Fractional vortex light phase retrieval and image restoration method based on deep learning

Abstract

The present invention provides a method for phase recovery and image restoration of fractional-order vortex light based on deep learning. It proposes a solution for obtaining the phase information of fractional-order vortex light at any transmission position, and constructs a model applicable to a wide range of light field patterns, thereby analyzing the phase evolution law of fractional-order vortex light during transmission. A color image restoration system is constructed based on the model. Combined with the phase evolution law of fractional-order vortex light during transmission, the phase information of any diffraction position can be accurately restored. According to the confusion matrix output by the model, it can be known that at the initial position, the model can accurately restore all phases. In the near-field diffraction area, the average accuracy is 99.3%. In the far-field diffraction area, the average accuracy is 97.8%.

Description

Technical Field

[0001] The present invention relates to the field of free-space optical communication and image processing technology, and in particular to a fractional-order vortex light phase recovery and image recovery method based on deep learning. Background Art

[0002] Obtaining the phase information of a vortex beam and thus its OAM mode is a key issue in vortex optical communication. Fractional-order vortex light, due to its unique phase evolution law, also contains richer phase information and OAM modes. However, the phase of a fractional-order vortex beam will continue to evolve during beam transmission. This makes demodulating the phase of the fractional-order vortex light at the receiving end a difficult task. Currently, the main methods for obtaining the phase information of fractional-order vortex light are as follows:

[0003] 1. GS Iterative Algorithm: An iterative diffraction calculation process between the initial input plane and the received output plane. Based on the known light field amplitude distribution on the input plane and the required light field amplitude distribution on the output plane, the required light field phase distribution on the input plane is calculated.

[0004] 2. TIE transmission equation: First, obtain the fractional vortex light intensity distribution and the intensity differential along the optical axis. Then, solve the second-order partial differential equation to obtain the specific in-plane phase distribution information at a specific location. Generally speaking, two or more defocused images can be used to predict the axial differential through finite differences. Summary of the Invention

[0005] To address the above-mentioned problems in the prior art, this application proposes a deep learning-based fractional vortex light phase recovery and image restoration method, which includes the following steps:

[0006] First, the RGB format image is channel-separated and decomposed into R, G, and B formats, and modulation is performed on the R, G, and B format images; the presence or absence of the fractional-order vortex beam pattern is used to represent the binary number of the pixel;

[0007] Based on a deep learning model, multiple axial measurements are performed to obtain intensity maps of the fractional vortex light field at different locations. The intensity maps at different locations are used to represent the image information under different channels. The obtained intensity maps are then input into the model to obtain the phase image of the corresponding light beam.

[0008] According to the vortex intensity value contained in the phase image, the pixels of different channels are decoded into binary numbers. After decoding, images under different channels are obtained, and then the channels are composited to obtain the corresponding original images.

[0009] Preferably, the deep learning model is:

[0010] Loss function:

[0011]

[0012] x represents the source domain image, y represents the real image, z represents the noise input to the generator G network, D(x,y) represents the probability that the discriminator D network judges whether the real image is real; G(x,z) represents the target domain image generated by the G network based on the source domain image and random noise; and D(x,G(x,z)) is the probability that the D network judges whether the image generated by G is real; E represents the mathematical expectation; V(D,G) is the objective function of the discriminator;

[0013] Based on the loss function, the deep learning model consists of a generator part and a discriminator part. In the generator part, the light field intensity map of the fractional-order vortex light at different positions is used as the input image, and the residual network convolution layer is the vortex beam image. The convolution kernel performs the convolution operation, followed by feature mapping and repeated convolution operations. The model generator uses the convolution layer. The convolution step size is set to a value greater than 1, allowing the network to learn the downsampling method on its own. The BN layer is used for batch normalization. The inverse recovery operation is performed by using the transposed convolution layer.

[0014] After the above steps, the generator realizes the conversion from image to data and then to image; the image obtained by the generator and the real image are input to the discriminator; the discriminator uses a Markov discriminator; after the convolution layer operates on the input image, it is finally averaged to obtain an image of size 1×1, and then determines whether the generated image is real or fake.

