Co-phase error detection method for sub-mirrors of spliced telescope

Abstract

The invention relates to the technical field of error detection of telescopes, in particular to a spliced telescope sub-mirror co-phase error detection method, which comprises the following steps of: firstly, designing a special mask, so that secondary peak values for representing sub-mirror co-phase errors in an MTF (Modulation Transfer Function) under wide-spectrum illumination are not overlapped; therefore, real secondary peak values representing co-phase errors of all sub-mirrors in the MTF under wide spectrum illumination can be calculated respectively; initializing a population optimization algorithm, taking an initial solution as a sub-mirror co-phase error under a certain condition, substituting the initial solution into the spliced telescope simulation model, calculating to obtain a simulation sub-peak value representing the sub-mirror co-phase error, and taking a variance between the simulation sub-peak value and a real sub-peak value as an evaluation index; and the optimal simulation quantity is selected according to the evaluation indexes, and repeated iteration is carried out, so that large-range high-precision real-time detection on the three-dimensional co-phase error of each sub-mirror is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of error correction of telescopes, and in particular to a method for detecting the co-phasing error of sub-mirrors of a segmented telescope. Background Art

[0002] The light-gathering power and resolution of a telescope are directly related to the size of its primary mirror. However, the increase in the size of the primary mirror has brought unprecedented challenges to the design, processing, manufacturing, testing, and launching of space telescopes. The emergence of the segmented primary mirror telescope provides a solution to the above problems. In order to make the overall imaging quality of the segmented telescope close to the diffraction limit, it is necessary to ensure a high co-phasing accuracy between the sub-mirrors. Therefore, it is necessary to detect the co-phasing error of each sub-mirror through wavefront sensing, and then use a high-precision displacement adjustment mechanism for correction.

[0003] Existing methods have established a functional relationship between the MTF secondary peak and the translational error of the segmented mirror under broadband illumination, and by designing a special mask, the secondary peaks representing the translational error of the sub-mirrors in the MTF do not overlap, so that this relationship can be used to calculate the translational error of each sub-mirror in the segmented telescope respectively, but the tilt errors in the other two directions of each sub-mirror cannot be calculated. Summary of the Invention

[0004] In order to solve the above problems, the present invention provides a method for detecting the co-phasing error of sub-mirrors of a segmented telescope, which realizes the identification of the three-dimensional co-phasing error of each sub-mirror by designing a special mask and combining a population optimization algorithm. Since the identification process of each sub-mirror is independent, the increase in the number of sub-mirrors will not increase the difficulty of the algorithm, and only the shape of the mask needs to be changed according to the design principle.

[0005] The method for correcting the co-phasing error of sub-mirrors of the segmented telescope proposed by the present invention specifically includes the following steps:

[0006] S1. Select one sub-mirror in the simulation model of the segmented telescope as the reference sub-mirror, and the remaining sub-mirrors as the sub-mirrors to be corrected; design a mask arranged at the pupil of the segmented telescope system; and calculate the true secondary peak MTF representing the co-phasing error of a certain sub-mirror to be corrected in the MTF of the segmented telescope system nph ;

[0007] S2. Initialize the population optimization algorithm, use the initial solution as the simulation quantity of the co-phasing error of the sub-mirror in a certain situation, and substitute the simulation quantity of the co-phasing error of the sub-mirror into the simulation model of the segmented telescope;

[0008] S3. According to N candidate simulation quantities of co-phasing errors, calculate N corresponding simulation secondary peaks to obtain a simulation secondary peak sequence:

[0009] {MTF nph1,MTF nph2 ,…MTF nphk ,…,MTF nphN};

[0010] S4. Compare each item in the simulated sub-peak sequence with the true sub-peak MTF nph to obtain the difference sequence gap:

[0011] gap[k] = |MTF nphk - MTF nph | 2 (1);

[0012] where k = {1, 2,..., N}, select the simulated sub-peak MTF nphk corresponding to the minimum value in the difference sequence gap as the optimal simulated sub-peak MTF nph-max , and the co-phase error simulation quantity corresponding to the optimal simulated sub-peak MTF nph-max is the current optimal simulation quantity;

[0013] S5. Taking the current optimal simulation quantity as a reference, update the co-phase error simulation quantity according to the update principle of the population optimization algorithm;

[0014] S6. Repeat the operations in steps S3 - S5:

[0015] If the same optimal simulation quantity appears more than the set number of times, stop the operation and set the optimal simulation quantity as the final simulation quantity;

[0016] If the same optimal simulation quantity does not appear more than the set number of times and the number of repeated operations reaches the set number of times, set the last optimal simulation quantity as the final simulation quantity;

[0017] S7. Repeat steps S2 - S6 until the final simulation quantities of all sub-mirrors to be corrected are obtained.

