All-optical diffraction network-based multiplexing coaxial hologram reconstruction method

Abstract

The invention relates to the field of computer technology and optics, and discloses a multiplexing coaxial hologram reconstruction method based on an all-optical diffraction network, which comprises the following steps: holographic recording: after a plane wave with the wavelength of lambda passes through a polarization splitting prism, splitting two beams of light with mutually orthogonal polarization states, and respectively irradiating the two beams of light onto pictures of two recorded objects, the two beams of light coincide through a prism, a holographic plate is placed at the coincidence position of the two light fields, and an overlapped recording multiplexing coaxial hologram after interference of object light waves and reference light waves is obtained by recording the intensity of the object light waves and the intensity of the reference light waves on a plane; and through the reproduction of the all-optical diffraction network, that is, the recording multiplexing coaxial holograms are irradiated by plane waves with the same wavelength, the recording multiplexing coaxial holograms are respectively sent into the parallel trained all-optical diffraction network by the polarization splitting prism, and the reconstruction and reproduction of the multiplexing coaxial holograms are completed. According to the method, the multiplexing coaxial hologram can be successfully reconstructed, and twin images are eliminated.

Description

Technical Field

[0001] The invention relates to the fields of computer technology and optics, and in particular to a multiplexed coaxial hologram reconstruction method based on an all-optical diffraction network. Background Art

[0002] Holography is a widely used technology with many applications in computational imaging, display devices, interferometry, and data storage. With the rapid development of modern computing science, digital holography has emerged. Its core is to reconstruct holograms with the help of advanced numerical algorithms and use phase recovery algorithms to reduce artifacts caused by twin images. As an innovation in the coaxial hologram reconstruction strategy, hologram reconstruction based on deep learning has also been proven to be effective. This method uses an optimized deep neural network to implement coaxial hologram reconstruction and effectively suppresses twin image interference.

[0003] In the early days of neural networks, several models were specifically designed for the task of coaxial hologram reconstruction, and their training process trained the network with holograms (as network input) and their corresponding object fields (as target images). Although the data generation and training process is time-consuming, this training process is one-time. Once the network training is completed, unknown new objects can be reconstructed through a single forward propagation without the need for additional processing and any optimization process. However, the reconstruction method of deep neural networks essentially relies on computer processing, and its reconstruction mechanism can be regarded as a hard mapping, which lacks a clear physical interpretation. This poses a major challenge to the application of deep neural networks in the field of holographic reconstruction.

[0004] An all-optical holographic reconstruction method established by Aydogan Ozcan's research team can solve the problems faced by the above-mentioned deep neural networks. The method processes the diffraction waves from the holographic recording through a series of transmission diffraction layers, which reconstruct the image of the unknown object on the output plane. These diffraction layers are also designed using deep learning to specifically reconstruct coaxial holograms and form a passive optical network. The training process of this network is similar to that of deep neural networks, using phase modulation to reconstruct coaxial holograms, and the entire training process is completed in one go. In addition to using illumination light with a wavelength of λ, this reconstruction scheme does not require any external power supply, and reconstructs the image of the unknown object at the speed of light propagation. This network architecture reflects the large connectivity of spatial optical diffraction. However, current diffraction neural networks can often only solve the reconstruction problem of a single hologram, which is far from meeting the needs of modern big data.

[0005] Therefore, this application proposes a method for reconstructing multiplexed coaxial holograms. This method uses a deep learning algorithm to optimize the all-optical diffraction network formed by two sets of parallel transmission diffraction layers, which can process the diffraction waves recorded by the multiplexed hologram and reconstruct the multiplexed coaxial holograms respectively, thereby solving the technical problem that the existing diffraction neural network can only solve the reconstruction of a single hologram. Summary of the invention

[0006] The present invention provides a method for reconstructing multiplexed coaxial holograms based on an all-optical diffraction network. The method fully utilizes the parallel processing potential of free-space optical diffraction through the all-optical diffraction network, improves the storage and reproduction capabilities of holograms, and transcends the traditional limitation of only carrying information of a single object. It provides an efficient solution for reconstructing multiplexed coaxial holograms, thereby solving the technical problem that the prior art can only solve the reconstruction of a single hologram.

