Dispersion fringe co-phase error inversion method and system based on vu decomposition
By using VU decomposition and iterative update, the common phase error is directly extracted from the dispersion fringe diagram, which solves the problems of reliance on preprocessing and sign insensitivity in the existing technology and realizes efficient and accurate common phase error inversion.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SUZHOU UNIV
- Filing Date
- 2026-05-18
- Publication Date
- 2026-07-31
AI Technical Summary
Existing methods for inverting dispersive fringe cophase error rely on complex preprocessing and are insensitive to the sign of cophase error, which affects inversion accuracy and efficiency.
A VU decomposition-based method is adopted. By acquiring the dispersive fringe pattern, VU decomposition and iterative update are performed to obtain the matrix V representing the orthogonal characteristic basis of the fringe spatial domain. The wrapped phase of the phase error modulation is obtained by combining the arctangent function, and the unwrapping and linear fitting are performed to obtain the phase error.
It can accurately invert co-phase error without preprocessing and auxiliary information, improving inversion efficiency and accuracy, solving the sign insensitivity problem, and simplifying the process.
Smart Images
Figure CN122237770B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of dispersive fringe cophase error inversion technology, and in particular to a method and system for dispersive fringe cophase error inversion based on VU decomposition. Background Technology
[0002] Co-phasing error refers to the systematic deviation caused by inconsistent optical path lengths between multiple sub-beams and sub-mirrors, which disrupts coherent superposition and significantly reduces image quality. Accurate measurement and effective correction of co-phasing error are core technologies for achieving high-resolution imaging, directly determining the system's wavefront quality, diffraction-limited imaging capability, and overall observation performance. Therefore, methods for measuring and correcting co-phasing error have significant theoretical and engineering application value.
[0003] Dispersion fringe cophase sensor is a device that encodes cophase errors based on the principle of spectral dispersion. A schematic diagram of the structure of a dispersion fringe cophase sensor is shown below. Figure 1 As shown, the acquired dispersive fringe signals can be used for co-phase error inversion. Dispersive fringe co-phase sensors are widely used in various synthetic aperture imaging systems due to their significant advantages of simple structure and large sensing range. Currently, the main methods for inverting dispersive fringe co-phase errors include: 1. Least squares method: Nonlinear fitting is performed on the one-dimensional dispersion fringe signal along the wavelength dispersion direction to obtain the corresponding co-phase error.
[0004] 2. The Fourier transform method obtains the corresponding co-phase error by extracting the separation interval between the side lobes and the main lobe in the spatial frequency domain of the dispersive fringes.
[0005] 3. Two-dimensional fringe analysis method: By analyzing the interference signals at multiple dispersion positions, the offset values of multiple side lobes are estimated in advance, thereby comprehensively solving the co-phase error.
[0006] 4. Slope method: linearly inverts the cophase error by analyzing the overall fringe slope of the dispersion fringes.
[0007] 5. Principal component analysis method: By jointly analyzing multiple sets of one-dimensional signals in the interference direction, and extracting their common principal components through the principal component analysis algorithm, the co-phase error can be inferred.
[0008] The first four methods are extremely complex to operate. The least squares method requires pre-calibration to eliminate the influence of light source spectral modulation; the Fourier transform method, two-dimensional fringe analysis method, and slope method require pre-calibration of the linear relationship between signal physical quantities and co-phase error. Principal component analysis requires pre-eliminating the background DC signal in the dispersive fringe signal to separate the core co-phase error modulation signal. In practice, a constant background signal is often assumed, which deviates from reality to some extent. Furthermore, the least squares method and principal component analysis method are not sensitive to the sign of the co-phase error, requiring additional determination based on the tilt direction of the dispersive fringes.
[0009] In summary, existing methods for inverting cophase errors in dispersion fringes have two significant drawbacks: firstly, these methods rely heavily on preprocessing, which directly affects the accuracy of cophase error inversion; secondly, they are insensitive to the sign of the cophase error and require auxiliary information to obtain a complete cophase error. Summary of the Invention
[0010] Therefore, the technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a method and system for inverting the cophase error of dispersive fringes based on VU decomposition, which can realize the inversion of cophase error without preprocessing or the aid of auxiliary information.
