CN113405676B - Correction method for micro-vibration influence in phase difference wavefront detection of space telescope - Google Patents
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Abstract
The invention relates to a correction method of micro-vibration influence in phase difference wavefront detection of a space telescope, which belongs to the field of optical detection and is characterized in that a Gaussian convolution is introduced to carry out statistical modeling on a random process of micro-vibration influence point diffusion function imaging so as to correct a functional relation between wavefront aberration and a point diffusion function acquired by a detector; determining parameters required for describing a two-dimensional Gaussian convolution template by using ground micro-vibration simulation data; collecting two point spread function images of different focal planes in a micro-vibration environment; establishing a nonlinear equation set for solving the wave front aberration coefficient by utilizing the functional relation between the corrected wave front aberration and the point spread function acquired by the detector and the point spread function images of different out-of-focus surfaces; and (3) converting the solution of the nonlinear equation set into a numerical optimization problem by establishing an objective function, and solving the wavefront aberration coefficient by using a related numerical optimization algorithm. The invention can improve the detection precision of the space telescope wavefront detection based on the phase difference method in the space micro-vibration environment.
Description
Technical Field
The invention belongs to the technical field of optical detection, and particularly relates to a correction method for micro-vibration influence in phase difference wavefront detection of a space telescope.
Background
The large-aperture telescope is an important astronomical observation instrument and plays an important role in the research of the problem of the leading edge of the great astronomy, particularly the space large-aperture astronomical telescope has the advantages that the imaging quality is not influenced by atmospheric disturbance, sensitive wave bands (such as infrared wave bands) are not influenced by atmospheric absorption, and compared with the ground astronomical telescope with the same aperture, the space large-aperture telescope has higher imaging performance.
During the in-orbit operation of the space large-caliber astronomical telescope, space thermal and mechanical environment disturbance factors continuously exist, the position precision of the mirror surface is difficult to guarantee for a long time by only relying on a fixing mechanism, and each mirror surface is gradually maladjusted to cause wavefront aberration and reduce the imaging quality. Therefore, it is necessary to correct the system wave aberration in-orbit to continuously maintain the in-orbit imaging quality of the spatial telescope.
High precision wavefront sensing is a prerequisite for on-track wavefront correction. Compared with a Hartmann sensor and a rectangular pyramid wave-front sensor, the phase difference method utilizes images (two images with known phase difference) formed by a focal plane detector to calculate the wave-front phase, does not need additional precise devices and a complex calibration process (the calibration process has errors) and is suitable for on-orbit application of a space telescope. However, the accuracy of the space telescope wavefront detection by using the phase difference method is easily influenced by the disturbance of the space environment, wherein the micro-vibration is typical space disturbance, particularly the near-earth orbit space telescope has high fluctuation frequency and large amplitude of the external heat flow, and the required refrigerating machine power is large; the track running period is short, the posture is adjusted frequently, the required power of a reaction wheel is high, and the conditions cause micro-vibration. The micro-vibration affects the image acquisition process of the focal plane detector, leads to image blurring, causes image information change and affects wavefront detection precision. The influence of the micro-vibration on the image of the focal plane detector has certain randomness, and mathematical modeling is difficult to perform in an analytic mode.
At present, the research on the influence of correcting the micro-vibration on the phase difference wavefront detection precision of the space telescope is not reported.
Disclosure of Invention
The invention provides a method for correcting the influence of micro-vibration in phase difference wavefront detection of a space telescope, which aims to correct the influence of the micro-vibration on the phase difference wavefront detection precision of the space telescope.