[0007] In order to achieve the above object, the technical solution of the present invention is as follows:

[0008] A multiplexed coaxial hologram reconstruction method based on an all-optical diffraction network, comprising:

[0009] Holographic recording: A plane wave with a wavelength of λ is passed through a polarization beam splitter prism to separate two beams of light with mutually orthogonal polarization states, which are respectively irradiated onto the images of two objects to be recorded. The holographic dry plate is placed at the overlap of the two light fields, and the intensity of the object light wave and the reference light wave on the recording plane are used to obtain the overlapping recorded multiplexed coaxial hologram after the interference of the object light wave and the reference light wave.

[0010] Reproduction through the all-optical diffraction network: the recorded multiplexed coaxial hologram is illuminated by a plane wave of the same wavelength, and the recorded multiplexed coaxial hologram is sent to a parallel trained all-optical diffraction network by a polarization beam splitter prism to complete the reconstruction and reproduction of the multiplexed coaxial hologram.

[0011] Further, the recording multiplexed coaxial hologram is represented as follows:

[0012]

[0013] Where (x, y) represents the spatial coordinates of the recording surface, O1 and O2 represent object light, O1(x, y) and O2(x, y) represent the amplitude of the object light wave, R(x, y) represents the amplitude of the reference light wave, * represents the complex conjugate sign, |O1(x, y)| 2 and |O2(x,y)| 2 represents the object light wave intensity, |R(x,y)| 2 Indicates the reference light wave intensity.

[0014] Furthermore, the holographic recording distance (the distance from the recording object to the holographic dry plate) used in recording the multiplexed coaxial hologram is 30λ, and the axial distance between the continuous transverse planes in the all-optical diffraction network is z m =37.5λ, m=1,...,N+1; the continuous transverse planes are the input holographic plane, two parallel diffraction network layers and the output plane in sequence, the number of layers N of the two parallel continuous transverse planes is 5, the width of each diffraction layer is 100λ, the size of the recorded object is 25λ, and the transverse range size of the recorded multiplexed coaxial hologram is 42λ.

[0015] Furthermore, before the reproduction through the all-optical diffraction network, a 1×1 convolutional layer needs to be placed in front of the diffraction layer, and the training of the all-optical diffraction network layer needs to be completed. Each diffraction layer has 200×200 trainable parameters, and the size of the diffraction feature on each diffraction layer is half the wavelength, that is, v i =λ / 2, i=1,...,40000, the diffraction feature is a neuron.

[0016] Furthermore, the light transmission between the diffraction layers in the all-optical diffraction network is realized by Rayleigh-Sommerfeld diffraction integral, wherein the wave emitted from the i-th neuron on the k-th diffraction layer It is expressed as follows:

[0017]

[0018] Where (x, y, z) represents the spatial coordinates of the diffraction layer; (x i ,y i ,z i ) represents the spatial coordinates of the i-th neuron; represents the wave incident on the i-th neuron on the k-th diffractive layer, which is generated by the previous diffractive layer k-1 layer; w and t represent the analogs of weights and biases, respectively, represents the weight of the neuron on the k-1 layer, t k (x i ,y i ,z i ) represents the complex-valued transmittance coefficient.

[0019] Further, the complex-valued transmittance coefficient is expressed as follows:

[0020]

[0021] Among them, a k (x i ,y i ,z i )and Represent the amplitude coefficient and phase coefficient of the i-th feature of the k-th layer, respectively, k (x i ,y i ,z i ) ranges from 0 to 1, The range of is 0 to 2π, and j represents the imaginary unit.

[0022] Furthermore, the loss function of the all-optical diffraction network layer training is

[0023]

[0024] L loss =L pixel +L fourier +L mse

[0025] Among them, Y p Represents the value of the pth pixel on the target image (object image), Represents the value of the pth pixel on the network output graph, N p represents the total number of image pixels, F{} represents the Fourier transform operation, L pixel Indicates pixel loss, L mse represents the mean square error loss, L fourier represents the Fourier loss function, L loss is the total loss function.

[0026] Furthermore, the loss function of the all-optical diffraction network layer training adopts the Adam optimization algorithm to obtain the minimized loss function, where φ1(x, y) and φ2(x, y) represent the first output and the second output of the parallel all-optical diffraction network layer, respectively, and the image reconstruction loss is defined as two φ r The minimum value in the error term, that is and The losses are as follows:

[0027]

[0028] Among them, φ p (x,y) and φ q (x, y) represent the first label image and the second label image of the multiplexed hologram respectively, L loss Represents the total loss of the loss function.

