CN115236848B - Full-caliber high-precision deformable mirror control method and device - Google Patents
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Abstract
The invention discloses a full-caliber high-precision deformable mirror control method, which comprises the following steps: acquiring an initial voltage; performing voltage iteration and voltage search on the initial voltage based on a voltage iteration and search fusion algorithm to obtain a target voltage; the calculated target voltage is input into a digital simulation model, so that the deformable mirror is controlled. When the iteration evaluation parameter is larger than the conversion threshold value, calculating through an iteration algorithm affecting the function matrix; when the iteration evaluation parameter is smaller than the conversion threshold value, performing voltage search optimization through a random parallel gradient descent method, and eliminating solving errors caused by influencing the self errors of the function matrix; the iterative evaluation parameters are represented by the deviation of standard Zernike coefficient vectors of the target surface shape and the current mirror surface shape. The invention can not only effectively improve the solving precision of control voltage, but also fully exert the capability of the large-caliber deformable mirror, improve the applicability of the large-caliber deformable mirror, and ensure the flexibility and the degree of freedom of the design of a control scheme.
Description
Technical Field
The invention relates to the technical field of deformable mirror control, in particular to a full-caliber high-precision deformable mirror control method and device.
Background
Deformable mirrors are an important wavefront corrector in the field of adaptive optics. A typical Adaptive Optics (AO) system is mainly composed of a wavefront sensor, a wavefront controller, a wavefront corrector and some additional optical components, as shown by the dashed box in fig. 1. The wavefront sensor detects and displays aberration components of distorted wavefront in real time, the detection result is fed back to the wavefront controller, the wavefront controller calculates the measured wavefront information, a control voltage signal for driving the wavefront corrector to work is solved, and the wavefront corrector carries out conjugate compensation on the wavefront with optical distortion. If the adaptive system is to be analogous to a human body, the wavefront sensor, wavefront controller, wavefront corrector act as "eyes", "brain" and "extremities", respectively.
The deformable mirror is widely applied in astronomical imaging, biomedical imaging, microscopic imaging, laser communication, inertial confinement fusion and other fields, and can change the surface shape of the deformable mirror according to a control voltage signal transmitted by the wavefront controller, so that the dynamic and rapid correction of distorted wavefront is realized, and the quality of light beams or the imaging effect is improved. The deformable mirror can be divided into two types of continuous type and spliced type according to whether the mirror surface of the deformable mirror is continuous, a splicing gap exists on the mirror surface of the spliced deformable mirror, the light beam propagation efficiency is affected during use, and the characteristics of lossless propagation of the continuous deformable mirror can be subdivided into the following types according to different actuators: film deformable mirror, piezoelectric deformable mirror and electromagnetic deformable mirror. Taking a piezoelectric stack deformable mirror as an example, the structure and the wave front correction principle of the piezoelectric stack deformable mirror are shown in fig. 2, and the piezoelectric stack deformable mirror comprises a mirror surface 1, a connecting column 2, a piezoelectric actuator 3 and a base 4.
The accuracy of the control voltage solution of the deformable mirror actuator is a key factor affecting the capacity of the deformable mirror to correct wavefront distortion. The existing control voltage solving algorithm can be divided into an open-loop algorithm and a closed-loop algorithm according to whether a feedback process is needed or not, wherein the open-loop algorithm mainly refers to an influence function matrix pseudo-inverse method; the closed-loop algorithm can be divided into two main types of iterative algorithm based on the influence function matrix and voltage search algorithm without influence function matrix according to the need of the influence function matrix, wherein the iterative algorithm based on the influence function matrix comprises a gradient descent method, an iterative learning control method and the like, and the voltage search algorithm without influence function matrix comprises a hill climbing method, a genetic algorithm, a simulated annealing method, a random parallel gradient descent method and the like. The research shows that the influence function matrix pseudo-inverse method has high calculation efficiency, but has poor calculation accuracy, the voltage search algorithm without influence function matrix has the highest solution accuracy, but has slower convergence and longest calculation time, and the calculation accuracy and the calculation time of the iterative algorithm based on the influence function matrix are both at intermediate level.
Disclosure of Invention
The invention aims to solve the technical problem of low control precision of a full-caliber deformable mirror, and provides a full-caliber high-precision deformable mirror control method and device.