The technical scheme adopted by the invention for solving the technical problem is as follows:
the invention relates to a correction method of micro-vibration influence in phase difference wavefront detection of a space telescope, which comprises the following steps:
step one, correcting an imaging model
Carrying out statistical modeling on a random process of micro-vibration influence point spread function imaging by introducing Gaussian convolution, and correcting a functional relation between wavefront aberration and a point spread function acquired by a detector;
step two, determining model parameters
Determining parameters required for describing a two-dimensional Gaussian convolution template by using ground micro-vibration simulation data;
step three, focal plane image acquisition
Collecting two point spread function images of different focal planes in a micro-vibration environment;
step four, equation establishment
Establishing a nonlinear equation set for solving the wave front aberration coefficient by utilizing the functional relation between the corrected wave front aberration and the point spread function acquired by the detector and the point spread function images of different out-of-focus surfaces;
step five, aberration coefficient solving
The solution of the nonlinear equation set is converted into a numerical optimization problem by establishing an objective function, and then the wavefront aberration coefficient is solved by utilizing a relevant numerical optimization algorithm.
Further, the step one specifically comprises the following steps:
according to the central limit theorem, the PSF image information of a certain field position under the micro-vibration condition is expressed as:
wherein s represents a two-dimensional PSF image matrix,
denotes an image plane coordinate vector, x denotes a wavefront aberration coefficient vector, λ denotes a center wavelength, FT-1Representing the inverse fourier transform, P the pupil plane aperture function matrix,
denotes a pupil plane coordinate vector, W denotes a pupil plane wave aberration matrix, i is an imaginary unit,
representing a convolution operation, G (σ)1,σ2) Representing a two-dimensional Gaussian convolution kernel, σ1,σ2The size of a Gaussian convolution kernel in two dimensions represents the strength of micro vibration in two different directions; w is expressed as a linear superposition of each of the individual wavefront aberration coefficients in x and the corresponding Zernike polynomial representation.
Further, the second step specifically comprises the following steps:
(1) generating a large number of scattered point positions where the visual axis intersects with the image plane according to a related micro-vibration simulation technology, wherein each scattered point represents the position where the visual axis intersects with the image plane at a certain moment;
(2) determining the center positions of a large number of scattered points according to a large number of scattered points generated by a related micro-vibration simulation technology, dividing a pixel grid by taking the center positions as the scattered points, wherein the grid interval is consistent with the size of a detector pixel;
(3) determining the size of a two-dimensional Gaussian convolution kernel according to the scatter point distribution and the grid size;
(4) and counting the number of scattered points in each grid, normalizing, wherein the sum of the weights of all elements in the two-dimensional Gaussian convolution kernel is 1, and obtaining the weight value of each element in the two-dimensional Gaussian convolution kernel.
Further, the third step specifically comprises the following steps:
under the micro-vibration environment, a beam splitter prism is adopted to simultaneously acquire two PSF images with defocusing difference, or two PSF images with different defocusing surfaces are acquired in a time-sharing manner in a focusing mode.
Further, the fourth step specifically comprises the following steps:
the relationship between two PSF images with different focal planes and wavefront aberration coefficients acquired under the micro-vibration environment is represented as follows:
wherein s is1And s2The two different-off-focus-plane PSF image data matrixes collected in the micro-vibration environment are respectively represented, the delta W represents an off-focus aberration difference data matrix between two different off-focus-plane positions, the delta W value is irrelevant to a wave front aberration coefficient to be solved, and G' is a Gaussian convolution kernel.
Further, the step five specifically comprises the following steps:
according to a nonlinear equation set, subtracting the left side and the right side of each equation in the nonlinear equation set, taking the square, integrating the left side and the right side of each equation in the nonlinear equation set in the whole image data area, and establishing an objective function related to a wavefront aberration coefficient vector x to be solved:
and then, solving the minimum value of the objective function E (x) by utilizing a related numerical optimization algorithm, wherein the corresponding wavefront aberration coefficient vector x is obtained.
Further, in the fifth step, the correlation value optimization algorithm is a gradient method, a newton method, or a particle swarm algorithm.
