A method for correcting a mirror translation error in a segmented target

Abstract

The application discloses a kind of patch mirror translation error correction methods for extended target, belong to optical imaging technical field.The method for realizing of the present application is: for the optical system of the block type primary mirror of having one piece reference mirror and one piece mirror to be adjusted, to any extended target imaging;Establish the relationship between the reciprocal of the power spectral density of image at the secondary peak position of optical transfer function under wideband spectrum illumination and the translation error of mirror to be adjusted, solve the translation error of mirror to be adjusted using the relationship;Adjust the translation of mirror to be adjusted;Repeat the process of calculating the translation error of mirror to be adjusted until the translation of mirror to be adjusted meets the threshold requirement;For the block type primary mirror optical system containing multiple mirrors, adjust the translation of mirror one by one in turn until all mirrors are adjusted, and the translation error correction is complete.The present application has the advantages of large dynamic range, few iteration times and fast convergence speed, and is suitable for on-orbit translation error correction of telescope with block type primary mirror.

Description

TECHNICAL FIELD

[0001] The application relates to a translation error correction method for sub-mirrors of a segmented primary mirror of an optical system, and belongs to the technical field of optical imaging. BACKGROUND

[0002] Increasing the aperture of a telescope is a main technical means to obtain higher resolution images, but due to the size of the rocket fairing and the limitation of processing cost, the aperture of the primary mirror of the telescope is generally not more than 4 meters. In order to break through this limitation, the primary mirror of a large-aperture telescope can be in the form of a segmented mirror, which is formed by arranging multiple small-aperture mirrors to form a large-aperture mirror as the primary mirror of the telescope. Due to the influence of mechanical structure and environment, there will be translation errors between the segmented sub-mirrors in the optical axis direction, which will directly lead to the decline of the imaging quality of the large-aperture telescope. Therefore, it is necessary to study the correction method of the translation error of the segmented mirror.

[0003] The existing translation error correction method of the segmented mirror mainly uses a point target as a beacon, and common methods include the Michelson interference method, the wide and narrow band Hartmann-Shack method, the dispersion fringe method, and the phase recovery method. The Michelson interference method is to interfere the wavefront with a reference light which has a common phase error, and the translation error is calculated according to the movement amount of the interference fringes. The wide and narrow band Hartmann-Shack method is to place a small lens at the edge position of the segmented mirror, and to move the adjustable mirror at the same step during the sensing process. The correlation coefficient of the obtained far-field image and the sample image is calculated and recorded, and the maximum value of the correlation coefficient is used to determine the translation error of the segmented mirror. The dispersion fringe method is to introduce a microlens array and a dispersion element-prism array at the pupil conjugate position, and to obtain a dispersion fringe in the far field. The translation error is obtained by fitting the light intensity signal. The phase recovery method uses multiple focal planes and defocused planes to recover the phase distribution of the pupil, and can recover the translation error between the segmented mirrors within one wavelength. When the observation object of the telescope is a single star point source beacon, the above methods can be used, but when the observation object of the telescope is a ground scene or multiple star extended targets, the above methods cannot be used.

[0004] The main methods for correcting the translation error of the segmented mirror using the extended target are the phase difference method, the evaluation function optimization method and the deep learning method. The phase difference method needs to introduce a specific phase change, and the solution is complex and the calculation amount is large. The measurement range of the translation error of the segmented mirror is limited to within 1 wavelength, and the measurement dynamic range is small. The evaluation function optimization method uses image sharpness as the evaluation function, and directly corrects the translation error of the segmented mirror using an optimization algorithm. The optimization algorithms that can be selected include the random parallel gradient descent method, the genetic algorithm and the particle swarm algorithm. These optimization algorithms are prone to fall into local extreme values when correcting the translation error of the segmented mirror, and the number of iterations is too large and the convergence speed is slow. The deep learning method uses a neural network to establish the mapping relationship between the focal plane image and the translation error, but the network structure is relatively complex, the network training time is long, and due to the limited network generalization ability, the reliability in actual application cannot be guaranteed. SUMMARY

[0005] In view of the small translation error measurement dynamic range, the large number of iterations and the slow convergence speed in the existing segmented mirror translation error correction method using an extended target as a beacon. The disclosed segmented mirror translation error correction method for an extended target derives the relationship between the translation error of the segmented mirror to be adjusted and the reciprocal of the power spectral density of the system acquired image at the secondary peak of the optical transfer function under wideband spectral illumination. Then, the translation error of the segmented mirror is solved and calculated according to the relationship, so that the method of the present application is not limited by monochromatic light and will not fall into local extreme values. The method has the advantages of large dynamic range, less number of iterations and fast convergence speed, thereby improving the adjustment efficiency and imaging resolution of the optical system with a segmented primary mirror.