The technical problems of the invention are solved by the following technical scheme:
a full-caliber high-precision deformable mirror control method comprises the following steps:
s1, acquiring an initial voltage;
s2, performing voltage iteration and voltage search on the initial voltage based on a voltage iteration and search fusion algorithm to obtain a target voltage;
s3, inputting the calculated target voltage into a digital simulation model so as to control the deformable mirror.
In some embodiments, the method further comprises the following technical characteristics:
in step S2, the voltage iterative and search fusion algorithm includes: defining an iteration evaluation parameter, setting a conversion threshold, and calculating through an iteration algorithm of the influence function matrix when the iteration evaluation parameter is greater than or equal to the conversion threshold; when the iteration evaluation parameter is smaller than the conversion threshold value, performing voltage search optimization through a random parallel gradient descent method, and eliminating solving errors caused by influencing the self errors of the function matrix; the iterative evaluation parameters are represented by the deviation of standard Zernike coefficient vectors of the target surface shape and the current mirror surface shape.
Further, in step S2, the formula of the voltage iteration and search fusion algorithm is:
wherein alpha isThe gain coefficient, the value size influences the iteration speed and the stability of the solving process, C n C is the current control voltage vector n+1 E is the control voltage vector after the next iteration n For iterative evaluation parameters, GT represents the transposed matrix of the influence function matrix G, γ is the gain coefficient, E is the evaluation function, δc is the randomly added bidirectional disturbance voltage signal, and t is the conversion threshold.
Further, the voltage iteration and search fusion algorithm comprises an influence function matrix iteration algorithm C n+1 ＝C n +αG T e n And the function matrix search algorithm C is not influenced n+1 ＝C n +γ(E + -E - )δC。
Further, step S2 further includes:
when iterating the evaluation parameter e n When the transformation threshold value is greater than or equal to the transformation threshold value, approximating the target voltage based on the influence function matrix iterative algorithm to locate a proper searching starting point;
when iterating the evaluation parameter e n And when the voltage is smaller than the conversion threshold value, performing voltage search by using a closed-loop voltage search algorithm without influencing the function matrix to obtain the target voltage.
In step S3, the digital simulation model is a continuous deformable mirror digital simulation model.
Further, the continuous deformable mirror digital simulation model is established through the following steps:
f1, establishing a finite element simulation model of a deformable mirror, and obtaining a coupling coefficient omega, a Gaussian index alpha and deformation A of an actuator under unit voltage;
f2, in the digital simulation platform, using the formulaEstablishing expressions of all actuator influence functions under a preset arrangement scheme on the basis, and representing the mirror surface shape under the action of multiple actuators through linear superposition of the influence functions; where i denotes the number of the actuator, A denotes the magnitude of the amplitude of the Gaussian function, exp denotes the exponential function based on the natural constant e, ln denotes the logarithmic function, ω denotes the inter-actuator distanceAlpha represents the gaussian index, r and d represent the point-to-actuator center distance on the mirror and the actuator distribution spacing, respectively, B represents the magnitude of the gaussian function used for correction, and beta is the radial adjustment width.
In step S3, the continuous deformable mirror digital simulation model outputs three-dimensional point cloud data, i.e. mirror surface shape, after the deformable mirror responds to the input control voltage.
Step S2 further comprises selecting a control voltage solving algorithm according to the relative size of the target surface shape caliber.
The target surface shape is a small-caliber surface shape when the number of the target surface shape caliber covering actuators does not exceed a first numerical value; the target surface shape caliber covering actuator number is a medium caliber surface shape when the target surface shape caliber covering actuator number is between a first value and a second value; and the target surface shape is a large-caliber surface shape when the number of the target surface shape caliber covering actuators is larger than a second value.
The invention also adopts the following technical scheme:
a full-caliber high-precision deformable mirror control device comprises a processor and a memory, wherein a computer program is stored in the memory, and the computer program can be executed by the processor to realize the method.
Compared with the prior art, the invention has the beneficial effects that:
the full-caliber high-precision deformable mirror control method provided by the invention has the advantages of integrating two major algorithms, namely an iterative algorithm based on an influence function matrix and a voltage search algorithm without an influence function matrix, and comprises two modules, namely voltage iteration and voltage search, and solving the control voltage when the deformable mirror is used for surface shape reconstruction, so that a plurality of novel control voltage solving algorithms can be quickly derived, the surface shape reconstruction error RMSE is obviously reduced, the control voltage solving precision can be effectively improved, the capability of the large-caliber deformable mirror can be fully exerted, the applicability of the large-caliber deformable mirror is improved, and the flexibility and the degree of freedom of control scheme design are ensured.