The invention has the beneficial effects that:
the invention discloses a correction method for micro-vibration influence in space telescope Phase difference wavefront detection, which is used for improving the detection precision of a space telescope wavefront detection method based on a Phase Diversity (Phase Diversity) principle in a space micro-vibration environment. The invention carries out statistical description on the random process of the micro-vibration influence by introducing Gaussian convolution, and provides a method for determining Gaussian convolution parameters, thereby having certain reference significance for improving the wavefront detection precision of a phase difference method in a space micro-vibration environment.
Drawings
FIG. 1 is a schematic diagram of the mechanism of the PSF imaging process.
FIG. 2 is a schematic diagram of the determination of a specific form of a two-dimensional Gaussian convolution kernel required to correct the effects of microvibration.
FIG. 3 is a flow chart of correcting the influence of micro-vibration on the detection accuracy of the phase difference wavefront of the space telescope.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention relates to a correction method of micro-vibration influence in phase difference wavefront detection of a space telescope, which has the following inventive principle:
although the change in the position of the visual axis caused by the microvibration has a certain randomness, a certain statistical law is obeyed. Specifically, for any time, the intersection position of the visual axis and the image plane follows a two-dimensional gaussian distribution, and the variance of the gaussian distribution is related to the intensity of the micro-vibration.
Compared with an ideal PSF in a non-microvibration environment, after being influenced by microvibration and integrated for a period of time, each pixel gray value of the PSF image contains other pixel information, and the effect has substantial similarity with the influence of a convolution effect.
By combining the two aspects, the influence of the micro-vibration on the PSF image acquired by the detector can be equivalent to the process of performing Gaussian convolution on the PSF image by a certain Gaussian kernel. Based on the principle, the imaging mathematical model of the PSF image under the influence of the micro-vibration can be modified.
And establishing an objective function by using the PSF image (under the influence of micro-vibration) acquired by the detector and the corrected imaging model, and solving by using a nonlinear optimization means to obtain a corrected wave aberration solving result.
The invention discloses a method for correcting the influence of micro-vibration in phase difference wavefront detection of a space telescope, which specifically comprises the following steps as shown in figure 3:
1. statistical modeling of stochastic processes of microvibration-affected Point Spread Function (PSF) imaging
And performing statistical modeling on a random process of micro-vibration influence point spread function imaging by introducing Gaussian convolution, and correcting the functional relation between the wave front aberration and the spread function of the acquisition point of the detector.
The micro-vibrations cause a change in the relative position between the intensity distribution of the point spread function PSF and the detector pixels at different times (t1, t2, t 3). In other words, for a particular pixel, the received point spread function PSF light intensity is different at different times. And (after exposure integration) finally, the total energy received by a certain pixel is a superposition value of the intensity of a certain area range of the point spread function PSF, and the homogenization can cause the actually obtained point spread function PSF image to be blurred, as shown in fig. 1 (here, in order to highlight the effect of vibration, the amplitude of the considered vibration is larger than the actual situation, and details are blurred), in fig. 1, a and b represent the original PSF image pair, a 'and b' represent the PSF image pair affected by micro-vibration, c represents position jitter caused by the effect of micro-vibration, d represents the PSF position at different moments, e represents a detector receiving surface, and f represents the integral superposition in the exposure imaging process of the detector.
According to the central limit theorem, the results of a large number of random experiments are limited to normal distributions. That is, the sum of a large number of random variables has an approximately normal distribution. According to this principle, although the above superimposition process is random, from the overall effect point of view, the superimposition weights are distributed in a gaussian function according to the distance from the target pixel element. Therefore, the micro-vibration effect is consistent with the gaussian convolution blur principle. Therefore, the PSF image information at a certain field position under the micro-vibration condition can be expressed as:
wherein s represents a two-dimensional PSF image matrix,
denotes an image plane coordinate vector, x denotes a wavefront aberration coefficient vector, λ denotes a center wavelength, FT-1Representing the inverse fourier transform, P the pupil plane aperture function matrix (1 in the aperture, 0 outside the aperture),
denotes a pupil plane coordinate vector, W denotes a pupil plane wave aberration matrix, i is an imaginary unit,
representing a convolution operation, G (σ)1,σ2) Representing a two-dimensional gaussian convolution kernel (typically 3 x 3 or 5 x 5 in size), σ1,σ2The magnitude of the gaussian convolution kernel in two dimensions is indicative of the magnitude of the microvibration in two different directions. W can be expressed as a linear superposition of each element in x (i.e., each of the monomial wavefront aberration coefficients) and the corresponding zernike polynomial representation.