[0006] The purpose of the present application is achieved by the following technical solutions:

[0007] The disclosed segmented mirror translation error correction method for an extended target is used for imaging an arbitrary extended target for a reference sub-mirror and a to-be-adjusted sub-mirror of an optical system with a segmented primary mirror. The relationship between the reciprocal of the power spectral density of the image at the secondary peak position of the optical transfer function under wideband spectral illumination and the translation error of the to-be-adjusted mirror is established, and the translation error of the to-be-adjusted sub-mirror is solved using the relationship. The translation of the to-be-adjusted sub-mirror is adjusted. The process of calculating the translation error of the to-be-adjusted sub-mirror is repeated until the translation of the to-be-adjusted sub-mirror meets the threshold requirement. For a segmented primary mirror optical system containing multiple sub-mirrors, the translation of the sub-mirrors is adjusted one by one in turn until all the sub-mirrors are adjusted and the system segmented mirror translation error correction is completed, and the imaging resolution is improved. The present application has the characteristics of large dynamic range, less number of iterations and fast convergence speed, and is suitable for on-orbit translation error correction of a telescope with a segmented primary mirror.

[0008] This invention discloses a method for correcting translation error of a segmented mirror for extended targets, used in an optical imaging system with a segmented primary mirror. The optical imaging system with a segmented primary mirror observes any extended target at ground level or at a distance. The optical imaging system with a segmented primary mirror mainly consists of segmented mirrors, detectors, and other optical elements. The segmented mirror is a sub-mirror array formed by two or more sub-mirrors.

[0009] The present invention discloses a method for correcting translation error of segmented mirrors for extended targets, comprising the following steps:

[0010] Step 1: Take the sub-mirror with the number k as the translation error reference sub-mirror, that is, the translation error of this sub-mirror is 0. For the reference sub-mirror with the number k and the sub-mirror to be adjusted with the number k+1, under broadband spectral illumination, establish the relationship between the image power spectral density of the image formed by the block mirror optical imaging system through the two sub-mirrors and the translation error of the sub-mirror to be adjusted for any extended target.

[0011] Based on the fact that the optical transfer function of an optical system is the autocorrelation of the system's pupil function, it is expressed as:

[0012]

[0013] Where OTF is the optical transfer function of the optical system under monochromatic light, m ​​is the spatial frequency, and P is the pupil function of the segmented mirror optical imaging system formed by the two sub-mirrors. * Let be the conjugate of the pupil function P, r be the spatial coordinates of the system's pupil surface, λ be the wavelength, f be the focal length of the optical system, and dA represent the integral over the pupil area.

[0014] P(r)=Π(r)exp[jΦ(r)] (2)

[0015] Π is the transmittance of the pupil plane, Φ is the wavefront phase within the pupil plane, and j represents a complex number. 2 =-1.

[0016] For a segmented mirror optical system with two sub-mirrors, the optical transfer function (OTF) in aberration-free conditions exhibits three peaks: a central highest peak and two lower, centrally symmetrical secondary peaks. The physical meaning of the secondary peak positions is the overlap position of the two sub-mirrors during autocorrelation. The two sub-mirrors have identical shapes and contain no higher-order aberrations, only translational errors between the two sub-mirrors. If the optical path difference caused by the translational error of the sub-mirror to be adjusted is p, then the OTF at the secondary peak is:

[0017]

[0018] Where S is the area of ​​each sub-mirror, and p is the optical path difference caused by the translation error of the sub-mirror to be adjusted. spThe spatial frequency of the second peak of the optical transfer function is determined by the center position vectors of the two sub-mirrors, the focal length of the optical system, and the center wavelength of the light entering the system.

[0019]

[0020] Where d is the center position vector of the two segmented mirrors, λ0 is the center wavelength, and f is the focal length of the optical system.

[0021] According to formula (3), the optical transfer function at the secondary peak under single wavelength is only affected by the phase component due to translation error, which is within 2π, meaning the optical path difference length of the translation error is within one wavelength. To avoid the phase interference under single wavelength and to expand the dynamic range of the translation error, broadband spectral illumination is used. The optical transfer function at the secondary peak under polychromatic light is expressed as:

[0022]

[0023] Where H is the optical transfer function of the optical system under polychromatic light, the wavelength of the polychromatic illumination light ranges from λ1 to λ2, and c(λ) is the proportion of different wavelengths within the polychromatic light wavelength range. dλ represents the integration over the wavelength range of the polychromatic illumination light.