[0011] To address the aforementioned technical problems, this invention provides a method for inverting the cophase error of dispersive fringes based on VU decomposition, comprising: Obtain the dispersion fringe pattern corresponding to the sub-aperture pair to be co-phased, and extract the effective dispersion fringe signal from the dispersion fringe pattern; The effective dispersive fringe signal is subjected to VU decomposition and iterative update to obtain the matrix V characterizing the orthogonal feature basis of the fringe spatial domain; Based on the matrix V representing the orthogonal characteristic basis of the fringe spatial domain, the wrapping phase of the co-phase error modulation is obtained through the arctangent function; The wrapped phase is unwrapped using a phase unwrapping function to obtain the unwrapped phase; The unwrapped phase and the effective dispersion fringe signal are linearly fitted along the wavenumber coordinates of the dispersion direction to obtain the cophase error.
[0012] Furthermore, the two-dimensional light intensity distribution of the dispersion fringe pattern corresponding to the sub-aperture pair to be co-phase is as follows: , In the formula, This represents the two-dimensional light intensity distribution of the dispersion fringe pattern corresponding to the desired co-phase sub-aperture pair. Given two-dimensional planar coordinates, the dispersion direction is... Direction, interference direction is direction; Background DC signal, This is the contrast function; The wavelength is related to the dispersive position. , Where λ is the center wavelength of the incident broadband light, and C is the dispersion coefficient. p represents the co-phase error to be determined. for Phase at the coordinate position.
[0013] Further, the effective dispersive fringe signal is subjected to VU decomposition and iterative update to obtain a matrix V characterizing the orthogonal feature basis of the fringe spatial domain, including: The valid dispersion fringe signal is denoted as , , express The dimension is N is the effective dispersive fringe signal. The number of coordinate points, M, represents the effective dispersive fringe signal. The number of coordinate points; Will The matrix obtained after transposition is denoted as ,right Perform VU decomposition to obtain matrices V and U. , Let V be a matrix. , Let U be a matrix. T is the matrix transpose; By iteratively updating matrices V and U, we obtain matrix V that represents the orthogonal characteristic basis of the fringe spatial domain.
[0014] Furthermore, the elements of the matrices V and U are composed as follows: , ; In the formula, Indicates the i-th Background DC signal at the coordinate location, , Indicates the i-th Contrast function at coordinate position Indicates the i-th The wavelength at the coordinate position, and p is the phase error to be determined. For the j-th Phase at coordinate position .
[0015] Further, the iterative update of matrices V and U to obtain matrix V representing the orthogonal feature basis of the fringe spatial domain includes: Randomly generate N The initial phase at the coordinate position is denoted as , , The initial matrix U is constructed as follows: , In the formula, Let U be the initial matrix; The initial matrix V is constructed based on the initial matrix U as follows: , In the formula, Let V be the initial matrix. This is a matrix inversion operation. The arctangent function is used to iteratively update matrices U and V until the error of matrix V is less than or equal to a preset error threshold or the number of iterations exceeds the set maximum number of iterations. The resulting iteratively updated matrix V, which satisfies the VU decomposition condition, is used as the matrix V representing the orthogonal feature basis of the fringe spatial domain.
[0016] Furthermore, the iterative update of matrices U and V using the arctangent function is specifically as follows: In the k-th iteration, the phase vector is calculated as follows: , In the formula, Let a_k represent the phase vector in the k-th iteration, and a_n be the arctangent function. Let V represent the matrix after the (k-1)th iteration update. express Column 3 express Column 2; The intermediate update matrix for calculating matrix V is: , In the formula, This represents the intermediate update matrix of matrix V. express Column 1; The updated matrix U is: , In the formula, Let U represent the matrix after the k-th iteration update. For matrix transpose, This is a matrix inversion operation. The updated matrix V is: , In the formula, Let V represent the matrix after the k-th iteration update.