Furthermore, in some embodiments, the following benefits are also provided:
according to the voltage solving algorithm self-adaptive selection method based on the target surface shape caliber, solving accuracy and solving cost are comprehensively considered in a full caliber range, the most suitable control voltage solving algorithm can be selected in a self-adaptive mode according to the relative size of the target surface shape caliber, and the method has high application value.
Other advantages of embodiments of the present invention are further described below.
Drawings
FIG. 1 is a schematic diagram of a typical adaptive optics system;
FIG. 2 is a schematic diagram of the principle of operation and structure of a piezo-electric stacked deformable mirror;
FIG. 3 is a flow chart of a voltage iteration and search fusion algorithm in an embodiment of the invention;
FIG. 4 is a flow chart of a method of selecting a voltage solving algorithm in an embodiment of the invention;
FIG. 5a is a schematic diagram of reconstruction errors for different apertures and different aberration profiles by pseudo-inverse;
FIG. 5b is a schematic diagram of the reconstruction errors of the gradient descent method for different apertures and different aberration profiles;
FIG. 5c is a schematic diagram of the reconstruction errors of the iterative learning control method for different apertures and different aberration profiles;
FIG. 5d is a schematic diagram of reconstruction errors for different apertures and different aberration profiles by a random parallel gradient descent method;
FIG. 6 is a schematic diagram of reconstruction accuracy for different algorithms at different target surface apertures;
FIG. 7 is a schematic diagram of reconstruction accuracy of different algorithms for different standard Zernike polynomial aberration profiles;
FIG. 8 is a schematic diagram of reconstruction errors of different apertures and different aberration profiles by the full aperture high precision deformable mirror control method in an embodiment of the present invention;
FIG. 9 is a diagram showing the comparison of the reconstruction accuracy of the full-aperture high-accuracy deformable mirror control method and the prior art method under different target surface apertures in the embodiment of the present invention;
FIG. 10 is a diagram showing the comparison of the reconstruction accuracy of the full aperture high accuracy deformable mirror control method and the prior art method for different standard Zernike polynomial aberration profiles in accordance with one embodiment of the present invention;
FIG. 11 is a schematic diagram showing the comparison of the calculation cost of the full-caliber high-precision deformable mirror control method and the calculation cost of the existing method in the embodiment of the invention;
FIG. 12 is a flow chart of a method for controlling a full aperture high precision deformable mirror in an embodiment of the invention.
Detailed Description
The invention will be further described with reference to the following drawings in conjunction with the preferred embodiments. It should be noted that, in the case of no conflict, the embodiments and features in the embodiments may be combined with each other.
Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include one or more such feature. In the description of the embodiments of the present invention, the meaning of "plurality" is two or more, unless explicitly defined otherwise.
Before describing the specific embodiments of the present invention, the following is a description of the concepts of the present invention:
in the prior art, the conclusion that the calculation accuracy of the influence function matrix pseudo-inverse method is poor and the voltage search algorithm without influence function matrix is slow and the calculation time is longest is obtained when the deformable mirror is in a general working caliber (namely about 80% of the caliber of a mirror surface), and in practice, in many optical systems, the working caliber of the deformable mirror is dynamically changed. For example, for a deformable mirror with a caliber of 100mm and 55 actuators, when working conditions only use a medium caliber (less than 60 mm), an iterative algorithm based on an influence function matrix has better reconstruction precision, and a voltage search algorithm without the influence function matrix is easy to fall into a local optimal value to cause precision reduction; when the working condition is used in a large caliber (60 mm), the situation that the voltage search algorithm without influencing the function matrix falls into a local optimal value is reduced, and the reconstruction accuracy is improved.
The invention builds a deformation mirror mathematical model with large caliber and multiple actuators based on a digital simulation platform, researches the precision and efficiency of different aberration surface shapes of the existing algorithm under different reconstructed calibers, and results show that the existing algorithm can not keep relatively stable control voltage solving precision under the whole caliber. The complete flow of the method of the present invention is shown in FIG. 12.