[0029] In summary, the present invention has the following beneficial effects:

[0030] 1. The present invention optimizes an all-optical diffraction network formed by two sets of parallel transmission diffraction layers through a deep learning algorithm, and utilizes the parallelized all-optical diffraction network to simultaneously modulate two sets of phase plates, so as to process the diffraction waves recorded by the multiplexed hologram and reconstruct the multiplexed coaxial holograms respectively. The input light field of the all-optical diffraction network projects two desired target fields on two output planes respectively through optical transmission, and can eliminate the related artifacts and conjugate images generated by the coaxial hologram while reconstructing the two target images. The network framework makes full use of the parallel processing potential of free-space optical diffraction, improves the storage and reproduction capabilities of holograms, transcends the traditional limitation of only carrying information of a single object, and provides an efficient solution for reconstructing multiplexed coaxial holograms.

[0031] 2. The present invention can not only separate and reconstruct overlapping multiplexed holograms, but also remove twin image artifacts. The structural similarity index of the simulated reconstruction can reach 0.80, and the peak signal-to-noise ratio reaches 20, which verifies the effectiveness of the all-optical diffraction network for the reconstruction of multiplexed holograms.

[0032] 3. The present invention compares the test results of the all-optical diffraction network and Y-Net under the salt and pepper noise density of 0.1 to 0.5. When the salt and pepper noise reaches 0.3 (the salt and pepper noise range is 0 to 1), the structural similarity of the reconstruction result of the all-optical diffraction network reaches 0.55, and the peak signal-to-noise ratio also reaches 13.5. In contrast, the structural similarity and peak signal-to-noise ratio of the Y-Net reconstruction result are 0.33 and 9, respectively. As the density of the salt and pepper noise increases, the reconstruction results of the Y-Net network become worse and worse. The results show that the all-optical diffraction network has strong robustness to salt and pepper noise.

[0033] 4. The present invention simulates occluded multiplexed holograms. The simulation results show that when the occlusion area of ​​the multiplexed coaxial hologram is 1 / 8 and 1 / 4, the network can reconstruct a clearer image. Even when the occlusion area exceeds 2 / 3, the diffraction network can still achieve image reconstruction. Although the image quality is reduced at this time, it is still better than the reconstruction result of the Y-Net network.

[0034] 5. The all-optical diffraction network structure designed in the present invention can successfully reconstruct the multiplexed coaxial hologram and eliminate the twin images. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 a is a coaxial multiplexed holographic recording image in the present invention;

[0036] Figure 1 b is a schematic diagram of the reproduction using the all-optical diffraction network in the present invention;

[0037] Figure 2It is the reconstruction image of the handwritten digital multiplexed coaxial hologram using the diffraction network of the present invention (the first column is the multiplexed coaxial hologram, the second column is the first target object image, the third column is the second target object image, the fourth column is the first reconstruction image of the object reconstructed by the designed diffraction network, the fifth column is the second reconstruction image of the object reconstructed by the diffraction network, and the sixth column is the reconstruction image of the object propagated in free space with an axial distance of 30λ between the object and the recording plane);

[0038] Figure 3 It is a reconstruction diagram of a multiplexed hologram with added noise using a diffraction network and a Y-Net in the present invention (Figure a is a blind test result of two networks when the salt and pepper noise density is 0.1, 0.3, and 0.5 respectively, the first column is a multiplexed coaxial hologram with added noise of 0.1, 0.3, and 0.5 density, the second and third columns are the reconstruction results of the diffraction network under different salt and pepper noise densities, the fourth column is a reconstruction diagram of an object propagating in free space with an axial distance of 30λ between the multiplexed coaxial hologram and the recording plane under different salt and pepper noise densities, the fifth and sixth columns are the reconstruction results of the Y-Net network under different salt and pepper noise densities. Figure b is an image quality evaluation index of the reconstruction result of adding different noises (0.1-0.5) to the multiplexed coaxial hologram);

