CN115097708B - Holographic display resolution expanding method based on optical diffraction neural network - Google Patents
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Abstract
The invention provides a holographic display resolution expanding method based on an optical diffraction neural network. The method expands the resolution of the holographic reconstruction image through the optical diffraction neural network in the holographic reconstruction process. By using the optical diffraction neural network on the low-resolution hologram reconstruction path, the resolution of the diffraction layer of the optical diffraction neural network is the target resolution, resampling and modulating the light fields with different distances in the hologram reconstruction are carried out, and finally the resolution of the reconstructed image is improved on the premise of ensuring the quality of the hologram reconstruction. The method can effectively expand the resolution of the holographic reconstructed image to generate the calculation time of the low-resolution hologram and obtain the display effect of the high-resolution hologram, and has the characteristics of high calculation speed and low power consumption.
Description
Technical Field
The invention relates to the technical field of optics and machine learning, in particular to a method for expanding holographic display resolution.
Background
Holography, which is capable of storing the amplitude and phase of light and reconstructing the entire information of the target light field, has been widely studied in many fields of application. In holographic display, a computer is used to generate a high-resolution hologram, which requires a large amount of data to be processed, and the generation of the high-resolution hologram is time-consuming, so that the speed of generating the hologram is always a hot spot for research in the field of holograms. Conventional methods of fast hologram generation use computer memory space in exchange for faster generation times, the computational process of which is also dependent on an electronic computer. If a low-resolution hologram is generated, then upsampling is performed at the holographic reconstruction end, a high-resolution reconstructed image can be obtained, and the advantages of light speed parallelism and low power consumption are achieved. However, how to reconstruct after sampling on holograms also preserves the quality of the reconstructed image, and little research has been done in this regard. Thus, achieving an expansion of resolution in the holographic reconstruction process remains a challenge.
Disclosure of Invention
Aiming at the problems that the generation of the high-resolution hologram is time-consuming and depends on an electronic computer, the invention provides a method for expanding the holographic display resolution based on an optical diffraction neural network. The method can use optical means to process images in parallel in the process of reconstructing the holograms, obtain high-resolution hologram display effect with low-resolution hologram generation time, and has convenient calculation and high calculation speed.
The method is generally divided into four steps, and the method is specifically described as follows: step one, calculating the diffraction field distribution of the holographic surface based on an optical diffraction algorithm: first, an object U0 having a resolution of m×n is subjected toThe line random phase modulation yields a complex amplitude distribution U1, the process of which is denoted u1=u0×exp (j× ϕ), where j is the imaginary unit and ϕ is at [0,2 pi ]]A random phase distributed among the plurality of cells; then, for the diffraction process that the object plane initial light field with complex amplitude distribution of U1 passes through a distance of z, calculating holographic plane diffraction field distribution U2 by adopting an optical diffraction propagation algorithm, wherein the process is expressed as U < 2 > = Prop { U1, z }, and the z } represents a diffraction process with the distance of z; step two, the diffraction field distribution of the holographic surface is encoded into a calculation hologram: encoding the obtained holographic plane diffraction field distribution U2 to obtain a hologram Holo which is used for loading and displaying on a spatial light modulation device, wherein the process is expressed as holo=Encode (U2), and Encode () represents an encoding process function for complex amplitude; and step three, improving the resolution of the reconstructed image by using an optical diffraction neural network in the hologram reconstruction process: adding an L-layer optical diffraction neural network between hologram Holo reconstruction distances z, and processing the hologram Holo by using the optical diffraction neural network trained by minimizing Loss function Loss () value to obtain a reconstructed image U with expanded resolution re The process is expressed as follows: u (U) re =ODN θ { Holo, z }, where ODN θ { (), z } represents the process of expanding the resolution of the holographic reconstructed image by the optical diffraction neural network; designing physical parameters of the optical diffraction neural network: according to the wavelength of light that generates the hologram𝜆The physical parameters of the optical diffraction neural network are designed according to the h and diffraction distance z of the hologram sampling interval, wherein the related parameters comprise: focal length of Fourier lensfThe number of diffraction layers L of the optical diffraction neural network, the number N and size p of neurons of each layer, and the interval D between the diffraction layers.
The random phase modulation is performed on the object U0, and in particular, if the phases of the random phases are all 0, no random phase is added, and no random phase is added as a special case of adding a random phase.
