CN105318847A - Aspheric non-zero digit circular subaperture stitching method based on system modeling - Google Patents

Abstract

The invention discloses a method for splicing non-zero annular sub-apertures of an aspheric surface based on system modeling. The present invention models the experimental interference system, establishes a multi-structure model corresponding to the aspheric positions of different rings, establishes an optimization function based on the multi-structure model, takes the actually measured wavefront Zernike coefficients of each ring as the optimization target at the same time, and uses the model The wavefront Zernike coefficients of each annular zone are the dependent variables, and the aspheric full-aperture surface error is the independent variable. Taking the position of the measured surface corresponding to each aspheric annulus as a constraint condition, and executing the optimization function to make the wavefront Zernike coefficients of each annulus in the model approach the actual measured value, it is considered that the full-aperture surface shape error of the measured surface in the model is close to the actual The measured value, so as to obtain the full-diameter surface error of the measured surface. The present invention does not require special morphological splicing operations and overlapping areas, reduces the number of sub-apertures that may be required, and increases splicing accuracy.

Description

Aspherical non-zero annular sub-aperture splicing method based on system modeling

technical field

The invention relates to a method for splicing non-zero annular sub-apertures of aspheric surfaces based on system modeling.

Background technique

At present, sub-aperture splicing interference detection technology is often used for large-aperture depth aspheric detection. Among various stitching methods, the annular sub-aperture stitching method is widely used in the detection of rotationally symmetric aspheric surfaces due to its simple detection structure. It uses a transmission spherical mirror to generate a standard spherical wave as a reference wavefront, matches different annulus areas of the aspheric surface at different detection positions, so that each matching area can reach an approximate zero-position detection condition, and then uses the sub-aperture splicing algorithm to splice the full-aperture surface shape error . However, since the radius of curvature of each ring area of the measured aspheric surface is different, it is difficult to make the measurement of each annular sub-aperture fully meet the zero position condition by using the spherical wave as the reference wave front, resulting in a return error; at the same time, each time in the detection The movement of the position of the aspheric surface will inevitably cause adjustment errors, making it difficult to unify the data of each sub-aperture. Therefore, the backhaul error and adjustment error of each sub-aperture must be corrected in the splicing of sub-aperture data. This is also the difficulty of various sub-aperture stitching algorithms.

Liu et al. proposed the earliest aspherical annular sub-aperture splicing method based on Zernike polynomials, using the Zernike coefficients of each sub-aperture measured by commercial interferometers to calculate the full-aperture surface Zernike coefficients. Subsequently, Melozzi and Granados-Agustin proposed sequential stitching and global stitching methods based on overlapping regions, respectively, and performed least squares fitting for the characteristics of consistent surface shapes in overlapping regions to correct the relative adjustment error between sub-apertures. Hou Xi et al. proposed a more accurate calculation method for the full-aperture surface coefficient based on the circular Zernike polynomial; Chen Shanyong et al. also proposed an iterative splicing algorithm for interactive overlapping area calculation and system structure optimization. However, the above-mentioned algorithms all need to rely on complicated mathematical calculation formulas or overlapping area fitting, and the backhaul error correction for each sub-aperture is not accurate.

Contents of the invention

The purpose of the present invention is to address the deficiencies of the prior art, and propose a method for splicing non-zero annular sub-apertures of aspheric surfaces based on system modeling, using ray tracing software to model the detection system, and measuring the obtained sub-apertures through experiments The wavefront aberration coefficient is optimized to solve the full-aperture surface error. The method replaces complex stitching algorithms with iterative ray tracing and does not require overlapping regions between sub-apertures.

The aspheric non-zero annular sub-aperture splicing method based on system modeling uses reverse optimization constrained by multiple structural models to directly obtain the Zernike coefficients representing the full-aperture surface error from the Zernike coefficients of each annular sub-aperture wavefront.

The multiple structure model is a combination of multiple independent system models established according to system parameters. Each sub-aperture measurement position corresponds to a heavy structure, and the positions of the measured surfaces corresponding to each heavy structure are different, that is, each sub-aperture measurement position Corresponds to an independent system model.