[0039] Figure 4 This is a diagram of the present invention using a diffraction network to reconstruct an occluded multiplexed hologram (Figure a is a blind test result of a multiplexed coaxial hologram with 1 / 8, 1 / 4 and 2 / 3 occluded, the first column is the multiplexed coaxial hologram with 1 / 8, 1 / 4 and 2 / 3 occluded, the second and third columns are the diffraction network reconstruction results of different occlusion areas, the fourth column is a reconstruction of an object propagating in free space with an axial distance of 30λ between the multiplexed coaxial hologram and the recording plane with 1 / 8, 1 / 4 and 2 / 3 occluded, and the fifth and sixth columns are Y-Net network reconstruction results. Figure b is an image quality evaluation index for the reconstruction results of the multiplexed hologram with 1 / 8, 1 / 4 and 2 / 3 occluded). DETAILED DESCRIPTION

[0040] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solution of the present invention will be further described in detail below in conjunction with the embodiments of the present invention and the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0041] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present invention can be combined with each other. The present invention will be described in detail below in conjunction with the embodiments.

[0042] Example:

[0043] A method for reconstructing a multiplexed coaxial hologram based on an all-optical diffraction network, that is, a schematic diagram of reconstructing a coaxial multiplexed hologram using an all-optical diffraction network is shown in FIG. Figure 1 As shown, including:

[0044] The holographic recording process is as follows Figure 1 As shown in a, it is similar to the coaxial holographic recording, that is, a plane wave with a wavelength of λ passes through a polarization splitter prism to separate two beams of light with mutually orthogonal polarization states, which are respectively recorded as object light O1 and object light O2, and irradiate onto the images of two recorded objects. The two beams of light are then overlapped by a prism, and the holographic dry plate is placed at the overlap of the two light fields. The object light wave intensity and the reference light wave intensity on the recording plane are used to obtain the overlapping recorded multiplexed coaxial hologram after the interference of the object light wave and the reference light wave.

[0045] The recorded multiplexed on-axis hologram I(x,y) can be expressed as follows:

[0046] I(x,y)=|O1(x,y)+O2(x,y)+R1(x,y)+R2(x,y) 2

[0047] Among them, (x, y) represents the spatial coordinates of the recording surface, O1 and O2 represent object light, O1(x, y) and O2(x, y) represent the amplitude of the object light wave, and R1(x, y) and R2(x, y) represent the amplitude of the reference light wave.

[0048] Since the two object beams are orthogonally polarized, O1 and O2 do not interfere with each other, and the two object beams share a reference beam, the recording of the multiplexed coaxial hologram can be rewritten as:

[0049]

[0050] Where (x, y) represents the spatial coordinates of the recording surface, O1 and O2 represent object light, O1(x, y) and O2(x, y) represent the amplitude of the object light wave, R(x, y) represents the amplitude of the reference light wave, * represents the complex conjugate sign, |O1(x, y)| 2 and |O2(x,y)| 2 represents the object light wave intensity, |R(x,y)| 2 Indicates the reference light wave intensity.

[0051] So |R 2 、O1R * RO1 * 、O2R * and They are all background noise. Generally, the twin image artifacts of the coaxial hologram are very strong, and the noise of the multiplexed hologram further reduces the image reconstruction quality.

[0052] In the process of reconstruction through the all-optical diffraction network ( Figure 1 b), the recorded multiplexed coaxial hologram is illuminated by a plane wave of the same wavelength, and the recorded multiplexed coaxial hologram is sent to a parallel trained all-optical diffraction network by a polarization beam splitter prism to complete the reconstruction and reproduction of the multiplexed coaxial hologram.

[0053] In the present invention, the holographic recording distance used in the holographic recording process is 30λ, which specifically refers to the distance from the recording object to the holographic dry plate. The axial distance between consecutive transverse planes is represented by z m Indicates that z m =37.5λ, m=1,...,N+1, N represents the number of diffraction layers, the continuous transverse planes are the input holographic plane, two parallel diffraction network layers and the output plane, the number of two parallel diffraction network layers (N1 and N2) are both 5, the width of each diffraction layer is 100λ, the size of the recorded object is 25λ, and the transverse range size of the recorded multiplexed coaxial hologram is 42λ.

