Imaging method for passing through random scattering medium in visible light based on diffractive optical neural network

Abstract

The invention discloses an imaging method for passing through a random scattering medium in visible light based on a diffractive optical neural network, and the method comprises the following steps: 1, carrying out the optical coding of an input image through a coherent or low-coherent monochromatic plane wave, and enabling a coded light field to pass through a random phase diffuser for scattering; and step 2, continuous wavefront modulation of the scattered light field is obtained through a coherent or incoherent diffractive optical neural network, and finally, high-fidelity original image reconstruction is generated on an output plane. The invention finds that the coherent diffraction neural network obtains dynamic phase modulation by introducing a randomly generated diffuser in the training process, enhances the adaptive capacity of the network to the spatial coherence change of the light source, realizes the high-quality reconstruction of the scattering image under the visible light, has the robustness to the low-coherence light source, and is suitable for large-scale popularization and application. The method can be applied to low-power-consumption and real-time imaging of the dynamic scattering medium under natural light.

Description

Technical Field

[0001] This invention relates to an imaging method for scattering media, specifically to an imaging method based on a diffractive optical neural network for imaging through a randomly scattering medium in visible light. Background Technology

[0002] Optical imaging in scattering media has always been a key challenge in fields such as biomedical imaging, environmental monitoring, and autonomous driving. Although various methods have been proposed to overcome this challenge, existing technologies still have significant limitations. Traditional optical methods, such as ballistic beam separation, wavefront shaping, transfer matrix measurement, and phase retrieval based on memory effects, often struggle to achieve a good balance between imaging depth and temporal resolution. Artificial neural networks, by learning and extracting scatterer features, have shown excellent potential for solving the inverse scattering problem; however, these data-driven methods typically rely on substantial computational resources, resulting in poor real-time performance and low energy efficiency.

[0003] Diffractive optical neural networks (DONs), as a novel all-optical computing architecture, have demonstrated remarkable advantages in imaging tasks involving unknown random scattering media. They can be designed as passive, all-optical devices, achieving light-speed computation and directly reconstructing hidden target information from speckle maps without additional digital post-processing. Their potential for imaging through scattering media has already been validated in the terahertz band. While this framework has been used for random diffuse compensation in the terahertz band, extending it to the visible light band, crucial for biomedical imaging and computer vision, remains a significant research challenge. Currently, existing Diffractive optical neural networks face two major challenges in the visible light band: firstly, achieving precise alignment of neuronal units at the subwavelength scale is difficult; secondly, the imaging performance of this architecture degrades significantly under incoherent light conditions, limiting its practical application in natural lighting environments. Summary of the Invention

[0004] This invention provides an imaging method based on diffractive optical neural networks for imaging through random scattering media in visible light. This method can be used to solve the problem of imaging through scattering media in both coherent and low-coherence visible light.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] An imaging method based on a diffractive optical neural network for imaging through a randomly scattering medium in visible light includes the following steps:

[0007] Step 1: The input image is first optically encoded using coherent or low-coherence monochromatic plane waves. The encoded light field is then scattered by a random phase diffuser, where:

[0008] For coherent light, scattered light with random phases interferes, forming a speckle pattern of alternating bright and dark areas; for incoherent light fields, the incoherent light field follows the principle of intensity superposition.

[0009] A random phase diffuser is a device that uses refractive index Using glass as the basic structure, the input end is designed as an ideal plane, and the output end is constructed from a random height map. The described smooth random Gaussian surface;

[0010] The transmittance of a random phase diffuser is defined as follows:

[0011]

[0012] in, This represents the transmittance function of a random phase diffuser. Represents two-dimensional spatial coordinates. This represents the difference in refractive index between the scattering material and air. Indicates wavelength. Represents the imaginary unit. It is a set that follows the mean. Standard deviation is The random height value selected from the normal distribution, i.e. , It is a value with a mean of zero and a standard deviation of Gaussian smoothing kernel;

