CN116184797A - A robust control method and system based on kinoform coding - Google Patents
A robust control method and system based on kinoform coding Download PDFInfo
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
- G03H1/04—Processes or apparatus for producing holograms
- G03H1/08—Synthesising holograms, i.e. holograms synthesized from objects or objects from holograms
- G03H1/0841—Encoding method mapping the synthesized field into a restricted set of values representative of the modulator parameters, e.g. detour phase coding
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- G—PHYSICS
- G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
- G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
- G03H1/04—Processes or apparatus for producing holograms
- G03H1/08—Synthesising holograms, i.e. holograms synthesized from objects or objects from holograms
- G03H1/0841—Encoding method mapping the synthesized field into a restricted set of values representative of the modulator parameters, e.g. detour phase coding
- G03H2001/085—Kinoform, i.e. phase only encoding wherein the computed field is processed into a distribution of phase differences
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Abstract
The invention discloses a robust control method and a robust control system based on a kinoform code, wherein the method comprises the steps of constructing a control system according to an incident light field, intensity distribution and corresponding phase distribution; generating an attraction domain by adopting a robust model predictive control algorithm and soft constraint based on a control system, and constructing a data set based on the attraction domain; expanding the data set according to the data set and based on a data density segmentation method; training a symmetric neural network according to the expanded data set, and determining a phase distribution prediction model; determining current phase distribution by adopting a phase distribution prediction model according to the current incident light field and intensity distribution; generating a phase hologram according to the current phase distribution can obtain a phase hologram with high precision.
Description
Technical Field
The invention relates to the field of robust control of optical systems, in particular to a robust control method and a robust control system based on kinoform coding.
Background
Computing holograms enables the recording of the amplitude and phase of the light wave field. For recorded objects, if the energy spread is made uniform by the random phase mask of the object itself, the mode recorded by the corresponding computed hologram is relatively unimportant, so that only the phase needs to be extracted, generating gray fringes. The encoding of the kinoform is based on one assumption: the phase distribution of the hologram plane carries most of the information and the amplitude is negligible. Such a hologram function can be expressed as:
where j is an imaginary unit, (x, y) is the light field sampling point coordinates, +.>
Is the corresponding phase; when the hologram is used for encoding the object wave, if the calculated object is a diffuse reflector, the phase distribution of all object points is relatively independent and random, and then the hologram function can accurately represent the object wave field.
The computational problem of the kinoform is the process of knowing the intensity distribution of the incident light field and the diffraction pattern and solving the phase distribution of the complex amplitude transmission coefficient. The existence, uniqueness and other conclusions of such a problem have not been demonstrated yet, but can only be translated into a numerical optimization problem and an optimal solution can be found under a certain norm.
Robust model predictive control (robustMPC) is a rolling optimization technology considering system uncertainty, can solve dynamic optimization problems on line, ensures the closed-loop stability of an uncertainty system, and can be applied to an optical system with uncertainty. In each optimization process, the robust MPC mainly considers the worst-case minimum problem, which greatly increases the robustness of problem solving. However, since the on-line solution of the optimization problem is to be obtained, a lot of time is required to apply the technique, and this robust optimization scheme weakens the advantages of the calculation of the kinoform due to the high accuracy of the optimization solution. Therefore, we propose a robust control method of symmetrical neural network for kinoform coding.
Therefore, how to obtain a high-precision phase hologram is still a problem to be solved.
Disclosure of Invention
The invention aims to provide a robust control method and a robust control system based on kinoform coding, which can obtain a high-precision phase hologram.
In order to achieve the above object, the present invention provides the following solutions:
a robust control method based on kinoform encoding, comprising:
constructing a control system according to the incident light field, the intensity distribution and the corresponding phase distribution;
generating an attraction domain by adopting a robust model predictive control algorithm and soft constraint based on a control system, and constructing a data set based on the attraction domain;
expanding the data set according to the data set and based on a data density segmentation method;
training a symmetric neural network according to the expanded data set, and determining a phase distribution prediction model;
determining current phase distribution by adopting a phase distribution prediction model according to the current incident light field and intensity distribution; and generating a kinoform according to the current phase distribution.