[0017] Furthermore, the error of the matrix V is: , In the formula, The error of matrix V, Let V represent the matrix after the k-th iteration update. express Column 3 express Column 2 It is the L2 norm. Let V represent the matrix after the (k-1)th iteration update. express Column 3 express In the second column, atan represents the arctangent function.
[0018] Furthermore, the wrapping phase of the co-phase error modulation is: , In the formula, The phase envelope is the modulated phase of the common-phase error, and atan is the arctangent function. To characterize the matrix V representing the orthogonal characteristic basis of the fringe spatial domain, express Column 3 express In the second column, atan represents the arctangent function; The unpacking phase is: , In the formula, To unwrap the phase, unwrap() is a one-dimensional phase unwrapping function.
[0019] Further, the wavenumber coordinates of the unwrapped phase and the effective dispersive fringe signal along the dispersion direction are linearly fitted to obtain the co-phase error, including: By linearly fitting the unwrapped phase and the effective dispersive fringe signal along the dispersion direction using wavenumber coordinates, the fitting formula is obtained as follows: , In the formula, To unwrap the phase, The wavenumber coordinates of the effective dispersive fringe signal along the dispersion direction are given, p is the co-phase error to be determined, 2p is the slope of the fitting formula, and the co-phase error to be determined is numerically equal to half of the slope.
[0020] This invention also provides a dispersion fringe cophase error inversion system based on VU decomposition, comprising: The image acquisition module is used to acquire the dispersion fringe pattern corresponding to the sub-aperture pair to be co-phase; The effective signal extraction module is used to extract the effective dispersion fringe signal from the dispersion fringe pattern. The VU decomposition module is used to perform VU decomposition and iterative update on the effective dispersive fringe signal to obtain a matrix V that characterizes the orthogonal feature basis of the fringe spatial domain. The wrapping phase calculation module is used to obtain the wrapping phase of the co-phase error modulation by means of the arctangent function based on the matrix V representing the orthogonal feature basis of the fringe spatial domain. The unwrapping phase calculation module is used to unwrap the wrapped phase using a phase unwrapping function to obtain the unwrapped phase; The co-phase error calculation module is used to linearly fit the wavenumber coordinates of the unwrapped phase and the effective dispersion fringe signal along the dispersion direction to obtain the co-phase error.
[0021] Compared with the prior art, the above-described technical solution of the present invention has the following advantages: This invention uses the background signal as a variable in the core iteration process of VU decomposition, eliminating the need for pre-elimination. This not only improves efficiency but also avoids a strong dependence on background signal elimination, thus overcoming the influence of the background signal on the accuracy of common-phase error inversion. VU decomposition solves the problem of insensitivity to the sign of common-phase errors, simultaneously acquiring both the absolute value and positive / negative information of the common-phase error without the need for fringe tilt direction assistance. By directly processing the acquired dispersion fringe pattern, pre-calibration steps related to the light source spectrum, signal physical quantities, and the linear relationship of common-phase errors are avoided, further simplifying the inversion process. Attached Figure Description
[0022] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein: Figure 1 This is a schematic diagram of the structure of a dispersive fringe cophase sensor.
[0023] Figure 2 This is a flowchart of a method in a preferred embodiment of the present invention.
[0024] Figure 3 This is a schematic diagram of the double rectangular aperture used in the simulation experiment of this invention.
[0025] Figure 4 This is a spectral curve of the Gaussian spectral light source used in the simulation experiment of this invention.
[0026] Figure 5 This is a noisy dispersion fringe pattern collected during the simulation experiment of this invention when the aperture of the cophase sub-aperture is p=-25μm.
[0027] Figure 6 In the simulation experiment of this invention, according to Figure 5 The image shown is a cut-out of the effective dispersion fringe signal from the noisy dispersion fringe pattern.
[0028] Figure 7 In the simulation experiment of this invention, according to Figure 6 The wrapped phase diagram of the effective dispersive fringe signal inversion is shown.
[0029] Figure 8 In the simulation experiment of this invention, according to Figure 7 The unwrapped phase diagram obtained from the wrapped phase is shown.