The reverse optimization of the multiple structural model constraints is carried out using a strictly constrained global optimization function; the global optimization function takes the experimentally obtained Zernike coefficients of each annulus as the optimization target; is the dependent variable, and the full-aperture surface shape error of the measured surface is the independent variable; by executing the global optimization function, the Zernike coefficients of each annulus wavefront in the model gradually approach the Zernike coefficients of each annulus wavefront in the experiment; when the global optimization function is executed , the full-aperture surface error of the measured surface in the model is consistent with the full-aperture surface error of the measured surface in the experiment; among them, the constraint condition of the global optimization function is the relative distance between each sub-aperture; the independent variable (full-aperture surface shape error) and the dependent variable (annular wavefront Zernike coefficient) are defined and enforced by ray tracing.

The aspherical non-zero annular sub-aperture splicing method based on system modeling, the specific steps are as follows:

Step 1. Build the experimental system;

Step 2. Establish a model and divide the sub-aperture according to the experimental system parameters: perform system modeling according to the experimental system parameters, complete the sub-aperture division of the annular zone according to the detector resolution, and record the position parameters of the measured surface corresponding to each annular zone on the optical axis , assuming that the number of divided sub-apertures is N, and N is a natural number;

Described modeling software is ray tracing software;

Step 3. Establish a multi-structure model: According to the sub-aperture division parameters, a multi-structure model is established. Each structure corresponds to a sub-aperture measurement position, that is, the number of aspheric rings and the number of structures in the multi-structure model are both N, and each structure The positions of the corresponding measured surfaces are different, that is, each sub-aperture measurement position corresponds to an independent system model;

3-1. According to the distance between the aspherical surface corresponding to the sub-aperture of the reference ring in the multi-structure model and the part of the zero mirror, the defocus coefficient of the return wavefront of the reference ring in the multi-structure model is used for precise positioning;

3-2. Collect the interferogram of the reference ring tape sub-aperture through the interferogram acquisition module, and use the phase shift algorithm to demodulate the phase of the interferogram in the computer to obtain the return wavefront phase of the reference ring tape sub-aperture received by the detector in the experiment;

3-3. According to the relative position between the other annular zone apertures and the reference subaperture in the multi-structure model, the displacement measurement interferometer is used to accurately control the relative movement of the aspheric surface and the measurement position of the reference annular zone for positioning;

3-4. Collect the interferograms of other ring-band sub-apertures through the interferogram acquisition module, and use the phase shift algorithm to demodulate the phase of the interferogram in the computer to obtain the return wavefront phase of other ring-band sub-apertures received by the detector in the experiment;

3-5. Repeat steps 3-3 and 3-4 until the aperture positioning of all other ring belts and the demodulation of their corresponding interferograms are completed;

Step 4, band subaperture wavefront fitting: according to the wavefront phases of all band subapertures, Zernike band fitting is carried out to obtain the band Zernike coefficients of all subapertures;

Step 5. Full-aperture surface shape optimization stitching: remove the first four items of the annular Zernike coefficients of each sub-aperture, and then use the annular Zernike coefficients of all sub-apertures as the optimization target, and use the Zernike coefficients of all annular bands in the multi-structure model is the dependent variable, and the full-aperture surface shape error of the measured surface is the independent variable; through the multi-structure optimization module, the Zernike coefficients of each annular wave front in the model are gradually approaching the Zernike coefficients of each annular wave front in the experiment, where the independent variable (full-aperture surface Shape error) and the function of the dependent variable (annular wavefront Zernike coefficient) are performed by ray tracing; thus, the full-aperture surface error of the measured surface in the model is consistent with the full-aperture surface error of the measured surface in the experiment.

In the aspherical non-zero annular sub-aperture splicing interference detection system, the experimental interference system is modeled using ray tracing software, and a multi-structural model is established corresponding to the aspheric positions of different annular zones, and an optimization function is established based on the multi-structural model. The actual measured Zernike coefficients of each annulus wavefront are used as optimization targets at the same time, with the Zernike coefficients of each annulus wavefront in the model as the dependent variable and the aspheric full-aperture surface shape error as the independent variable. Taking the position of the measured surface corresponding to each aspheric annulus as a constraint condition (the position parameter is controlled by the precision displacement guide rail), and executing the optimization function to make the wavefront Zernike coefficients of each annulus in the model approach the actual measured value, it is considered that the measured surface in the model is The full-aperture surface error of the measured surface is close to the actual measured value, so that the full-aperture surface error of the measured surface is obtained.