[0015] Preferably, the deep learning model adopts a similarity comparison scheme to quantify the model recovery effect. First, the probability distribution of the two images on the histogram is calculated respectively, the probabilities of the same position are multiplied, and then the square root is taken, and the square root results are accumulated; if the distribution probability of the two images at a certain point is exactly the same, then the calculation result of the two images at the said point is the same as the distribution probability of any image at the said point. If the two images are exactly the same, then the calculation result is exactly the same as the distribution probability of any image on the histogram, and the accumulated result must be 1; the calculation formula is:

[0016]

[0017] Where p(i) and p'(i) represent the image histogram data of the source and candidate respectively. The result of adding the square root of the product of each identical data point i is the image similarity value.

[0018] Preferably, the decoding method is: taking the pattern with the largest initial topological charge value as the highest bit, and arranging them from high to low; sending the arrangement of the intensity image into the PRN model, and performing phase recovery on the intensity images in three formats respectively; decoding according to the recovered phase image; after decoding, converting the obtained binary value into decimal, importing the decimal matrix into MATLAB, and obtaining the restored image after three demodulations.

[0019] Preferably, the training method of the deep learning model is:

[0020] A laser is used to emit a linearly polarized fundamental mode Gaussian beam, which is then irradiated onto a reflective spatial light modulator.

[0021] A reflective spatial light modulator modulates the laser beam based on the principle of a multi-field phase mask, generating fractional vortex beams with different topological charges. These vortex beams are carefully recorded by a CCD camera through a 2-f lens system.

[0022] The image formed on the focal plane is the Fraunhofer diffraction pattern of the light beam. The focal plane is the first measurement position. The Fresnel diffraction pattern of the fractional vortex beam is obtained at the second measurement position in front of the focal plane and after the lens. The third measurement position is in front of the lens, where the light beam propagates in free space without being diffracted by the lens.

[0023] The obtained intensity image is fed into the constructed deep learning model for training.

[0024] Preferably, the wavelength of the linearly polarized fundamental mode Gaussian beam emitted by the laser is λ=532nm, the beam waist radius ω0=5λ, and the intensity of the incident beam is controlled by a combination of a half-wave plate and a beam polarization beam splitter; the beam expansion system located between the half-wave plate and the beam polarization beam splitter includes a pair of lenses and an aperture, which expands the beam waist to 1mm.

[0025] The above technical features can be combined in various suitable ways or replaced by equivalent technical features, as long as the purpose of the present invention can be achieved.

[0026] The present invention provides a method for phase recovery and image restoration of fractional vortex light based on deep learning. Compared with the existing technology, it has at least the following advantages:

[0027] By combining the phase evolution of fractional-order vortex light during transmission, the phase information at any diffraction position can be accurately recovered. The confusion matrix output by the model shows that at the initial position, the model can accurately recover all phases, with an average accuracy of 99.3% in the near-field diffraction region and 97.8% in the far-field diffraction region.

[0028] This model has a wider range of recognition for fractional vortex light and works well for initial topological charges of 1.7-4.7, which is three times wider than the previous model's 1.1-2.1.

[0029] This model can be actually used in free-space optical communications to realize information recovery of color images, which can recover more information than previous gray image recovery. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The present invention will be described in more detail below based on embodiments and with reference to the accompanying drawings, wherein:

[0031] Figure 1 This is a diagram of the internal principles of a deep learning model and the architecture of the entire solution. A deep learning model consists of two parts: a generator and a discriminator. The generator is responsible for generating samples to confuse the discriminator as much as possible, while the discriminator is responsible for distinguishing between the samples generated by the generator and real samples as much as possible.

[0032] Figure 2 It is a diagram of the experimental scheme for obtaining the model training set;

[0033] Figure 3 are the numerical simulation results of the constructed model; the intensity and phase information of the initial position corresponding to series 1 (A1-D1); the information of near-field diffraction corresponding to series 2 (A2-D2); and the information of far-field diffraction corresponding to series 3 (A3-D3); A, B, C, and D correspond to topological charges of 1.7, 2.3, 3.3, and 4.7, respectively;

[0034] Figure 4 This is a design diagram for color image restoration;

[0035] Figure 5 It is a comparison between the final restored color image and the original image, including the comparison of the grayscale histogram of the two images, and gives the Bhattacharyya coefficient of the two (the closer to 1, the more similar). DETAILED DESCRIPTION

[0036] The present invention will be further described below with reference to the accompanying drawings.