[0030] Figure 9 In the simulation experiment of this invention, according to Figure 8 The figure shown is a result of linear fitting of the unwrapped phase and the wavenumber coordinates of the effective dispersive fringe signal along the dispersion direction.
[0031] Figure 10 This is a noisy dispersion fringe pattern collected during the simulation experiment of this invention when the aperture of the cophase sub-phase is p=25μm.
[0032] Figure 11 In the simulation experiment of this invention, according to Figure 10 The image shown is a cut-out of the effective dispersion fringe signal from the noisy dispersion fringe pattern.
[0033] Figure 12 In the simulation experiment of this invention, according to Figure 11 The wrapped phase diagram of the effective dispersive fringe signal inversion is shown.
[0034] Figure 13 In the simulation experiment of this invention, according to Figure 12 The unwrapped phase diagram obtained from the wrapped phase is shown.
[0035] Figure 14 In the simulation experiment of this invention, according to Figure 13 The figure shown is a result of linear fitting of the unwrapped phase and the wavenumber coordinates of the effective dispersive fringe signal along the dispersion direction. Detailed Implementation
[0036] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.
[0037] Reference Figure 2As shown, this invention discloses a method for inverting the cophase error of dispersive fringes based on VU decomposition, comprising the following steps: S1: Obtain the dispersion fringe pattern corresponding to the aperture pair of the phase to be co-phase.
[0038] In this embodiment, when acquiring the dispersion fringe pattern corresponding to the sub-aperture pair to be co-phase, the recording medium used can be a charge-coupled detector (CCD) camera or a complementary metal-oxide-semiconductor (CMOS) camera. The processed dispersion fringes can be generated by a broadband light source with a uniform, Gaussian, or other arbitrary spectral distribution; that is, the method of the present invention is not limited by the spectral type of the light source.
[0039] The two-dimensional intensity distribution of the dispersion fringe pattern corresponding to the co-phase sub-aperture pair is as follows: , In the formula, This represents the two-dimensional light intensity distribution of the dispersion fringe pattern corresponding to the desired co-phase sub-aperture pair. Given two-dimensional planar coordinates, the dispersion direction is... Direction, interference direction is direction; Background DC signal, This is the contrast function; The wavelength is related to the dispersive position. , Where λ is the center wavelength of the incident broadband light, and C is the dispersion coefficient. p represents the co-phase error to be determined. for Phase at the coordinate position.
[0040] C is the dispersion coefficient, and its value is determined by the parameters of the hardware device itself. Specifically, the quantization value of C can be obtained from... This is obtained by calculating the spatial position of the wavelength. The rate of change is obtained. That is, by obtaining the spatial distribution of the centroids of two adjacent wavelengths in the incident broadband light, and the corresponding wavelengths of the light spot centroids. Coordinates, calculate the difference between two adjacent wavelengths in the incident broadband light, and divide by the coordinates corresponding to the two adjacent wavelengths. The difference in coordinates yields the quantized value of C. In practical applications, this involves two adjacent wavelengths in the incident broadband light, and the spatial coordinates of the centroids of the corresponding light spots. The coordinates are values obtained through direct measurement.
[0041] S2: Extract the valid dispersion fringe signal from the dispersion fringe pattern.
[0042] An effective dispersion fringe signal satisfies: The coordinates satisfy: , The minimum wavelength of the incident broadband light. The maximum wavelength of the incident broadband light; The coordinates satisfy: , For the preset threshold, The value should be adjusted according to the actual situation.
[0043] S3: Perform VU decomposition and iterative update on the effective dispersive fringe signal to obtain matrix V, which characterizes the orthogonal feature basis of the fringe spatial domain. Matrix V can be used to purify the phase error modulation interference information, decouple noise and background components, and provide core data support for subsequent high-precision demodulation of piston error and tilt error, as well as system closed-loop correction.
[0044] S3-1: Denote the valid dispersion fringe signal as... , , express The dimension is N is the effective dispersive fringe signal. The number of coordinate points, M, represents the effective dispersive fringe signal. The number of coordinate points; that is, N is the number of points that satisfy the above requirements. The number of elements, M, is the number of elements that satisfy the above requirements. The number of.