[0054] Based on the above hyperparameters, firstly, a 1×1 convolutional layer is placed in front of the diffraction layer to extract more detailed features; secondly, a parallelized all-optical diffraction network layer is trained, each diffraction layer has 200×200 trainable parameters, and the size of the diffraction feature (neuron) on each diffraction layer is half the wavelength, that is, v i =λ / 2, i=1,...,40000. Therefore, using deep learning technology, the present invention optimizes a total of 400,000 independent diffraction neurons, distributed in the transmissive diffraction layer with N1 and N2 being 5 respectively, to form a parallelized all-optical diffraction network ( Figure 1 b) For the training image data of the present invention, the Mnist handwriting data set is used. The total number of multiplexed holograms in the training data set is 17,000, and none of these images in the data set are used for blind testing of the final diffraction network model.

[0055] When building the diffraction network model, the Rayleigh-Sommerfeld diffraction integral is used to simulate the light transmission between the diffraction layers. This integral assumes that the propagating light can be represented as a scalar field. The prior art has reported various experimental demonstrations of designing 3D diffraction networks using the same scalar field, proving the feasibility of this assumption. According to the Rayleigh-Sommerfeld diffraction theory, the light transmission between the diffraction layers is i ,y i ,z i ) can be regarded as a secondary wave source.

[0056]

[0057] Among them, (x i ,y i,z i ) represents the spatial coordinates of the ith neuron, (x, y, z) represents the spatial coordinates of the diffraction layer, represents the weight of the neuron on layer k, and r represents the radial distance j represents the imaginary unit; based on this, the wave emitted from the i-th neuron on the k-th layer It can be written as:

[0058]

[0059] Among them, (x i ,y i ,z i ) represents the spatial coordinates of the ith neuron, represents the wave incident on the i-th neuron on the k-th layer, which is generated by the previous k-1 layers. The formula is similar to a feedforward neural network; w and t represent the analogs of weights and (multiplicative) biases, respectively. The multiplicative bias t of the neuron is trainable because it is determined by the physical parameters of the diffraction surface; represents the weight of the neuron on the k-1 layer, t k (x i ,y i ,z i ) represents the complex-valued transmittance coefficient.

[0060] Since the trainable diffractive layers are not polarization sensitive, the complex-valued modulation generated by these diffractive layers is the same for two orthogonal polarization states. Assume that the diffractive layers are thin optical modulators where at position (x i ,y i ,z i The i-th feature on the k-th diffraction layer at ) represents the complex-valued transmittance coefficient t k It is expressed as follows:

[0061]

[0062] Among them, a k (x i ,y i ,z i )and They represent the amplitude coefficient and phase coefficient of the i-th feature of the k-th layer respectively. The amplitude coefficient and phase coefficient of the diffraction neuron are both trainable. k (x i ,y i ,z i ) allows a range of 0 to 1, The allowed range is 0 to 2π, where j represents the imaginary unit.

[0063] In order to train the diffraction network for multiplexed hologram reproduction, the present invention numerically simulates the propagation of plane waves scattered by two objects from the object plane to the holographic recording plane, and calculates the multiplexed coaxial hologram corresponding to the overlap of the two training objects. Assuming that the amplitude transmittance of the multiplexed coaxial hologram is proportional to the recording intensity, the amplitude of the input light field is the normalized intensity of the multiplexed hologram. The reconstructed patterns are the intensities of the output light fields respectively. The loss function for training is defined as follows:

[0064]

[0065] L loss =L pixel +L fourier +L mse

[0066] Among them, Y p Represents the value of the pth pixel on the target image (object image), Represents the value of the pth pixel on the network output graph, N p represents the total number of image pixels, F{} represents the Fourier transform operation, L pixel Indicates pixel loss, L mse represents the mean square error loss, L fourier represents the Fourier loss function, L loss is the total loss function.

[0067] The present invention adopts the Adam optimization algorithm to obtain the minimized loss function, and represents φ1(x, y) and φ2(x, y) as the first output and the second output of the parallel all-optical diffraction network layer, respectively. Then the image reconstruction loss is defined as two φ r The minimum value in the error term, that is and The losses are as follows:

[0068]

[0069] Among them, φ p (x,y) and φ q (x, y) represent the first label image and the second label image of the multiplexed hologram respectively, L loss represents the total loss of the loss function. Since there is no difference in hierarchy and priority between input objects, this loss function allows the network to choose priorities about the activation order.