The optical diffraction neural network expands the ODN of the holographic reconstruction image resolution θ { (), z } is characterized in that the structure of the optical diffraction neural network is formed by combining a plurality of diffraction layers, and the optical field propagates to the diffraction layers and passes through the amplitude of the parameters of the diffraction layersAnd phase modulation, the output of the neurons of each layer becomes again diffracted by the secondary wave source to the next layer. In the reconstruction process of the hologram, the reconstruction distance z is divided into L parts, L represents the diffraction layer number of the optical diffraction neural network, the reconstruction light fields with different distances and the diffraction layers are subjected to convolution operation, the resolutions of all the diffraction layers are r [ m ] m [ r ] n, wherein r represents the final expanded target resolution multiplicative factor, and the aim of expanding the resolution is fulfilled through the modulation of the L-layer optical diffraction neural network, and meanwhile, the reconstruction quality of the hologram is guaranteed. Wherein the output function of any one of the diffraction layers is expressed as: u (U) i = FT -1 (A i ×exp(j×φ i )×FT(Prop{U i-1 , D i }), U, where i-1 And U i Respectively represent the output light fields modulated by the ith-1 layer and the ith diffraction layer, D i Represents the diffraction distance from the i-1 th layer to the i-th layer, A i Represent the firstiAmplitude modulation factor of diffraction layer, phi i Represent the firstiPhase modulation coefficient of diffraction layer, FT () is Fourier transform, FT -1 () Is an inverse fourier transform.
The Loss function Loss (), which is characterized in that the Loss between the target image and the image processed by the optical diffraction neural network is calculated by mean square error, and the specific formula is as follows: loss=sum { (U) re − U t ) 2 (Sum/N), where Sum is the method of solving the Sum of all elements entered, U t For the target image, U re And N is the number of pixels of the image, wherein the image is processed by the optical diffraction neural network. And (3) performing a model training process in a computer, updating the modulation parameters of the network by using a gradient descent method, and performing multiple iterations to enable the Loss function value to be converged and obtain an optimized optical diffraction neural network model.
The design process of the physical parameters of the optical diffraction neural network is characterized in that the focal length of the Fourier lensfThe diffraction layer number L of the optical diffraction neural network is determined according to multiple simulation experiments; the number of neurons N in the diffraction layer is determined from the hologram resolution m×n and the spreading factor r, and the neuron size fatp is fatted according to the formula fatp =𝜆×fAnd (3) performing calculation to obtain the product; spacing between diffraction layersD is greater than or equal to the formula DN 1/2 ∆p×(4×∆p 2 ∕𝜆 2 -1) 1/2 And (5) calculating to obtain the product.
The method has the beneficial effects that: the invention creatively uses the optical diffraction neural network in the field of holographic display, and improves the resolution of the reconstructed image when being used at a holographic reconstruction end, and simultaneously maintains the acceptable reconstruction quality of human eyes. The method provided by the invention can effectively improve the resolution of the reconstructed image of the hologram, reduce the hologram generation time, and has the advantages of simple model training, high calculation speed and low power consumption.
Drawings
FIG. 1 is a schematic diagram of an expanded holographic display resolution based on an optical diffraction neural network of the present invention.
FIG. 2 is a graph showing the reconstruction performance of a low resolution hologram according to the present invention.
FIG. 3 is a graph showing the performance of the direct reconstruction and the reconstruction via the optical diffraction neural network after the low resolution hologram is filled with the high resolution hologram according to the present invention.
Note that: the figures are merely schematic and are not drawn to scale.
Detailed Description
An exemplary embodiment of a method for expanding holographic display resolution based on an optical diffraction neural network according to the present invention is described in detail below, and the method is described in further detail. It is noted herein that the following examples are given by way of further illustration only and are not to be construed as limiting the scope of the present invention, as those skilled in the art will make numerous insubstantial modifications and adaptations of the process in light of the above teachings, and yet remain within the scope of the invention.