[0045] S3-2: Matrix The matrix obtained after transposition is denoted as ,Right now: , This is the matrix transpose.
[0046] S3-3: For the matrix Perform VU decomposition to obtain matrices V and U. , , , where T is the matrix transpose.
[0047] The elements of matrices V and U are composed based on Specifically, the results are as follows: , ; In the formula, Indicates the i-th Background DC signal at the coordinate location, , Indicates the i-th Contrast function at coordinate position Indicates the i-th The wavelength at the coordinate position, and p is the phase error to be determined. For the j-th Phase at coordinate position .
[0048] S3-4: Iteratively update matrices V and U to obtain matrix V that represents the orthogonal characteristic basis of the fringe spatial domain.
[0049] S3-4-1: Randomly generate N items The initial phase at the coordinate position is denoted as , , The initial matrix U is constructed as follows: , In the formula, The initial matrix U is used; in this embodiment, it is randomly generated. It is not necessary to use the true value corresponding to the dispersive fringe signal; It should be as dispersed as possible to avoid clustering, that is, it should have a large variance.
[0050] S3-4-2: Construct the initial matrix V based on the initial matrix U as follows: , In the formula, Let V be the initial matrix. This is the matrix inverse operation.
[0051] S3-4-3: Iteratively update matrices U and V using the arctangent function until the error of matrix V is less than or equal to a preset error threshold or the number of iterations exceeds the set maximum number of iterations, at which point the iterative update stops.
[0052] S3-4-3-1: In the k-th iteration, the phase vector is calculated as follows: , In the formula, Let a_k represent the phase vector in the k-th iteration, and a_n be the arctangent function. Let V represent the matrix after the (k-1)th iteration update. express Column 3 express The second column.
[0053] S3-4-3-2: The intermediate update matrix of matrix V is calculated as follows: , In the formula, This represents the intermediate update matrix of matrix V. express The first column.
[0054] S3-4-3-3: The updated matrix U is: , In the formula, Let U represent the matrix after the k-th iteration update. For matrix transpose, This is the matrix inverse operation.
[0055] S3-4-3-4: The updated matrix V is: , In the formula, Let V represent the matrix after the k-th iteration update.
[0056] S3-4-3-5: The error in calculating matrix V is: , In the formula, The error of matrix V, It is the L2 norm. Let V represent the matrix after the (k-1)th iteration update. express Column 3 express In the second column, atan represents the arctangent function.
[0057] The iteration update stops when the error of matrix V is less than or equal to the preset error threshold or the number of iterations exceeds the set maximum number of iterations.
[0058] S3-4-4: The final iteratively updated matrix V that satisfies the VU decomposition conditions is obtained as the matrix V representing the orthogonal feature basis of the fringe spatial domain.
[0059] S4: Based on the matrix V representing the orthogonal characteristic basis of the fringe spatial domain, the wrapping phase of the co-phase error modulation is obtained through the arctangent function.
[0060] The wrapping phase of the common-phase error modulation is: , In the formula, The phase envelope is the modulated phase of the common-phase error, and atan is the arctangent function. To characterize the matrix V representing the orthogonal characteristic basis of the fringe spatial domain, express Column 3 express In the second column, atan represents the arctangent function.
[0061] S5: Unwrap the wrapped phase using a one-dimensional phase unwrapping function to obtain the unwrapped phase.
[0062] The unwrapping phase is: , In the formula, To unwrap the phase, unwrap() is a one-dimensional phase unwrapping function.
[0063] S6: Linearly fit the wavenumber coordinates of the unwrapped phase and the effective dispersion fringe signal along the dispersion direction to obtain the co-phase error.
[0064] By linearly fitting the unwrapped phase and the effective dispersive fringe signal along the dispersion direction using wavenumber coordinates, the fitting formula is obtained as follows: , In the formula, To unwrap the phase, The wavenumber coordinates of the effective dispersive fringe signal along the dispersion direction are given, p is the co-phase error to be determined, and 2p is the slope of the fitted formula, that is, the co-phase error to be determined is numerically equal to half of the fitted slope.
