective sub-aperture are obtained by calculating the difference between the coordinates of each pixel in the sub-aperture and the corresponding geometric center of the sub-aperture. Secondly, calculate the Euclidean distance R from each pixel to the geometric center of the sub-aperture, and then... The region is set to 1. The effective diameter of the sub-apertures is introduced to introduce tilt error, and the rest are set to 0, thereby generating a binary mask for each sub-aperture. Finally, a logical OR operation is performed on the binary masks of all sub-apertures in the generated binary mask set to construct an overall pupil mask with a value of 1 only in the effective light-transmitting area and 0 in the background area.

[0047] To verify the accuracy of the technical solution provided by this invention, an error can be applied to a specific sub-aperture. For example, any two sub-apertures from multiple sub-apertures can be selected, and a piston error can be introduced into one sub-aperture while a tilting error is introduced into the other. The calculation process for the piston error injection is as follows: The piston error in the form of a physical optical path is set. (Unit: meters), Piston error That is, the rigid displacement optical path difference along the optical axis. Based on the physical relationship between phase and optical path, the piston error is calculated. Phase delay at two laser wavelengths (i.e., two single wavelengths) and and the phase delay amount and The phase delay is superimposed on the wavefront phase of the corresponding sub-aperture. and The calculation is as follows:

[0048] ;

[0049] ;

[0050] in, The first laser wavelength, The second laser wavelength, For the first laser wavelength The phase delay generated below, For the second laser wavelength The amount of phase delay generated below.

[0051] The formula for calculating tilt error is as follows:

[0052] ;

[0053] in, For coordinates The tilt error phase value at that location, This is the preset tilt strength coefficient along the X-axis direction. The preset tilt strength coefficient along the Y-axis direction. and These are the x and y coordinates of the pixel, respectively. and These are the x and y coordinates of the geometric center of the sub-aperture, which introduces tilt error. The effective diameter of the sub-aperture to introduce tilt error.

[0054] In step S3, the process of multiplying with the overall pupil mask is to perform a dot product operation, which forces the phase of the background area with a mask value of 0 to zero, and only retains the phase data of the effective aperture area, in order to remove background noise interference.

[0055] Step S5 includes: using a traversal method, spatially indexing the synthesized wavefront optical path for each binary mask in the binary mask set to obtain the local wavefront optical path corresponding to each sub-aperture; performing piecewise Zernike polynomial fitting based on the local wavefront optical path corresponding to each sub-aperture to obtain the piston error and tilt error of each sub-aperture, thereby obtaining the co-phase error.

[0056] Specifically, piecewise Zernike polynomial fitting is performed based on the local wavefront optical path length corresponding to each sub-aperture to obtain the piston error and tilt error of each sub-aperture. This includes: for each sub-aperture, the local wavefront optical path length of the corresponding sub-aperture is used as the observation vector W; for each sub-aperture, an observation matrix Z is constructed based on the Zernike polynomial; based on the observation vector W and the observation matrix Z, the overdetermined equation system is solved using the least squares method to obtain the coefficient vector A; and based on the coefficient vector A, the piston error and tilt error of each sub-aperture are obtained.

[0057] The observation matrix Z is constructed based on Zernike polynomials, including: using the first three terms of the Zernike polynomials as basis functions for fitting, where the first term of the basis function is a constant 1, representing a piston term translated along the optical axis, and the second term of the basis function is... , represents a linear function that slopes along the horizontal coordinate axis, and the third term of the basis functions is , represents a linear function inclined along the direction perpendicular to the coordinate axis, where, This represents the normalized distance from a point within a sub-aperture to the geometric center of that sub-aperture. The rotation angle of a point within a sub-aperture relative to the geometric center of the corresponding sub-aperture is represented; where the observation matrix Z is composed of basis functions, the horizontal axis represents the direction of increase of the row vector of the pixel, and the vertical axis represents the direction of increase of the column vector of the pixel.

