A mode voltage constraint control method for improving the correction ability of a deformable mirror

Abstract

The application discloses a mode voltage constraint control method for improving correction capability of a deformable mirror, mode decomposition is performed on a control voltage based on a mode method, a recovery matrix without a constraint term is constructed, and the control voltage obtained through a direct slope method does not accumulate constraint residual errors through a proportional integral controller, so that the constrained deformable mirror does not generate translation and tilt aberration in a closed-loop correction process, coupling with a tilt mirror is avoided, and waste of a driver stroke is caused. Compared with an existing vector projection suppression method, the mode voltage constraint control method can obtain a more optimal control voltage, the deformable mirror is further controlled through the proportional integral controller to fit a more accurate recovery wave surface, and a better far-field image can be obtained.

Description

Technical Field

[0001] This invention relates to adaptive optics technology in the field of astronomical observation, specifically to a mode voltage constraint control method for improving the correction capability of deformable mirrors. Background Technology

[0002] Adaptive optics technology, a relatively new technology developed in the 1970s, has seen widespread application in various adaptive optics systems, with deformable mirrors serving as the core correction device. In astronomical observation, a combination of tilting and deformable mirrors is typically used to achieve joint correction of overall tilt and higher-order aberrations. The tilting mirror corrects tilt aberrations, while the deformable mirror corrects higher-order aberrations. However, in systems using a single deformable mirror, the mirror itself has the ability to generate low-order tilt. Therefore, during closed-loop correction, if the corrector control signal is not constrained, the deformable mirror may generate tilt aberrations, and the tilting and deformable mirrors will mutually correct each other's tilt. Since the deformable mirror actuator has a limited stroke, tilting significantly weakens the system's ability to correct higher-order aberrations. Furthermore, higher-order errors exist in the tilt or translation aberrations fitted by the deformable mirror, reducing far-field imaging brightness. The mutual correction of tilt by the tilting and deformable mirrors creates coupling between the two mirrors. To avoid this coupling, the deformable mirror must not tilt. Meanwhile, since the Hartmann wavefront sensor is not sensitive to translational aberration detection, the deformable mirror needs to not fit the translational aberration to avoid wasting the actuator's travel and reducing the system's ability to correct higher-order aberrations.

[0003] The aforementioned problem requires constraining the overall tilt and translation aberrations through the deformable mirror control voltage in the adaptive optics system. Traditional control algorithms, after closed-loop control, use a proportional-integral controller to remove the voltage within the constraint vector space from the control voltage, thus constraining the deformable mirror to correct only higher-order aberrations. However, due to the coupling inherent in the deformable mirror's influence function, the control voltage calculated using the direct slope method contains errors and is not optimal. Furthermore, the integral action accumulates these errors, failing to completely remove the voltage within the constraint vector space. Summary of the Invention

[0004] The technical problem to be solved by this invention is that during the correction process of the deformable mirror, the deformable mirror itself has the ability to generate low-order tilt, and the deformable mirror and the tilt mirror will correct each other for the generated tilt. The two mirrors are coupled together. Since the stroke of the deformable mirror actuator is limited, the tilt of the deformable mirror will greatly weaken the system's ability to correct high-order aberrations. At the same time, there are high-order errors in the tilt or translation aberration fitted by the deformable mirror, which reduces the brightness of the far-field imaging. It is necessary to constrain the deformable mirror to not generate translation or tilt aberrations during the correction process.

[0005] To solve the above technical problems, the technical solution adopted by this invention is to provide a mode voltage constraint control method to improve the correction capability of deformable mirrors. This method constructs x and y vectors based on the coordinate values ​​of the effective actuators of the deformable mirror in the x and y directions within a unit circle. The number of effective actuators generates a translation vector p. Vectors x, y, and p are respectively derived from {x...} i}, {y i The voltage vector V is composed of elements {1} and {2}. The projection vectors of the voltage vector V onto the x, y, and translation directions are respectively: V x =V·x,V y =V·y,V p =V·p, to prevent tilt and translation aberrations in the deformable mirror, considering the symmetry of the actuator distribution, the three constraint vectors are orthogonal vectors, and the actual applied voltage is the voltage vector after removing the projection. The actual voltage V does not include translation and tilt aberrations. actual =(IP x (IP) y (IP) piston V = MV, where I is the identity matrix consisting of the number of effective drivers, and P... x P y P piston It is the projection matrix onto the subspace composed of constraint vectors p, x, and y, with the first three terms denoted by matrix M. M is an n×n symmetric matrix that describes the correlation between the aberrations of the responses of each effective actuator. This is achieved by performing singular value decomposition on matrix M. For the slope-based orthogonal basis response matrix of deformable mirrors R is the original response matrix of the deformable mirror, a i These are the voltage coefficients for each mode. After obtaining the wavefront slope g to be corrected, they are obtained through a = D. + g obtains the coefficients of each mode voltage, and then the voltage coefficients of each mode voltage can be calculated by the action of the integral controller. Since the deformation mirror needs to be coupled and suppressed, the actual voltage control vector is equal to the superposition of the coefficients of each mode voltage after constraint and the characteristic vectors of each mode voltage.

