CN111652372B - Wavefront restoration method and system based on diffractive optical neural network - Google Patents
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Abstract
The invention discloses a wavefront restoration method and a system based on a diffractive optical neural network. The method comprises the following steps: 1) selecting or constructing a data set consisting of wave front-coefficient data pairs containing the first N-order Zernikes; 2) constructing an optical neural network model, and fitting a data set to obtain two-dimensional phase distribution of each phase modulation plate in the model; determining the thickness of the corresponding phase modulation plate according to the two-dimensional phase distribution of each phase modulation plate, the wavelength of the light wave to be detected, and the refractive index and the transmittance of the required phase modulation plate; 3) manufacturing corresponding phase modulation plates according to the thickness of each phase modulation plate determined in the step 2), respectively placing the phase modulation plates behind the wavefront to be measured according to the positions in the optical neural network model, modulating the complex amplitude of the optical wave, then detecting the light intensity distribution passing through each phase modulation plate, and performing wavefront restoration according to the light intensity distribution. The invention avoids the photoelectric conversion and the dependence on an electronic computer, and has the advantages of low energy consumption, high speed and the like.
Description
Technical Field
The present invention relates to a wavefront reconstruction method, and more particularly, to a wavefront reconstruction method and system based on a diffractive optical neural network.
Background
Adaptive Optics (AO) aims at correcting a wavefront (hereinafter, "wavefront" and "phase" are not distinguished) causing distortion of an optical system, thereby improving the imaging capability of the optical system, and is widely used in the fields of laser systems, astronomical observation, medical imaging and the like. If the technical route of wavefront detection is adopted, the distorted wavefront needs to be detected and then corrected.
Because the phase of the light wave cannot be directly detected, an optical detection system is usually constructed to detect the light intensity, and then a certain wave front recovery algorithm is used for inverting the wave front. The wave-front restoration algorithm has two technical routes at present: one is that modeling is firstly carried out on the forward imaging process of the optical system, and then an optimization algorithm is used to solve the inverse problem by taking the distorted wavefront as a parameter; the other method is to train a neural network on an electronic computer, fit a data set formed by a pair of data of wavefront-facula and then use the neural network as a recovery algorithm.
Diffractive optical neural networks (D2NN) have proven useful for machine learning tasks of a certain complexity, which encode an input into a light beam of a certain wavelength band, diffract layer by layer, and output task labels.
The existing wavefront restoration needs to perform photoelectric conversion (namely photoelectric detection) firstly, and then data is input into an electronic computer for wavefront restoration, so that the problems of high energy consumption, low speed and phase information loss in the middle detection link exist.
Disclosure of Invention
In view of the technical problems in the prior art, the present invention aims to provide a wavefront reconstruction method and system based on a diffractive optical neural network. The invention directly receives the wavefront to be measured as input and outputs the wavefront restoration result represented by the Zernike coefficient, thereby avoiding the photoelectric conversion and the dependence on an electronic computer and having the advantages of low energy consumption, high speed and the like.
The technical scheme of the invention is as follows:
a wavefront restoration method based on a diffractive optical neural network comprises the following steps:
1) selecting or constructing a data set consisting of wave front-coefficient data pairs containing the front N-order Zernike;
2) constructing an optical neural network model, and fitting a data set to obtain two-dimensional phase distribution of each phase modulation plate in the optical neural network model; determining the thickness of the corresponding phase modulation plate according to the two-dimensional phase distribution of each phase modulation plate, the wavelength of the light wave to be detected, and the refractive index and the transmittance of the required phase modulation plate;
3) manufacturing corresponding phase modulation boards according to the thicknesses of the phase modulation boards determined in the step 2), respectively placing the phase modulation boards behind the wave front to be measured according to the positions in the optical neural network model, modulating the complex amplitude of the optical wave, and then detecting the light intensity distribution passing through each phase modulation board; and then wavefront restoration is performed based on the detected light intensity distribution.