[0058] Specifically, the coordinate system of this invention is established as follows: the X-axis and Y-axis are defined in a plane perpendicular to the laser propagation direction. The X-axis is the direction of increase of the row vector of the pixel, and the Y-axis is the direction of increase of the column vector of the pixel. The X-axis is the horizontal axis, i.e., the horizontal coordinate axis, and the Y-axis is the vertical axis, i.e., the vertical coordinate axis.

[0059] The coefficient vector A includes three coefficients: a first coefficient, a second coefficient, and a third coefficient. The first coefficient is the piston error of the corresponding sub-aperture, the second coefficient is the horizontal axis tilt error of the corresponding sub-aperture, and the third coefficient is the vertical axis tilt error of the corresponding sub-aperture. The first coefficient corresponds to the first term of the basis function, the second coefficient corresponds to the second term of the basis function, and the third coefficient corresponds to the third term of the basis function.

[0060] Specifically, piecewise Zernike polynomial fitting is performed based on the local wavefront optical path length corresponding to each sub-aperture mask, including: constructing an observation matrix in a normalized coordinate system for each sub-aperture. Among them, the normalized radial coordinates The calculation formula is:

[0061] ;

[0062] in, For the first Geometric center coordinates of individual apertures For the first The effective radius of each aperture.

[0063] Solving the overdetermined system of equations using the least squares method Directly output the piston and tilt coefficient vectors for each sub-aperture. And based on this, the cophase error value is obtained.

[0064] in, This is the first coefficient, representing the piston error for the corresponding sub-aperture. The second coefficient represents the horizontal axis tilt error of the corresponding sub-aperture. The third coefficient represents the vertical coordinate axis tilt error of the corresponding sub-aperture, where the second coefficient... With the second term of the basis function Correspondingly, the tilt error of the corresponding sub-aperture along the X-axis (horizontal direction) is represented by the third coefficient. With the third term of the basis function Correspondingly, this represents the tilt error of the corresponding sub-aperture along the Y-axis (vertical direction).

[0065] The method for measuring the co-phase error of a spliced ​​diffraction system based on dual-wavelength interference provided by the present invention further includes: taking the sub-aperture located at the geometric center of the multiple sub-apertures of the diffractive optical element as the reference sub-aperture; and calculating the relative co-phase error of all sub-apertures based on the piston error, horizontal coordinate axis tilt error, and vertical coordinate axis tilt error of the reference sub-aperture, as well as the piston error, horizontal coordinate axis tilt error, and vertical coordinate axis tilt error of all sub-apertures.

[0066] The specific calculation formula is as follows:

[0067] ;

[0068] ;

[0069] ;

[0070] in, Indicates the first Relative piston error of individual orifice diameter Indicates the first Relative X-axis tilt error of individual apertures Indicates the first The relative Y-axis tilt error of each aperture, Indicates the first The piston error obtained by fitting the individual apertures using Zernike (the first) (the first coefficient corresponding to each aperture) Indicates the first The tilt error in the X-axis direction (horizontal direction) obtained by Zernike fitting for each aperture (the first... (the second coefficient corresponding to each aperture) Indicates the first The tilt error in the Y-axis direction (vertical direction) obtained by Zernike fitting for each aperture (the first... (the third coefficient corresponding to each aperture) This represents the piston error (the first coefficient corresponding to the specific sub-aperture) obtained by Zernike fitting for a specific sub-aperture (index 1). This represents the tilt error in the X-axis direction (horizontal direction) obtained by Zernike fitting for a specific sub-aperture (index 1) (the second coefficient corresponding to the specific sub-aperture). This represents the tilt error in the Y-axis direction (vertical direction) obtained by Zernike fitting for a specific sub-aperture (index 1) (the third coefficient corresponding to the specific sub-aperture).

[0071] In a stitched diffraction system, the relative phase mismatch between sub-apertures affects the system's co-phase state and imaging quality. Therefore, alignment is required using a specific sub-aperture as a physical reference. By calculating the relative co-phase error of each sub-aperture relative to the reference sub-aperture, global rigid body displacement interference introduced by the measurement environment can be filtered out and directly used as the feedback driving quantity for error compensation, thereby completing high-precision co-phase measurement.