In the aspherical non-zero ring sub-aperture splicing interference detection system, the thin beam emitted by the frequency-stabilized laser is expanded into a wide beam of parallel light through the collimation system, and the parallel light travels forward to the beam splitter and is divided into two paths. Light. One path propagates forward to the reference plane mirror and then returns to the original path as the reference wave; the other path propagates forward to a part of the zero mirror and then converges and then diverges. The divergent light is approximately perpendicular to the aspheric surface to be measured and returns, and passes through the part of the zero mirror again. into the detection wave. The two interfere at the beam splitter, and image the image at the detector through the imaging mirror. Among them, the measured aspheric surface is installed on the guide rail by the clamping mechanism, and can move along the direction of the guide rail (optical axis), so that the interference fringes between the wavefronts returned by different rings and the reference light can be distinguished by the detector until the rings are covered. Measuring surface full bore.

The partial zero mirror is a commonly used component in non-zero interference detection systems, similar to the standard mirror in zero detection. The aspheric wavefront generated by part of the null mirror is used as the reference wavefront to compensate most of the aspheric normal aberrations. The aspheric surface will produce interference fringes of different densities at different positions on the optical axis. Because the partial zero mirror can only compensate part of the aberration of the measured surface, each ring phase includes a return error.

The displacement measurement interferometer is composed of an interferometer host, a half-reflective prism, a linear reflective prism (fixed) and a measuring reflective prism (movable). The laser light emitted by the interferometer host passes through the half-reflective prism, part of which is reflected to the linear reflective prism, and then reflected back to the half-reflective prism; the other part passes through the half-reflective prism, enters the measuring mirror, and is reflected back to the half-transparent In a half-reflecting prism, the two beams of reflected light interfere. The measuring mirror can move along the direction of the optical axis, and its moving distance is directly expressed as the change of interference fringes, and its moving distance can be accurately measured by counting the interference fringes.

The measuring mirror in the displacement measuring interferometer is fixed to the clamping mechanism of the measured aspheric surface, and the clamping mechanism of the aspheric surface can move along the direction of the guide rail (optical axis), and the moving distance is accurately measured and monitored by the displacement measuring interferometry system.

The computer data processing module includes image acquisition, wavefront fitting module, system multi-structure modeling module and full aperture optimization module. Firstly, the ray tracing software is used to input the experimental system parameters for system modeling. At the same time, the aspheric position parameters corresponding to each measurement ring can be simulated, and then multi-structure simultaneous modeling can be carried out. The obtained position parameters of the aspheric surface are input into the precision displacement measurement interferometry system, which is used to monitor the movement of the aspheric surface along the optical axis in the experiment. After the aspheric surface moves along the optical axis in the experiment, a four-step phase-shifting interferogram is collected at each position, and the four-step phase-shifting interferogram of each annular zone is received from the CCD through the image acquisition module and output to the wavefront fitting module. The wavefront fitting module restores the sub-aperture wavefront phase through a four-step phase-shifting algorithm, and fits it to the annular Zernike coefficient. The full-aperture optimization module is established based on the multi-structure model, which includes a least squares optimization function. This function takes the Zernike coefficient of each annulus as the optimization target, and takes the wavefront Zernike coefficient of each annulus in the model as the dependent variable. The full-aperture of the measured surface Surface error is an independent variable. Functions of independent and dependent variables are performed by ray tracing. Execute the function of the optimization module, so that the Zernike coefficients of each annular wave front in the model gradually approach the Zernike coefficients of each annular wave front in the experiment, so that the full-aperture surface shape error of the measured surface in the model approaches the real value.

Beneficial effects of the present invention:

The sub-aperture stitching method replaces the complex mathematical algorithm in the traditional sub-aperture stitching through system modeling, and uses the multi-structural model co-optimization method to replace the traditional return error and adjustment error removal, without special morphological stitching operations, and without The need for overlapping regions reduces the number of sub-apertures that may be required and increases stitching accuracy.

Description of drawings

Fig. 1 is a device diagram of the method of the present invention;

Fig. 2 is experimental sub-aperture interferogram among the present invention;

Fig. 3 annular sub-aperture wavefront Zernike coefficient (Zernike annular polynomial coefficient);

Figure 4 Zernike coefficient of the full-aperture surface shape error of the measured surface (Zernike standard polynomial coefficient);

Figure 5. The full-aperture surface shape error of the measured surface.

detailed description

The present invention is described in detail with reference to FIG. 1 and FIG. 2 .

As shown in Fig. 1, the implementation device of the aspherical non-zero annular sub-aperture splicing method based on system modeling of the present invention consists of a non-zero interference detection system, a displacement measurement interference system, and a data processing module.