[0024] Discretizing the wavelength, when the translation error is relatively small compared to the coherence length of the polychromatic illumination light, we use a Taylor series expansion to expand the optical transfer function at the second peak under polychromatic light, neglecting higher-order terms, to obtain...

[0025]

[0026] Where N is the number of wavelength samples, λ i For the i-th wavelength after wavelength discretization, i = 1:N, c(λ) i Let be the weight of the i-th wavelength. Since the modulation transfer function of the optical system is the modulus of the optical transfer function, squaring the modulation transfer function of the system under polychromatic light at the second peak and ignoring terms higher than the power of 2, we get:

[0027]

[0028] in,

[0029]

[0030] λ j Let c(λ) be the j-th wavelength after discretization. j ) represents the weight of the j-th wavelength.

[0031] Formula (7) is accurate when the translation error is relatively small compared to the coherence length of the broadband spectral illumination light. However, for translation errors with a relatively large coherence length compared to the polychromatic illumination light, Formula (7) is not accurate enough due to the use of Taylor series expansion. Furthermore, as the translation error increases, the square of the modulation transfer function |H(m) of the system under the polychromatic light at the secondary peak becomes even more inaccurate. sp )| 2 Negative values ​​may occur, while in practice, the square of the modulation transfer function of the system under polychromatic light at the secondary peak is |H(m)|. sp )| 2 It will approach zero. At this point, a more suitable approximation is the Lorentz function, where the square of the modulation transfer function of the system under polychromatic light at the second peak of the Lorentz function is |H(m)|. sp )| 2 Always positive, that is

[0032]

[0033] For an optical imaging system observing an extended target, the Fourier transform of the acquired spatial image is equal to the product of the Fourier transform of the observed extended target and the system's optical transfer function, i.e.

[0034] J(m)=T(m)H(m) (10)

[0035] Where J and T are the Fourier transforms of the acquired image and the observed extended target, respectively, and m is the spatial frequency, i.e., within the entire frequency domain. The power spectral density of the acquired image is the square of the modulus of the image's Fourier transform. Combining formulas (9) and (10), we can obtain the power spectral density at the second peak m. sp Get

[0036]

[0037] The reciprocal of the obtained image power spectral density at the second peak is used as the evaluation function G. That is, the relationship between the evaluation function G (the reciprocal of the image power spectral density at the second peak of the optical transfer function) and the translation error p of the sub-mirror to be adjusted is:

[0038]

[0039] Step 2: Using the relationship between the image power spectral density established in Step 1 and the translation error of the sub-mirror to be adjusted, solve for the translation error of the sub-mirror to be adjusted.

[0040] Preferably, the translation error of the sub-mirror to be adjusted is solved in step 2 using the bidirectional bias method. The specific method is as follows:

[0041] Step 2.1: For the reference sub-mirror with index k and the sub-mirror to be adjusted with index k+1, the segmented mirror optical imaging system formed by these two sub-mirrors will extend the target image onto the detector. The optical image received by the detector is the image obtained without applying translation error bias. Perform a Fourier transform on the image, and take the square of the modulus after the Fourier transform to obtain the power spectral density of the image. The reciprocal of the power spectral density at the secondary peak is the evaluation function G0 without applying translation error bias.

[0042]

[0043] Where J0 is the Fourier transform of the image obtained without applying translation error bias, and I0 is the image obtained without applying translation error bias. is the symbol for the Fourier transform, and m is the spatial frequency.

[0044] Step 2.2: For the reference sub-mirror with index k and the sub-mirror to be adjusted with index k+1, apply a translation bias of +b to the translation of the sub-mirror to be adjusted with index k+1. Then, the segmented mirror optical imaging system formed by these two sub-mirrors will image the extended target onto the detector. The detector receives the optical image, which is the image obtained under the applied positive translation error bias. Perform a Fourier transform on the image, and take the square of the modulus after the Fourier transform to obtain the power spectral density of the image. The reciprocal of the power spectral density at the secondary peak is the evaluation function G under the applied positive translation error bias. + :

[0045]

[0046] J + For the Fourier transform of the image obtained under a positive translation error bias, I + The image obtained with a positive translation error bias applied.

[0047] Step 2.3: For the reference sub-mirror with index k and the sub-mirror to be adjusted with index k+1, after adjusting the state of the sub-mirror to be adjusted with index k+1 to the unbiased state, apply a translation bias of magnitude -b to the translation of the sub-mirror to be adjusted with index k+1. Then, the segmented mirror optical imaging system formed by these two sub-mirrors will image the extended target onto the detector. The detector receives the optical image, which is the image obtained under the negative translation error bias. Perform a Fourier transform on the image, and take the square of the modulus after the Fourier transform to get the power spectral density of the image. The reciprocal of the power spectral density at the secondary peak is the evaluation function G under the negative translation error bias. _ :

[0048]

[0049] J _For the Fourier transform of the image obtained under a negative translation error bias, I _ The image obtained with a negative translation error bias applied.

