Method for optimizing arrangement of deformable mirror actuators

Abstract

The application relates to a method for optimizing the arrangement of a deformable mirror actuator, which comprises the following steps: obtaining an influence function matrix between the actuator control voltage of a deformable mirror and the mirror deformation; selecting a Zernike polynomial order, dividing to obtain a basic region, and performing'region folding' on the actuator of the deformable mirror; determining the optimal arrangement of the actuator in the basic region according to the obtained influence function matrix and the obtained basic region; and performing overall 'unfolding' on the'region folded' actuator of the deformable mirror to obtain the optimal topological arrangement of the entire deformable mirror. The application can reduce the calculation amount and complexity of the actuator control system in the actual wavefront correction process, and relieve the fatigue of the actuator during long-time work.

Description

Technical Field

[0001] This invention relates to the field of optical imaging technology, and in particular to a method for optimizing the arrangement of deformable mirror actuators. Background Technology

[0002] Deformable mirrors are a typical wavefront aberration correction device, widely used in various adaptive optics systems. They change the phase structure of the incident light wavefront by altering the optical path length of the light wave or the refractive index of the transmission medium, thereby improving the imaging quality of the optical system.

[0003] The deformation of a deformable mirror is achieved by multiple actuators under the control of an applied driving voltage. The number of actuators, response time, deformation amount, and the distribution of actuators on the mirror surface all directly affect the deformation accuracy of the deformable mirror.

[0004] When using Zernike polynomials to describe wavefront aberrations, generally speaking, the more actuators, the larger the effective aperture, and the more electrode rings a deformable mirror of the same aperture has, the higher its spatial resolution and the better its correction effect. However, the higher the order of the fitted Zernike polynomial, the greater the computational load for wavefront correction and control, and the more complex the actuator control becomes. This is because the actuator deformation is alternating between positive and negative values, operating at speeds of hundreds or even thousands of times per second. The enormous cyclic stress and high-frequency, high-speed repeated deformation directly affect the actuator's service life, thereby impacting the deformable mirror's operational stability and surface shape control accuracy.

[0005] Existing deformable mirrors typically perform wavefront correction with a fixed number and arrangement topology of actuators. In actual operation, the system control bandwidth and spatial resolution of the same optical system vary under different application environments. To reduce the computational load and complexity of wavefront correction under certain conditions and to reduce actuator fatigue, it is necessary to study different actuator arrangement optimization methods for deformable mirrors based on actual operating conditions. Summary of the Invention

[0006] In view of this, it is necessary to provide a method for optimizing the arrangement of deformable mirror actuators, which can design the optimal topology of actuator arrangement under different requirements from two scales, "overall" and "region", based on the idea of ​​"regional folding-overall unfolding" according to the wavefront correction accuracy requirements.

[0007] This invention provides a method for optimizing the arrangement of deformable mirror actuators, the method comprising the following steps:

[0008] S1. Obtain the influence function matrix between the actuator control voltage of the deformable mirror and the mirror deformation;

[0009] S2. Select the Zernike polynomial order, divide the basic region, and perform "region folding" on the actuator of the deformable mirror;

[0010] S3. Based on the obtained influence function matrix and the obtained basic region, determine the optimal arrangement of actuators within the basic region;

[0011] S4. Unfold the actuators of the deformable mirror with “regional folding” as a whole to obtain the optimal topological arrangement of the entire deformable mirror.

[0012] Preferably, step S1 includes:

[0013] By applying the same control voltage v to each actuator individually, the corresponding mirror surface shape change data are obtained. An influence function f between any actuator and the mirror surface shape change is then established using a super-Gaussian function. j Mathematical description of (x,y):

[0014]

[0015] Where: ω is the cross-linking value between actuators, α is the Gaussian exponent, and x... j ,y j is the coordinate of the j-th actuator, and d is the distance between the actuators.

[0016] Preferably, step S2 includes:

[0017] When all actuators of the deformable mirror are operational, the Zernike polynomial order that the deformable mirror can fit within the accuracy range calculated by simulation is n0; when the spatial resolution requirement for wavefront correction is low, the Zernike polynomial order that the deformable mirror can fit is n. i n i ≤n0;

[0018] Using n i The angular symmetry of the Zernike polynomial divides the surface of the deformable mirror into equal angles along the angular direction. Q regions, Each region contains N / Q actuators with the same actuator distribution.