[0065] This invention also discloses a dispersion fringe cophase error inversion system based on VU decomposition, comprising: The image acquisition module is used to acquire the dispersion fringe pattern corresponding to the sub-aperture pair to be co-phase; The effective signal extraction module is used to extract the effective dispersion fringe signal from the dispersion fringe pattern. The VU decomposition module is used to perform VU decomposition and iterative update on the effective dispersive fringe signal to obtain a matrix V that characterizes the orthogonal feature basis of the fringe spatial domain. The wrapping phase calculation module is used to obtain the wrapping phase of the co-phase error modulation by means of the arctangent function based on the matrix V representing the orthogonal feature basis of the fringe spatial domain. The unwrapping phase calculation module is used to unwrap the wrapped phase using a phase unwrapping function to obtain the unwrapped phase; The co-phase error calculation module is used to linearly fit the wavenumber coordinates of the unwrapped phase and the effective dispersion fringe signal along the dispersion direction to obtain the co-phase error.
[0066] The present invention also discloses a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a method for inverting the cophase error of dispersion fringes based on VU decomposition.
[0067] The present invention also discloses an apparatus including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a method for inverting the cophase error of dispersive fringes based on VU decomposition.
[0068] This invention overcomes the shortcomings of existing technologies, such as reliance on complex preprocessing and sign insensitivity, thereby improving the practicality and scenario adaptability of the dispersive fringe cophase error inversion method. Compared with existing technologies, its advantages include: 1. By treating the background signal as a variable in the core iteration process of VU decomposition, this invention eliminates the need for precise pre-elimination, thereby improving efficiency and avoiding the strong dependence on background signal elimination in existing principal component analysis techniques. This also overcomes the impact of the background signal on the accuracy of co-phase error inversion.
[0069] 2. The VU decomposition solves the problem of insensitivity to the sign of the cophase error, and can simultaneously obtain the absolute value and positive / negative information of the cophase error without the need for fringe tilt direction assistance.
[0070] 3. This invention directly processes the acquired dispersive fringe pattern, avoiding the pre-calibration steps in traditional methods, such as those related to the light source spectrum, signal physical quantities, and the linear relationship of co-phase error. This greatly simplifies the inversion process and improves the practicality and scene adaptability of the dispersive fringe co-phase sensing method.
[0071] To further demonstrate the beneficial effects of the present invention, in this embodiment, a dual rectangular aperture and dispersive fringe co-phase sensor generates dispersive fringes corresponding to the sub-aperture to be co-phased, and a simulation experiment is conducted. A schematic diagram of the dual rectangular aperture used is shown below. Figure 3 As shown. The spectral curve of the Gaussian spectral source used is as follows. Figure 4 As shown in Table 1, the hardware parameters of the dual rectangular aperture and dispersive fringe cophase sensor are as follows.
[0072] Table 1 Hardware parameters of the dual rectangular aperture and dispersion fringe cophase sensor
[0073] The noisy dispersion fringe pattern acquired when the aperture spacing between cophase particles is p=-25μm is shown below. Figure 5 As shown, according to Figure 5 The effective dispersion fringe signal extracted from the noisy dispersion fringe pattern shown is as follows: Figure 6 As shown, according to Figure 6 The wrapped phase inverted from the effective dispersive fringe signal is shown as follows: Figure 7 As shown, according to Figure 7 The unwrapped phase obtained from the wrapped phase shown is as follows: Figure 8 As shown. According to Figure 8The results of linear fitting of the unwrapped phase and the effective dispersive fringe signal along the dispersion direction are shown below. Figure 9 As shown, the fitted slope was found to be -49.971 μm, meaning the cophase error was -24.986 μm and the measurement error was 14 nm.