Optionally, the construction of the control system according to the incident light field and the intensity distribution and the corresponding phase distribution specifically includes the following formulas:
y(k)＝[0 1]x(k)+0.1；
wherein x (k) represents an incident light field of k sampling time, which is a control system state, x (k+1) represents an incident light field of k+1 sampling time, u (k) represents a phase distribution, which is a control system input, ω is a random number, ω e (0, 1), and a (k) and B (k) are system models of different sampling moments.
Optionally, the control system generates an attraction domain by adopting a robust model predictive control algorithm and soft constraint, and constructs a data set based on the attraction domain, and specifically comprises the following formula:
F(k)＝YQ -1 ；
wherein F (k) is the attraction domain q=γp (k) -1 P (k) is a positive weighting matrix, and gamma is a number greater than 0.
Optionally, the expanding the data set according to the data set and based on the segmentation method of the data density specifically includes:
defining a data density as a number of samples per unit area;
determining the data density according to the sampling step length;
and sampling the data set according to the data density to obtain an expanded data set.
A robust control system based on kinoform encoding, comprising:
the control system construction module is used for constructing a control system according to the incident light field, the intensity distribution and the corresponding phase distribution;
the data set construction module is used for generating an attraction domain by adopting a robust model predictive control algorithm and soft constraint based on the control system and constructing a data set based on the attraction domain;
the data set expansion module is used for expanding the data set according to the data set and based on a data density segmentation method;
the phase distribution prediction model determining module is used for training the symmetrical neural network according to the expanded data set to determine a phase distribution prediction model;
the phase diagram generation module is used for determining current phase distribution by adopting a phase distribution prediction model according to the current incident light field and the intensity distribution; and generating a kinoform according to the current phase distribution.
A robust control system based on kinoform encoding, comprising: at least one processor, at least one memory, and computer program instructions stored in the memory, which when executed by the processor, implement the method.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
according to the robust control method and system based on the kinoform coding, based on the control system, the robust model predictive control algorithm and the soft constraint are adopted to generate the attraction domain, and the data set is constructed based on the attraction domain, so that the environmental interference is realized; and soft constraint is introduced, so that the feasibility of the optimization problem is improved. The data samples are ensured to be distributed uniformly in different data sets by a data density segmentation method. According to the extended data set, the symmetrical neural network is trained, a phase distribution prediction model is determined, and further phase distribution is accurately determined, so that high precision of the phase hologram is guaranteed.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a robust control method based on the kinoform coding provided by the invention;
FIG. 2 is a schematic drawing of an attraction domain;
FIG. 3 is a schematic diagram of a symmetric neural network;
FIG. 4 is a schematic diagram of a control principle of a symmetric neural network;
fig. 5 is a schematic diagram of a symmetric neural network training process.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a robust control method and a robust control system based on kinoform coding, which can obtain a high-precision phase hologram.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
As shown in fig. 1, the robust control method based on the kinoform coding provided by the invention comprises the following steps:
s101, constructing a control system according to an incident light field, intensity distribution and corresponding phase distribution;
s101 specifically includes the following formula:
the process of converting an incident light field into a kinoform is regarded as a system to be controlled, the current light field and the intensity distribution are in a system state, and the phase distribution is the system input;
y(k)＝[01]x(k)+0.1(1.2)
wherein x (k) represents the incident light field of k sampling time, which is the control system state, x (k+1) represents the incident light field of k+1 sampling time, u (k) represents the phase distribution, which is the control system input, and A (k) and B (k) are the system models of different sampling moments.
S102, generating an attraction domain by adopting a robust model predictive control algorithm and soft constraint based on a control system, and constructing a data set based on the attraction domain; as shown in fig. 2, the original attraction domain is extended to the rule area, and if the mapping relation between the state and the control action in the attraction domain can be learned, a display control rate can be obtained, so as to avoid online solving of the optimization problem.