[0006] The advantages of this invention compared to the prior art are:

[0007] 1. This invention can effectively constrain the deformation mirror from generating translational and tilting aberrations during the correction process, avoid the problem of coupling with the tilting mirror, and improve the correction capability.

[0008] 2. This invention obtains a better control voltage through a new restoration matrix, which has a better correction effect than the prior art and results in a better imaging image.

[0009] 3. This invention can be further applied to dual deformable mirror systems, allocating reasonable aberrations, and effectively improving the deformable mirror correction capability without changing the deformable mirror parameters or adding a actuator, thus saving costs from a manufacturing process perspective. Attached Figure Description

[0010] Figure 1 This is an optical schematic diagram of an experimental system based on a mode voltage constraint control algorithm for improving the correction capability of deformable mirrors according to the present invention.

[0011] Figure 2 This invention presents a residual surface profile image after correction based on a mode voltage constraint control algorithm and an existing vector projection suppression algorithm to improve the correction capability of deformable mirrors.

[0012] Figure 3 This invention presents a far-field Strell ratio diagram after correction based on a mode voltage constraint control algorithm and an existing vector projection suppression algorithm to improve the correction capability of deformable mirrors. Detailed Implementation

[0013] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0014] First, let me introduce the basic principles of this invention:

[0015] For a single deformable mirror adaptive optics system, the wavefront aberrations to be corrected can be divided into tilt aberrations corrected by the tilt mirror and higher-order aberrations corrected by the deformable mirror. In the Zernike mode method, translation can be written as Φ0, and tilt aberrations can be written as Φ1(x-tilt) and Φ2(y-tilt), where the deformable mirror influence function corresponding to the k-th actuator is denoted by f. k (x, y) represents the value. The control voltage applied to the k-th driver is V. k .

[0016] To prevent tilt and translation aberrations in the deformable mirror, constraints need to be imposed on it. Since the Zernike polynomials are orthogonal within the unit circle, the deformable mirror suppresses the i-th order Zernike polynomial aberration Z. i The inhibition condition is:

[0017]

[0018] Numerical integration of formula (1) yields:

[0019]

[0020] Convert equation (2) to vector mode:

[0021]

[0022] In the formula, V is the voltage vector composed of all voltages, and the vectors p,x and y are {1},{x}. i},{y i The vector formed by combining elements is ·, which represents the dot product of vectors. Equation (3) indicates that in order to constrain the deformable mirror from producing translational and tilt aberrations, the overall tilt constraint condition is that the projection of the actual control voltage onto the three vectors p, x, and y should be 0. To prevent the deformable mirror from producing tilt and translational aberrations, considering the symmetry of the actuator distribution, the three constraint vectors are orthogonal vectors, and the actual applied voltage is the voltage vector after removing the projection.

[0023] V actual =(IP x (IP) y (IP) piston V = MV (4)

[0024] Where I is an identity matrix consisting of the number of effective drivers, and P x P y P piston It is the projection matrix onto the subspace composed of constraint vectors p, x, and y, with the first three terms denoted by matrix M. M is an n×n symmetric matrix that describes the correlation between the aberrations of the responses of each effective actuator. This is achieved by performing singular value decomposition on matrix M.

[0025]

[0026] Where U1 is the left singular value vector generated by the singular value decomposition of M in mathematics. Since M is a symmetric matrix, U1 = V1. S1 is a diagonal matrix composed of the eigenvalues ​​of matrix M, and V1 is a unitary matrix composed of the eigenvectors of matrix M. Due to the constraints of translation and tip / tilt aberrations, the last three eigenvalues ​​are filtered out, that is, the last three columns of eigenvectors of matrix V1 are deleted.

[0027]

[0028]

[0029] Among them, V 11 Each column is the characteristic vector of the mode voltage at each order, and a i It is the voltage coefficient vector for each mode, where n represents the number of eigenvalues, corresponding to the number of effective drivers, and λ. nn These represent the eigenvector coefficients corresponding to different eigenvalues. According to the pattern method, the control voltage V of each effective driver... k Equal to the superposition of the mode voltage eigenvector and the mode voltage coefficient, the voltage slope response matrix R and matrix V of the deformable mirror. 11A new response matrix D is formed. To stabilize the dynamic characteristics of the system, the condition number of the response matrix D is restricted based on matrix perturbation theory, and singular value decomposition is performed on the response matrix D.