[0019] Preferably, step S2 further includes:

[0020] Because n i The Zernike polynomial of order 1 represents the symmetry of the surface, with the q-th region as the base region Θ. q The surface shape described in other areas Based on the basic area shape Rotate by a certain angle around a certain coordinate axis The transformation yields:

[0021]

[0022] Preferably, step S3 includes:

[0023] In the basic region Θ q Within, based on the fitting order n i A finite number of actuators, selected in size and distributed within multiple electrode rings, are designated as basic actuators. The number of these basic actuators is [number missing]. Simultaneously, ensure that there are at least three electrode rings within the base region to guarantee the accuracy of the deformable mirror fitting low-order Zernike polynomials; based on the fitting order n... i The relationship between the maximum fitting order n0 and the remaining actuators is used to select a certain number of actuators as candidate actuators. The number of candidate actuators is...

[0024]

[0025] in, Is with A positively correlated function, because n i ∈[1,n0], therefore Where g is a constant.

[0026] Preferably, step S3 further includes:

[0027] With n i The fundamental region Θ described by the Zernike polynomial of order 1 q The face shape is an ideal face shape Combining the basic actuator and the candidate actuators, K different actuator arrangement topologies are generated within the region using traversal or discrete topology optimization. Under the k-th actuator arrangement (k≤K), each driving voltage is controlled to generate the actual surface shape according to the desired ideal surface shape.

[0028]

[0029] in, Basic region Θ q The set of all actuators under the k-th actuator arrangement scheme.

[0030] Preferably, step S3 further includes:

[0031] Calculate the fitting residuals between the actual surface shape and the ideal surface shape:

[0032]

[0033] Let ζ be the fitting error of the k-th actuator arrangement scheme. k To fit the residuals Root mean square and ideal surface shape The ratio of root mean square:

[0034]

[0035] in, The average value of the surface residuals. The average value of the ideal face shape. It is the set containing all actuators of the deformable mirror.

[0036] Preferably, step S3 further includes:

[0037] Taking the minimum fitting error shown in formula (6) as the objective function for actuator layout topology optimization, calculate the fitting n i The region Θ of the Zernike polynomial of order q Internal optimal actuator layout topology The number of working actuators under this topology is:

[0038] Preferably, step S4 includes:

[0039] With region Θ q of Based on the topological arrangement, the inverse transformation of the folding transformation using formula (2) is used to transform the actuator of the deformable mirror that "folds the region". The topological arrangement is "unfolded" to obtain the optimal topological arrangement T of the entire deformable mirror. i :

[0040]

[0041] Preferably, step S4 includes:

[0042] In actual wavefront correction, the desired Zernike polynomial order is selected online according to actual needs, and wavefront correction is performed based on the optimal topology arrangement of the corresponding actuators stored in the system.

[0043] This invention, based on the accuracy requirements of wavefront correction, utilizes the angular symmetry and correlation between aberrations of different orders described by Zernike polynomials to design the optimal actuator arrangement topology at both the global and regional scales, using the concept of "regional folding-global unfolding." This invention reduces the computational load and complexity of the actuator control system during actual wavefront correction and alleviates actuator fatigue during long-term operation, making deformable mirrors suitable for a wider range of applications. Attached Figure Description

[0044] Figure 1 This is a flowchart of the method for optimizing the arrangement of deformable mirror actuators according to the present invention;

[0045] Figure 2This is a schematic diagram of the actuator "regional folding" of the deformable mirror according to an embodiment of the present invention;

[0046] Figure 3 This is a schematic diagram illustrating the optimal arrangement of actuators within the basic region of an embodiment of the present invention;

[0047] Figure 4 This is a schematic diagram showing the actuator of the deformable mirror in an embodiment of the present invention being "unfolded" as a whole. Detailed Implementation

[0048] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0049] See Figure 1 The diagram shown is a flowchart of a preferred embodiment of the deformable mirror actuator arrangement optimization method of the present invention.

[0050] In this embodiment, a hexahedron is selected as the basic unit of the actuator for the deformable mirror, and multiple actuators are evenly distributed on the deformable mirror to form the actuator for wavefront correction of the deformable mirror. Let the number of actuators in the deformable mirror be N, and the spacing between the actuators be d. Specifically, this invention includes:

[0051] Step S1: Obtain the influence function matrix between the actuator control voltage of the deformable mirror and the mirror deformation. Specifically:

[0052] The movement of the actuators under the driving voltage causes the mirror surface to deform. The distribution of this deformation on the mirror surface is defined as an influence function. The linear superposition of the influence functions of all actuators under different voltage coefficients yields the surface shape of the entire deformable mirror. By applying the same control voltage v to each actuator individually, the corresponding mirror surface shape change data are obtained. An influence function f between any actuator and the mirror surface shape change is then established using a super-Gaussian function. j Mathematical description of (x,y):

[0053]

[0054] Where: ω is the cross-linking value between actuators, α is the Gaussian exponent, and x... j ,y j It is the coordinate of the j-th actuator.

