A method for correcting co-phasing errors of a segmented telescope mirror

Abstract

The present application relates to the field of error correction technology of telescope, and especially relates to a kind of spliced telescope mirror co-phase error correction method, first design special mask, so that the secondary peak value in MTF under wide spectrum illumination representing each mirror co-phase error does not overlap, so that the secondary peak value in MTF under wide spectrum illumination representing each mirror co-phase error can be calculated separately, then this value is used as evaluation function, and a plurality of correction amounts to be selected for mirror co-phase error under certain conditions are generated by population optimization algorithm, and the evaluation function value corresponding to the actual correction of the mirror is obtained to evaluate the correction amount;Select the optimal correction amount, and iterate repeatedly, to achieve wide range high-precision real-time correction of three-dimensional co-phase error of each mirror without accurate modeling of optical system.

Description

Technical Field

[0001] This invention relates to the field of telescope error correction technology, and in particular to a method for correcting the co-phase error of sub-mirrors in a spliced ​​telescope. Background Technology

[0002] A telescope's light-gathering ability and resolution are directly related to the size of its primary mirror aperture. However, the increase in primary mirror size has brought unprecedented challenges to the design, fabrication, manufacturing, testing, and launch of space telescopes. The emergence of modular primary mirror telescopes has provided a solution to these problems. To ensure that the overall imaging quality of a modular telescope approaches the diffraction limit, it is necessary to guarantee high co-phase accuracy between the individual sub-mirrors. Therefore, wavefront sensing is used to detect the co-phase error of each sub-mirror, and then a high-precision displacement adjustment mechanism is used for correction.

[0003] Existing methods have established a functional relationship between the second peak value of the MTF and the translation error of the segmented mirrors under broadband illumination. By designing a special mask, the second peak value of the MTF characterizing the translation error of the sub-mirrors does not overlap. Thus, this relationship can be used to calculate the translation error of each sub-mirror in the spliced ​​telescope separately.

[0004] However, the existing method cannot calculate the tilt error in the other two directions of each sub-mirror, and this method requires accurate registration between the optical system simulation model and the real model. After obtaining the co-phase error of the sub-mirrors, it still needs to rely on a high-precision displacement adjustment mechanism for correction. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a method for correcting the phase error of sub-mirrors in a spliced ​​telescope. By designing a special mask and combining it with a population optimization algorithm, this method achieves real-time correction of the three-dimensional phase error of each sub-mirror over a wide range with high precision without requiring accurate modeling of the optical system.

[0006] The proposed method for correcting phase error of sub-mirrors in a spliced ​​telescope includes the following steps:

[0007] S1. Select one sub-mirror from the spliced ​​telescope system as the reference sub-mirror, and the remaining sub-mirrors as sub-mirrors to be calibrated; design a mask to be placed at the pupil of the spliced ​​telescope system; and calculate the second-peak MTF representing the co-phase error of a certain sub-mirror to be calibrated in the MTF of the spliced ​​telescope system. nph ;

[0008] S2. Initialize the population optimization algorithm and use the initial solution as the N phase error candidate correction quantities for the current sub-mirror to be corrected;

[0009] S3. Correct the current sub-mirror to be corrected based on N possible co-phase error correction values, and calculate the evaluation value sequence {MTF}. nph1MTF nph2 ,…,MTF nphN};

[0010] S4. Select the evaluation value series {MTF} nph1 MTF nph2 ,…,MTF nphN The maximum rating value (MTF) in} nph-max And set the maximum evaluation value MTF. nph-max The corresponding co-phase error correction value to be selected is the current optimal correction value;

[0011] S5. Restore the current sub-mirror to be calibrated to its state before calibration. Using the current optimal calibration amount as a reference, update the co-phase error candidate calibration amount according to the update principle of the population optimization algorithm.

[0012] S6. Repeat steps S3 to S5:

[0013] If the same optimal correction value is repeated more than the set number of times, the operation will stop, and the optimal correction value will be set as the final correction value.