[0030]

[0031] D = RV 11 V2 (9)

[0032] U2 and V2 are the left and right singular value vectors after singular value decomposition of matrix D, respectively. Like U1 and V1 above, they are mathematical expressions. Here, the singular value decomposition is performed on D, hence the subscript 2 distinguishes them from the U1 and V1 generated by the singular value decomposition of M above. The command matrix is ​​obtained by first calculating the singular value decomposition of the interaction matrix to constrain the condition number, and then obtaining the generalized inverse in the least squares sense. After obtaining the wavefront slope g to be corrected, the voltage coefficients of each mode can be calculated through the action of the integral controller. Because coupling suppression of the deformable mirror is required, the actual voltage control vector is equal to the superposition of the constrained coefficients of each mode voltage and the eigenvectors of each mode voltage.

[0033] a = D + g (10)

[0034] A(j+1)=pi_a×A(j)+pi_b×a(k) (11)

[0035] V(j+1)=V 11 V2A(j+1) (12)

[0036] pi_a and pi_b are the control parameters of the PI controller, representing the integral coefficient of the current control quantity and the cumulative proportional coefficient of the correction quantity, respectively. + It is the inverse matrix of the response matrix D, also called the restoration matrix. a is the coefficient vector of the mode voltage; j represents the current closed-loop frame number in the closed-loop control, and j+1 represents the next frame.

[0037] The optical path distribution diagram in this embodiment is as follows: Figure 1 As shown, the experimental platform includes an imaging light source, a tilting mirror, a deformable mirror, a Hartmann sensor, a reflecting mirror, a lens, a beam splitter, and a photoelectric detection system. The imaging light source is a 650nm wavelength laser point source. The Hartmann sensor and deformable mirror can synchronously detect and compensate for system aberrations. The deformable mirror actuator has 185 units and a limited stroke of ±2.6μm. Figure 1 It includes an imaging point source with a wavelength of 650nm, a deformable mirror type of continuous surface discrete-driven deformable mirror, 177 effective actuators, a Gaussian exponent of 2.0, a crossover value of 10%, and a wavefront sensor that is a Hartmann sensor with a 15×15 sub-aperture.

[0038] The input wavefront profile and the residual wavefront profiles corrected using the mode voltage constraint control method and the existing vector projection suppression method, respectively, are as follows: Figure 2 As shown, the minimum RMS value of the residual wavefront using the mode voltage constraint control method is 0.011 μm.

[0039] The Strell ratio, calculated as the ratio of the peak value of the far-field image after loop closure to the peak value of the far-field image without aberrations, is used as the evaluation metric. The mode voltage constraint control method demonstrates superior correction performance compared to the traditional vector projection suppression method. The correction capabilities of different methods are as follows: Figure 3 As shown.

[0040] In summary, this invention provides a mode voltage constraint control method to improve the correction capability of deformable mirrors. It can constrain translational and tilting aberrations during the correction process without changing the deformable mirror parameters and actuator density, thus avoiding wasted actuator travel and improving correction capability. This invention provides technical guidance for further optimization of deformable mirror decoupling control methods.

[0041] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A mode voltage constraint control method for improving the correction capability of deformable mirrors, characterized in that: Based on the coordinates of each effective actuator of the deformable mirror in the x and y directions within the unit circle, construct x and y vectors. The number of effective actuators generates a translation vector p. Vectors x, y, and p are respectively... , and It is composed of elements, where i represents the i-th valid driver; The actual applied voltage is the voltage vector after removing the projection, and does not include the actual voltage due to translation and tilt aberrations. ,in It is an identity matrix consisting of the number of effective drivers. , , M is the projection matrix on the subspace composed of constraint vectors p, x, and y. The three constraint vectors are orthogonal vectors. M is an n×n symmetric matrix that describes the correlation between the response aberrations of each effective actuator. Actual voltage In Using matrices This means that by performing singular value decomposition on matrix M, ,in, V1 is a diagonal matrix composed of the eigenvalues ​​of matrix M, and V1 is a unitary matrix composed of the eigenvectors of matrix M. = , It is the left singular vector after the singular value decomposition of M; Due to the constraints of translation and tip / tilt aberrations, the last three eigenvalues ​​are filtered out, that is, the last three columns of eigenvectors of the unitary matrix V1 are deleted. According to the mode method, the control voltage of each effective driver is equal to the superposition of the mode voltage eigenvector and the mode voltage coefficient. The voltage slope response matrix and unitary matrix V1 of the deformable mirror generate a new response matrix. The condition number of the new response matrix is ​​restricted based on the perturbation theory of the matrix, and singular value decomposition is performed on the new response matrix. After obtaining the wavefront slope g to be corrected, the voltage coefficients of each mode can be calculated by the action of the integral controller. Since the deformation mirror needs to be coupled and suppressed, the actual voltage control vector is equal to the superposition of the coefficients of each mode voltage after constraint and the characteristic vectors of each mode voltage.

2. The mode voltage constraint control method for improving the correction capability of deformable mirrors according to claim 1, characterized in that: Voltage vector The projection vectors onto vectors x, y, and translation vector p are divided into: , , .

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