[0037] The present invention provides a method for phase recovery and image restoration of fractional-order vortex light based on deep learning, comprising the following steps:

[0038] First, the RGB format image is channel-separated and decomposed into R, G, and B formats, and modulation is performed on the R, G, and B format images; the presence or absence of the fractional-order vortex beam pattern is used to represent the binary number of the pixel;

[0039] Based on a deep learning model, multiple axial measurements are performed to obtain intensity maps of the fractional vortex light field at different locations. The intensity maps at different locations are used to represent the image information under different channels. The obtained intensity maps are then input into the model to obtain the phase image of the corresponding light beam.

[0040] According to the vortex intensity value contained in the phase image, the pixels of different channels are decoded into binary numbers. After decoding, images under different channels are obtained, and then the channels are composited to obtain the corresponding original images.

[0041] In one embodiment, an RGB color image is first channel-separated into three RGB formats, and three modulations are performed on the three formats. The presence or absence of a fractional-order vortex beam pattern is used to represent the binary number of the pixel.

[0042] Based on the model's more powerful phase recovery capabilities, three axial measurements were performed to obtain intensity maps of the fractional vortex light field at three different locations. These intensity maps were used to represent the image information under the three channels. The obtained intensity maps were then input into the model to obtain the phase image of the corresponding light beam.

[0043] According to the vortex intensity value contained in the phase image, the pixels of the three channels are decoded into binary numbers. After three decodings are completed, the images under the three channels are obtained, and then the channels are composited to obtain the corresponding original images.

[0044] In one embodiment, a deep learning-based fractional vortex optical phase recovery method includes the following steps: a laser emits a linearly polarized fundamental mode Gaussian beam with a wavelength of λ = 532nm (beam waist radius ω0 = 5λ). The intensity of the incident beam is controlled by a combination of a half-wave plate and a beam polarization beam splitter to prevent excessive beam intensity from damaging the spatial light modulator. A beam expander, consisting of a pair of lenses and an aperture, expands the beam waist to approximately 1mm. The expanded and collimated beam is then directed onto a reflective spatial light modulator.

[0045] The reflective spatial light modulator modulates the laser beam based on the principle of a multi-field phase mask, and then generates fractional vortex beams with different topological charges. The topological charge is selected based on the phase evolution law of fractional-order vortex light discussed previously. After modulation by the spatial light modulator, the light field becomes the expected vortex beam with various topological charges, which can be carefully recorded by the CCD camera through the 2-f lens system. In this experimental design, in order to reduce the measurement error, a converging lens with a large focal length should be selected as much as possible, because this will ensure that the diffraction pattern of the fractional-order vortex light is clearer. Here, a lens with f = 300mm is selected to measure the intensity distribution near or on their focal plane. At the same time, the 2-f lens system needs to be precisely adjusted so that the distance from the spatial light modulator to the lens and the distance from the lens to the CCD are both equal to f.

[0046] According to coherent optical system theory, the image formed at the focal plane is the Fraunhofer diffraction pattern of the beam. Therefore, the focal plane is the first measurement position, i.e., z1 in the figure. After measuring the intensity at the focal plane, according to diffraction theory, the Fresnel diffraction pattern of the fractional vortex beam is obtained at z2, 150 mm in front of the focal plane, or 150 mm behind the lens. The third measurement position is z3, 50 mm in front of the lens. The beam propagates in free space without lens diffraction. The resulting intensity image is fed into the constructed model for training.

[0047] In one embodiment, the loss function is:

[0048]

[0049] x represents the source image, y represents the real image, z represents the noise input to the generator network G, and D(x,y) represents the probability that the discriminator network D determines whether the real image is real (because y is real, the closer this value is to 1, the better for D). G(x,z) represents the target image generated by the G network based on the source image and random noise. And D(x,G(x,z)) is the probability that the D network determines whether the image generated by G is real. E represents the mathematical expectation.