[0014] If the same optimal correction value does not appear more than the set number of times, and the number of repeated operations reaches the specified number, then the last optimal correction value is set as the final correction value.

[0015] The current sub-mirror to be calibrated is calibrated based on the final calibration value;

[0016] S7. Repeat steps S2 to S6 until all sub-mirrors to be calibrated have been calibrated.

[0017] Furthermore, the mask design process is as follows:

[0018] S11. Make the number of sub-apertures of the mask the same as the number of sub-mirrors in the spliced ​​telescope system. Define the baseline between the sub-aperture corresponding to the reference sub-mirror and the sub-aperture of each sub-mirror to be corrected as the main baseline. Define the baseline between the sub-apertures of each sub-mirror to be corrected as the sub-baseline.

[0019] S12, the directions of the main baselines are different, without affecting the secondary peak MTF generated by each pair of sub-apertures. nph In this case, partial overlap in the side lobes is allowed, thus obtaining a mask.

[0020] Furthermore, the process of obtaining the side lobe is as follows:

[0021] The reflected wavelet of the sub-aperture is sampled, and the incident light is a broad spectrum with a center wavelength of λ0 and a spectral width of Δλ; if the weight of each wavelength is equal, the PSF of the optical system is... b It can be expressed by equation (1):

[0022]

[0023] Among them, PSF m (x,y,λ) represents the PSF under monochromatic light, which can be expressed by equation (2):

[0024]

[0025] Where B represents the distance between the centers of every two sub-pupils in the sub-aperture; J1(·) represents the first-order Bessel function; p represents the piston error; D represents the secondary pupil diameter; and f represents the focal length of the imaging lens.

[0026] Therefore, the differential of equation (1) is approximately the sum of integrals over n intervals, i.e.:

[0027]

[0028] Therefore, the MTF is obtained according to equation (4):

[0029]

[0030] Among them, f x =x0 / λf,f y =y0 / λf; MTF sub The side lobes of the MTF are specifically:

[0031]

[0032] Where FT[·] represents Fourier calculation;

[0033] Sidelobe MTF sub The amplitude of the central peak is normalized to obtain the secondary peak MTF. nph Thus, the second peak MTF is obtained. nph The relationship between the error and the translation error of the sub-mirror is as follows:

[0034]

[0035] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0036] 1) This invention evaluates the correction amount by calculating the actual evaluation function after online correction, thus eliminating the need to establish an accurate optical system model;

[0037] 2) Based on the design of a special mask, this invention combines a population optimization algorithm to calculate and correct tilt errors while calculating common translation errors, thereby enabling large-scale and high-precision calculation and correction of the three-dimensional co-phase error of each sub-mirror. Attached Figure Description

[0038] Figure 1 This is a flowchart of a method for correcting the phase co-occurrence error of a spliced ​​telescope sub-mirrors according to an embodiment of the present invention;

[0039] Figure 2 This is a design flowchart of a mask according to an embodiment of the present invention;

[0040] Figure 3 This is a schematic diagram of the mask for a spliced ​​telescope provided according to an embodiment of the present invention. Detailed Implementation

[0041] 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 specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0042] The method for correcting the phase error of sub-mirrors in a spliced ​​telescope provided in this invention first designs a special mask and calculates the second peak value in the MTF representing the phase error of each sub-mirror under broadband illumination. This value is then used as an evaluation index, and the method is repeatedly optimized and iterated through a population optimization algorithm to achieve real-time correction of the three-dimensional phase error of each sub-mirror with a wide range and high precision without accurately modeling the optical system.

[0043] Figure 1 A flowchart of a method for correcting phase error of sub-mirrors in a spliced ​​telescope according to an embodiment of the present invention is shown.

[0044] like Figure 1 As shown, the method for correcting the phase error of the sub-mirrors of a spliced ​​telescope provided in this embodiment of the invention specifically includes the following steps:

[0045] S1. Select one sub-mirror from the spliced ​​telescope system as the reference sub-mirror, and the remaining sub-mirrors as sub-mirrors to be calibrated; design a mask to be placed at the pupil of the spliced ​​telescope system; and calculate the second-peak MTF representing the co-phase error of a certain sub-mirror to be calibrated in the MTF of the spliced ​​telescope system. nph .