[0074] The noisy dispersion fringe pattern collected when the aperture spacing between cophase particles is 25 μm is shown below. Figure 10 As shown, according to Figure 10 The effective dispersion fringe signal extracted from the noisy dispersion fringe pattern shown is as follows: Figure 11 As shown, according to Figure 11 The wrapped phase inverted from the effective dispersive fringe signal is shown as follows: Figure 12 As shown, according to Figure 12 The unwrapped phase obtained from the wrapped phase shown is as follows: Figure 13 As shown. According to Figure 13 The results of linear fitting of the unwrapped phase and the effective dispersive fringe signal along the dispersion direction are shown below. Figure 14 As shown, the fitting slope was found to be 49.932 μm, the cophase error was 24.966 μm, and the measurement error was -34 nm.
[0075] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0076] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0077] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0078] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0079] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.
Claims
1. A method for dispersion fringe co-phase error inversion based on VU decomposition, characterized in that, include: Obtain the dispersion fringe pattern corresponding to the sub-aperture pair to be co-phased, and extract the effective dispersion fringe signal from the dispersion fringe pattern; The effective dispersive fringe signal is subjected to VU decomposition and iterative update to obtain the matrix V characterizing the orthogonal feature basis of the fringe spatial domain; Based on the matrix V representing the orthogonal characteristic basis of the fringe spatial domain, the wrapping phase of the co-phase error modulation is obtained through the arctangent function; The wrapped phase is unwrapped using a phase unwrapping function to obtain the unwrapped phase; The unwrapped phase and the effective dispersive fringe signal are linearly fitted along the wavenumber coordinates of the dispersion direction to obtain the cophase error; The effective dispersive fringe signal is subjected to VU decomposition and iterative update to obtain a matrix V representing the orthogonal characteristic basis of the fringe spatial domain, including: Let the effective dispersion fringe signal be , , represent the dimension of , N is the number of coordinate points of the effective dispersion fringe signal , and M is the number of coordinate points of the effective dispersion fringe signal . Will The matrix obtained after transposition is denoted as ,right Perform VU decomposition to obtain matrices V and U. , Let V be a matrix. , Let U be a matrix. T is the matrix transpose; By iteratively updating matrices V and U, we obtain matrix V that represents the orthogonal characteristic basis of the fringe spatial domain; The elements of the matrices V and U are composed of: ， ； In the formula, Indicates the i-th Background DC signal at the coordinate location, , Indicates the i-th Contrast function at coordinate position Indicates the i-th The wavelength at the coordinate position, and p is the phase error to be determined. For the j-th Phase at coordinate position .
2. The VU-decomposition-based dispersion-striation common- phase-error inversion method of claim 1, wherein: The two-dimensional light intensity distribution of the dispersion fringe pattern corresponding to the sub-aperture pair to be co-phase is as follows: ， In the formula, This represents the two-dimensional light intensity distribution of the dispersion fringe pattern corresponding to the desired co-phase sub-aperture pair. Given two-dimensional planar coordinates, the dispersion direction is... Direction, interference direction is direction; Background DC signal, This is the contrast function; The wavelength is related to the dispersive position. , Let λ be the center wavelength of the incident broadband light, C be the dispersion coefficient, and p be the co-phase error to be determined. for Phase at the coordinate position.
3. The VU-decomposition-based dispersion-striation co-phase-error inversion method according to claim 1, wherein: The iterative update of matrices V and U to obtain matrix V representing the orthogonal characteristic basis of the fringe spatial domain includes: N random generated The initial phase at the coordinate position, denoted as , , The initial matrix U is constructed as: ， In the formula, is the initial matrix U; The initial matrix V is constructed based on the initial matrix U as follows: ， wherein is the initial matrix V, is the matrix inverse operation; The arctangent function is used to iteratively update matrices U and V until the error of matrix V is less than or equal to a preset error threshold or the number of iterations exceeds the set maximum number of iterations. The resulting iteratively updated matrix V, which satisfies the VU decomposition condition, is used as the matrix V representing the orthogonal feature basis of the fringe spatial domain.