In the aspheric non-zero position interference detection system, the thin beam emitted by the frequency-stabilized laser L1 is expanded into a wide-beam parallel light by the collimation beam expansion system L2, and the parallel light propagates forward to the beam splitter L3 and is divided into two paths Light. One path propagates forward to the reference plane mirror L4 and then returns to the original path as the reference wave; the other path propagates forward to the partial zero mirror L8 and then converges and then diverges. The divergent light is basically perpendicular to the measured aspheric surface L9 and then returns, passing through the partial zero position again. The mirror L8 enters backward to form a detection wave. The two interfere at the beam splitter L3, and are imaged at the detector L7 through the imaging mirror L6. L5 is a piezoelectric ceramic used for phase shifting. Among them, the aspheric surface L9 is fixed on its clamping mechanism L10, and the aspheric surface clamping mechanism L10 is installed on the guide rail L11, and can move along the guide rail L11 (in the direction of the optical axis of the system), and the moving distance is precisely controlled by the displacement measurement interferometric system L12.

The displacement measurement interference system L12 is mainly composed of an interferometer host 1, a half mirror 2, a linear reflection prism 3 (fixed) and a measuring mirror 4 (movable). The main optical axis of the displacement measurement system L11 is parallel to the main optical axis of the aspheric surface measurement system, and the measuring mirror 4 is fixed to the aspheric surface clamping mechanism L10, that is, the measuring mirror 4 and the measured aspheric surface L9 move along the respective optical axis directions, The moving distance of the aspheric surface L9 is the moving distance of the measuring reflector 4 . The laser light emitted by the interferometer host 1 passes through the half-reflective prism 2, and part of it is reflected to the linear reflective prism 3, and is reflected back to the half-reflective prism 2; the other part passes through the half-reflective prism 2 and enters the measuring mirror 4 , is also reflected back to the half-reflective prism 2, and the two beams of reflected light interfere. The measuring mirror can move along the direction of the optical axis, and its moving distance is directly expressed as the change of interference fringes, and its moving distance can be accurately measured by counting the interference fringes.

Figure 2 shows the steps of the aspherical non-zero annular sub-aperture splicing method based on system modeling, as follows:

Step 1. Build the experimental system;

Step 2. Establish a model and divide the sub-aperture according to the experimental system parameters: perform system modeling according to the experimental system parameters, complete the sub-aperture division of the annular zone according to the detector resolution, and record the position parameters of the measured surface corresponding to each annular zone on the optical axis , assuming that the number of divided sub-apertures is N, and N is a natural number;

Described modeling software is ray tracing software;

Step 3. Establish a multi-structure model: According to the sub-aperture division parameters, a multi-structure model is established. Each structure corresponds to a sub-aperture measurement position, that is, the number of aspheric rings and the number of structures in the multi-structure model are both N, and each structure The positions of the corresponding measured surfaces are different, that is, each sub-aperture measurement position corresponds to an independent system model;

3-1. According to the distance between the aspherical surface corresponding to the sub-aperture of the reference ring in the multi-structure model and the part of the zero mirror, the defocus coefficient of the return wavefront of the reference ring in the multi-structure model is used for precise positioning;

3-2. Collect the interferogram of the reference ring tape sub-aperture through the interferogram acquisition module, and use the phase shift algorithm to demodulate the phase of the interferogram in the computer to obtain the return wavefront phase of the reference ring tape sub-aperture received by the detector in the experiment;

3-3. According to the relative position between the other annular zone apertures and the reference subaperture in the multi-structure model, the displacement measurement interferometer is used to accurately control the relative movement of the aspheric surface and the measurement position of the reference annular zone for positioning;

3-4. Collect the interferograms of other ring-band sub-apertures through the interferogram acquisition module, and use the phase shift algorithm to demodulate the phase of the interferogram in the computer to obtain the return wavefront phase of other ring-band sub-apertures received by the detector in the experiment;

3-5. Repeat steps 3-3 and 3-4 until the aperture positioning of all other ring belts and the demodulation of their corresponding interferograms are completed;

Step 4, band subaperture wavefront fitting: according to the wavefront phases of all band subapertures, Zernike band fitting is carried out to obtain the band Zernike coefficients of all subapertures;

Step 5. Full-aperture surface shape optimization stitching: remove the first four items of the annular Zernike coefficients of each sub-aperture, and then use the annular Zernike coefficients of all sub-apertures as the optimization target, and use the Zernike coefficients of all annular bands in the multi-structure model is the dependent variable, and the full-aperture surface shape error of the measured surface is the independent variable; through the multi-structure optimization module, the Zernike coefficients of each annular wave front in the model are gradually approaching the Zernike coefficients of each annular wave front in the experiment, where the independent variable (full-aperture surface Shape error) and the function of the dependent variable (annular wavefront Zernike coefficient) are performed by ray tracing; thus, the full-aperture surface error of the measured surface in the model is consistent with the full-aperture surface error of the measured surface in the experiment.