[0055] Step S2: Select the Zernike polynomial order, divide the basic region, and perform "region folding" on the actuator of the deformable mirror. Specifically:

[0056] When all actuators of the deformable mirror are operational, simulation tests show that the deformable mirror can fit a Zernike polynomial of order n0 within the accuracy range. When the system has low requirements for wavefront correction spatial resolution, the design of the fitting Zernike polynomial of order n... i (n i≤n0).

[0057] Using n i The angular symmetry of the Zernike polynomial divides the surface of the deformable mirror into equal angles along the angular direction. Q regions Each region contains N / Q actuators with the same actuator distribution. Since n i The Zernike polynomial of order 1 represents the symmetry of the surface, with the q-th region as the base region Θ. q The surface shape described in other areas Based on the basic area shape Rotate by a certain angle around a certain coordinate axis The transformation yields:

[0058]

[0059] like Figure 2 As shown, taking the surface corresponding to the third-order Zernike polynomial as an example, considering its symmetry, the entire surface is divided into 4 regions. The upper left region 1 is the base region (q=1), and the regions Θ2, Θ3, and Θ4 are rotated and folded to the base region Θ1 through axis-angle rotation, thereby realizing the "fan-shaped region folding" of the entire deformed mirror surface.

[0060] Step S3: Based on the obtained influence function matrix and the derived base region, determine the optimal arrangement of actuators within the base region. Please refer to [link to relevant documentation]. Figure 3 Specifically:

[0061] In the basic region Θ q Within, based on the fitting order n i A finite number of actuators, each of which is selected and distributed within multiple electrode rings, are used as the basic actuators (the number is...). Simultaneously, ensure that there are at least three electrode rings within the region to guarantee the accuracy of the deformable mirror fitting the low-order Zernike polynomial. Based on the fitting order n... i The relationship between the maximum fitting order n0 and the remaining actuators is used to select a certain number of actuators as candidate actuators (the number is...). ):

[0062]

[0063] in, Is with A positively correlated function, because n i ∈[1,n0], therefore Where g is a constant.

[0064] Specifically, in the basic region Θ qWithin the candidate actuator, the actuators other than the basic actuators are selected by a random method.

[0065] With n i The fundamental region Θ described by the Zernike polynomial of order 1 q The face shape is an ideal face shape Combining the basic actuator and the candidate actuators, different actuator arrangement topologies (a total of K) are generated within the region using either traversal or discrete topology optimization. Under the k-th actuator arrangement (k≤K), each driving voltage is controlled to generate the actual surface shape according to the desired ideal surface shape.

[0066]

[0067] in, Basic region Θ q Given the k-th actuator arrangement, find the set of all actuator-containing schemes. Calculate the fitting residual between the actual surface shape and the ideal surface shape:

[0068]

[0069] Let ζ be the fitting error of the k-th actuator arrangement scheme. k To fit the residuals Root mean square and ideal surface shape The ratio of root mean square:

[0070]

[0071] in, The average value of the surface residuals. The average value of the ideal face shape. It is the set containing all actuators of the deformable mirror.

[0072] Taking the minimum fitting error shown in formula (6) as the objective function for actuator layout topology optimization, calculate the fitting n i The region Θ of the Zernike polynomial of order q Internal optimal actuator layout topology The number of working actuators under this topology is:

[0073] Step S4 involves "unfolding" the actuators of the "region-folded" deformable mirror as a whole to obtain the optimal topological arrangement of the entire deformable mirror. Please refer to [link / reference]. Figure 4 Specifically:

[0074] With region Θ q of Based on the topological arrangement, the inverse transformation of the folding transformation using formula (2) is used to transform the actuator of the deformable mirror that "folds the region". The topological arrangement is "unfolded" to obtain the optimal topological arrangement T of the entire deformable mirror. i .

[0075]

[0076] In some embodiments, when generating the actuator sub-arrangement topology scheme using a traversal method, the basic actuator is used as a basis to include a number of (0 to N) ws The two variables, distribution location and location, are used to traverse all topological arrangements containing candidate actuators, totaling... kind.

[0077] In some embodiments, when using discrete topology optimization methods to generate the driving sub-arrangement topology scheme, relaxation methods, simulated annealing methods, topology optimization based on genetic algorithms, and other topology optimization methods with the same or similar characteristics are selected.

[0078] In actual wavefront correction, the desired Zernike polynomial order is selected online according to actual needs, and wavefront correction is performed based on the optimal topology arrangement of the corresponding actuators stored in the system.