[0070] Test example:

[0071] 1. Blind test results of reconstructing multiplexed coaxial holograms

[0072] The present invention uses the parallelized training of the all-optical diffraction network for the optical reconstruction of the multiplexed hologram. After the all-optical diffraction network is trained, it is blindly tested using the coaxial multiplexed holograms calculated using two new unknown objects. Figure 2 Two numerical simulation reconstruction images obtained after the multiplexed hologram is input into the all-optical diffraction network are shown. The first column in the figure is the multiplexed coaxial hologram, the second and third columns are the target images, the fourth and fifth columns are the reconstruction results obtained by the network reconstruction of the multiplexed coaxial hologram, and the last column is the result of free space propagation. The reconstructed images show that the problems of overlapping images that cannot be separated and twin-image related artifacts in free space propagation are solved. On the output plane, the all-optical diffraction network successfully separates the multiplexed hologram, and related artifacts such as twin images are eliminated.

[0073] According to the blind test results of the network Figure 2 As shown. All blind tested multiplexed coaxial holograms were not presented to the diffraction network during the training phase. The test results show that the twin images that usually appear in the free space propagation of the input hologram are eliminated in the diffraction network, and the overlapping multiplexed coaxial holograms are separated and reconstructed. The present invention uses structural similarity (SSIM) and peak signal-to-noise ratio (PSNR) values ​​to quantify the similarity between the target image and the reconstructed image. In the report of the all-optical diffraction network reconstructing the coaxial hologram, the SSIM value is about 0.7 and the PSNR value is about 16. In contrast, the diffraction network of the present invention has significant improvements in both SSIM and PSNR values, reaching about 0.8 and 20 respectively, which shows that the diffraction network can generate highly fidelity reconstructed images. This result not only proves that the trained diffraction network has a strong generalization ability for processing grayscale and low-contrast images, but also shows that the diffraction network can retain various spatial features and detail information lost in the free space propagation of the hologram during the training process.

[0074] 2. Influence of noise on the reconstruction results of multiplexed coaxial holograms

[0075] Due to the high coherence of lasers, the reflected light of light waves irradiating objects will be coherently superimposed, so in general, salt and pepper noise is inevitable on holograms. The factor that has the greatest impact on the quality of the reconstructed image of the hologram is the salt and pepper noise in the holographic image. In order to further prove the reconstruction performance of the diffraction network, the ability to optically reconstruct and analyze the multiplexed hologram with added noise was tested in the above-trained all-optical diffraction neural network. Figure 3 As shown in a, the first column is the multiplexed coaxial hologram with added salt and pepper noise of density 0.1, 0.3 and 0.5 respectively. Due to the strong twinning artifact, this causes the input salt and pepper noise multiplexed coaxial hologram to present stronger background artifact noise and loss of detail information in free space propagation, so that the free space propagation is more blurred and the image cannot be distinguished. Figure 3 The fifth and sixth columns are the reconstruction results of the traditional neural network Y-Net network. Although the traditional neural network can restore the hologram without salt and pepper noise, Figure 3 a As can be seen from the fifth and sixth columns, the traditional neural network is limited in its ability to restore noisy holograms. The second and third columns are the results of diffraction network reconstruction under different salt and pepper noise densities. Although the quality of the results reproduced by the present invention is reduced compared to those without noise, and the greater the noise density, the worse the quality, the correct results can still be clearly obtained. The present invention compares the SSIM and PSNR values ​​of the diffraction neural network and the traditional neural network in reproducing noisy multiplexed holograms, as shown in Figure 2. Figure 3 As shown in b. Under the salt and pepper noise density of 0.1, the SSIM value between the diffraction network reconstructed image and the target image reaches about 0.75, and the PSNR is about 16.5. Under the salt and pepper noise density of 0.3, the SSIM value is about 0.55, and the PSNR value is 13.5. When the salt and pepper noise density is 0.5, the SSIM and PSNR values ​​drop to about 0.35 and 11, respectively. In comparison, the SSIM values ​​of the reconstructed image of the Y-Net network at the same noise level are 0.58, 0.33 and 0.15, and the PSNR values ​​are 13, 9 and 9.5, respectively. Although the increase in noise inevitably leads to a decline in the quality of image reconstruction, by comparing the SSIM and PSNR curves of the two, it can be seen that even on the multiplexed coaxial hologram with high-density salt and pepper noise, the diffraction network can still show a strong ability to separate and reconstruct multiplexed coaxial holograms. This study strongly confirms the strong robustness of the diffraction network in dealing with noise disturbances, and demonstrates its robust performance and excellent performance in complex environments.