[0046] Figure 2 and Figure 3 The design process and schematic diagram of the mask provided according to the embodiments of the present invention are shown respectively.

[0047] like Figure 2 and Figure 3 As shown, the mask design process is as follows:

[0048] S11. Make the number of sub-apertures of the mask the same as the number of sub-mirrors in the spliced ​​telescope system. Define the baseline between the sub-aperture corresponding to the reference sub-mirror and the sub-aperture of each sub-mirror to be corrected as the main baseline. Define the baseline between the sub-apertures of each sub-mirror to be corrected as the sub-baseline.

[0049] S12. Since the directions of the main baselines are different, the distribution of MTF sidelobes on the main baselines should be discrete, without affecting the secondary peak MTF generated by each pair of sub-apertures. nph In this case, partial overlap in the side lobes is allowed, thus obtaining a mask.

[0050] The process of obtaining the side lobe is as follows:

[0051] The reflected wavelet of the sub-aperture is sampled, and the incident light is a broad spectrum with a center wavelength of λ0 and a spectral width of Δλ; if the weight of each wavelength is equal, the PSF of the optical system is... b It can be expressed by equation (1):

[0052]

[0053] Among them, PSF m (x,y,λ) represents the PSF under monochromatic light, which can be expressed by equation (2):

[0054]

[0055] Where B represents the distance between the centers of every two sub-pupils in the sub-aperture; J1(·) represents the first-order Bessel function; p represents the piston error; D represents the secondary pupil diameter; and f represents the focal length of the imaging lens.

[0056] Therefore, the differential of equation (1) is approximately the sum of integrals over n intervals, i.e.:

[0057]

[0058] Therefore, the MTF is obtained according to equation (4):

[0059]

[0060] Among them, f x =x0 / λf,f y =y0 / λf; MTF sub The side lobes of the MTF are specifically:

[0061]

[0062] Where FT[·] represents Fourier calculation;

[0063] Sidelobe MTF subThe amplitude of the central peak is normalized to obtain the secondary peak MTF. nph Thus, the second peak MTF is obtained. nph The relationship between the error and the translation error of the sub-mirror is as follows:

[0064]

[0065] S2. Initialize the population optimization algorithm and use the initial solution as the N phase error candidate correction quantities for the current sub-mirror to be corrected.

[0066] S3. Correct the current sub-mirror to be corrected based on N possible co-phase error correction values, and calculate the evaluation value sequence {MTF}. nph1 MTF nph2 ,…,MTF nphN}

[0067] S4. Select the evaluation value series {MTF} nph1 MTF nph2 ,…,MTF nphN The maximum rating value (MTF) in} nph-max And set the maximum evaluation value MTF. nph-max The corresponding cophase error candidate correction amount is the current optimal correction amount.

[0068] S5. Restore the current sub-mirror to be calibrated to its state before calibration. Using the current optimal calibration amount as a reference, update the co-phase error candidate calibration amount according to the update principle of the population optimization algorithm.

[0069] S6. Repeat steps S3 to S5.

[0070] If the same optimal correction value is repeated more than the set number of times, the operation will stop and the optimal correction value will be set as the final correction value.

[0071] If the same optimal correction value does not appear more than the set number of times, and the number of repeated operations reaches the set number, then the last optimal correction value is set as the final correction value.

[0072] The current sub-mirror to be calibrated is calibrated based on the final calibration value.

[0073] S7. Repeat steps S2 to S6 until all sub-mirrors to be calibrated have been calibrated.

[0074] To clearly illustrate the phase error correction method for the sub-mirrors of the spliced ​​telescope provided by this invention, the cuckoo algorithm and particle swarm optimization algorithm are selected as population optimization algorithms, and corresponding specific embodiments are given. Specific Implementation Example 1:

[0076] When the Cuckoo Optimization Algorithm is selected as the population optimization algorithm in this invention, the following calculation process is performed for optimization and iterative calculation during steps S2 to S6:

[0077] A1. Initialize the Cuckoo algorithm, setting the maximum number of iterations N, population size Q, search space dimension, and search upper and lower bounds, and generating N initial solutions. These serve as N initial co-phase errors to be corrected for the sub-mirror to be corrected.