[0013] The scattering characteristics of random phase diffusion are derived from random height maps. Decision, through change Values ​​are used to generate phase diffusers with different randomization properties for training and testing diffraction neural networks, using a two-dimensional autocorrelation function. Used to calculate the correlation length of a random phase diffuser. As a quantitative indicator of the degree of randomization of the diffuser, it is defined as follows:

[0014]

[0015] The relevant length of the diffuser It is given by the following formula: ,in The size of a single diffraction layer;

[0016] Step 2: The scattered light field is continuously modulated via a coherent or incoherent diffractive optical neural network to finally generate a high-fidelity original image reconstruction on the output plane, wherein:

[0017] Both coherent and incoherent diffractive optical neural networks consist of three cascaded diffraction layers;

[0018] The physical process by which a coherently scattered light field obtains wavefront modulation through a coherent diffraction optical neural network includes:

[0019] (1) The coherent scattered light field propagates through free space diffraction into the first diffraction layer. The neurons on the diffraction layer apply phase modulation to the scattered light field. The coherent scattered light field is transmitted sequentially between adjacent diffraction layers through free space diffraction, realizing interlayer information transmission. Finally, the output image modulated by the three diffraction layers is obtained on the output plane. This process is expressed by the formula:

[0020]

[0021] in, Indicates the first The modulation effect of the diffraction layer on the light field. This represents free diffraction propagation from the scattering medium to the first diffraction layer. Indicates from the first The output of the diffraction layer to the first layer Free diffraction propagation between layer inputs in layer diffraction. This represents the final output light field of the coherent diffraction optical neural network. ;

[0022] (2) By employing the complex random screen method to realize the incoherent light field and simulate its propagation process, this method can generate a quasi-monochromatic Gaussian Sher beam with low spatial coherence, wherein:

[0023] Cross spectral density function of quasi-monochromatic Gauss-Sher model Represented as:

[0024]

[0025] in, and These represent the positions of two points in space. Indicates the position of the beam waist. Indicates the coherence length;

[0026] The complex random screen method includes the following steps: applying a random complex amplitude screen of a Gauss-Sherlock model beam to a coherent source field, causing the light field to propagate sequentially through a random phase diffuser and an incoherent diffractive optical neural network to the output plane. Repeat the above process with several different random complex amplitude screens, ultimately by... The propagation result of the incoherent light field is obtained by averaging the intensity of the independent coherent output light. This process can be expressed by the formula:

[0027]

[0028] in, It is the first The random complex amplitude screen used in the subcoherent simulation. It is a coherent transport transform matrix that incorporates diffuser scattering and diffraction layer modulation effects. It is the total number of coherent simulations. This represents the output light intensity of an incoherent diffractive optical neural network.

[0029] The random complex amplitude screen of the Gauss-Schwarz model beam is described as follows:

[0030]

[0031] in, It is the first The random complex amplitude screen used in the subcoherent simulation. Represents circular complex Gaussian noise. It is a power spectral function that follows a Gaussian distribution. Represents spatial frequency domain coordinates, This represents the inverse Fourier transform operator.

[0032] Compared with the prior art, the present invention has the following advantages:

[0033] 1. In this invention, when the diffuser's relevant length is 4... -14 ,in Indicating the size of a single neuron, coherent diffraction optical neural networks reconstruct coherent scattering images, achieving Pearson correlation coefficients (PCC) of 0.863–0.971 for the reconstructed images; when the diffuser correlation length is 2... -5 At that time, the incoherent diffraction optical neural network can reconstruct the incoherent scattering image, and the PCC of the reconstructed image can reach 0.861~0.899.

[0034] 2. This invention discovers that coherent diffraction neural networks obtain dynamic phase modulation by introducing randomly generated diffusers during the training process, which enhances the network's adaptability to changes in the spatial coherence of the light source. This enables high-quality reconstruction of scattering images under visible light and also has robustness to low-coherence light sources. It can be applied to low-power, real-time imaging of dynamic scattering media under natural light. Attached Figure Description

[0035] Figure 1This invention describes the workflow of imaging in visible light through a random scattering medium based on a diffractive optical neural network. An optically encoded digital image is illuminated by a monochromatic plane wave, transmitted through a random phase diffuser, and scattered. It undergoes phase modulation within the diffractive layer, ultimately forming the target digital image at the output. The image within the red border represents the coherent light input and output image, while the image within the blue border represents the incoherent light input and output image.