2. Determining the specific form of two-dimensional Gaussian convolution kernel approximately according to the micro-vibration intensity data
Parameters (the magnitude of each weight in the convolution kernel) required for describing the two-dimensional Gaussian convolution template are determined by using the ground micro-vibration simulation data. As shown in fig. 2, the specific form of the two-dimensional gaussian convolution kernel required for describing the micro-vibration characteristics can be determined according to the following steps:
(1) and generating a large number of scattered point positions A at which the visual axis intersects with the image plane according to a related micro-vibration simulation technology, wherein each scattered point represents the position at which the visual axis intersects with the image plane at a certain moment.
(2) According to a large number of scattered points generated by a related micro-vibration simulation technology, the central positions of the large number of scattered points are determined, the central positions are used as scattered point centers O to divide a pixel grid B, and the grid interval is consistent with the size of a detector pixel.
(3) And determining the size of a two-dimensional Gaussian convolution kernel (namely a convolution template) according to the scatter point distribution and the grid size. Generally speaking, visual axis jitter caused by micro-vibration is not too large, the jitter amount is generally smaller than the size of one detector pixel, and the size of a two-dimensional Gaussian convolution kernel is 3 multiplied by 3, so that the requirement can be met.
(4) And counting the number of scattered points in each grid, normalizing, wherein the sum of the weights of all elements in the two-dimensional Gaussian convolution kernel is 1, and obtaining the weight value of each element in the two-dimensional Gaussian convolution kernel.
3. Collecting two PSF images with different focal planes in micro-vibration environment
Under the micro-vibration environment, a beam splitter prism can be adopted to simultaneously acquire two PSF images with defocusing difference (the position interval of the focal plane is known), or two PSF images with different defocusing planes (the position interval of the focal plane is known) can be acquired in a time-sharing manner in a focusing manner.
4. Establishing a nonlinear equation set for solving wavefront aberration coefficients in a micro-vibration environment
And establishing a nonlinear equation system for solving the wave front aberration coefficient by utilizing the functional relation between the wave front aberration and the point spread function acquired by the detector after correction (micro-vibration influence) and the acquired point spread function images of different (off) focal planes.
The relationship between two PSF images of different out-of-focus planes acquired under the micro-vibration environment and the wavefront aberration coefficient can be expressed as follows:
wherein s is1And s2The method comprises the steps of respectively representing two PSF image data matrixes of different off-focus surfaces acquired under a micro-vibration environment, wherein the delta W represents a data matrix of the difference (generally a known fixed value) of the off-focus aberration between the two different off-focus surface positions, the delta W value is irrelevant to a wave front aberration coefficient to be solved, and G' is a Gaussian convolution kernel determined by the previous method.