Considering model uncertainty, at each sampling time, the optimization problem that should be considered is as follows:
consider that the closed loop system is stable, i.e.:
wherein,,
and->
Representing constraints on control actions and system states, respectively; ψ is a transformation matrix; x (k+i) =x (k+i|k+i), x (k+i|k) representing the predicted state at the kth sampling instant for the k+i instant; Ω=co { [ a 1 B 1 ],[A 2 B 2 ],…,[A G B G ]And G is the number of multi-packet top points. . Gamma > 0 represents the robust performance index function. Definition q=γp (k) -1 And F (k) =YQ -1 According to the lyapunov stability criterion, the following linear matrix inequality can be obtained for the above equation:
s∈{1,…,q},g∈{1,…,G}
wherein q=γp (k) -1 ，F(k)＝YQ -1 The method comprises the steps of carrying out a first treatment on the surface of the I is an identity matrix; [ A ] g B g ]Representing the vertices of a multipack system, the j(s) th diagonal element of Z (Γ) is represented as Z if and only if Q > 0, Y=FQ and γ are present jj (Γ ss )；β j And beta s Is a correlation factor. Thus, equation (1.3) can be converted into the constraint-containing optimization problem as follows:
s103, expanding the data set according to the data set and the segmentation method based on the data density; training samples are made up of system state and control inputs, obtained by sampling in the suction domain. In principle, as long as the sampling step is sufficiently small. A complete set of system states can be generated from the attraction domain to generate a complete set of system states from the attraction domain. However, periodic sampling can result in a relatively single data set. And the result of dividing it into training and testing sets is that the data distribution is inconsistent between the different data sets. In addition, shuffling the data sets and destroying the original data distribution pattern. Making accurate approximation of the training model more challenging. Specifically, in some cases, taking too small a sampling step within a fixed range and taking too small a sampling step within a fixed range can result in a lack of diversity in the data. Resulting in limited variation between training and testing sets. This increases the risk of model overfitting during training. In order to solve the problems occurring in the construction of data sets, a segmentation method (DDSD) based on data density is proposed.
S103 specifically comprises the following steps:
defining a data density as a number of samples per unit area;
determining the data density according to the sampling step length;
and sampling the data set according to the data density to obtain an expanded data set.
Let the sampling step length be s respectively 1 Sum s 2 The data density is:
setting a reference data density as ρ o ＝10 8 And uses this as a reference to define a sample set
Phase of (2)Density is measured. For ease of expression and description, the data density of a data set is expressed as a relative value with respect to a predetermined reference. This allows the data density discussed later to be understood with respect to this reference.
The extended dataset is composed of three subsets: training set
Verification set->
And test set->
Furthermore, it is sufficient that the selected data density coincides with the numerical accuracy of the state. The data set generated based on this data density is relatively small compared to the total number of samples.
S104, training a symmetrical neural network according to the expanded data set, and determining a phase distribution prediction model;
as shown in fig. 3 and 4, n= [ N ] 1 ,…,n l ,…,n L ]To represent a symmetric neural network, where n l Representing the number of neurons of layer i; w= [ W ] 1 ,…,W l ,…,W L ]For a weight matrix sequence of the network, W l Is a weight matrix connecting layer l and layer l-1, which is in the form:
in the method, in the process of the invention,
is the weight connecting the c-th neuron of layer l and the r-th neuron of layer l-1; the network bias is b= [ B ] 1 ,...,b l ,...,b L ]Wherein->
Is the bias of layer i. W and B form network parametersθ, the objective function of the network can thus be expressed as:
wherein p represents a sample number, m s The total number of samples in the dataset;
is the predicted value of the network for the p-th sample, y (p) Is the tag value of the p-th sample. In the method, the sampling momentum gradient descent algorithm updates network parameters in the following specific updating mode: />
W l :＝W l -αv dWl
bl:＝bl-αv dbl
Wherein, beta is a super parameter for controlling weighted average, and alpha represents learning law; parameters (parameters)
And->
Respectively represent the first layer->
And->
Momentum of (c) is provided.