4. The VU-decomposition-based dispersion-striation common- phase-error inversion method of claim 3, wherein: The iterative update of matrices U and V using the arctangent function is specifically as follows: In the k-th iteration, the phase vector is calculated as follows: ， wherein denotes the phase vector in the kth iteration, atan is the arctangent function, denotes the matrix V updated in the k-1th iteration, denotes the 3rd column of denotes the 2nd column of The intermediate update matrix for calculating matrix V is: ， wherein denotes the intermediate update matrix of matrix V, denotes the 1st column of The updated matrix U is: ， In the formula, denotes the updated matrix U of the kth iteration, is the matrix transpose, is the matrix inverse operation; The updated matrix V is: ， In the formula, denotes the matrix V updated after the kth round of iteration.
5. The method for inverting dispersive fringe cophase error based on VU decomposition according to claim 3, characterized in that: The error of matrix V is: ， In the formula, The error of matrix V, Let V represent the matrix after the k-th iteration update. express Column 3 express Column 2 It is the L2 norm. Let V represent the matrix after the (k-1)th iteration update. express Column 3 express In the second column, atan represents the arctangent function.
6. The VU-decomposition-based dispersive stripe common phase error inversion method of claim 1, wherein: The encapsulation phase of the co-phase error modulation is: ， In the formula, The phase envelope is the modulated phase of the common-phase error, and atan is the arctangent function. To characterize the matrix V representing the orthogonal characteristic basis of the fringe spatial domain, express Column 3 express In the second column, atan represents the arctangent function; The unpacking phase is: ， In the formula, unwrap is a one-dimensional phase unwrapping function for unwrapping the phase.
7. The VU-decomposition-based dispersion-striation common- phase-error inversion method according to any one of claims 1-6, characterized in that: The unwrapped phase and the effective dispersive fringe signal are linearly fitted along the wavenumber coordinates of the dispersion direction to obtain the cophase error, including: By linearly fitting the unwrapped phase and the effective dispersive fringe signal along the dispersion direction using wavenumber coordinates, the fitting formula is obtained as follows: ， wherein is the unwrapped phase, is the wave number coordinate of the effective dispersion fringe signal along the dispersion direction, p is the sought common phase error, 2p is the slope of the fitting formula, the sought common phase error is equal to half of the slope in value.
8. A VU decomposition based dispersive stripe common phase error retrieval system, characterized in that, include: The image acquisition module is used to acquire the dispersion fringe pattern corresponding to the sub-aperture pair to be co-phased; The effective signal extraction module is used to extract the effective dispersion fringe signal from the dispersion fringe pattern. The VU decomposition module is used to perform VU decomposition and iterative update on the effective dispersive fringe signal to obtain a matrix V that characterizes the orthogonal feature basis of the fringe spatial domain. The wrapping phase calculation module is used to obtain the wrapping phase of the co-phase error modulation by means of the arctangent function based on the matrix V representing the orthogonal feature basis of the fringe spatial domain. The unwrapping phase calculation module is used to unwrap the wrapped phase using a phase unwrapping function to obtain the unwrapped phase; The co-phase error calculation module is used to linearly fit the wavenumber coordinates of the unwrapped phase and the effective dispersion fringe signal along the dispersion direction to obtain the co-phase error; The effective dispersive fringe signal is subjected to VU decomposition and iterative update to obtain a matrix V representing the orthogonal characteristic basis of the fringe spatial domain, including: The valid dispersion fringe signal is denoted as , , express The dimension is N is the effective dispersive fringe signal. The number of coordinate points, M, represents the effective dispersive fringe signal. The number of coordinate points; Will The matrix obtained after transposition is denoted as ,right Perform VU decomposition to obtain matrices V and U. , Let V be a matrix. , Let U be a matrix. T is the matrix transpose; The matrix V and the matrix U are iteratively updated to obtain a matrix V representing a stripe space orthogonal characteristic basis; The elements of the matrix V and the matrix U are composed of: ， ； In the formula, Indicates the i-th Background DC signal at the coordinate location, , Indicates the i-th Contrast function at coordinate position Indicates the i-th The wavelength at the coordinate position, and p is the phase error to be determined. For the j-th Phase at coordinate position .