[0036] Figure 2 This is a schematic diagram illustrating the design and optimization process of the diffractive optical neural network for imaging through a random scattering medium according to the present invention.

[0037] Figure 3 This is a numerical simulation reconstructed image based on a coherent diffraction optical neural network according to the present invention. (a) is a partially reconstructed image, with the first column describing the stochastic phase diffuser correlation lengths of 14. 10 7 and 4 The first column shows the situation; the second, fifth, and eighth columns show the speckle image (Non) generated by the free space propagation of the coherent light field after scattering by the random diffuser; the third, sixth, and ninth columns show the imaging result (Lens) of the lens imaging system after the coherent light field is scattered by the random diffuser; the fourth, seventh, and tenth columns show the image reconstructed by the coherent diffraction optical neural network (DONN). The number in the lower right corner of the image represents the PCC value of that image. (b) is the average PCC value of 10,000 images tested blindly.

[0038] Figure 4 This is a numerical simulation image reconstructed based on an incoherent diffraction optical neural network according to the present invention. (a) is a partially reconstructed image, with the first column describing the stochastic phase diffuser correlation lengths of 5. 4 3 and 2 The first column shows the image of the incoherent light field after it has been scattered by a random diffuser and propagated in free space (Non); the second, fifth, and eighth columns show the image of the incoherent light field after it has been scattered by a random diffuser and propagated in free space (Lens); the third, sixth, and ninth columns show the image of the incoherent light field after it has been scattered by a random diffuser and then imaged by a lens imaging system (Lens); the fourth, seventh, and tenth columns show the image reconstructed by an incoherent diffraction optical neural network (IC-DONN). The number in the lower right corner of the image represents the PCC value of that image. (b) is the average PCC value of 10,000 images tested blindly.

[0039] Figure 5 This paper compares the reconstruction performance of coherent and incoherent diffractive optical neural networks of the present invention. (a)-(d) use a correlation length of 5. 4 3 and 2 Reconstructed images of coherent and incoherent diffractive optical neurons trained on diffusers. The first row shows the reconstructed images of each model under incoherent light conditions, and the second row shows the reconstructed images of each model under coherent light conditions. (e)-(h) are the average PCC values ​​of 10,000 blind test images using the same test scheme as (a)-(d).

[0040] Figure 6 The interference pattern of the random phase diffuser in the double-slit interference of the present invention is shown. (a)-(h) have coherence lengths of 20. 14 10 7 5 4 3 and 2 The interference pattern output by the diffuser under an incoherent optical field through double-slit interference. Detailed Implementation

[0041] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0042] This invention provides an imaging method for visible light through a random scattering medium based on a diffractive optical neural network, such as... Figure 1 As shown, the method includes the following steps:

[0043] Step 1: The input image is first optically encoded using a coherent or low-coherence monochromatic plane wave. The encoded light field is scattered as it passes through a random phase diffuser, whose surface has a randomly varying height distribution. This introduces a position-dependent random phase delay in front of the incident wave, resulting in scattering of the light field.

[0044] Step 2: The scattered light field is processed by a coherent or incoherent diffractive optical neural network. The coherent or incoherent diffractive optical neural network consists of three cascaded diffraction layers. The three cascaded diffraction layers perform continuous wavefront modulation on the scattered light field, and finally generate a high-fidelity original image reconstruction on the output plane.

[0045] In this invention, the random phase diffuser used is one that employs a refractive index... Using glass as the basic structure, the input end is designed as an ideal plane, and the output end is constructed from a random height map. The description refers to a smooth, random Gaussian surface. The transmittance of a random phase diffuser is defined as follows:

[0046]

[0047] in, This represents the transmittance function of a random phase diffuser. Represents two-dimensional spatial coordinates. This represents the difference in refractive index between the scattering material and air. Indicates wavelength. It represents the imaginary unit. It is a set that follows the mean. Standard deviation is The random height value selected from the normal distribution, i.e. , It is a value with a mean of zero and a standard deviation of Gaussian smoothing kernel.