5. Objective function establishment and nonlinear equation system solution
According to the nonlinear equation set, the left side and the right side of each equation in the nonlinear equation set are subtracted and squared, and then the left side and the right side of each equation in the nonlinear equation set are integrated in the whole image data area (namely, the left side and the right side of all equations are subtracted and the squared results are added), so that an objective function related to a wavefront aberration coefficient vector x to be solved is established, and the following steps are performed:
then, the minimum value of the objective function e (x) is solved by using a correlation numerical optimization algorithm (such as a gradient method, a newton method, a particle swarm optimization, etc.), and the corresponding wavefront aberration coefficient vector x is obtained.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (2)
1. The method for correcting the micro-vibration influence in the phase difference wavefront detection of the space telescope is characterized by comprising the following steps of:
step one, correcting an imaging model
Carrying out statistical modeling on a random process of micro-vibration influence point spread function imaging by introducing Gaussian convolution, and correcting a functional relation between wavefront aberration and a point spread function acquired by a detector;
the first step specifically comprises the following steps:
according to the central limit theorem, the PSF image information of a certain field position under the micro-vibration condition is expressed as:
wherein s represents a two-dimensional PSF image matrix,
denotes an image plane coordinate vector, x denotes a wavefront aberration coefficient vector, λ denotes a center wavelength, FT-1Representing the inverse fourier transform, P the pupil plane aperture function matrix,
denotes a pupil plane coordinate vector, W denotes a pupil plane wave aberration matrix, i is an imaginary unit,
representing a convolution operation, G (σ)1,σ2) Representing a two-dimensional Gaussian convolution kernel, σ1,σ2The size of a Gaussian convolution kernel in two dimensions represents the strength of micro vibration in two different directions; w is expressed as the linear superposition of each single wave front aberration coefficient in x and the corresponding Zernike polynomial expression surface shape;
step two, determining model parameters
Determining parameters required for describing a two-dimensional Gaussian convolution template by using ground micro-vibration simulation data;
the second step specifically comprises the following steps:
(1) generating a large number of scattered point positions where the visual axis intersects with the image plane according to a related micro-vibration simulation technology, wherein each scattered point represents the position where the visual axis intersects with the image plane at a certain moment;
(2) determining the center positions of a large number of scattered points according to a large number of scattered points generated by a related micro-vibration simulation technology, dividing a pixel grid by taking the center positions as the scattered points, wherein the grid interval is consistent with the size of a detector pixel;
(3) determining the size of a two-dimensional Gaussian convolution kernel according to the scatter point distribution and the grid size;
(4) counting the number of scattered points in each grid, normalizing, wherein the sum of the weights of all elements in the two-dimensional Gaussian convolution kernel is 1, and obtaining the weight value of each element in the two-dimensional Gaussian convolution kernel;
step three, focal plane image acquisition
Collecting two point spread function images of different focal planes in a micro-vibration environment;
the third step specifically comprises the following steps:
under the micro-vibration environment, a beam splitter prism is adopted to simultaneously acquire two PSF images with defocusing difference, or two PSF images with different defocusing surfaces are acquired in a time-sharing manner in a focusing manner;
step four, equation establishment
Establishing a nonlinear equation set for solving the wave front aberration coefficient by utilizing the functional relation between the corrected wave front aberration and the point spread function acquired by the detector and the point spread function images of different out-of-focus surfaces;
the fourth step specifically comprises the following steps:
the relationship between two PSF images with different focal planes and wavefront aberration coefficients acquired under the micro-vibration environment is represented as follows:
wherein s is1And s2Respectively representing two PSF image data matrixes of different off-focus surfaces acquired in a micro-vibration environment, wherein delta W represents an off-focus aberration difference data matrix between two different off-focus surface positions, the delta W value is irrelevant to a wave front aberration coefficient to be solved, and G' is a Gaussian convolution kernel;
step five, aberration coefficient solving
The solution of the nonlinear equation set is converted into a numerical optimization problem by establishing an objective function, and then the wavefront aberration coefficient is solved by utilizing a related numerical optimization algorithm;
the fifth step specifically comprises the following steps:
according to a nonlinear equation set, subtracting the left side and the right side of each equation in the nonlinear equation set, taking the square, integrating the left side and the right side of each equation in the nonlinear equation set in the whole image data area, and establishing an objective function related to a wavefront aberration coefficient vector x to be solved:
and then, solving the minimum value of the objective function E (x) by utilizing a related numerical optimization algorithm, wherein the corresponding wavefront aberration coefficient vector x is obtained.
2. The method for correcting the micro-vibration influence in the phase difference wavefront detection of the space telescope according to claim 1, wherein in the fifth step, the correlation value optimization algorithm is a gradient method, a Newton method or a particle swarm optimization algorithm.
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