[0076] 3. The influence of occlusion on the reconstruction results of multiplexed coaxial holograms

[0077] Due to the unique recording method of holographic technology, the hologram can reproduce the original image information when some information is missing. The diffraction neural network retains the wavefront reconstruction ability of the light beam propagating in free space. The present invention numerically simulates the results of the diffraction neural network in processing the partial missing of the multiplexed coaxial hologram. First, different random areas of the multiplexed coaxial hologram are painted black to simulate the information loss that may occur in actual applications to evaluate the performance of the hologram reconstructed using the diffraction network in the missing state. The random parts of the multiplexed coaxial hologram are covered (black treatment), and the covered areas are 1 / 8, 1 / 4 and 2 / 3 as shown in the first column of Figure a. When the covered multiplexed hologram is allowed to propagate freely in space, it can be seen that due to a large black part in the image, the black part still exists after propagation in free space, and the specific values ​​in the image are blocked by the black part and cannot be distinguished, as shown in the fourth column of Figure a. The present invention uses an unobstructed training set to train a parallelized diffraction network model. Then, we used the datasets with occlusion areas of 1 / 8, 1 / 4, and 2 / 3 to test, and randomly selected images. The test results are as follows: Figure 4 As shown in the second and third columns of a. For comparison, the present invention also shows the results of reconstruction using the Y-Net network, as shown in the fifth and sixth columns of FIG. a. In addition, in order to quantify the reconstruction performance of the network, the structural similarity and peak signal-to-noise ratio are used to evaluate the reconstruction quality of the diffraction network and the Y-Net network. Figure 4 As shown in b. The results of numerical simulation show that the diffraction network realizes the reconstruction of the occluded multiplexed coaxial hologram. When the occlusion area is 1 / 8, 1 / 4 and 2 / 3, the SSIM values ​​are 0.62, 0.49 and 0.37 respectively, and the PSNR values ​​are 14, 12 and 11 respectively. In contrast, the SSIM values ​​of the Y-Net network reach 0.55, 0.24 and 0.22 respectively, and the PSNR values ​​are 12, 9 and 8 respectively under the same occlusion ratio. The reconstruction results prove its success in the occluded multiplexed coaxial hologram. In reconstructing the incomplete multiplexed coaxial hologram, the diffraction network can not only reconstruct the image that eliminates the twin image artifact according to the only remaining hologram information (unoccluded part), but also realize the separate reconstruction of overlapping holograms according to the designed model. Therefore, the present invention can conclude that the diffraction network also has a certain robustness for the incomplete multiplexed coaxial hologram. This discovery is of great significance for reconstruction in practical applications.

[0078] In summary, the present invention proposes a scheme for multiplexed coaxial holographic reconstruction based on an all-optical diffraction network, which uses a parallelized all-optical diffraction network to simultaneously modulate two sets of phase plates, and can achieve reconstruction of multiplexed coaxial holograms. The designed all-optical diffraction network structure can successfully reconstruct multiplexed coaxial holograms and eliminate twin images. This network structure provides a new idea and possibility for real-time reconstruction of multiplexed coaxial holograms.

[0079] The above-described embodiments only express the preferred implementation modes of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present invention. It should be pointed out that, for those of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

Claims

1. A multiplexed coaxial hologram reconstruction method based on an all-optical diffraction network, characterized in that: include: Holographic recording: A plane wave with a wavelength of λ is passed through a polarization beam splitter prism to separate two beams of light with mutually orthogonal polarization states, which are respectively irradiated onto the images of two objects to be recorded. The two beams of light are then overlapped by a prism, and a holographic dry plate is placed at the overlap of the two light fields. By recording the intensity of the object light wave and the intensity of the reference light wave on the plane, a recorded multiplexed coaxial hologram of the overlapped object light wave and the reference light wave after interference is obtained. Reproduction through the all-optical diffraction network: the recorded multiplexed coaxial hologram is illuminated by a plane wave of the same wavelength, and the recorded multiplexed coaxial hologram is sent to a parallel trained all-optical diffraction network by a polarization beam splitter prism to complete the reconstruction and reproduction of the multiplexed coaxial hologram.