The invention aims to provide an optical diffraction neural network processing method for expanding resolution in a holographic reconstruction process, which adopts the following technical scheme:
the method is generally divided into four steps, and the method is specifically described as follows: step one, calculating the diffraction field distribution of the holographic surface based on an optical diffraction algorithm: first, an object U0 having a resolution of m×n is randomly phase-modulated to obtain a complex amplitudeDistribution U1, the process of which is denoted u1=u0×exp (j× ϕ), where j is the imaginary unit and ϕ is at [0,2 pi ]]A random phase distributed among the plurality of cells; then, for the diffraction process that the object plane initial light field with complex amplitude distribution of U1 passes through a distance of z, calculating holographic plane diffraction field distribution U2 by adopting an optical diffraction propagation algorithm, wherein the process is expressed as U < 2 > = Prop { U1, z }, and the z } represents a diffraction process with the distance of z; step two, the diffraction field distribution of the holographic surface is encoded into a calculation hologram: encoding the obtained holographic plane diffraction field distribution U2 to obtain a hologram Holo which is used for loading and displaying on a spatial light modulation device, wherein the process is expressed as holo=Encode (U2), and Encode () represents an encoding process function for complex amplitude; and step three, improving the resolution of the reconstructed image by using an optical diffraction neural network in the hologram reconstruction process: adding an L-layer optical diffraction neural network between hologram Holo reconstruction distances z, and processing the hologram Holo by using the optical diffraction neural network trained by minimizing Loss function Loss () value to obtain a reconstructed image U with expanded resolution re The process is expressed as follows: u (U) re =ODN θ { Holo, z }, where ODN θ { (), z } represents the process of expanding the resolution of the holographic reconstructed image by the optical diffraction neural network; designing physical parameters of the optical diffraction neural network: according to the wavelength of light that generates the hologram𝜆The physical parameters of the optical diffraction neural network are designed according to the h and diffraction distance z of the hologram sampling interval, wherein the related parameters comprise: focal length of Fourier lensfThe number of diffraction layers L of the optical diffraction neural network, the number N and size p of neurons of each layer, and the interval D between the diffraction layers.
The random phase modulation is performed on the object U0, and in particular, if the phases of the random phases are all 0, no random phase is added, and no random phase is added as a special case of adding a random phase.
The optical diffraction neural network expands the ODN of the holographic reconstruction image resolution θ { (), z }, as shown in fig. 1, wherein the structure of the optical diffraction neural network is formed by combining a plurality of diffraction layers, the optical field propagates to the diffraction layers, the amplitude and the phase of the parameters of the diffraction layers are modulated,the output of the neurons of each layer in turn becomes a secondary wave source that diffracts to the next layer. In the reconstruction process of the hologram, the reconstruction distance z is divided into L parts, L represents the diffraction layer number of the optical diffraction neural network, the reconstruction light fields with different distances and the diffraction layers are subjected to convolution operation, the resolutions of all the diffraction layers are r [ m ] m [ r ] n, wherein r represents the final expanded target resolution multiplicative factor, and the aim of expanding the resolution is fulfilled through the modulation of the L-layer optical diffraction neural network, and meanwhile, the reconstruction quality of the hologram is guaranteed. Wherein the output function of any one of the diffraction layers is expressed as: u (U) i = FT -1 (A i ×exp(j×φ i )×FT(Prop{U i-1 , D i }), U, where i-1 And U i Respectively represent the output light fields modulated by the ith-1 layer and the ith diffraction layer, D i Represents the diffraction distance from the i-1 th layer to the i-th layer, A i Represent the firstiAmplitude modulation factor of diffraction layer, phi i Represent the firstiPhase modulation coefficient of diffraction layer, FT () is Fourier transform, FT -1 () Is an inverse fourier transform.
The Loss function Loss (), which is characterized in that the Loss between the target image and the image processed by the optical diffraction neural network is calculated by mean square error, and the specific formula is as follows: loss=sum { (U) re − U t ) 2 (Sum/N), where Sum is the method of solving the Sum of all elements entered, U t For the target image, U re In order to obtain an image processed by the optical diffraction neural network, N is the number of pixels of the image, a model training process is carried out in a computer, the modulation parameters of the network are updated by using a gradient descent method, and the Loss function value is converged through multiple iterations, so that an optimized optical diffraction neural network model is obtained.
The design process of the physical parameters of the optical diffraction neural network is characterized in that the focal length of the Fourier lensfThe diffraction layer number L of the optical diffraction neural network is determined according to multiple simulation experiments; the number of neurons N in the diffraction layer is determined from the hologram resolution m×n and the spreading factor r, and the neuron size fatp is fatted according to the formula fatp =𝜆×fAnd (3) performing calculation to obtain the product; the interval D between the diffraction layers is more than or equal to the formula D N 1/2 ∆p×(4×∆p 2 ∕𝜆 2 -1) 1/2 And (5) calculating to obtain the product.