Further, in step 3), dividing a detection surface of the detector into different regions according to the pixel and the Zernike orders of the detector, wherein the intensity of each region represents a Zernike coefficient of a corresponding order; then reading out the total energy of the light intensity of each region of the detector to recover the wave front Zernike coefficient, and synthesizing the wave front according to the recovered wave front Zernike coefficient to finish wave front recovery.
Further, the thickness Δ of the phase modulation plate is λ Φ/2 pi (n-1); wherein n is the refractive index of the phase modulation plate, phi is the phase value of the phase modulation plate obtained by training, and lambda is the optical wavelength.
Further, under a deep learning framework, the optical neural network model is constructed, the size and the interval of each phase modulation plate are set, and the phase distribution of the phase plates is used as a parameter to train the data set; and adjusting the phase value of the phase modulation plate according to the comparison result to make the loss function converge to the minimum, and finally obtaining the two-dimensional phase distribution of each phase modulation plate.
Further, the method for generating the data set comprises the following steps: the wavefront W is decomposed into zernike polynomials and then several zernike orders within the first N zernike orders are randomly selected to generate a mixed wavefront, thereby generating a data set of multiple wavefront-coefficient data pairs.
A wave front based on diffraction optics nerve network recovers the system, characterized by that, include a diffraction optics nerve network and a detector formed by a plurality of phase modulation boards; determining two-dimensional phase distribution of each phase modulation plate according to a trained optical neural network model, and then determining the thickness of the corresponding phase modulation plate according to the two-dimensional phase distribution of each phase modulation plate, the wavelength of the light wave to be detected, and the refractive index and the transmittance of the required phase modulation plate; training the optical neural network model by using a data set consisting of wave front-coefficient data pairs containing front N-order Zernikes to obtain two-dimensional phase distribution of each phase modulation plate in the optical neural network model;
the diffraction optical neural network is placed behind the wavefront to be measured and is used for modulating the complex amplitude distribution of the incident wavefront;
the detector is placed behind the diffraction optical neural network and used for receiving the light intensity distribution passing through each phase modulation plate; and then wavefront restoration is performed according to the detected light intensity distribution.
Furthermore, a focusing lens is arranged between the diffractive optical neural network and the incident wavefront to be measured and is used for converging the wavefront to be measured and then irradiating the wavefront to be measured into the diffractive optical neural network; and a focusing lens is arranged between the diffraction optical neural network and the detector and is used for converging the light beams passing through the diffraction optical neural network to the detection surface of the detector.
The optical neural network is composed of phase modulation plates, each phase modulation plate is a flat plate with two-dimensional thickness distribution designed for a specific waveband, the light wave to be detected passes through the M phase modulation plates, no energy is consumed in the whole process, and finally the light intensity distribution is detected by a detector.
Due to arbitrary distortion the wavefront W can be decomposed into Zernike polynomials
Wherein Z is a Zernike basis function, a represents the corresponding Zernike coefficient, i represents the Zernike order, and r, θ form a polar coordinate system.
According to the pixel and the Zernike order of the detector, the detection surface of the detector is divided into different areas, and the intensity of each area represents the Zernike coefficient of the corresponding order.
First, a data set comprising pairs of wavefront-nth order coefficient data of the first nth order zernike is constructed as required by the particular application.
Secondly, an optical neural network model is constructed under a deep learning framework such as Tensorflow, a data set is fitted, two-dimensional phase distribution of each phase modulation plate is finally obtained, the two-dimensional phase distribution is converted into the thickness of each phase modulation plate according to the refractive index, and the phase plate material is selected according to the wavelength, the refractive index and the transmittance. If the refractive index of the phase plate is n, the phase value is trained to be phi, the optical wavelength is lambda, and the thickness delta is equal to lambda phi/2 pi (n-1).