[0048] In this invention, the scattering characteristics of random phase diffusion are derived from random height maps. Decision, through change Values ​​are used to generate phase diffusers with different randomization properties for training and testing diffraction neural networks. Two-dimensional autocorrelation function. Used to calculate the correlation length of a random phase diffuser. As a quantitative indicator of the degree of randomization of the diffuser, it is defined as follows:

[0049]

[0050] The relevant length of the diffuser It is given by the following formula: ,in This refers to the size of a single diffraction layer.

[0051] In this invention, the input light field is scattered by a random phase diffuser, including: for coherent light, the scattered light with random phase interferes to form alternating bright and dark speckles. For incoherent light fields, the incoherent light field follows intensity superposition. Therefore, after free-space diffraction, the incoherent light field does not produce a distinct speckle pattern, but gradually evolves into a more uniform intensity distribution, leading to degradation of the original light field information.

[0052] In this invention, both coherent and incoherent diffractive optical neural networks employ three diffraction layers. The coherent scattered light field propagates through free-space diffraction into the first diffraction layer. Neurons on the diffraction layer apply phase modulation to the scattered light field. The coherent scattered light field is then sequentially transmitted between adjacent diffraction layers through free-space diffraction, achieving inter-layer information transmission. Finally, an output image modulated by the three diffraction layers is obtained on the output plane. This process can be expressed by the following formula:

[0053]

[0054] in, Indicates the first The modulation effect of the diffraction layer on the light field. This represents free diffraction propagation from the scattering medium to the first diffraction layer. Indicates from the first The output of the diffraction layer to the first layer Free diffraction propagation between layer inputs in layer diffraction. This represents the final output light field of the coherent diffraction optical neural network. .

[0055] In this invention, an incoherent optical field is realized and its propagation process is simulated using the complex random screen method. This method can generate a quasi-monochromatic Gauss-Schelle model beam with low spatial coherence. The cross-spectral density function of the quasi-monochromatic Gauss-Schelle model is described. It can be represented as:

[0056]

[0057] in, and These represent the positions of two points in space. Indicates the position of the beam waist. This parameter represents the coherence length and is used to quantify the maximum distance between any two points in a quasi-monochromatic Gauss-Schelle model beam that can maintain coherence.

[0058] In this invention, the complex random screen method includes the following steps: applying a random complex amplitude screen of a Gauss-Schwarz model beam to a coherent light source field, so that the light field propagates sequentially through a random phase diffuser and an incoherent diffraction optical neural network to the output plane. Repeat the above process with several different random complex amplitude screens, ultimately by... The propagation result of the incoherent light field is obtained by averaging the intensity of the independent coherent output light. This process can be expressed by the formula:

[0059]

[0060] in, It is the first The random complex amplitude screen used in the subcoherent simulation. It is a coherent transport transform matrix that incorporates diffuser scattering and diffraction layer modulation effects. It is the total number of coherent simulations. This represents the output light intensity of the incoherent diffraction optical neural network. Considering limited computational resources, we set... .

[0061] The random complex amplitude screen of the Gauss-Schwarz model beam can be described as follows:

[0062]

[0063] in, It is the first The random complex amplitude screen used in the subcoherent simulation. Represents circular complex Gaussian noise. It is a power spectral function that follows a Gaussian distribution. Represents spatial frequency domain coordinates, This represents the inverse Fourier transform operator.

[0064] Figure 2 The paper presents training schemes for coherent diffractive optical neural networks and incoherent diffractive optical neural networks. In model training, both coherent and incoherent diffractive neural networks use MSE as the loss function for optimization. Loss function Represented as:

[0065]

[0066] in, This represents the target output light intensity of the diffractive optical neural network. This represents the actual output light intensity of the diffractive optical neural network. and They respectively represent the network in and Number of sampling points in each direction.