Example 1
A method for establishing a continuous deformable mirror digital simulation model is specifically described as follows:
for a continuously deformable mirror, the mirror surface shape under the action of a single actuator is called the influence function of the actuator, and can be generally fitted by a super Gaussian function:
where i denotes the number of the actuator, a denotes the magnitude of the amplitude of the gaussian function, exp denotes an exponential function based on a natural constant e, ln denotes a logarithmic function, ω denotes the coupling coefficient between the actuators, α denotes the gaussian index, and r and d denote the point-to-actuator center distance on the mirror surface and the actuator distribution pitch, respectively. Because of the large difference in rigidity between the actuator and the mirror, when a single actuator acts, a phenomenon that the mirror deforms in the opposite direction to the movement of the actuator exists in a section of the area outside the adjacent actuator, and as a result, the conventional Gaussian function shown in the formula (1) cannot fit the deformation of the mirror well. To this end, researchers have proposed using another gaussian function to modify the original hypersurface to characterize the influence function of the actuator:
where B represents the magnitude of the gaussian function used for correction and β (6 in the case of a hexagonal arrangement of actuators) is the radial adjustment width. The embodiment of the invention provides a method for establishing a deformable mirror digital simulation model with any caliber and any actuator number on the basis of a formula (2). The conventional step of establishing a deformable mirror simulation model comprises the following steps: 1. determining the caliber of the deformable mirror, the number of actuators and the arrangement scheme of the actuators; 2. determining material parameters, setting piezoelectric polarization directions of actuators, and determining boundary conditions of a deformable mirror simulation model; 3. establishing a finite element simulation model of the deformable mirror in finite element simulation software, and meshing the model; 4. and adjusting structural parameters of the deformable mirror finite element simulation model to enable the coupling coefficient omega and the Gaussian index alpha to be in a reasonable range. The embodiment considers the inherent problems of high finite element simulation calculation cost and low simulation efficiency, and improves the following on the basis of traditional deformation mirror simulation model establishment: 1. establishing a traditional deformable mirror finite element simulation model, and obtaining a coupling coefficient omega, a Gaussian index alpha and the deformation A of an actuator under unit voltage; 2. in the digital simulation platform, the expression of all actuator influence functions under a preset arrangement scheme is established based on the formula (2), and the linear superposition of the influence functions is used for representing the mirror surface shape under the action of multiple actuators, so that the digital simulation model of the deformable mirror is completed. The input of the digital simulation model is the control voltage magnitude (in volts) of all actuators, and the output is three-dimensional point cloud data, namely the mirror surface shape, after the deformable mirror responds to the input control voltage. The meaning of two a in the formulas (1) and (2) is identical, and the deformation amount of the actuator per unit voltage is physically expressed (the magnitude of the amplitude of the gaussian function in the model is different, and the angles are substantially the same).
Compared with the traditional finite element simulation model, the deformation mirror digital simulation model established in the embodiment has the advantages that the calculation efficiency is greatly improved while the surface shape control precision is maintained (the finite element simulation calculation cost is related to the grid division density, more than 1 hour is usually required for completing one-time surface shape response output of control voltage on the finite element simulation model, and the time for completing one-time surface shape response output of control voltage by the digital simulation model is less than 1 second).
Example 2
A high-precision and high-efficiency voltage iteration and search fusion algorithm is specifically described as follows:
the existing control voltage solving algorithm mainly comprises an influence function matrix pseudo-inverse method, a gradient descent method, an iterative learning control method, a random parallel gradient descent method and the like.
The influence function matrix pseudo-inverse method belongs to an open-loop voltage solving algorithm based on an influence function matrix, and a formula for solving control voltage according to a standard Zernike coefficient of a target surface shape is as follows:
C＝G -1 S (3)
wherein G is an influence function matrix of the deformable mirror, S is a standard Zernike coefficient of a target surface shape to be reconstructed, and C is a control voltage vector of all actuators obtained through solving.