And finally, manufacturing a phase modulation plate, placing the phase modulation plate behind the wavefront to be detected, and detecting the light intensity distribution passing through the phase modulation plate. And reading out a reset wavefront Zernike coefficient according to the total energy of the light intensity of each region, and synthesizing the wavefront by the coefficient.
The invention has the beneficial effects that:
the fitting capability of the diffraction optical neural network is utilized, forward motion is calculated at the same time, the wavefront to be measured is directly received as input, and a wavefront restoration result represented by a Zernike coefficient is output, so that photoelectric conversion and dependence on an electronic computer are avoided, the energy consumption is low, the speed is high, and the system is simplified.
Drawings
FIG. 1 is a schematic diagram of a single-order example of a wavefront reconstruction system based on a diffractive optical neural network;
FIG. 2 is a schematic diagram of a multi-order example of a wavefront reconstruction system based on a diffractive optical neural network;
fig. 3 is a schematic diagram of detector surface area division.
Detailed Description
The invention provides a wavefront restoration method based on a diffractive optical neural network, which is described in the following with reference to the accompanying drawings and embodiments:
1. detailed description of the preferred embodiment 1
The system diagram of embodiment 1 is shown in fig. 1, and a detailed implementation process of the technical solution of embodiment 1 is described with reference to fig. 1.
First, the wavefront W is decomposed into Zernike polynomials, within the first 10 Zernike orders, 3 Zernike orders are randomly selected, from
A mixed wavefront is generated which forms a data pair with the corresponding coefficient, and the above process is repeated to generate a data set of about 20000 wavefront-coefficient data pairs.
Secondly, an optical neural network model is constructed under a deep learning framework such as Tensorflow, the size and the interval of the phase plate are set, and the phase distribution of the phase plate is used as a parameter to train a data set. And taking the phase in the data set as the input of the neural network to obtain corresponding output, comparing the output with the N-order Zernike coefficient in the data set by using a loss function, and continuously adjusting the phase value of the phase plate by using an optimization algorithm to ensure that the loss function is converged to the minimum, thereby obtaining the trained phase distribution of the phase plate. The training process may use the Tensorflow's mature tool. And finally, converting the two-dimensional phase distribution of each phase plate into the thickness of the phase plate according to the refractive index.
And finally, manufacturing a phase plate, respectively placing the phase plate behind the wavefront to be detected according to the position in the optical neural network model, and detecting the light intensity distribution passing through the phase plate. The reconstructed wavefront Zernike coefficients are read from the total intensity of each region and the wavefront is synthesized from the coefficients.
2. Specific example 2
The system diagram of embodiment 2 is shown in fig. 2, and a detailed implementation process of the technical solution of embodiment 2 is described with reference to fig. 2.
First, a mixed wavefront is generated by randomly selecting 3-order zernikes within the first 10-order zernikes, thereby generating a data set of about 20000 wavefront-coefficient data pairs.
In order to overcome the situation that the energy distribution in the light wave propagation process exceeds the size of the phase plate, which may occur in the multi-order phase, focusing mirrors are arranged in front and at the back for collecting the light waves.
Secondly, an optical neural network model is constructed under a deep learning framework such as Tensorflow, a data set is trained, two-dimensional phase distribution of each phase plate is finally obtained, and the two-dimensional phase distribution is converted into the thickness of the phase plate according to the refractive index.
And finally, manufacturing a phase plate, placing the phase plate behind the wavefront to be measured, modulating the complex amplitude of the optical wave, and finally detecting the light intensity distribution passing through the phase plate.
Reading the restored wavefront Zernike coefficients from the total intensity of each region
The wavefronts are synthesized.
The invention has not been described in detail and is part of the common general knowledge of a person skilled in the art.