[0079] Although the present invention has been described with reference to the present preferred embodiments, those skilled in the art should understand that the above preferred embodiments are only used to illustrate the present invention and are 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 optimizing the arrangement of deformable mirror actuators, characterized in that, The method includes the following steps: S1. Obtain the influence function matrix between the actuator control voltage of the deformable mirror and the mirror deformation; S2. Select the Zernike polynomial order, divide the basic region, and perform "region folding" on the actuator of the deformable mirror; S3. Based on the obtained influence function matrix and the obtained basic region, determine the optimal arrangement of actuators within the basic region; S4. Unfold the actuators of the deformable mirror with "regional folding" as a whole to obtain the optimal topological arrangement of the entire deformable mirror.

2. The method for optimizing the arrangement of deformable mirror actuators as described in claim 1, characterized in that, Step S1 includes: Apply the same control voltage to all actuators individually. The corresponding mirror surface shape change data are obtained, and the influence function between any actuator and the mirror surface shape change is established using the super-Gaussian function. Mathematical description: （1） in: The crosslinking value between actuators. For Gaussian exponents, It is the first j The coordinates of each actuator are given, where d is the distance between the actuators.

3. The method for optimizing the arrangement of deformable mirror actuators as described in claim 2, characterized in that, Step S2 includes: When all actuators of the deformable mirror are activated, the Zernike polynomial order that the deformable mirror can fit within the fitting accuracy range is calculated to be... When the spatial resolution requirement for wavefront correction is low, the deformable mirror can be fitted with a Zernike polynomial of order [order missing]. , ; use The angular symmetry of the Zernike polynomial divides the surface of the deformable mirror into equal angles along the angular direction. of Each region Each region contains Each actuator and the same actuator distribution, This represents the number of actuators for the deformable mirror.

4. The method for optimizing the arrangement of deformable mirror actuators as described in claim 3, characterized in that, Step S2 further includes: because The Zernike polynomial of order X represents the symmetry of a surface, with the first X representing the symmetry of the surface. Each region is a basic region The surface shape described in other areas Based on the basic area shape Rotate by a certain angle around a certain coordinate axis The transformation yields: （2）。 5. The method for optimizing the arrangement of deformable mirror actuators as described in claim 4, characterized in that, Step S3 includes: In the basic area Internally, based on the fitting order A finite number of actuators, selected in size and distributed within multiple electrode rings, are designated as basic actuators. The number of these basic actuators is [number missing]. Simultaneously, ensure that there are at least three electrode rings within the base region to guarantee the accuracy of the deformable mirror fitting low-order Zernike polynomials; based on the fitting order... With the order of maximum fit Based on the relationship between the actuators, a certain number of actuators are selected from the remaining actuators as candidate actuators, wherein the number of candidate actuators is... : （3） in, Is with Positively correlated functions, because ,so ,in It is a constant.

6. The method for optimizing the arrangement of deformable mirror actuators as described in claim 5, characterized in that, Step S3 further includes: by The fundamental region described by the Zernike polynomial of order 1 The face shape is an ideal face shape By combining basic actuators and candidate actuators, different actuators within the region are generated through traversal or discrete topology optimization. One arrangement topology scheme; the first k Under this actuator arrangement scheme, Control each driving voltage to generate the actual surface shape according to the desired ideal surface shape. : （4） in, Basic area Inner k The set of all actuators under a given actuator arrangement scheme.

7. The method for optimizing the arrangement of deformable mirror actuators as described in claim 6, characterized in that, Step S3 further includes: Calculate the fitting residuals between the actual surface shape and the ideal surface shape: （5） Order No. k Fitting error of various actuator arrangement schemes To fit the residuals Root mean square and ideal surface shape The ratio of root mean square: （6） in, The average value of the surface residuals. The average value of the ideal face shape. It is the set containing all actuators of the deformable mirror.

8. The method for optimizing the arrangement of deformable mirror actuators as described in claim 7, characterized in that, Step S3 further includes: Taking the minimum fitting error shown in formula (6) as the objective function for actuator layout topology optimization, the fitting error is calculated. Regions of Zernike polynomials of order Internal optimal actuator layout topology The number of working actuators under this topology is , .

9. The method for optimizing the arrangement of deformable mirror actuators as described in claim 8, characterized in that, Step S4 includes: By region of Based on the topological arrangement, the inverse transformation of the folding transformation using formula (2) is used to transform the actuator of the deformable mirror that "folds the region". The topological arrangement is "unfolded" to obtain the optimal topological arrangement of the entire deformable mirror. : （7）。 10. The method for optimizing the arrangement of deformable mirror actuators as described in claim 9, characterized in that, Step S4 includes: In actual wavefront correction, the desired Zernike polynomial order is selected online according to actual needs, and wavefront correction is performed based on the optimal topology arrangement of the corresponding actuators stored in the system.

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