[0072] Figure 3 A comparison chart of common phase error measurement results obtained through simulation is provided for embodiments of the present invention, such as... Figure 3 As shown, Figure 3 This paper presents a comparison chart of 100 random co-phase error measurement results obtained through simulation using the technical solution of this invention. Figure 3 It can be seen that the phase error measurement value calculated by the technical solution of this invention is in high agreement with the preset actual value (theoretical value). Within a large range of 10 micrometers to 20 micrometers, the curve formed by the measurement value maintains a very high consistency and accurate tracking with the curve formed by the actual value (theoretical value). There is no phase unpacking error or deviation due to the large range, which intuitively verifies the accuracy and reliability of this invention in measuring phase error under a large dynamic range.

[0073] The optional embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the embodiments of the present invention are not limited to the specific details in the above embodiments. Within the scope of the technical concept of the embodiments of the present invention, various simple modifications can be made to the technical solutions of the embodiments of the present invention, and these simple modifications all fall within the protection scope of the embodiments of the present invention.

[0074] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the embodiments of the present invention will not describe the various possible combinations separately.

[0075] Furthermore, various different implementations of the present invention can be combined arbitrarily, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed in the present invention.

Claims

1. A method for measuring the phase error of a spliced ​​diffraction system based on dual-wavelength interference, characterized in that, The method includes: Step S1: Based on the layout and effective radius of the multiple sub-apertures of the diffractive optical element, generate a binary mask for each sub-aperture and generate an overall pupil mask for the diffractive optical element. Step S2: Obtain interference frame sequences for two laser wavelengths using a four-step phase-shifting sequence; Step S3: The four-step phase-shifting algorithm is used to demodulate the phase of the interference frame sequences of the two laser wavelengths respectively, and multiply them by the overall pupil mask to calculate the single-wavelength effective phase of each laser wavelength in the two laser wavelengths respectively. Step S4: Calculate the composite wavefront optical path of the diffractive optical element using the single-wavelength effective phase of the two laser wavelengths. Step S5: Perform piecewise Zernike polynomial fitting on the synthesized wavefront optical path according to the binarized mask corresponding to each sub-aperture to obtain the piston error and tilt error of each sub-aperture, thereby obtaining the co-phase error.

2. The method for measuring the common phase error of a spliced ​​diffraction system based on dual-wavelength interference as described in claim 1, characterized in that, In step S4, the optical path length of the synthesized wavefront is calculated as follows: ； in, To synthesize the wavefront optical path, The composite wavelength is formed by combining two laser wavelengths. , The first laser wavelength, The second laser wavelength is included in the two laser wavelengths, which are the first laser wavelength. Second laser wavelength , This indicates the argument operation. This represents an exponential function with base e. The imaginary unit, For the first laser wavelength The first single-wavelength effective phase is obtained by performing phase demodulation using a four-step phase-shift sequence and multiplying it with a pupil mask. To the second laser wavelength The second single-wavelength effective phase is obtained by performing phase demodulation using a four-step phase-shift sequence and multiplying it with the pupil mask.

3. The method for measuring the common phase error of a spliced ​​diffraction system based on dual-wavelength interferometry according to claim 2, characterized in that, Generating a binary mask for each sub-aperture includes: The geometric center coordinates and effective radius of each sub-aperture are determined based on the layout of the multiple sub-apertures of the diffractive optical element. The Euclidean distance from each pixel in the sub-aperture to the center of the corresponding sub-aperture is calculated for each sub-aperture to generate a binarized mask for each sub-aperture. The binarized masks of all sub-apertures constitute a set of binarized masks.