[0078] A2. Based on the initial cophase error, select the correction amount. The current sub-mirror to be calibrated is calibrated, and the evaluation value series is calculated:

[0079]

[0080] A3. Select the evaluation value series The highest evaluation value in And set the maximum evaluation value The corresponding co-phase error candidate correction amount is the optimal correction amount.

[0081] A4. Restore the current sub-mirror to be calibrated to its state before calibration, with the optimal calibration amount. For reference, based on the Lévy flight mechanism in the cuckoo optimization algorithm, equation (7) is used to select the correction amount for the co-phase error. Update:

[0082]

[0083] Where i = {0, 1, ..., M-1}, M represents the iteration number, and z best-i This represents the correction amount at the i-th iteration, and α represents the step size control factor. In this specific embodiment, α = 0.01. This represents point-to-point multiplication; Levy(λ) is the Levy flight formula.

[0084] The Levi flight formula is as follows:

[0085]

[0086] Where β = 1.5, v ~ N(0,1), while the standard deviation σ of the normal distribution μ According to equation (9), we can obtain:

[0087]

[0088] Generate a random number r and compare it with a given probability pa = 0.25:

[0089] If r > pa, then the parameters are updated randomly using equation (10); otherwise, the parameters remain unchanged.

[0090]

[0091] Where η represents the compression factor, and η ~ U[0,1]; and Let represent two random correction values ​​in the i-th iteration.

[0092] A5. Based on the current cophase error, select the appropriate correction amount. The current sub-mirror to be calibrated is calibrated, and a series of N evaluation values ​​are calculated.

[0093] A6. Select the evaluation value series The highest evaluation value in And set the maximum evaluation value The corresponding co-phase error candidate correction amount is the current optimal correction amount.

[0094] A7. Repeat steps A4 to A6:

[0095] If the same optimal correction value appears more than M times, the operation is stopped and the optimal correction value is set as the final correction value.

[0096] If the same optimal correction value does not appear more than the set number of times, and the number of repeated operations reaches the set number, then the last optimal correction value is set as the final correction value; the current sub-mirror to be corrected is corrected according to the final correction value. Specific Implementation Example 2:

[0098] When the particle swarm optimization algorithm is selected as the population optimization algorithm in this invention, the following calculation process is performed for optimization and iterative calculation during steps S2 to S6:

[0099] B1. Initialize the particle swarm optimization algorithm, set the maximum number of iterations M, and set the initial update rate group. and N initial solutions These serve as N initial co-phase errors to be corrected for the sub-mirror to be corrected.

[0100] B2. Selected correction amount based on initial cophase error The current sub-mirror to be calibrated is calibrated, and the evaluation value series is calculated:

[0101]

[0102] B3. Selecting the evaluation value series The highest evaluation value in And set the maximum evaluation value The corresponding co-phase error candidate correction amount is the optimal correction amount. set up The j-th optimal correction value among the candidate correction values ​​Z0 for cophase error j = {1, 2, ..., M}.

[0103] B4. Restore the current sub-mirror to be calibrated to its pre-calibration state, with the optimal calibration amount. For reference, the candidate correction amount for cophase error is updated using the particle swarm optimization algorithm. As shown in the following formula:

[0104] Z i+1 =Z i +α·V i (11);

[0105] Where i = {0, 1, ..., N-1}, Z i α represents the co-phase error to be corrected in the i-th iteration; α represents the constraint factor that controls the influence of speed.

[0106] Regarding update speed Update using the following formula:

[0107]

[0108] Where c1 and c2 are acceleration constants, representing the influence factors of group memory and individual memory on individual behavior, w represents the inertia factor that enables the algorithm to maintain its search direction during the search process, and γ1 and γ2 represent randomly generated random numbers in the range of [0 to 1].