[0050] Step 2.4: Based on the evaluation function G0 without applying translation error bias in Step 2.1, and the evaluation function G with positive translation error bias in Step 2.2... + The evaluation function G under the negative translation error bias in step 2.3 - The translation error of the sub-mirror is calculated using equation (12) in step 1.

[0051]

[0052] Therefore, the optical path difference caused by the translation error of the sub-mirror to be adjusted is

[0053]

[0054] Step 2.5: Adjust the state of the sub-mirror with serial number k+1 to the unbiased state.

[0055] Step 3: Use the translation error calculated in Step 2 to adjust the translation of the sub-mirror to be adjusted.

[0056] Step 4: Repeat steps 2 and 3 until the translation of the sub-mirror to be adjusted meets the threshold requirement.

[0057] The preferred threshold requirement is that the translation adjustment amount is less than 1 / 50 of the center wavelength.

[0058] Step 5: Using the sub-mirror with serial number k = k+1 as the reference sub-mirror, adjust the sub-mirror with serial number k+1 to be adjusted, and repeat steps 2-4 until the serial number of the reference sub-mirror is K-1, where K is the number of sub-mirrors in the segmented primary mirror. That is, all sub-mirrors in the sub-mirror array of the segmented primary mirror in the segmented primary mirror optical system have been adjusted, thereby improving the imaging resolution of the segmented primary mirror optical system.

[0059] Beneficial effects:

[0060] 1. The present invention discloses a method for correcting the translation error of a segmented mirror for extended targets. It utilizes the mathematical relationship between the reciprocal of the image power spectral density of the extended target at the second peak of the optical transfer function under broadband spectral illumination and the translation error of the segmented mirror to be adjusted. Compared with model-free optimization algorithms that use image sharpness as the evaluation function, it does not get trapped in local extrema, has fewer iterations, faster convergence speed, and larger dynamic range, and thus has higher adjustment efficiency.

[0061] 2. The present invention discloses a segmented mirror translation error correction method for extended targets. It uses an optical system under broadband optical illumination to image the extended targets. Compared with the phase change method, which cannot calculate translation error of more than one wavelength using single-wavelength imaging, it has a larger dynamic range for translation error correction.

[0062] 3. The present invention discloses a method for correcting the translation error of a segmented mirror for extended targets. It utilizes the quadratic mathematical relationship between the reciprocal of the image power spectral density at the second peak of the optical transfer function under broadband spectral illumination and the translation error of the segmented mirror to be adjusted to calculate the translation error of the segmented mirror. Compared with the phase change method, it has the advantages of small computational load, small data processing load, fast calculation speed, and higher adjustment efficiency. Attached Figure Description

[0063] Figure 1 This is a schematic diagram of the optical imaging system of the present invention for observing any extended target using a segmented primary mirror;

[0064] Figure 2 This is a flowchart of the operation of a segmented mirror translation error correction method for an extended target according to the present invention;

[0065] Figure 3 This is a flowchart of a preferred bidirectional offset method for calculating translation error in a segmented mirror translation error correction method for an extended target, according to the present invention.

[0066] Figure 4 This is a curve showing the change of translation error with the number of iterations under different initial translation errors when the target is a USAF-1951 resolution board, using the correction method of the present invention;

[0067] Figure 5 These are comparison images of images before and after correction using the correction method of this invention. Detailed Implementation

[0068] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0069] Example 1:

[0070] This embodiment discloses a method for correcting translation errors of a segmented primary mirror for extended targets, applicable to optical imaging systems with segmented primary mirrors, such as... Figure 1 As shown, the optical imaging system with a segmented primary mirror observes any extended target at ground level or at a distance. The optical imaging system with a segmented primary mirror mainly consists of segmented mirrors, detectors, and other optical elements used to balance the aberrations of the optical system. The segmented mirror is a sub-mirror array formed by two sub-mirrors.

[0071] like Figure 2 As shown in the figure, this embodiment discloses a method for correcting the translation error of a segmented mirror for an extended target, which includes the following steps:

[0072] Step 1: Take the sub-mirror with serial number 1 as the translation error reference sub-mirror, that is, the translation error of this sub-mirror is 0. For the reference sub-mirror with serial number 1 and the sub-mirror to be adjusted with serial number 2, under broadband spectral illumination, establish the relationship between the image power spectral density of the segmented mirror optical imaging system formed by the two sub-mirrors for imaging any extended target and the translation error of the sub-mirror to be adjusted.