The gradient descent method belongs to a closed-loop voltage solving algorithm based on an influence function matrix, and the control voltage iteration formula is as follows:
C n+1 ＝C n +αG T e n (4)
wherein alpha is a gain coefficient, the value affects the iteration speed and the stability of the solving process, C n C is the current control voltage vector n+1 For the control voltage vector after the next iteration, G T A transpose matrix e representing an influence function matrix G n For iterative evaluation parameters, the deviation of the standard zernike coefficient vector of the target surface shape and the current mirror surface shape can be used for representing:
f(x)＝e n ＝S d -S n ＝S d -GC n (5)
where Sd represents the standard zernike coefficient of the target profile and Sn represents the standard zernike coefficient of the deformed mirror profile at the current iteration voltage. The iterative learning control method belongs to a closed-loop voltage solving algorithm based on an influence function matrix, and the iterative formula of the control voltage is as follows:
C n+1 ＝C n +(G T G+βI) -1 G T e n (6)
wherein beta is a gain coefficient, the value affects the iteration speed and the stability of the solving process, I is a unit matrix, and the iteration evaluation parameter e n The expression of (2) is the same as that of (5).
The random parallel gradient descent method belongs to a closed loop voltage search algorithm without influencing function matrix, and the control voltage search formula is as follows:
C n+1 ＝C n +γ(E + -E-)δC (7)
wherein gamma is a gain coefficient, the value size influences the iteration speed and the stability of the solving process, E is an evaluation function, and is selected as the RMS value of the error between the target surface shape and the current surface shape of the deformable mirror, and δC is a randomly added bidirectional disturbance voltage signal and can be expressed as δC= [ δc ] 1 ,δc 2 ,…,δc N ](plus or minus), N is the number of actuators.
The open-loop influence function matrix pseudo-inverse method is easy to solve extreme values because no iterative process exists, has poor solving precision, and can cause that an actuator of a deformable mirror cannot work or is damaged; the closed loop voltage solving algorithm based on the influence function matrix, such as a gradient descent method and an iterative learning control method, has more stable solving process, but the solving precision is highly related to the calculating precision of the influence function matrix; the voltage search algorithm of the closed loop, such as the random parallel gradient descent method, without influencing the function matrix eliminates the influence of the influence function matrix on the solving precision of the control voltage, but the phenomenon that the solving precision is lowered due to the fact that the iteration process falls into a local optimal value possibly occurs.
In order to further improve the reconstruction precision of the deformable mirror to the target surface shape, the embodiment of the invention provides a high-precision and high-efficiency voltage iteration and search fusion algorithm, which can effectively solve the problem that the random parallel gradient descent method is easy to sink into a local optimal value to cause the reduction of the solution precision, and gradually eliminates the solution error of an influence function matrix in the process of voltage search optimization. A schematic diagram of the algorithm is shown in fig. 3, and the voltage iteration formula can be expressed as follows:
wherein t is a preset conversion threshold value, and when the iteration evaluation parameter e n When the transformation threshold is greater than or equal to the transformation threshold, an iterative algorithm based on an influence function matrix (the gradient descent method is shown in the formula (8), and other iterative algorithms based on the influence function matrix can be used), and the parameter e is evaluated by iteration n And after the voltage is smaller than the conversion threshold value, performing further voltage searching optimization by using a random parallel gradient descent method, and eliminating solving errors caused by influencing the errors of the function matrix.
Example 3
A voltage solving algorithm self-adaptive selection method based on the number of actuators covered by a target surface shape caliber is specifically described as follows:
the research finds that the calculation cost of some embodiments of the method is reduced by about 42% compared with a random parallel gradient descent method and is about 6-8 times of that of a gradient descent method or an iterative learning control method, and when the number of the action centers of the target surface caliber coverage actuator is small (less than or equal to 13), the calculation accuracy of some embodiments of the method is improved by less than (< 5%) compared with that of the gradient descent method or the iterative learning control method, so that other embodiments of the invention provide a self-adaptive selection method of a voltage solving algorithm based on the target surface caliber, as shown in fig. 4, a proper control voltage solving algorithm can be selected according to the relative size of the target surface caliber, and thus, the calculation cost and the calculation accuracy are both realized in the full caliber working range of the deformable mirror. The number of the target surface shape caliber covering actuators is defined to be a small-caliber surface shape when not more than 13, a medium-caliber surface shape when between 14 and 31, and a large-caliber surface shape when more than 31.