In the embodiment of the invention, when the diffraction field distribution of the holographic surface is calculated based on an optical diffraction algorithm, prop { (), a z } diffraction algorithm is specifically an angular spectrum method, and the formula is expressed as follows: u (U) e (x 1 , y 1 ) = FT -1 {FT[U s (x, y)] × exp[j×k×z×(1-(𝜆×fx) 2 -(𝜆×fy) 2 ) 1/2 ]U, where s To input a light field, U e For the diffraction field, k=2𝜋 ∕ 𝜆The wave number is represented by a number of waves,𝜆is the wavelength of light, z represents the diffraction distance, x 1 And y 1 Representing the abscissa, the ordinate, f of the airspace x And f y Representing the abscissa of the frequency domain.
In the example of the invention, the encoding process function encod () of the holographic diffraction field, in particular the phase-taking function.
According to the model training method, a COCO2014 open source image library is selected as implementation data, and 1000 images are randomly selected as a training set. The training set image is uniformly processed into an initial image U0 with resolution m x n, which is used for generating a low-resolution hologram, and the target resolution with the resolution of rM x r n is up-sampled as a target image U during model training t . The training environment of the proposed method is a PyTorch framework under an Instrata RTX TiTitan GPU, an Adam optimizer is adopted, the initial learning rate lr is set to be 0.01, the training period epoch is 200, and the batch_size is 50. Finally, the test images are selected from 'moto.jpg' and 'UASF.jpg' for model performance test.
In the example of the present invention, the hologram resolution m×n used is 512×512. Light wavelength in the parameters𝜆671nm, a hologram sampling interval of 8 μm, a hologram generation and reconstruction diffraction distance z of 30cm, a Fourier lens focal lengthfThe number of layers L of the optical diffraction neural network is 5cm, the resolution expansion factor r is 2, the size of the neuron is 4 mu m, the propagation distance from the hologram to the first diffraction layer is 10cm, and then the interval D between the layers of the optical diffraction neural network is 5cm.
Fig. 2 is a result of generating a low resolution hologram using a low resolution image and hologram reconstruction, and fig. 3 is a result of filling the low resolution hologram of fig. two with a high resolution hologram, and then reconstructing directly and reconstructing using an optical diffraction neural network. As can be seen from fig. 3, the hologram directly enlarged resolution reconstruction quality is poor, and the image high frequency information is seriously lost. The high-frequency information of the image reconstructed by the optical diffraction neural network is recovered, and the quality of the reconstructed image is maintained while the holographic display resolution is expanded. The quality of the reconstructed image was evaluated using Structural Similarity (SSIM). Fig. 2 and 3 illustrate that the method of the present invention obtains a display effect of a high resolution hologram with a generation time of a low resolution hologram, reduces the generation time of the hologram, and simultaneously ensures reconstruction quality of the hologram.
The invention has the beneficial effects that: the invention creatively uses the optical diffraction neural network in the field of holographic display, and improves the resolution of the reconstructed image when being used at a holographic reconstruction end, and simultaneously maintains the acceptable reconstruction quality of human eyes. The method provided by the invention can effectively improve the resolution of the reconstructed image of the hologram, reduce the hologram generation time, and has the advantages of simple model training, high calculation speed and low power consumption.