[0073] Based on the fact that the optical transfer function of an optical system is the autocorrelation of the system's pupil function, it is expressed as:

[0074]

[0075] Where OTF is the optical transfer function of the optical system under monochromatic light, m ​​is the spatial frequency, and P is the pupil function of the segmented mirror optical imaging system formed by the two sub-mirrors. * Let be the conjugate of the pupil function P, r be the spatial coordinates of the system's pupil surface, λ be the wavelength, f be the focal length of the optical system, and dA represent the integral over the pupil area.

[0076] P(r)=Π(r)exp[jΦ(r)] (19)

[0077] Π is the transmittance of the pupil plane, Φ is the wavefront phase within the pupil plane, and j represents a complex number. 2 =-1.

[0078] For a segmented mirror optical system with two sub-mirrors, the optical transfer function (OTF) in aberration-free conditions exhibits three peaks: a central highest peak and two lower, centrally symmetrical secondary peaks. The physical meaning of the secondary peak positions is the overlap position of the two sub-mirrors during autocorrelation. The two sub-mirrors have identical shapes and contain no higher-order aberrations, only translational errors between the two sub-mirrors. If the optical path difference caused by the translational error of the sub-mirror to be adjusted is p, then the OTF at the secondary peak is:

[0079]

[0080] Where S is the area of ​​each sub-mirror, and p is the optical path difference caused by the translation error of the sub-mirror to be adjusted. sp The spatial frequency of the second peak of the optical transfer function is determined by the center position vectors of the two sub-mirrors, the focal length of the optical system, and the center wavelength of the light entering the system.

[0081]

[0082] Where d = 10.4 mm is the center position vector of the two segmented mirrors, λ0 = 600 nm is the center wavelength, and f = 400 mm is the focal length of the optical system.

[0083] According to formula (3), the optical transfer function at the secondary peak under single wavelength is only affected by the phase component due to translation error, which is within 2π, meaning the optical path difference length of the translation error is within one wavelength. To avoid the phase interference under single wavelength and to expand the dynamic range of the translation error, broadband spectral illumination is used. The optical transfer function at the secondary peak under polychromatic light is expressed as:

[0084]

[0085] Where H is the optical transfer function of the optical system under polychromatic light, the wavelength of the polychromatic illumination light ranges from λ1 to λ2, and c(λ) is the proportion of different wavelengths within the polychromatic light wavelength range. dλ represents the integration over the wavelength range of the polychromatic illumination light. The polychromatic light wavelength range is 590nm to 610nm, with a center wavelength of 600nm, and the intensity of each wavelength is uniformly distributed.

[0086] Discretizing the wavelength, when the translation error is relatively small compared to the coherence length of the polychromatic illumination light, we use a Taylor series expansion to expand the optical transfer function at the second peak under polychromatic light, neglecting higher-order terms, to obtain...

[0087]

[0088] Where N is the number of wavelength samples, λ i For the i-th wavelength after wavelength discretization, i = 1:N, c(λ) i Let be the weight of the i-th wavelength. Since the modulation transfer function of the optical system is the modulus of the optical transfer function, squaring the modulation transfer function of the system under polychromatic light at the second peak and ignoring terms higher than the power of 2, we get:

[0089]

[0090] in,

[0091]

[0092] λ j Let c(λ) be the j-th wavelength after discretization. j ) represents the weight of the j-th wavelength.

[0093] Formula (7) is accurate when the translation error is relatively small compared to the coherence length of the broadband spectral illumination light. However, for translation errors with a relatively large coherence length compared to the polychromatic illumination light, Formula (7) is not accurate enough due to the use of Taylor series expansion. Furthermore, as the translation error increases, the square of the modulation transfer function |H(m) of the system under the polychromatic light at the secondary peak becomes even more inaccurate. sp )| 2 Negative values ​​may occur, while in practice, the square of the modulation transfer function of the system under polychromatic light at the secondary peak is |H(m)|. sp )| 2 It will approach zero. At this point, a more suitable approximation is the Lorentz function, where the square of the modulation transfer function of the system under polychromatic light at the second peak of the Lorentz function is |H(m)|. sp )| 2 Always positive, that is

[0094]

[0095] For an optical imaging system observing an extended target, the Fourier transform of the acquired spatial image is equal to the product of the Fourier transform of the observed extended target and the system's optical transfer function, i.e.