Verification example
For a large-caliber deformable mirror, when the focal length of an optical system where the deformable mirror is positioned is changed, the caliber of a target surface shape which is required to be reconstructed of the deformable mirror is also changed, in order to explore the control voltage solving precision of the various algorithms when the different calibers and different standard Zernike polynomial aberration term surface shapes are reconstructed, a large-caliber (100 mm) deformable mirror mathematical model base with 55 actuators is established by using the method of the embodiment of the invention, the control voltage solving precision (namely, the surface shape reconstructing precision) is shown to be smaller, the smaller the control voltage is, the more accurate the error between the reconstructed standard Zernike polynomial surface shape and the target surface shape is shown, and the smaller the error between the reconstructed standard Zernike polynomial surface shape and the target surface shape is shown to be solved by using a pseudo-inverse method, a gradient descent method, an iterative learning control method and a random parallel gradient descent method. And then gradually expanding the caliber of the target surface shape at intervals of 2mm, keeping the standard Zernike polynomial composition and the PV value of the target surface shape unchanged, and repeating the simulation reconstruction of the aberration surface shape until the caliber of the surface shape reaches 80mm (80% of the mirror surface caliber). The number of the target surface shape caliber covering actuators is defined to be small caliber when the number is not more than 13, medium caliber when the number is between 14 and 31, and large caliber when the number is more than 31.
The error distribution of reconstruction of different aberration profiles under different calibers by various existing algorithms is shown in figures 5a-5d, wherein the abscissa represents the standard zernike term number; the ordinate represents the caliber of the target surface shape, and the unit is mm; the gray values on the right indicate the size of the reconstruction error RMSE in μm, with darker colors indicating a larger reconstruction error. 5a-5d respectively show reconstruction errors of different calibers and different aberration profiles based on a pseudo-inverse method, a gradient descent method, an iterative learning control method and a random parallel gradient descent method of an influence function matrix, and can be seen that the reconstruction accuracy of the pseudo-inverse method on a small caliber and high order target profile is poor, so that the open loop control method is unstable, the gradient descent method and the iterative learning control are relatively close to each other in overall reconstruction errors, the reconstruction errors of the random parallel gradient descent method are relatively high when the 5 th item (defocus profile) and the 13 th item (spherical aberration profile) of a standard Zernike polynomial are reconstructed, and the errors of the reconstruction other aberration profiles are relatively stable, so that the reconstruction method is not suitable for reconstructing profiles with more defocus and spherical aberration components.
Calculating the average value of reconstruction errors RMSE of the existing various algorithms on the surface shapes of the same caliber and different aberration components to represent the surface shape reconstruction capability of the algorithm under the current caliber, as shown in figure 6, wherein the abscissa represents the caliber of the target surface shape and the unit is mm; the ordinate indicates the reconstruction error RMSE in μm. The statistical result shows that the solving precision of the pseudo-inverse method, the gradient descent method and the iterative learning control method based on the influence function matrix has the overall trend of firstly improving, then descending and then improving along with the increase of the caliber of the target surface shape, wherein the solving precision of the control voltage of the pseudo-inverse method when reconstructing the small-caliber surface shape is lower, and the precision of the pseudo-inverse method is gradually close to that of the gradient descent method and the iterative learning control method along with the increase of the caliber; the solving precision of the random parallel gradient descent method without influencing the function matrix is superior to that of the pseudo-inverse method in the small caliber, the solving precision is worst in the medium caliber, and the solving precision is optimal in the large caliber.
Calculating the average value of reconstruction errors RMSE of the current various algorithms on the surface shapes of different calibers and the same aberration components to represent the surface shape reconstruction capability of the algorithm on the current aberration components, as shown in figure 7, wherein the abscissa represents the standard Zernike term number; the ordinate indicates the reconstruction error RMSE in μm. As can be seen, as the number of standard zernike terms increases, the control voltage solving precision of the existing algorithm shows a decreasing trend, wherein the precision of the pseudo-inverse method based on the influence function matrix is worst when the higher-order aberration surface shape is reconstructed, and the random parallel gradient decreasing method without influence function matrix greatly improves the reconstruction error when the 5 th term (defocusing surface shape) and the 13 th term (spherical aberration surface shape) of the standard zernike polynomial are reconstructed, which means that the partial optimal value is extremely easy to be trapped when the two surface shapes are reconstructed, so that the voltage searching optimizing precision is reduced.