2. The method for reconstructing a multiplexed coaxial hologram based on an all-optical diffraction network according to claim 1, characterized in that: The recorded multiplexed coaxial hologram is represented as follows: Among them, (x, y) represents the spatial coordinates of the recording surface, O1 and O2 represent the object light, O1(x, y) and O2(x, y) represent the amplitude of the object light wave, R(x, y) represents the amplitude of the reference light wave, * represents the complex conjugate sign, O1(x, y) 2 and |O2(x,y) 2 Represents the object light wave intensity, |R(x,y) 2 Indicates the reference light wave intensity.

3. The method for reconstructing a multiplexed coaxial hologram based on an all-optical diffraction network according to claim 1, characterized in that: The holographic recording distance used for recording the multiplexed coaxial hologram is 30λ, and the axial distance between the continuous transverse planes in the all-optical diffraction network is z m =37.5λ, m=1,...,N+1; the continuous transverse planes are the input holographic plane, two parallel diffraction network layers and the output plane in sequence, the number of layers N of the two parallel continuous transverse planes is 5, the width of each diffraction layer is 100λ, the size of the recorded object is 25λ, and the transverse range size of the recorded multiplexed coaxial hologram is 42λ.

4. The method for reconstructing a multiplexed coaxial hologram based on an all-optical diffraction network according to claim 3, characterized in that: Before the reproduction through the all-optical diffraction network, a 1×1 convolutional layer needs to be placed in front of the diffraction layer, and the training of the all-optical diffraction network layer needs to be completed. Each diffraction layer has 200×200 trainable parameters, and the size of the diffraction feature on each diffraction layer is half the wavelength, that is, v i =λ / 2, i=1,...,40000, the diffraction feature is a neuron.

5. The method for reconstructing a multiplexed coaxial hologram based on an all-optical diffraction network according to claim 4, characterized in that: The light transmission between the diffraction layers in the all-optical diffraction network is realized by Rayleigh-Sommerfeld diffraction integration, where the wave emitted from the i-th neuron on the k-th diffraction layer It is expressed as follows: Where (x, y, z) represents the spatial coordinates of the diffraction layer; (x i ,y i ,z i ) represents the spatial coordinates of the i-th neuron; represents the wave incident on the i-th neuron on the k-th diffraction layer, which is generated by the previous diffraction layer k-1 layer; w i k-1 (x, y, z) represents the weight of the neuron on the k-1 layer, t k (x i ,y i ,z i ) represents the complex-valued transmittance coefficient.

6. The method for reconstructing a multiplexed coaxial hologram based on an all-optical diffraction network according to claim 5, characterized in that: The complex-valued transmittance coefficient is expressed as follows: Among them, a k (x i ,y i ,z i )and Represent the amplitude coefficient and phase coefficient of the i-th feature of the k-th layer, respectively, k (x i ,y i ,z i ) ranges from 0 to 1, The range of is 0 to 2π: j represents the imaginary unit.

7. The method for reconstructing a multiplexed coaxial hologram based on an all-optical diffraction network according to claim 1 or 6, characterized in that: The loss function of the all-optical diffraction network layer training is L loss =L pixel +L fourier +L mse Among them, Y p Represents the value of the pth pixel on the target image, Represents the value of the pth pixel on the network output graph, N p represents the total number of image pixels, F{} represents the Fourier transform operation, L pixel Indicates pixel loss, L mse represents the mean square error loss, L fourier represents the Fourier loss function, L loss is the total loss function.

8. The method for reconstructing a multiplexed coaxial hologram based on an all-optical diffraction network according to claim 7, characterized in that: The loss function of the all-optical diffraction network layer training adopts the Adam optimization algorithm to obtain the minimized loss function, where φ1(x, y) and φ2(x, y) represent the first output and the second output of the parallel all-optical diffraction network layer, respectively. The image reconstruction loss is defined as two φ r The minimum value in the error term, that is and The losses are as follows: Among them, φ p (x,y) and φ q (x, y) represent the first label image and the second label image of the multiplexed hologram respectively, L loss Represents the total loss of the loss function.

Images