[0096] J(m)=T(m)H(m) (27)

[0097] Where J and T are the Fourier transforms of the acquired image and the observed extended target, respectively, and m is the spatial frequency, i.e., within the entire frequency domain. The power spectral density of the acquired image is the square of the modulus of the image's Fourier transform. Combining formulas (9) and (10), we can obtain the power spectral density at the second peak m. sp Get

[0098]

[0099] The reciprocal of the obtained image power spectral density at the second peak is used as the evaluation function G. That is, the relationship between the evaluation function G (the reciprocal of the image power spectral density at the second peak of the optical transfer function) and the translation error p of the sub-mirror to be adjusted is:

[0100]

[0101] Step 2: Using the relationship between the image power spectral density established in Step 1 and the translation error of the sub-mirror to be adjusted, solve for the translation error of the sub-mirror to be adjusted.

[0102] In step 2, the translation error of the sub-mirror to be adjusted is solved using the bidirectional bias method. The flowchart is as follows: Figure 3 As shown, the expanded target is as follows Figure 4 The resolution panel in the upper right corner is explained in the following steps:

[0103] Step 2.1: For the reference sub-mirror (number 1) and the sub-mirror to be adjusted (number 2), the segmented mirror optical imaging system formed by these two sub-mirrors will extend the target image onto the detector. The optical image received by the detector is the image obtained without applying translation error bias. Perform a Fourier transform on the image, and take the square of the modulus after the Fourier transform to obtain the power spectral density of the image. The reciprocal of the power spectral density at the secondary peak is the evaluation function G0 without applying translation error bias.

[0104]

[0105] Where J0 is the Fourier transform of the image obtained without applying translation error bias, and I0 is the image obtained without applying translation error bias. is the symbol for the Fourier transform, and m is the spatial frequency.

[0106] Step 2.2: For the reference sub-mirror (number 1) and the sub-mirror to be adjusted (number 2), apply a translation bias of +5λ0 to the translation of the sub-mirror to be adjusted (number 2). Then, the segmented mirror optical imaging system formed by these two sub-mirrors will image the extended target onto the detector. The detector receives the optical image, which is the image obtained under the applied positive translation error bias. Perform a Fourier transform on the image, and take the square of the modulus after the Fourier transform to obtain the power spectral density of the image. The reciprocal of the power spectral density at the secondary peak is the evaluation function G under the applied positive translation error bias. + :

[0107]

[0108] J + For the Fourier transform of the image obtained under a positive translation error bias, I + The image obtained with a positive translation error bias applied.

[0109] Step 2.3: For the reference sub-mirror (number 1) and the sub-mirror to be adjusted (number 2), after adjusting the state of the sub-mirror to be adjusted (number k+1) to the unbiased state, apply a translation bias of -5λ0 to the translation of the sub-mirror to be adjusted (number 2). Then, the segmented mirror optical imaging system formed by these two sub-mirrors will image the extended target onto the detector. The detector receives the optical image, which is the image obtained under the negative translation error bias. Perform a Fourier transform on the image, and take the square of the modulus after the Fourier transform to obtain the power spectral density of the image. The reciprocal of the power spectral density at the secondary peak is the evaluation function G under the negative translation error bias. _ :

[0110]

[0111] J _For the Fourier transform of the image obtained under a negative translation error bias, I _ The image obtained with a negative translation error bias applied.

[0112] Step 2.4: Based on the evaluation function G0 without applying translation error bias in Step 2.1, and the evaluation function G with positive translation error bias in Step 2.2... + The evaluation function G under the negative translation error bias in step 2.3 _ The translation error of the sub-mirror is calculated using equation (12) in step 1.

[0113]

[0114] Therefore, the optical path difference caused by the translation error of the sub-mirror to be adjusted is

[0115]

[0116] Step 2.5: Adjust the state of the sub-mirror with serial number 2 to the unbiased state.

[0117] Step 3: Use the translation error calculated in Step 2 to adjust the translation of the sub-mirror to be adjusted.

[0118] Step 4: Repeat steps 2 and 3 until the translation of the sub-mirror to be adjusted is less than λ0 / 50.

[0119] like Figure 4 The graph shows the translation error changes in step 4 under different initial segmented mirror translation errors. Specifically, when the initial error is 24λ0, steps 2 and 3 are repeated 8 times; when the initial error is 15λ0, steps 2 and 3 are repeated 5 times; and when the initial error is 5λ0, steps 2 and 3 are repeated 3 times.

[0120] Step 5: The number of sub-mirrors in the segmented primary mirror is 2. Therefore, all sub-mirrors in the sub-mirror array of the segmented primary mirror in the segmented primary mirror optical system are adjusted, and the imaging resolution of the segmented primary mirror optical system is improved.

[0121] like Figure 5 The image shown is a comparison of the imaging results of the imaging system with segmented mirrors for striped targets before and after translation error correction. The translation error is 24λ0, and the translation error after correction is 0.012λ0, thus improving the system's imaging resolution.