The algorithm provided by the embodiment of the invention is used for researching the reconstruction accuracy of target surface shapes with different calibers and different aberration components, and the statistical result is shown in figure 8, wherein the abscissa represents the standard Zernike term number; the ordinate represents the caliber of the target surface shape in mm. Compared to the prior art algorithm in fig. 5a-5d, it can be seen that the reconstruction errors of the proposed algorithm are all at a smaller level in the global scope.
The average value of the reconstruction errors RMSE of the surface shapes of the components of the same caliber and different aberrations is counted by the algorithm provided by the embodiment of the invention to represent the surface shape reconstruction capability of the algorithm under the current caliber, and the result is compared with the prior algorithm, as shown in figure 9, wherein the abscissa represents the caliber of the target surface shape and the unit is mm; the ordinate indicates the reconstruction error RMSE in μm. Meanwhile, the average value of the reconstruction errors RMSE of the current various algorithms on the surface shapes of different calibers and the same aberration components is counted to represent the reconstruction capability of the algorithm on the surface shape of the current aberration components, and the results are compared with the existing algorithm, and are shown in a figure 10, wherein the abscissa represents the standard Zernike term number; the ordinate indicates the reconstruction error RMSE in μm. As can be seen from FIGS. 9 and 10, compared with the existing algorithm, the calculation accuracy of the method of the embodiment of the invention is kept optimal under the condition of full caliber, and meanwhile, the best reconstruction accuracy is provided for the target surface shape of all aberration components, thereby proving the effectiveness and superiority of the new algorithm.
Comparing the calculation efficiency of the existing algorithm with that of the method according to the embodiment of the invention by taking the calculation cost of the open-loop influence function matrix pseudo-inverse method as a unit, wherein the statistical result is shown in figure 11, and the abscissa sequentially represents the pseudo-inverse method, the gradient descent method, the iterative learning control method, the random parallel gradient descent method and the method according to the embodiment of the invention based on the influence function matrix from left to right; the ordinate represents the computational cost (normalized to the pseudo-inverse). It can be seen that the computational cost of the method of the embodiments of the present invention is reduced by about 42% compared to the random parallel gradient descent method, which is about 6-8 times that of the gradient descent method or the iterative learning control method.
Through comparison and verification with the prior art, the embodiment of the invention solves the control voltage when the deformable mirror is used for surface shape reconstruction, and has the following four advantages:
1) High applicability. Compared with the existing algorithm, the control voltage solving algorithm provided by the embodiment of the invention has higher solving precision under the full caliber, the surface shape reconstruction error RMSE is obviously reduced, the capability of the large caliber deformable mirror can be fully exerted, and the applicability of the large caliber deformable mirror is improved.
2) High stability. The control voltage solving algorithm provided by the embodiment of the invention belongs to a closed-loop convergence algorithm, wherein the control voltages of all actuators are gradually increased in the solving process, the phenomenon that the actuators cannot work or even damage devices due to extreme values can not occur, the working stability of a deformable mirror can be improved to a certain extent, and the robustness of the whole optical system is further ensured.
3) High degree of freedom. The control voltage solving algorithm provided by the embodiment of the invention combines the advantages of two major algorithms, namely an iterative algorithm based on an influence function matrix and a voltage searching algorithm without influence function matrix, and comprises two voltage iteration and voltage searching modules, wherein each module is provided with a plurality of specific control algorithms which can be selected, so that a plurality of novel control voltage solving algorithms can be quickly derived, and the flexibility and the degree of freedom of control scheme design are ensured.
4) And the calculation precision and the calculation cost are both considered. According to the voltage solving algorithm self-adaptive selection method based on the target surface shape caliber, solving accuracy and solving cost are comprehensively considered in a full caliber range, the most suitable control voltage solving algorithm can be selected in a self-adaptive mode according to the relative size of the target surface shape caliber, and the method has high application value.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may 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, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may 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, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing is a further detailed description of the invention in connection with specific/preferred embodiments, and it is not intended that the invention be limited to such description. It will be apparent to those skilled in the art that several alternatives or modifications can be made to the described embodiments without departing from the spirit of the invention, and these alternatives or modifications should be considered to be within the scope of the invention. In the description of the present specification, reference to the terms "one embodiment," "some embodiments," "preferred embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Those skilled in the art may combine and combine the features of the different embodiments or examples described in this specification and of the different embodiments or examples without contradiction. Although embodiments of the present invention and their advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the scope of the invention as defined by the appended claims.