[0018] Furthermore, the design process of the mask is as follows:

[0019] S11. Make the number of sub-apertures of the mask the same as the number of sub-mirrors in the segmented telescope system. Define the baseline between the sub-aperture corresponding to the reference sub-mirror and the sub-apertures of each sub-mirror to be corrected as the main baseline, and define the baseline between the sub-apertures of each pair of sub-mirrors to be corrected as the sub-baseline;

[0020] S12. The directions of the main baselines are different. Without affecting the sub-peak MTF nph generated by each pair of sub-apertures, partial overlap in the sidelobes is allowed, and then the mask is obtained.

[0021] Furthermore, the specific process of obtaining the sidelobes is as follows:

[0022] Sample the reflected sub - wave of the sub - aperture. The incident light is a broadband spectrum with a central wavelength of λ0 and a spectral width of Δλ. If the weights of each wavelength are the same, the PSF of the optical system b can be expressed by Equation (2):

[0023]

[0024] where PSF m (x, y, λ) is the PSF in the case of monochromatic light and can be expressed by Equation (3):

[0025]

[0026] 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 diameter of the secondary pupil, and f represents the focal length of the imaging lens;

[0027] Therefore, the differential of Equation (2) is approximately the integral sum of n intervals, that is:

[0028]

[0029] Furthermore, the MTF is obtained according to Equation (5):

[0030]

[0031] where f x = x0 / λf, f y = y0 / λf; MTF sub represents the sidelobe of the MTF, specifically:

[0032]

[0033] where FT[·] represents the Fourier calculation;

[0034] Normalize the amplitude of the central peak of the sidelobe MTF sub to obtain the sub - peak MTF nph , and then obtain the sub - peak MTF nph The relationship with the translational error of the secondary mirror is:

[0035]

[0036] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0037] 1) The present invention does not require repeated adjustment of the optical system and is not affected by the number of secondary mirrors. The error calculation is completed through theoretical calculation, reducing the operational complexity of the error experiment;

[0038] 2) Based on the design of a special mask and combined with a population optimization algorithm, the present invention calculates the tilt error while calculating the common translational error, and realizes the large-range and high-precision calculation of the three-dimensional co-phase error of each sub-mirror. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flowchart of a method for detecting the co-phase error of sub-mirrors of a segmented telescope according to an embodiment of the present invention;

[0040] Figure 2 is a flowchart of the design of a mask according to an embodiment of the present invention;

[0041] Figure 3 is a schematic diagram of a mask of a segmented telescope according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0042] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present 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 only used to explain the present invention, and do not constitute a limitation to the present invention.

[0043] A method for detecting the co-phase error of sub-mirrors of a segmented telescope provided by an embodiment of the present invention first designs a special mask, obtains and calculates the simulated secondary peaks in the MTF under broadband spectral illumination that characterize the co-phase error of each sub-mirror, and then uses the difference between the simulated secondary peaks and the real secondary peaks as an evaluation index, and repeatedly searches and iterates through a population optimization algorithm to achieve real-time detection of the three-dimensional co-phase error of each sub-mirror with a large range and high precision.

[0044] Figure 1 shows a flowchart of a method for detecting the co-phase error of sub-mirrors of a segmented telescope according to an embodiment of the present invention.

[0045] As Figure 1 shown, the method for detecting the co-phase error of sub-mirrors of a segmented telescope provided by an embodiment of the present invention specifically includes the following steps:

[0046] S1. Select one sub-mirror in the simulation model of the segmented telescope as the reference sub-mirror, and the remaining sub-mirrors as the sub-mirrors to be corrected; design a mask arranged at the pupil of the segmented telescope system; and calculate the real secondary peak MTF in the MTF of the segmented telescope system that characterizes the co-phase error of a certain sub-mirror to be corrected nph .

[0047] Figure 2 and Figure 3 respectively show the design process of the mask and the schematic diagram of the mask according to an embodiment of the present invention.