[0122] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for correcting translation error of a segmented mirror for extended targets, used in an optical imaging system with a segmented primary mirror, wherein the optical imaging system with a segmented primary mirror observes any extended target at ground level or at a distance, the optical imaging system with a segmented primary mirror mainly consists of segmented mirrors, detectors, and other optical elements, wherein the segmented mirror is a sub-mirror array formed by two or more sub-mirrors; characterized in that: Includes the following steps, Step 1: Take the sub-mirror with the number k as the translation error reference sub-mirror. The translation error of the reference sub-mirror is 0. For the reference sub-mirror with the number k and the sub-mirror to be adjusted with the number k+1, under broadband spectral illumination, establish the relationship between the image power spectral density of the image formed by the block mirror optical imaging system through the two sub-mirrors and the translation error of the sub-mirror to be adjusted for any extended target. Step 2: Using the relationship between the image power spectral density established in Step 1 and the translation error of the sub-mirror to be adjusted, solve for the translation error of the sub-mirror to be adjusted; Step 3: Adjust the translation of the sub-mirror to be adjusted using the translation error calculated in Step 2; Step 4: Repeat steps 2 and 3 until the translation of the sub-mirror to be adjusted meets the threshold requirement; Step 5: Using the sub-mirror with serial number k+1 as the reference sub-mirror, adjust the sub-mirror with serial number k+2 to be adjusted. Repeat steps 2 to 4 until the reference sub-mirror's serial number is K-1, where K is the number of sub-mirrors in the segmented primary mirror. All sub-mirrors in the sub-mirror array of the segmented primary mirror in the segmented primary mirror optical system are adjusted, thereby improving the imaging resolution of the segmented primary mirror optical system.

2. The method for correcting translation error of segmented mirrors for extended targets as described in claim 1, characterized in that: Step 1 is implemented as follows: Based on the autocorrelation of the optical transfer function of an optical system as the pupil function, it can be expressed as: Where OTF is the optical transfer function of the optical system under monochromatic light, m ​​is the spatial frequency, and P is the pupil function of the segmented mirror optical imaging system formed by the two sub-mirrors. * Let be the conjugate of the pupil function P, r be the spatial coordinates of the system's pupil surface, λ be the wavelength, f be the focal length of the optical system, and dA represent the integral over the pupil area; where P(r)=Π(r)exp[jΦ(r)] (2) Π is the transmittance of the pupil plane, Φ is the wavefront phase within the pupil plane, and j represents a complex number. 2 =-1; For a segmented mirror optical system with two sub-mirrors, the optical transfer function (OTF) in aberration-free conditions exhibits three peaks: a central highest peak, two centrally symmetrical lower secondary peaks, and the physical meaning of the secondary peak positions is the overlap position of the two sub-mirrors during autocorrelation. The two sub-mirrors have identical shapes and contain no higher-order aberrations, only translational errors between the two sub-mirrors. If the optical path difference caused by the translational error of the sub-mirror to be adjusted is p, then the OTF at the secondary peak is: Where S is the area of ​​each sub-mirror, p is the optical path difference caused by the translation error of the sub-mirror to be adjusted; m sp The spatial frequency of the second peak of the optical transfer function is determined by the center position vectors of the two sub-mirrors, the focal length of the optical system, and the center wavelength of the light entering the system. Where d is the center position vector of the two segmented mirrors, λ0 is the center wavelength, and f is the focal length of the optical system; According to formula (3), the optical transfer function at the secondary peak under single wavelength is only affected by the phase component due to translation error, which is within 2π. The optical path difference length of the translation error is within one wavelength. To avoid the phase interference under single wavelength and to expand the dynamic range of the translation error, broadband spectral illumination is used. The optical transfer function at the secondary peak under polychromatic light is expressed as: Where H is the optical transfer function of the optical system under polychromatic light, the wavelength of the polychromatic illumination light ranges from λ1 to λ2, and c(λ) is the proportion of different wavelengths within the polychromatic light wavelength range. dλ represents the integration over the wavelength range of the polychromatic illumination light; Discretizing the wavelength, when the translation error is relatively small compared to the coherence length of the polychromatic illumination light, we use a Taylor series expansion to expand the optical transfer function at the second peak under polychromatic light, neglecting higher-order terms, to obtain... Where N is the number of wavelength samples, λ i For the i-th wavelength after wavelength discretization, i = 1:N, c(λ) i ) represents the weight of the i-th wavelength; since the modulation transfer function of the optical system is the modulus of the optical transfer function, squaring the modulation transfer function of the system under polychromatic light at the second peak and ignoring terms higher than the power of 2, we obtain: in, λ j Let c(λ) be the j-th wavelength after discretization. j ) represents the weight of the j-th wavelength; Formula (7) is accurate when the translation error is relatively small compared to the coherence length of the broadband spectral illumination light; however, for translation errors with a relatively large coherence length compared to the polychromatic illumination light, Formula (7) is not accurate enough due to the use of Taylor series expansion. Furthermore, as the translation error increases, the square of the modulation transfer function |H(m) of the system under the polychromatic light at the secondary peak becomes even more inaccurate. sp )| 2 Negative values ​​may occur, while in practice, the square of the modulation transfer function of the system under polychromatic light at the secondary peak is |H(m)|. sp )| 2 It will approach zero; at this point, a more suitable approximation is the Lorentz function, and the square of the modulation transfer function of the system under polychromatic light at the second peak of the Lorentz function is |H(m)|. sp )| 2 Always positive, that is For an optical imaging system observing an extended target, the Fourier transform of the acquired spatial image is equal to the product of the Fourier transform of the observed extended target and the system's optical transfer function, i.e. J(m)=T(m)H(m) (10) Where J and T are the Fourier transforms of the acquired image and the observed extended target, respectively, and m is the spatial frequency, i.e., in the entire frequency domain; the power spectral density of the acquired image is the square of the modulus of the image Fourier transform, and combining formulas (9) and (10), i.e., at the second peak m sp Get The reciprocal of the obtained image power spectral density at the second peak is used as the evaluation function G. That is, the relationship between the evaluation function G (the reciprocal of the image power spectral density at the second peak of the optical transfer function) and the translation error p of the sub-mirror to be adjusted is:

3. The method for correcting translation error of segmented mirrors for extended targets as described in claim 2, characterized in that: In step 2, the translation error of the sub-mirror to be adjusted is solved using the bidirectional bias method. The specific method is as follows: Step 2.1: For the reference sub-mirror with index k and the sub-mirror to be adjusted with index k+1, the segmented mirror optical imaging system formed by these two sub-mirrors will extend the target image onto the detector. The optical image received by the detector is the image obtained without applying translation error bias. Perform a Fourier transform on the image, and take the square of the modulus after the Fourier transform to obtain the power spectral density of the image. The reciprocal of the power spectral density at the secondary peak is the evaluation function G0 without applying translation error bias. Where J0 is the Fourier transform of the image obtained without applying translation error bias, and I0 is the image obtained without applying translation error bias. is the symbol for the Fourier transform, and m is the spatial frequency; Step 2.2: For the reference sub-mirror with index k and the sub-mirror to be adjusted with index k+1, apply a translation bias of +b to the translation of the sub-mirror to be adjusted with index k+1. Then, the segmented mirror optical imaging system formed by these two sub-mirrors will image the extended target onto the detector. The detector receives the optical image, which is the image obtained under the applied positive translation error bias. Perform a Fourier transform on the image, and take the square of the modulus after the Fourier transform to obtain the power spectral density of the image. The reciprocal of the power spectral density at the secondary peak is the evaluation function G under the applied positive translation error bias. + : J + For the Fourier transform of the image obtained under a positive translation error bias, I + The image obtained with a positive translation error bias applied; Step 2.3: For the reference sub-mirror with index k and the sub-mirror to be adjusted with index k+1, after adjusting the state of the sub-mirror to be adjusted with index k+1 to be adjusted to an unbiased state, apply a translation bias of magnitude -b to the translation of the sub-mirror to be adjusted with index k+1. Then, the segmented mirror optical imaging system formed by these two sub-mirrors will image the extended target onto the detector. The detector receives the optical image, which is the image obtained under the negative translation error bias. Perform a Fourier transform on the image, and take the square of the modulus after the Fourier transform to get the power spectral density of the image. The reciprocal of the power spectral density at the secondary peak is the evaluation function G under the negative translation error bias. J - For the Fourier transform of the image obtained under a negative translation error bias, I - The image obtained with a negative translation error bias applied; Step 2.4: Based on the evaluation function G0 without applying translation error bias in Step 2.1, and the evaluation function G with positive translation error bias in Step 2.2... + The evaluation function G under the negative translation error bias in step 2.3 - And use equation (12) in step 1 to calculate the translation error of the sub-mirror; Therefore, the optical path difference caused by the translation error of the sub-mirror to be adjusted is Step 2.5: Adjust the state of the sub-mirror with serial number k+1 to the unbiased state.

4. The method for correcting translation error of segmented mirrors for extended targets as described in claim 3, characterized in that: In step 4, the threshold requirement is that the translation error adjustment amount is less than 1 / 50 of the center wavelength.

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