[0050] This objective function can be understood in two parts: The discriminator is optimized by implementing V(D, G) as the discriminator's objective function. The first expectation in the formula is the mathematical expectation of the probability that the discriminator determines a sample from the true data distribution to be a true sample. For real data samples, the closer the predicted probability is to 1, the better, so this expectation value should be large. The second expectation refers to the expected value of the negative logarithm of the predicted probability of the generated image obtained after the sample sampled from the noise distribution passes through the generator and is then sent to the discriminator. The larger this value, the better. The larger this value, the closer it is to 0 overall, and the better the discriminator's performance. The generator is optimized by minimizing the maximum value of the objective function. It is worth noting that the generator does not minimize the discriminator's objective function, but rather minimizes the maximum value of the discriminator's objective function.

[0051] Based on the loss function, the specific framework of the model construction is as follows: In the generator, the convolutional layer of the residual network uses a 256×256 vortex bundle image. Convolution operations are performed with kernel 4 and a stride of 2. This results in a 64×128 feature map. Similar to the above principle, the convolution operation is repeated to obtain a 128×64 feature map. When downsampling these feature maps, although the fully connected layers are replaced by convolutions, as in CNNs, the model generator uses convolutional layers instead of spatial pooling layers, unlike typical CNNs. Specifically, the convolution stride is set to a value greater than 1. The significance of this improvement is that the downsampling process no longer requires fixed pixel values ​​to be discarded at certain locations, but rather allows the network to learn the downsampling method. Furthermore, a BN layer is used for batch normalization, a common normalization method after convolutional layers, which helps the network converge. A transposed convolutional layer is used to perform the inverse recovery operation. Through these steps, the generator achieves the transformation from image to data and back to image. The images obtained by the generator and the real images are input to the discriminator. The discriminator uses a Markov discriminator. This structure is very similar to a typical CNN, but the final output data differs. The Markov discriminator converts the input into an N×N matrix and then calculates the average to determine the discriminator's final output. As shown in the figure, after the convolutional layer operates on the input image, we obtain a 30×30 matrix. Through averaging, we ultimately obtain a 1×1 matrix, which determines whether the generated image is real or fake.

[0052] In one embodiment, in order to accurately quantify the error size of the drawing result, a similarity comparison scheme is adopted to quantify the model recovery effect, which provides a basis for the subsequent construction of the confusion matrix. The principle of calculating image similarity is: first find the probability distribution of the two images on the histogram respectively, multiply the probabilities of the same position (if the distribution probability of a certain image at this location is 0, the product result is 1, indicating that they are completely different at this location), then take the square root, and then accumulate the square root results. If the distribution probability of the two images at a certain location is exactly the same, then the calculation result at this location is the same as the distribution probability of any image at this location. If the two images are exactly the same, then the calculation result is exactly the same as the distribution probability of any image on the histogram, and the cumulative result must be 1. The calculation formula is:

[0053]

[0054] Where p(i) and p'(i) represent the image histogram data of the source and candidate respectively. The result of adding the square root of the product of each identical data point i is the image similarity value.

[0055] A 50×50, 8-bit, 256-color image was selected for simulation. This image contains 2500 pixels, each represented by an 8-bit binary number. Therefore, when encoding the pixels, two initial topological charges were selected for each of the four phase evolution patterns of fractional vortex light. Here, we selected 1.6, 1.8; 2.2, 2.4; 3.2, 3.4; and 4.6, 4.8.

[0056] The pattern with the largest initial topological charge is used as the highest bit, and the images are arranged from highest to lowest. The intensity image arrangement is fed into the PRN model, and phase recovery is performed on the intensity images in each of the three formats. Decoding is performed based on the recovered phase images. After decoding, the resulting binary value is converted to decimal, and the decimal matrix is ​​imported into MATLAB to obtain the restored image after three demodulations.

[0057] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be employed in conjunction with other described embodiments.