[0048] As Figure 2 andFigure 3 As shown in the figure, the design process of the mask is as follows:

[0049] S11. Make the number of sub-apertures of the mask the same as the number of sub-mirrors in the segmented telescope system. Define the baseline between the sub-aperture corresponding to the reference sub-mirror and the sub-apertures of each sub-mirror to be corrected as the main baseline, and define the baseline between the sub-apertures of each pair of sub-mirrors to be corrected as the sub-baseline;

[0050] S12. The directions of the main baselines are different, and the distribution of the MTF sidelobes on the main baselines should be discrete. Without affecting the secondary peak MTF generated by each pair of sub-apertures nph partial overlap in the sidelobes is allowed, and thus the mask is obtained.

[0051] The specific process for obtaining the sidelobes is as follows:

[0052] Sample the reflected sub-waves of the sub-apertures. The incident light is a broad spectrum with a central wavelength of λ0 and a spectral width of Δλ; if the weights of each wavelength are the same, the PSF of the optical system b can be expressed by Equation (1):

[0053]

[0054] where PSF m (x, y, λ) is the PSF in the case of monochromatic light and can be expressed by Equation (2):

[0055]

[0056] 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 diameter of the secondary pupil, and f represents the focal length of the imaging lens;

[0057] Therefore, the differential approximation of Equation (1) is the integral summation of n intervals, that is:

[0058]

[0059] Furthermore, the MTF is obtained according to Equation (4):

[0060]

[0061] where f x = x0 / λf, f y = y0 / λf; MTF sub represents the sidelobe of the MTF and is specifically:

[0062]

[0063] where FT[·] represents the Fourier calculation;

[0064] Normalize the amplitude of the central peak of the sidelobe MTF sub to obtain the sub-peak MTF nph , and further obtain the sub-peak MTF nph The relationship with the segment mirror translation error is:

[0065]

[0066] S2. Initialize the population optimization algorithm, use the initial solution as the segment mirror phasing error simulation quantity in a certain case, and substitute the segment mirror phasing error simulation quantity into the stitching telescope simulation model.

[0067] S3. According to N candidate simulation quantities of phasing errors, calculate N corresponding simulation sub-peaks to obtain a simulation sub-peak sequence:[[]]

[0068] {MTF nph1 , MTF nph2 , … MTF nphk , …, MTF nphN}.

[0069] S4. Compare each item in the simulation sub-peak sequence with the true sub-peak MTF nph according to the following formula to obtain a difference sequence gap:

[0070] gap[k] = |MTF nphk - MTF nph | 2 (7);

[0071] where k = {1, 2, ..., N}, select the simulation sub-peak MTF nphk corresponding to the minimum value in the difference sequence gap as the optimal simulation sub-peak MTF nph-max , and the phasing error simulation quantity corresponding to the optimal simulation sub-peak MTF nph-max is the current optimal simulation quantity.

[0072] S5. Using the current optimal simulation quantity as a reference, update the candidate simulation quantities of phasing errors according to the update principle of the population optimization algorithm.

[0073] S6. Repeat the operations in steps S3 - S5:

[0074] If the same optimal simulation quantity appears more than the set number of times, stop the operation and set this optimal simulation quantity as the final simulation quantity;

[0075] If the same optimal simulation quantity does not appear more than the set number of times and the number of repeated operations reaches the set number of times, set the last optimal simulation quantity as the final simulation quantity.

[0076] S7. Repeat steps S2 - S6 until the final simulation values of all sub - mirrors to be corrected are obtained.

[0077] To clearly describe the co - phase error correction method for the segmented telescope sub - mirrors provided by the present invention, the cuckoo algorithm and the particle swarm algorithm are selected as the population optimization algorithms, and corresponding specific embodiments are given. Specific Embodiment 1:

[0079] When the cuckoo optimization algorithm is selected as the population optimization algorithm in the present invention, when performing steps S2 - S6, the following calculation process is carried out for optimization and iterative calculation:

[0080] A1. Initialize the cuckoo algorithm, set the maximum number of iterations N, population size Q, search space dimension, search upper and lower bounds, and use the N initial solutions as the N initial candidate simulation values of the co - phase errors of the sub - mirrors to be corrected.

[0081] A2. Calculate the initial simulation sub - peak value sequence according to the initial candidate simulation values of the co - phase errors

[0082] A3. Compare each item in the initial simulation sub - peak value sequence with the true sub - peak MTF nph to obtain the difference sequence gap 0 :

[0083]

[0084] where k = {1, 2,..., N}, select the simulation sub - peak value 0 corresponding to the minimum value in the difference sequence gap as the optimal simulation sub - peak value and the co - phase error simulation quantity corresponding to the optimal simulation sub - peak value is the current optimal simulation quantity

[0085] A4. Taking the optimal simulation quantity as a reference, based on the Lévy flight mechanism in the cuckoo optimization algorithm, use Equation (9) to update the candidate simulation quantities of the co - phase errors :

[0086]

[0087] where i = {0, 1,..., M - 1}, M represents the number of iterations, z best-i represents the simulation quantity at the i - th iteration, α represents the step - size control factor, and in this specific embodiment, α = 0.01; ​Denotes point-to-point multiplication; Levy(λ) is the Levy flight formula.