Claims (9)
1. A wavefront restoration method based on a diffractive optical neural network comprises the following steps:
1) selecting or constructing a data set consisting of wave front-coefficient data pairs containing the front N-order Zernike;
2) constructing an optical neural network model, and fitting a data set to obtain two-dimensional phase distribution of each phase modulation plate in the optical neural network model; determining the thickness of the corresponding phase modulation plate according to the two-dimensional phase distribution of each phase modulation plate, the wavelength of the light wave to be detected, and the refractive index and the transmittance of the required phase modulation plate;
3) manufacturing corresponding phase modulation plates according to the thickness of each phase modulation plate determined in the step 2), respectively placing the phase modulation plates after the wavefront to be measured according to the position in the optical neural network model, modulating the complex amplitude of the optical wave, and then detecting the light intensity distribution after passing through each phase modulation plate; and then wavefront restoration is performed according to the detected light intensity distribution.
2. The method according to claim 1, wherein in step 3), the detection surface of the detector is divided into different regions according to the pixel and the Zernike order of the detector, and the intensity of each region represents the corresponding Zernike coefficient; then reading out the total energy of the light intensity of each region of the detector to recover the wave front Zernike coefficient, and synthesizing the wave front according to the recovered wave front Zernike coefficient to finish wave front recovery.
3. A method as claimed in claim 1 or 2, characterized in that the thickness of the phase modulation plate Δ ═ λ Φ/2 pi (n-1); wherein n is the refractive index of the phase modulation plate, phi is the phase value of the phase modulation plate obtained by training, and lambda is the optical wavelength.
4. The method of claim 1, wherein the optical neural network model is constructed in a deep learning framework, the size and spacing of each phase modulation plate are set, and the data set is trained using phase plate phase distribution as a parameter; and adjusting the phase value of the phase modulation plate according to the comparison result to make the loss function converge to the minimum, and finally obtaining the two-dimensional phase distribution of each phase modulation plate.
5. The method of claim 1, wherein the data set is generated by: the wavefront W is decomposed into zernike polynomials and then several orders of zernike are randomly selected within the first N order of zernike to generate a mixed wavefront, thereby generating a data set of a plurality of wavefront-coefficient data pairs.
6. A wave front recovery system based on a diffraction optical neural network is characterized by comprising a diffraction optical neural network and a detector, wherein the diffraction optical neural network is composed of a plurality of phase modulation plates; determining two-dimensional phase distribution of each phase modulation plate according to a trained optical neural network model, and then determining the thickness of the corresponding phase modulation plate according to the two-dimensional phase distribution of each phase modulation plate, the wavelength of the light wave to be detected, and the refractive index and the transmittance of the required phase modulation plate; training the optical neural network model by using a data set consisting of wave front-coefficient data pairs containing first N-order Zernikes to obtain two-dimensional phase distribution of each phase modulation plate in the optical neural network model;
the diffraction optical neural network is placed behind the wavefront to be measured and used for modulating the complex amplitude distribution of the incident wavefront;
the detector is placed behind the diffraction optical neural network and used for receiving the light intensity distribution passing through each phase modulation plate; and then wavefront restoration is performed according to the detected light intensity distribution.
7. The system of claim 6, wherein the detector is divided into different regions on the detector plane based on detector pixel and Zernike order, each region intensity representing a respective order Zernike coefficient; then reading out the total energy of the light intensity of each region of the detector to recover the wave front Zernike coefficient, and synthesizing the wave front according to the recovered wave front Zernike coefficient to finish wave front recovery.
8. The system of claim 6, wherein the thickness of the phase modulating plate Δ ═ λ Φ/2 pi (n-1); wherein n is the refractive index of the phase modulation plate, phi is the phase value of the phase modulation plate obtained by training, and lambda is the optical wavelength.
9. The system as claimed in claim 6, wherein a focusing lens is disposed between the diffractive optic neural network and the incident wavefront to be measured, for converging the wavefront to be measured and then making the converged wavefront incident on the diffractive optic neural network; and a focusing lens is arranged between the diffraction optical neural network and the detector and is used for converging the light beams passing through the diffraction optical neural network to the detection surface of the detector.
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