Example

An example of the application of the present invention to stitching of aspherical non-null annular sub-apertures is described as follows.

Figure 1 is a diagram of a measurement device for the radius of curvature of an aspheric vertex in a non-zero interferometric system. The laser wavelength is λ=632.8nm. The thin beam emitted by the laser L1 is expanded into a wide beam of parallel light by the collimator beam expander system L2, and the parallel light travels forward to the beam splitter L3 and is divided into two beams. One path propagates forward to the reference flat mirror L5 and then returns to the original path as a reference wave; the other path propagates forward to the partial zero mirror L8 and then converges and then diverges. The divergent light is basically perpendicular to the measured aspheric surface L9 and then returns, passing through the partial zero again. The mirror L8 enters backward to form a detection wave. The two interfere at the beam splitter and are imaged at the detector L7 through the imaging mirror L6. The parameters of some zero mirrors in Figure 1 are as follows:

Table 1 Part of the zero mirror parameters in Figure 1

According to the experimental system parameters, the system modeling is carried out in the ray tracing software Zemax. Considering the influence of noise in the experiment, the return wavefront slope of each sub-aperture shall not be greater than 1/8 Nyquist sampling frequency. By moving the aspheric surface L9, the center The annulus is the initial condition. When the aspheric surface is positioned at 302.2155mm from the partial zero mirror, the normalized area of the central (reference) annulus is determined to be 0-0.6. With 0.6 as the lower bound, when moving the aspheric surface to 302.0473mm from the partial zero mirror, the normalized area of the second ring is 0.6-0.9; when continuing to move the aspheric surface to 302.0241mm from the partial zero mirror, the third ring is normalized The zone is 0.6-1. At this point the division of the ring is complete. Table 2 shows the three sub-aperture division parameters in the simulation.

Table 2 Three sub-aperture parameters

subaperture 1 2 Distance between aspheric surface and compensation mirror (mm) 302.2155 302.0473 normalized width [0, 0.75] [0.65, 1]

According to the above-mentioned sub-aperture division parameters, a triple structure model is established, each structure corresponds to an aspheric annular zone measurement, the system parameters in the triple structure are the same, the difference is that the distance between the aspheric surface and the compensation mirror is 302.2155mm, 302.0473mm, and 302.0241mm respectively. The aspheric surface is positioned according to the distance between the aspheric surface corresponding to the aperture of each annulus and part of the zero mirror in the modeling. Including the positioning of the aspheric surface when measuring the reference zone and the positioning of the aspheric surface when measuring other zones. When measuring the reference ring, the defocus coefficient of the return wavefront of the aspheric surface at this position in the modeling can be used for precise positioning. When measuring other rings, the relative movement between the aspheric surface and the reference position can be accurately controlled according to the displacement measurement interference shift to locate. The interferograms of three annular band sub-apertures are collected by the interferogram acquisition module, as shown in Fig. 2 . The phase-shifting interferogram collected by each zone measurement is processed by a phase-shifting algorithm to extract the wavefront phase of the zone sub-aperture, and the Zernike zone fitting is performed to obtain the zone Zernike coefficient, as shown in Figure 3. The Zernike coefficients of each annulus are taken as the optimization target, the wavefront Zernike coefficients of each annulus in the model are taken as the dependent variable, and the full-aperture surface shape error of the measured surface is used as the independent variable. Note that the first four items (displacement, tilt, and defocus) are excluded from all Zernike coefficients used, because they represent adjustment errors and therefore do not participate in optimization. Execute the function function in the optimization module, so that the Zernike coefficients of each annular wave front in the model gradually approach the Zernike coefficients of each annular wave front in the experiment, where the independent variable (full-aperture surface shape error) and the dependent variable (the annular wave front Zernike coefficient ) functions are performed by ray tracing. As a result, the full-aperture surface error of the measured surface in the model is approached to the true value, and the final aspheric full-aperture surface shape Zernike coefficient (37 items) is obtained, as shown in Figure 4, the 37 standard Zernike coefficients are simulated by least squares Combined to get the final full-aperture surface shape error, as shown in Figure 5, the splicing is completed.