4. The method for measuring the common phase error of a spliced ​​diffraction system based on dual-wavelength interferometry according to claim 3, characterized in that, The overall pupil mask for generating diffractive optical elements includes: Perform a logical OR operation on the binary mask corresponding to each sub-aperture in the binary mask set to generate a pupil mask covering all sub-apertures, so as to form the overall pupil mask of the diffractive optical element.

5. The method for measuring the common phase error of a spliced ​​diffraction system based on dual-wavelength interference according to claim 4, characterized in that, For each sub-aperture, calculate the Euclidean distance from each pixel in the sub-aperture to the center of the corresponding sub-aperture to generate a binary mask for each sub-aperture. This includes: assigning the corresponding pixel a value of 1 if the Euclidean distance is less than or equal to the effective radius of the corresponding sub-aperture, and otherwise assigning a value of 0.

6. The method for measuring the common phase error of a spliced ​​diffraction system based on dual-wavelength interference according to claim 5, characterized in that, Step S5 includes: By employing a traversal approach, the synthesized wavefront optical path is spatially indexed for each binary mask in the set of binary masks to obtain the local wavefront optical path corresponding to each sub-aperture; Piecewise Zernike polynomial fitting is performed based on the local wavefront optical path corresponding to each sub-aperture to obtain the piston error and tilt error of each sub-aperture, thereby obtaining the co-phase error.

7. The method for measuring the common phase error of a spliced ​​diffraction system based on dual-wavelength interferometry according to claim 6, characterized in that, Piecewise Zernike polynomial fitting was performed based on the local wavefront optical path length corresponding to each sub-aperture to obtain the piston error and tilt error of each sub-aperture, including: For each sub-aperture, the local wavefront optical path of the corresponding sub-aperture is used as the observation vector W; For each sub-aperture, an observation matrix Z is constructed based on Zernike polynomials; Based on the observation vector W and the observation matrix Z, the overdetermined system of equations is solved using the least squares method, and the coefficient vector A is obtained by calculation. The piston error and tilt error for each sub-aperture are obtained from the coefficient vector A.

8. The method for measuring the common phase error of a spliced ​​diffraction system based on dual-wavelength interferometry according to claim 7, characterized in that, The observation matrix Z is constructed based on Zernike polynomials, including: The first three terms of the Zernike polynomial are used as basis functions for fitting, wherein the first term of the basis function is a constant 1, representing a piston term translated along the optical axis, and the second term of the basis function is... , representing a linear function inclined along the horizontal coordinate axis, wherein the third term of the basis function is , represents a linear function inclined along the direction perpendicular to the coordinate axis, where, This represents the normalized distance from a point within a sub-aperture to the geometric center of that sub-aperture. This indicates the rotation angle of a point within a sub-aperture relative to the geometric center of the corresponding sub-aperture. The observation matrix Z is composed of the basis functions, the horizontal coordinate axis is the direction of increase of the row vector of the pixel, and the vertical coordinate axis is the direction of increase of the column vector of the pixel.

9. The method for measuring the co-phase error of a spliced ​​diffraction system based on dual-wavelength interferometry according to claim 8, characterized in that, The coefficient vector A includes three coefficients: a first coefficient, a second coefficient, and a third coefficient. The first coefficient is the piston error of the corresponding sub-aperture, the second coefficient is the horizontal axis tilt error of the corresponding sub-aperture, and the third coefficient is the vertical axis tilt error of the corresponding sub-aperture. The first coefficient corresponds to the first term of the basis function, the second coefficient corresponds to the second term of the basis function, and the third coefficient corresponds to the third term of the basis function.

10. The method for measuring the common phase error of a spliced ​​diffraction system based on dual-wavelength interference according to claim 9, characterized in that, The method also includes: The sub-aperture located at the center of the geometric layout among the multiple sub-apertures of the diffractive optical element is used as the reference sub-aperture. The relative cophase error of all sub-apertures is calculated based on the piston error, horizontal axis tilt error, and vertical axis tilt error of the reference sub-aperture, as well as the piston error, horizontal axis tilt error, and vertical axis tilt error of all sub-apertures.

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