[0109] B5. Select the current cophase error to be corrected. Corresponding value sequence The highest evaluation value in And set the maximum evaluation value The corresponding co-phase error candidate correction amount is the current optimal correction amount.

[0110] Compare the possible correction values ​​for each common phase error corresponding With the j-th optimal correction amount For the corresponding second peak value, the larger value of the co-phase error candidate correction value is selected and updated as the (j+1)th optimal correction value.

[0111] B6. Repeat steps B4 to B5:

[0112] If the same optimal correction value is repeated more than the set number of times, the operation will stop and the optimal correction value will be set as the final correction value.

[0113] If the same optimal correction value does not appear more than the set number of times, and the number of repeated operations reaches the set number, then the last optimal correction value is set as the final correction value; the current sub-mirror to be corrected is corrected according to the final correction value.

[0114] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0115] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for correcting the phase error of sub-mirrors in a spliced ​​telescope, characterized in that, Specifically, the following steps are included: S1. Select one sub-mirror from the spliced ​​telescope system as the reference sub-mirror, and the remaining sub-mirrors as sub-mirrors to be calibrated; design a mask to be placed at the pupil of the spliced ​​telescope system; and calculate the second-highest value of the co-phase error characterizing a certain sub-mirror to be calibrated in the MTF of the spliced ​​telescope system. The design process of the mask is as follows: S11. Make the number of sub-apertures of the mask the same as the number of sub-mirrors in the spliced ​​telescope system, define the baseline between the sub-aperture corresponding to the reference sub-mirror and the sub-aperture of each sub-mirror to be corrected as the main baseline, and define the baseline between the sub-apertures of each sub-mirror to be corrected as the sub-baseline. S12. The directions of the main baselines are different, so as not to affect the secondary peak values ​​generated by each pair of sub-apertures. In this case, partial overlap in the side lobes is allowed, thereby obtaining the mask; S2. Initialize the population optimization algorithm and use the initial solution as the N phase error candidate correction quantities of the current sub-mirror to be corrected. The population optimization algorithm adopts the cuckoo algorithm or the particle swarm algorithm. S3. Correct the current sub-mirror to be corrected based on N possible co-phase error correction values, and calculate the evaluation value series. ; S4. Select the evaluation value sequence. The highest evaluation value in And set the maximum evaluation value. The corresponding co-phase error correction value to be selected is the current optimal correction value; S5. Restore the current sub-mirror to be corrected to its state before correction, and update the co-phase error candidate correction amount according to the update principle of the population optimization algorithm, with the current optimal correction amount as a reference. S6. Repeat steps S3 to S5: If the same optimal correction value is repeated more than a set number of times, the operation is stopped, and the optimal correction value is set as the final correction value. If the same optimal correction value does not appear more than the set number of times, and the number of times the operation is repeated reaches the set number, then the last optimal correction value is set as the final correction value. The current sub-mirror to be corrected is corrected according to the final correction amount; S7. Repeat steps S2 to S6 until all sub-mirrors to be calibrated have been calibrated.

2. The method for correcting the phase co-occurrence error of sub-mirrors in a spliced ​​telescope according to claim 1, characterized in that, The process of obtaining the side lobes is as follows: The reflected wavelet of the sub-aperture is sampled, and the incident light has a center wavelength of and spectral width is A broad spectrum; if each wavelength has the same weight, then the optical system... It can be expressed by equation (1): in, The PSF under monochromatic light can be expressed by equation (2): in, This represents the distance between the centers of every two sub-pupils in the sub-aperture; Represents the first-order Bessel function. Indicates piston error. Indicates the diameter of the secondary pupil. Indicates the focal length of the imaging lens; Therefore, the derivative of equation (1) is approximately: The summation of integrals over intervals is: Therefore, according to equation (4), the MTF is obtained: in, , ; express The secondary lobes are specifically: in, Indicates Fourier calculation; The side lobe The amplitude of the central peak is normalized to obtain the secondary peak value. Thus, the secondary peak value is obtained. The relationship between the error and the translation error of the sub-mirror is as follows:

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