Claims (5)
1. The method for expanding the resolution of holographic display based on the optical diffraction neural network is characterized in that the optical diffraction neural network is used for expanding the resolution at a hologram reconstruction end, and the method is specifically described as follows: step one, calculating the diffraction field distribution of the holographic surface based on an optical diffraction algorithm: first, an object U0 having a resolution of m×n is subjected to random phase modulation to obtain a complex amplitude distribution U1, the process of which is represented by u1=u0×exp (j×ω), where j is an imaginary unit and ω is a value of [0,2 pi ]]A random phase distributed among the plurality of cells; then, for the diffraction process that the object plane initial light field with complex amplitude distribution of U1 passes through a distance of z, calculating holographic plane diffraction field distribution U2 by adopting an optical diffraction propagation algorithm, wherein the process is expressed as U < 2 > = Prop { U1, z }, and the z } represents a diffraction process with the distance of z; step two, the diffraction field distribution of the holographic surface is encoded into a calculation hologram: encoding the obtained holographic plane diffraction field distribution U2 to obtain a hologram Holo for loading and displaying on a spatial light modulation device, wherein the hologram Holo has a process tableShown as holo=encode (U2), where Encode () represents the encoding process function for complex amplitude; and step three, improving the resolution of the reconstructed image by using an optical diffraction neural network in the hologram reconstruction process: adding an L-layer optical diffraction neural network between hologram Holo reconstruction distances z, and processing the hologram Holo by using the optical diffraction neural network trained by minimizing Loss function Loss () value to obtain a reconstructed image U with expanded resolution re The process is expressed as follows: u (U) re ＝ODN θ { Holo, z }, where ODN θ { (), z } represents the process of expanding the resolution of the holographic reconstructed image by the optical diffraction neural network; designing physical parameters of the optical diffraction neural network: physical parameters of the optical diffraction neural network are designed according to the optical wavelength lambda for generating the hologram, the hologram sampling interval delta h and the diffraction distance z, wherein the related parameters comprise: the focal length f of the Fourier lens, the number L of diffraction layers of the optical diffraction neural network, the number N and the size deltap of neurons of each layer, and the interval D between the diffraction layers.
2. The method for expanding holographic display resolution based on optical diffraction neural network as claimed in claim 1, wherein the object U0 is randomly phase modulated, if the phases of the random phases are all 0, then no random phase is added, and no random phase is a special case of adding a random phase.
3. The method for expanding holographic display resolution based on optical diffraction neural network as claimed in claim 1, wherein the optical diffraction neural network expands the process ODN of the resolution of the holographic reconstructed image θ { (), z } is as follows: the structure of the optical diffraction neural network is formed by combining a plurality of diffraction layers, an optical field propagates to the diffraction layers, and the output of neurons of each layer becomes a secondary wave source to diffract to the next layer after the amplitude and the phase of parameters of the diffraction layers are modulated; in the reconstruction process of the hologram, the reconstruction distance z is divided into L parts, L represents the diffraction layer number of the optical diffraction neural network, the reconstruction light field with different distances and the diffraction layers are subjected to convolution operation, the resolutions of all the diffraction layers are r.m multiplied by r.n, wherein r represents the final expanded target resolution multiplication factor,the aim of expanding resolution is fulfilled through the modulation of the L-layer optical diffraction neural network, and the reconstruction quality of the hologram is guaranteed; wherein the output function of any one of the diffraction layers is expressed as:wherein U is i-1 And U i Respectively represent the output light fields modulated by the ith-1 layer and the ith diffraction layer, D i Represents the diffraction distance from the i-1 th layer to the i-th layer, A i Represents the amplitude modulation factor of the i-th diffraction layer, a +.>The phase modulation factor representing the i-th diffraction layer, FT () is the Fourier transform, FT -1 () Is an inverse fourier transform.
4. The method for expanding holographic display resolution based on optical diffraction neural network as claimed in claim 1, wherein the Loss function Loss () calculates the Loss between the target image and the processed image of the optical diffraction neural network by using a mean square error, and the specific formula is: loss=sum { (U) re -U t ) 2 [ N ] } where Sum { } is a method of solving the Sum of all elements input, U t For the target image, U re In order to obtain an image processed by the optical diffraction neural network, N is the number of pixels of the image, a model training process is carried out in a computer, the modulation parameters of the network are updated by using a gradient descent method, and the Loss function value is converged through multiple iterations, so that an optimized optical diffraction neural network model is obtained.
5. The method for expanding holographic display resolution based on optical diffraction neural network as claimed in claim 1, wherein the physical parameters of the optical diffraction neural network are designed as follows: the diffraction layer number L of the Fourier lens focal length f and the optical diffraction neural network is determined according to a plurality of simulation experiments; the number N of the neurons of the diffraction layer is determined according to the resolution m multiplied by N of the hologram and the expansion factor r, and the size deltap of the neurons is calculated according to the formula deltap=lambda multiplied by f/(deltah multiplied by N multiplied by r); diffraction layerThe interval D between the two is greater than or equal to N through the formula D 1/2 Δp×(4×Δp 2 /λ 2 -1) 1/2 And (5) calculating to obtain the product.
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