Claims

1. A fractional-order vortex light phase recovery and image restoration method based on deep learning, characterized in that: The following steps are involved: First, the RGB format image is channel-separated and decomposed into R, G, and B formats, and modulation is performed on the R, G, and B format images; The presence or absence of a fractional vortex beam pattern is used to characterize the binary number of a pixel; Based on the deep learning model, multiple axial measurements are performed to obtain the intensity maps of the fractional vortex light field at different positions. The intensity maps at different positions are used to represent the image information under different channels. The obtained intensity maps are then input into the model to obtain the phase image of the corresponding light beam. The loss function of the deep learning model is: x represents the source domain image, y represents the real image, z represents the noise input to the generator G network, D(x,y) represents the probability that the discriminator D network judges whether the real image is real; G(x,z) represents the target domain image generated by the G network based on the source domain image and random noise; and D(x,G(x,z)) is the probability that the D network judges whether the image generated by G is real; E represents the mathematical expectation; V(D,G) is the objective function of the discriminator; According to the vortex intensity value contained in the phase image, the pixels of different channels are decoded into binary numbers. After decoding, images under different channels are obtained, and then the channels are composited to obtain the corresponding original images.

2. The fractional-order vortex light phase recovery and image restoration method based on deep learning according to claim 1 is characterized in that: Based on the loss function, the deep learning model consists of a generator part and a discriminator part. In the generator part, the light field intensity map of fractional-order vortex light at different positions is used as the input image, and the residual network convolution layer is the vortex beam image. The convolution kernel performs a convolution operation, followed by feature mapping and repeated convolution operations. The model generator uses a convolution layer. The convolution step size is set to a value greater than 1, allowing the network to learn the downsampling method on its own. Batch normalization is performed using a BN layer. The inverse recovery operation is performed by using a transposed convolution layer. After the above steps, the generator realizes the conversion from image to data and then back to image; The image obtained by the generator and the real image are input to the discriminator; the discriminator adopts Markov discriminator; after the convolution layer operates on the input image, it is finally obtained by averaging to obtain an image of size 1×1, and then determines whether the generated image is real or fake.

3. The fractional-order vortex light phase recovery and image restoration method based on deep learning according to claim 2 is characterized in that: The deep learning model uses a similarity comparison scheme to quantify the model recovery effect. First, the probability distribution of the two images on the histogram is calculated separately, the probabilities of the same position are multiplied, and then the square root is taken. The square root results are then accumulated. If the distribution probability of the two images at a certain point is exactly the same, then the calculation result of the two images at that point is the same as the distribution probability of any image at that point. If the two images are exactly the same, then the calculation result is exactly the same as the distribution probability of any image on the histogram, and the accumulated result must be 1. The calculation formula is: Where p(i) and p'(i) represent the image histogram data of the source and candidate respectively. The result of adding the square root of the product of each identical data point i is the image similarity value.

4. The method for phase recovery and image restoration of fractional-order vortex light based on deep learning according to claim 1, characterized in that: The decoding method comprises: taking the pattern with the largest initial topological charge value as the highest bit and arranging them from high to low; feeding the arrangement of the intensity image into the PRN model, performing phase recovery on the intensity images in the three formats respectively; and performing decoding based on the recovered phase image; After decoding, the binary value is converted into decimal, and the matrix of decimal numbers is imported into MATLAB to obtain the restored image after three demodulations.

5. The fractional-order vortex light phase recovery and image restoration method based on deep learning according to claim 2, characterized in that: The training method of the deep learning model is: A laser is used to emit a linearly polarized fundamental mode Gaussian beam, which is then irradiated onto a reflective spatial light modulator. A reflective spatial light modulator modulates the laser beam based on the principle of a multi-field phase mask, generating fractional vortex beams with different topological charges. These vortex beams are carefully recorded by a CCD camera through a 2-f lens system. The image formed on the focal plane is the Fraunhofer diffraction pattern of the light beam. The focal plane is the first measurement position. The Fresnel diffraction pattern of the fractional vortex beam is obtained at the second measurement position in front of the focal plane and after the lens. The third measurement position is in front of the lens, where the light beam propagates in free space without being diffracted by the lens. The obtained intensity image is fed into the constructed deep learning model for training.

6. The fractional-order vortex light phase recovery and image restoration method based on deep learning according to claim 1, characterized in that: The wavelength of the linearly polarized fundamental mode Gaussian beam emitted by the laser is λ = 532nm, and the beam waist radius ω0 = 5λ. The intensity of the incident beam is controlled by a combination of a half-wave plate and a beam polarization beam splitter; the beam expansion system located between the half-wave plate and the beam polarization beam splitter includes a pair of lenses and an aperture, which expands the beam waist to 1mm.

Images