Claims (4)

1. The aspherical non-zero annular sub-aperture splicing method based on system modeling is characterized in that: the reverse optimization constrained by multiple structural models is used to directly obtain the full-aperture surface error from the Zernike coefficients of each annular sub-aperture wavefront Zernike coefficient. 2. the aspheric surface non-zero annular sub-aperture splicing method based on system modeling according to claim 1, is characterized in that: The multiple structure model is a combination of multiple independent system models established according to system parameters. Each sub-aperture measurement position corresponds to a heavy structure, and the positions of the measured surfaces corresponding to each heavy structure are different, that is, each sub-aperture measurement position Corresponds to an independent system model. 3. The aspherical non-zero annular sub-aperture splicing method based on system modeling according to claim 1, characterized in that: the reverse optimization of the constraints of the multiple structural models utilizes a global optimization function with strict constraints to perform The global optimization function takes the Zernike coefficients of each annulus obtained from the experiment as the optimization target; takes the wavefront Zernike coefficients of each annulus in the model as the dependent variable, and the full-aperture surface error of the measured surface as the independent variable; by executing the global optimization function , so that the Zernike coefficients of each annulus wave front in the model gradually approach the Zernike coefficients of each annulus wave front in the experiment; The surface error is consistent; the constraint condition of the global optimization function is the relative distance between each sub-aperture; the functional relationship between the independent variable (full-aperture surface error) and the dependent variable (annular wavefront Zernike coefficient) is determined by ray tracing to define and execute. 4. the aspheric surface non-zero annular sub-aperture splicing method based on system modeling according to claim 1, is characterized in that concrete steps are as follows: Step 1. Build the experimental system; Step 2. Establish a model and divide the sub-aperture according to the experimental system parameters: perform system modeling according to the experimental system parameters, complete the sub-aperture division of the annular zone according to the detector resolution, and record the position parameters of the measured surface corresponding to each annular zone on the optical axis , assuming that the number of divided sub-apertures is N, and N is a natural number; Described modeling software is ray tracing software; Step 3. Establish a multi-structure model: According to the sub-aperture division parameters, a multi-structure model is established. Each structure corresponds to a sub-aperture measurement position, that is, the number of aspheric rings and the number of structures in the multi-structure model are both N, and each structure The positions of the corresponding measured surfaces are different, that is, each sub-aperture measurement position corresponds to an independent system model; 3-1. According to the distance between the aspherical surface corresponding to the sub-aperture of the reference ring in the multi-structure model and the part of the zero mirror, the defocus coefficient of the return wavefront of the reference ring in the multi-structure model is used for precise positioning; 3-2. Collect the interferogram of the reference ring tape sub-aperture through the interferogram acquisition module, and use the phase shift algorithm to demodulate the phase of the interferogram in the computer to obtain the return wavefront phase of the reference ring tape sub-aperture received by the detector in the experiment; 3-3. According to the relative position between the other annular zone apertures and the reference subaperture in the multi-structure model, the displacement measurement interferometer is used to accurately control the relative movement of the aspheric surface and the measurement position of the reference annular zone for positioning; 3-4. Collect the interferograms of other ring-band sub-apertures through the interferogram acquisition module, and use the phase shift algorithm to demodulate the phase of the interferogram in the computer to obtain the return wavefront phase of other ring-band sub-apertures received by the detector in the experiment; 3-5. Repeat steps 3-3 and 3-4 until the aperture positioning of all other ring belts and the demodulation of their corresponding interferograms are completed; Step 4, band subaperture wavefront fitting: according to the wavefront phases of all band subapertures, Zernike band fitting is carried out to obtain the band Zernike coefficients of all subapertures; Step 5. Full-aperture surface shape optimization stitching: remove the first four items of the annular Zernike coefficients of each sub-aperture, and then use the annular Zernike coefficients of all sub-apertures as the optimization target, and use the Zernike coefficients of all annular bands in the multi-structure model is the dependent variable, and the full-aperture surface error of the measured surface is the independent variable; through the multi-structure optimization module, the Zernike coefficients of each annular wave front in the model are gradually approaching the Zernike coefficients of each annular wave front in the experiment, where the independent variable (and the dependent variable The function of is performed by ray tracing; thus, the full-aperture surface error of the measured surface in the model is consistent with the full-aperture surface error of the measured surface in the experiment.