A deep neural network with 10 hidden layers (3,10,25,80,400,400,80,25,10,3) is constructed, wherein the network input is a system state, and the network output is a control function;
to obtain high performance network parameters, the neural network is trained using three phases. In one stage, we have adopted a ten-fold cross-validation experiment, while obtaining penalty factors for the regularization term in the two-stage training process. In two phases, a measurement function is proposed to evaluate the performance of the network:
wherein x (p) represents a sample to be evaluated, F DNN (x (p)) is a predicted value of DNN, and F (x (p)) is a calculated value of a robust algorithm; a solution with η being robust MPC may allow for input perturbation. If it is
Then the specific algorithm effect is shown in fig. 5, representing that the sample being evaluated meets the robust constraint requirement, the specific algorithm is as follows:
s105, determining current phase distribution by adopting a phase distribution prediction model according to the current incident light field and intensity distribution; and generating a kinoform according to the current phase distribution.
As another specific embodiment, the present invention further provides a robust control system based on kinoform encoding, including:
the control system construction module is used for constructing a control system according to the incident light field, the intensity distribution and the corresponding phase distribution;
the data set construction module is used for generating an attraction domain by adopting a robust model predictive control algorithm and soft constraint based on the control system and constructing a data set based on the attraction domain;
the data set expansion module is used for expanding the data set according to the data set and based on a data density segmentation method;
the phase distribution prediction model determining module is used for training the symmetrical neural network according to the expanded data set to determine a phase distribution prediction model;
the phase diagram generation module is used for determining current phase distribution by adopting a phase distribution prediction model according to the current incident light field and the intensity distribution; and generating a kinoform according to the current phase distribution.
In order to execute the corresponding method of the above embodiment to achieve the corresponding functions and technical effects, the present invention further provides a robust control system based on the kinoform encoding, which is characterized by comprising: at least one processor, at least one memory, and computer program instructions stored in the memory, which when executed by the processor, implement the method.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (6)
1. A robust control method based on kinoform encoding, comprising:
constructing a control system according to the incident light field, the intensity distribution and the corresponding phase distribution;
generating an attraction domain by adopting a robust model predictive control algorithm and soft constraint based on a control system, and constructing a data set based on the attraction domain;
expanding the data set according to the data set and based on a data density segmentation method;
training a symmetric neural network according to the expanded data set, and determining a phase distribution prediction model;
determining current phase distribution by adopting a phase distribution prediction model according to the current incident light field and intensity distribution; and generating a kinoform according to the current phase distribution.
2. The robust control method based on the kinoform coding according to claim 1, wherein the constructing a control system according to the incident light field and the intensity distribution and the corresponding phase distribution specifically comprises the following formula:
y(k)＝[0 1]x(k)+0.1；
wherein x (k) represents an incident light field of k sampling time, which is a control system state, x (k+1) represents an incident light field of k+1 sampling time, u (k) represents a phase distribution, which is a control system input, ω is a random number, ω e (0, 1), and a (k) and B (k) are system models of different sampling moments.
3. The robust control method based on the kinoform coding according to claim 2, wherein the robust model predictive control algorithm and soft constraint are adopted to generate an attraction domain based on the control system, and a data set is constructed based on the attraction domain, and the method specifically comprises the following formula:
F(k)＝YQ -1 ；
wherein F (k) is the attraction domain q=γp (k) -1 P (k) is a positive weighting matrix, and gamma is a number greater than 0.
4. The robust control method based on the kinoform coding according to claim 1, wherein the expanding the data set according to the data set based on the segmentation method of the data density specifically comprises:
defining a data density as a number of samples per unit area;
determining the data density according to the sampling step length;
and sampling the data set according to the data density to obtain an expanded data set.
5. A robust control system based on kinoform encoding, comprising:
the control system construction module is used for constructing a control system according to the incident light field, the intensity distribution and the corresponding phase distribution;
the data set construction module is used for generating an attraction domain by adopting a robust model predictive control algorithm and soft constraint based on the control system and constructing a data set based on the attraction domain;
the data set expansion module is used for expanding the data set according to the data set and based on a data density segmentation method;
the phase distribution prediction model determining module is used for training the symmetrical neural network according to the expanded data set to determine a phase distribution prediction model;
the phase diagram generation module is used for determining current phase distribution by adopting a phase distribution prediction model according to the current incident light field and the intensity distribution; and generating a kinoform according to the current phase distribution.
6. A robust control system based on kinoform encoding, comprising: at least one processor, at least one memory, and computer program instructions stored in the memory, which when executed by the processor, implement the method of any one of claims 1-4.
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