[0088] The specific Levy flight formula is as follows:

[0089]

[0090] Among them, β = 1.5, v ∼ N(0,1), and the standard deviation σ of the normal distribution μ According to Equation (11), it can be obtained that:

[0091]

[0092] Randomly generate a random number r and compare r with the set probability pa = 0.25:

[0093] If r > pa, then randomly update the parameters using Equation (12), otherwise the parameters remain unchanged.

[0094]

[0095] Among them, η represents the compression factor, η ∼ U[0,1]; and Denotes two random simulation quantities in the i-th iteration.

[0096] A5. According to the current common-phase error, candidate simulation quantities Calculate the current simulation sub-peak value sequence

[0097] A6. According to the following formula, compare each item in the current simulation sub-peak value sequence with the true sub-peak value MTF nph to obtain the difference sequence gap i :

[0098]

[0099] Select the simulation sub-peak value corresponding to the minimum value in the difference sequence gap i as the optimal simulation sub-peak value and the common-phase error simulation quantity corresponding to the optimal simulation sub-peak value is the current optimal simulation quantity

[0100] A7. Repeat the operations in steps A4 - A6:

[0101] If the same optimal simulation quantity appears more than M times, stop the operation and set this optimal simulation quantity as the final simulation quantity;

[0102] ​If the same optimal simulation quantity does not repeat more than the set number of times and the number of repeated operations reaches the set number of times, then set the last optimal simulation quantity as the final simulation quantity. Specific Embodiment 2:

[0104] When the particle swarm algorithm is selected as the population optimization algorithm in the present invention, when performing steps S2 to S6, the following calculation process is carried out for optimization and iterative calculation:

[0105] B1. Initialize the particle swarm algorithm, set the maximum number of iterations M, the initial update speed group and take N initial solutions as the N initial co-phase error candidate simulation quantities of the sub-mirrors to be calibrated.

[0106] B2. Calculate the initial simulation sub-peak value sequence according to the initial co-phase error candidate simulation quantity :

[0107]

[0108] B3. Compare the gap between each item in the initial simulation sub-peak value sequence and the true sub-peak value MTF nph according to Equation (8) to obtain the gap sequence gap 0 , and select the simulation sub-peak value 0 corresponding to the minimum value in the gap sequence gap as the optimal simulation sub-peak value and the co-phase error simulation quantity corresponding to the optimal simulation sub-peak value is the current optimal simulation quantity Set as the j-th optimal simulation in the co-phase error candidate simulation quantity Z0 j = {1, 2,..., M}.

[0109] B4. Using the optimal simulation quantity as a reference, update the co-phase error candidate simulation quantity using the particle swarm algorithm as follows:

[0110] Z i+1 = Z i + α·V i (14);

[0111] where i = {0, 1,..., N - 1}, Z i represents the co-phase error candidate simulation quantity at the i-th iteration; α represents the constraint factor that controls the influence of the speed.

[0112] For the update speed update it as follows:

[0113]

[0114] Among them, c1 and c2 are acceleration constants, representing the influence factors of individual behavior by group memory and individual memory, w is the inertia factor representing the ability to maintain its own search direction during the algorithm search process, and γ1 and γ2 are randomly generated random numbers within the range of [0 to 1].

[0115] B5. Candidate simulation quantity according to the current universal error Calculate the current simulation sub-peak value sequence

[0116] B6. Compare each item in the current simulation sub-peak value sequence with the true sub-peak value MTF according to formula (13) nph to obtain the difference sequence gap i , and select the simulation sub-peak value corresponding to the minimum value in the difference sequence gap i as the optimal simulation sub-peak value and the universal error simulation quantity corresponding to the optimal simulation sub-peak value is the current optimal simulation quantity and the optimal simulation sub-peak value The corresponding universal error simulation quantity is the current optimal simulation quantity

[0117] Compare each candidate simulation quantity of the universal error according to formula (13) corresponding with the simulation sub-peak value corresponding to the j-th optimal simulation quantity , and select the candidate simulation quantity of the universal error corresponding to the larger value to update as the (j + 1)-th optimal simulation quantity

[0118] B7. Repeat the operations in steps B4 to B6:

[0119] If the same optimal simulation quantity appears more than the set number of times, stop the operation and set the optimal simulation quantity as the final simulation quantity;

[0120] If the same optimal simulation quantity does not appear more than the set number of times and the number of repeated operations reaches the set number of times, set the last optimal simulation quantity as the final simulation quantity.