[0067] By calculating the mean squared error between the coherent or incoherent output image and the target reconstructed image, and using error backpropagation and gradient descent algorithms, the error is propagated layer by layer in reverse. This iteratively optimizes the phase parameters of neurons in each diffraction layer until the error between the output image and the target image converges to a minimum. To enhance the generalization ability of the coherent or incoherent diffractive optical neural network to random phase diffusers, the diffusers through which the input image passes are randomly generated in each training iteration. This iterative training strategy enables the network to extract intrinsic features unaffected by diffuser perturbations and achieves effective generalization after completing a full training cycle.

[0068] Figure 3 The paper presents the results of reconstructing digital images occluded by unknown random phase diffusers using a coherent diffraction optical neural network under coherent light conditions, and compares them with free-space propagation without optical systems or components and traditional lens-based imaging systems. The Pearson correlation coefficient (PCC) is used to quantitatively evaluate the image reconstruction fidelity, defined as follows:

[0069]

[0070] in, This represents the target output light intensity of the diffractive optical neural network. This represents the actual output light intensity of the diffractive optical neural network. and They represent and The average value.

[0071] Figure 3 The visual assessment results in (a) indicate that for a correlation length of 14 10 7 and 4 The phase diffuser and diffractive optical neural network can effectively compensate for phase distortion caused by different diffusers, and outperform traditional optical systems in image restoration performance. Figure 3 (b) Quantitatively analyzed the statistical results based on 10,000 digital test images, showing that the PCC value significantly increased from 0.518–0.621 (lens) to 0.863–0.971 (diffractive optical neural network).

[0072] Figure 4 The results presented are shown in the paper, which reconstruct digital images of unknown random phase diffuser occlusion using an incoherent diffractive optical neural network under incoherent light conditions. This demonstrates the excellent recovery capability of the incoherent diffractive optical neural network for optical field distortions caused by strongly scattering media.

[0073] exist Figure 5 In this paper, the reconstruction performance of the proposed coherent diffraction neural network under coherent and incoherent illumination conditions was compared through cross-validation. The results show that even under incoherent illumination, the coherent diffraction neural network maintains excellent imaging capabilities. This finding demonstrates that a coherent diffraction neural network trained with a random phase diffuser can naturally adapt to incoherent optical environments. Compared to incoherent diffraction neural networks specifically trained for incoherent light fields, the training strategy employed in this invention reduces the optimization cycle of incoherent optical systems to one-twentieth of the original.

[0074] The training strategy for coherent diffraction neural networks achieves dynamic phase modulation by introducing randomly generated pure phase diffusers into the input optical field. This method forces the network to actively learn feature representation capabilities insensitive to phase fluctuations during training, thereby enabling the network parameters to automatically adapt to the propagation characteristics of low-coherence optical fields. Figure 6 In this invention, a double-slit interference experiment further demonstrates that using a pure phase diffuser can effectively reduce the coherence of the optical field. By applying random phase diffusers with different correlation lengths to the input optical field, a gradual decrease in the contrast of the interference fringes can be observed, verifying that the pure phase diffuser has a good modulation capability for the spatial coherence of the optical field.

Claims

1. A method of imaging in the visible light through a random scattering medium based on a diffractive optical neural network, characterized in that The method comprises the following steps: Step 1, the input image is firstly optically encoded by coherent or low-coherent monochromatic plane wave, and the encoded light field is scattered through a random phase diffuser; Step 2, the scattered light field is subjected to continuous wavefront modulation through a coherent or incoherent diffractive optical neural network, and finally generates a high-fidelity original image reconstruction on an output plane.

2. The method of imaging in visible light through a random scattering medium based on a diffractive optical neural network according to claim 1, characterized in that In the step 1, for coherent light, the scattered light with random phase interferes to form speckles with light and dark alternation; for incoherent light field, the incoherent light field follows intensity superposition.

3. The method of imaging in visible light through a random scattering medium based on a diffractive optical neural network according to claim 1, characterized in that In step 1, the random phase diffuser is a glass material with refractive index as the base structure, the input end is designed as an ideal plane, and the output end is constructed as a smooth random Gaussian surface described by a random height map .