Claims (10)
1. The full-caliber high-precision deformable mirror control method is characterized by comprising the following steps of:
s1, acquiring an initial voltage;
s2, performing voltage iteration and voltage search on the initial voltage based on a voltage iteration and search fusion algorithm to obtain a target voltage;
s3, inputting the calculated target voltage into a digital simulation model so as to control the deformable mirror.
In step S2, the voltage iterative and search fusion algorithm includes: defining an iteration evaluation parameter, setting a conversion threshold, and calculating through an iteration algorithm affecting a function matrix when the iteration evaluation parameter is greater than or equal to the conversion threshold; when the iteration evaluation parameter is smaller than the conversion threshold value, performing voltage search optimization through a random parallel gradient descent method, and eliminating solving errors caused by influencing the self errors of the function matrix; the iterative evaluation parameters are represented by the deviation of standard Zernike coefficient vectors of the target surface shape and the current mirror surface shape.
2. The method for controlling a full-caliber high-precision deformable mirror according to claim 1, wherein in step S2, the formula of the voltage iteration and search fusion algorithm is as follows:
wherein alpha is a gain coefficient, the value affects the iteration speed and the stability of the solving process, C n C is the current control voltage vector n+1 E is the control voltage vector after the next iteration n For iterative evaluation parameters, GT represents the transposed matrix of the influence function matrix G, γ is the gain coefficient, E is the evaluation function, δc is the randomly added bidirectional disturbance voltage signal, and t is the conversion threshold.
3. The method for controlling a full-caliber high-precision deformable mirror according to claim 2, wherein the voltage iteration and search fusion algorithm comprises an influence function matrix iteration algorithm C n+1 ＝C n +αG T e n And the function matrix search algorithm C is not influenced n+1 ＝C n +γ(E + -E - )δC。
4. The method for controlling a full-caliber high-precision deformable mirror according to claim 3, wherein the step S2 further comprises:
when iterating the evaluation parameter e n When the transformation threshold value is greater than or equal to the transformation threshold value, approximating the target voltage based on the influence function matrix iterative algorithm to locate a proper searching starting point;
when iterating the evaluation parameter e n And when the voltage is smaller than the conversion threshold value, performing voltage search by using a closed-loop voltage search algorithm without influencing the function matrix to obtain the target voltage.
5. The method according to claim 1, wherein in step S3, the digital simulation model is a continuous deformable mirror digital simulation model.
6. The method for controlling a full-caliber high-precision deformable mirror according to claim 5, wherein the continuous deformable mirror digital simulation model is established by the following steps:
f1, establishing a finite element simulation model of a deformable mirror, and obtaining a coupling coefficient omega, a Gaussian index alpha and deformation A of an actuator under unit voltage;
f2, in the digital simulation platform, using the formulaEstablishing expressions of all actuator influence functions under a preset arrangement scheme on the basis, and representing the mirror surface shape under the action of multiple actuators through linear superposition of the influence functions; where i denotes the number of the actuator, a denotes the magnitude of the gaussian function amplitude, exp denotes an exponential function based on a natural constant e, ln denotes a logarithmic function, ω denotes the coupling coefficient between the actuators, α denotes the gaussian index, r and d denote the point-to-actuator center distance on the mirror surface and the actuator distribution pitch, respectively, B denotes the amplitude of the gaussian function used for correction, and β is the radial adjustment width.
7. The method for controlling a full-caliber high-precision deformable mirror according to claim 5, wherein in step S3, the continuous deformable mirror digital simulation model outputs three-dimensional point cloud data after the deformable mirror responds to the input control voltage, and the three-dimensional point cloud data is in a mirror surface shape.
8. The method of claim 1, wherein step S2 further comprises selecting a control voltage solving algorithm according to the relative size of the target surface aperture.
9. The method of claim 8, wherein the target profile is a small-profile when the number of the target profile aperture overlay actuators does not exceed a first value; the target surface shape caliber covering actuator number is a medium caliber surface shape when the target surface shape caliber covering actuator number is between a first value and a second value; and the target surface shape is a large-caliber surface shape when the number of the target surface shape caliber covering actuators is larger than a second value.
10. A full bore high precision deformable mirror control device comprising a processor and a memory, the memory having stored therein a computer program executable by the processor to implement the method of any of claims 1-9.
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