[0121] It should be understood that various forms of the processes shown above can be used, reordering, adding or deleting steps. For example, the steps recorded in the disclosure of the present invention can be executed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in the present invention can be achieved, and no limitation is made herein.

[0122] The above specific embodiments do not constitute a limitation to the protection scope of the present 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 principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for detecting the coaxiality error of the secondary mirror of a segmented telescope, characterized in that, Specifically, it includes the following steps: S1. Select one sub - mirror in the segmented telescope simulation model as the reference sub - mirror, and the remaining sub - mirrors as the sub - mirrors to be corrected; design a mask set at the pupil of the segmented telescope system; and calculate the true secondary peak MTF representing the phase - error of a certain sub - mirror to be corrected in the MTF of the segmented telescope system nph ; S2. Initialize the population optimization algorithm, take the initial solution as the simulation quantity of the sub-mirror co-phasing error in a certain situation, and substitute the simulation quantity of the sub-mirror co-phasing error into the simulation model of the segmented telescope; S3. According to N candidate simulation quantities of the co-phasing error, calculate N corresponding simulation sub-peaks to obtain a simulation sub-peak sequence: {MTF nph1 ,MTF nph2 ,…MTF nphk ,…,MTF nphN}; S4. Compare each item in the simulated sub-peak sequence with the true sub-peak MTF according to the following formula to obtain a difference sequence gap: nph ​ gap[k] = |MTF nphk -MTF nph | 2 (1); where k = {1, 2,..., N}, select the simulated sub-peak MTF corresponding to the minimum value in the difference sequence gap nphk as the optimal simulated sub-peak MTF nph-max , and the co-phase error simulation quantity corresponding to the optimal simulated sub-peak MTF nph-max is the current optimal simulation quantity; S5. Taking the current optimal simulation quantity as a reference, update the simulation quantity of the co-phasing error according to the update principle of the population optimization algorithm; S6. Repeat the operations in steps S3 - S5: If the same optimal simulation quantity appears more than the set number of times, stop the operation and set the optimal simulation quantity as the final simulation quantity; If the same optimal simulation quantity does not appear more than the set number of times and the number of times of repeating the operation reaches the set number of times, set the last optimal simulation quantity as the final simulation quantity; S7. Repeat steps S2 - S6 until the final simulation quantities of all sub-mirrors to be corrected are obtained.

2. The method for detecting the coaxiality error of the secondary mirror of a segmented telescope according to claim 1, characterized in that, 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 segmented telescope system. Define the baseline between the sub-aperture corresponding to the reference sub-mirror and the sub-apertures of each sub-mirror to be corrected as the main baseline, and define the baseline between the sub-apertures of each pair of sub-mirrors to be corrected as the sub-baseline; S12. The directions of the main baselines are different. Without affecting the secondary peak MTF generated by each pair of sub-apertures, partial overlap is allowed in the sidelobes, thereby obtaining the mask. nph ​ 3. The method for detecting the coaxiality error of the secondary mirror of a segmented telescope according to claim 2, characterized in that, The specific process of obtaining the sidelobe is as follows: Sampling the reflected sub - wavelets of the sub - apertures, where the incident light is a broad spectrum with a central wavelength of λ0 and a spectral width of Δλ; if the weights of each wavelength are the same, the PSF of the optical system b can be expressed by Equation (2): Among them, PSF m (x, y, λ) is the PSF in the case of monochromatic light and can be expressed by Equation (3): 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 diameter of the secondary pupil, and f represents the focal length of the imaging lens; Therefore, the differential approximation of formula (2) is the integral summation of n intervals, that is: Furthermore, obtain the MTF according to formula (5): where f x = x0 / λf, f y = y0 / λf; MTF sub represents the sidelobe of MTF, specifically: Where FT[·] represents the Fourier calculation; Normalize the amplitude of the central peak of the sidelobe MTF sub to obtain the sub-peak MTF nph , and further obtain the sub-peak MTF nph . The relationship between the sub-peak MTF and the segment translation error is as follows:

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