4. The method of imaging in visible light through a random scattering medium based on a diffractive optical neural network according to claim 3, characterized in that The transmittance of the random phase diffuser is defined as follows: wherein, denotes the transmittance function of the random phase diffuser, denotes the two-dimensional spatial coordinate, denotes the difference in refractive index between the scattering material and air, denotes the wavelength, denotes the imaginary unit, is a set of random height values selected from a normal distribution with mean and standard deviation , i.e. , is a Gaussian smoothing kernel with mean zero and standard deviation . Scattering properties of random phase diffusers from random height maps determined by changing values, generating phase diffusers with different randomized properties for training and testing of a diffractive neural network, two-dimensional autocorrelation function for calculating the correlation length of a random phase diffuser as a quantitative indicator of the degree of randomization of the diffuser, defined as follows: 。 5. The method of imaging in visible light through a random scattering medium based on a diffractive optical neural network according to claim 4, characterized in that The is given by where is the size of the single-layer diffractive layer.

6. The method of imaging in visible light through a random scattering medium based on a diffractive optical neural network according to claim 1, wherein In the step 2, the coherent or incoherent diffractive optical neural network is composed of three cascaded diffractive layers.

7. The method of imaging in visible light through a random scattering medium based on a diffractive optical neural network according to claim 1, characterized in that In the step 2, the physical process of wavefront modulation of the coherent scattered light field through the coherent diffractive optical neural network comprises: (1) the coherent scattered light field is transmitted into the first layer of diffractive layer through free-space diffraction propagation, the neurons on the diffractive layer exert phase modulation on the scattered light field, the coherent scattered light field is transmitted between adjacent diffractive layers through free-space diffraction in turn to realize interlayer information transmission, and finally the output image modulated by the three layers of diffractive layer is obtained on the output plane, and this process is expressed by formula as follows: wherein, represents the modulation effect of the light field by the layer diffractive layer, represents the free-diffraction propagation between the scattering medium and the first layer diffractive layer, represents the free-diffraction propagation between the layer diffractive layer output to the layer diffractive layer input, represents the final output light field of the coherent diffractive optical neural network, ; (2) the complex random screen method is used to realize the incoherent light field and simulate the propagation process thereof.

8. The method of imaging in visible light through a random scattering medium based on a diffractive optical neural network according to claim 7, characterized in that In the (2), the cross-spectral density function of the quasi-monochromatic Gaussian Schell-model is expressed as: where and denote the position of two points in space, denotes the waist position of the beam, denotes the coherence length.

9. The method of imaging in visible light through a random scattering medium based on a diffractive optical neural network according to claim 7, characterized in that In the (2), the complex random screen method includes the following steps: applying a random complex amplitude screen of a Gaussian Schell model light beam to a coherent light source field, making the light field propagate to an output plane via a random phase diffuser and an incoherent diffractive optical neural network in turn, and obtaining a complex random amplitude screen of the output light field. The above process is repeated for a plurality of different random complex amplitude screens, and finally the propagation result of the incoherent light field is obtained by averaging a plurality of independent coherent output light intensities, which is expressed by a formula as follows: The above process is repeated for a plurality of different random complex amplitude screens, and finally the propagation result of the incoherent light field is obtained by averaging a plurality of independent coherent output light intensities, which is expressed by a formula as follows: wherein, is the random complex amplitude screen used in the is the coherent propagation transform matrix including the diffuser scattering and diffraction layer modulation effects, is the total number of coherent simulations, represents the output light intensity of the incoherent diffractive optical neural network.​ 10. The method of imaging in visible light through a random scattering medium based on a diffractive optical neural network according to claim 9, characterized in that The random complex amplitude screen of the Gaussian Schell model light beam is described as follows: wherein is the random complex amplitude screen used in the denotes a circular complex Gaussian noise, is a power spectral function following a Gaussian distribution, denotes a spatial frequency domain coordinate, denotes an inverse Fourier transform operator.

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