A method for extracting digital holographic object light waves based on machine learning

Abstract

The present invention discloses a digital holographic object light wave extraction method based on machine learning, which is characterized in that it includes the following steps: step one: establishing a training set; step one: constructing a curved surface as the object surface input of the holographic system, and the reference light is plane light; step one two: obtaining the phase distribution and complex amplitude distribution of the object surface light wave; step two: building a neural network; step three: phase reconstruction. The present invention relates to the field of object light wave extraction methods, specifically, to a digital holographic object light wave extraction method based on machine learning. The technical problem to be solved by the present invention is to provide a digital holographic object light wave extraction method based on machine learning, which completes holographic recording and reproduction simulation on MATLAB, and is used to produce the training set, verification set, and test set required for training the neural network; the model after training is verified using the test set; the verified neural network is used to extract the phase shift value, and then the original object light wave is reconstructed according to the phase shift algorithm based on the phase shift value and the interference pattern, and finally the reconstruction quality is analyzed.

Description

Technical Field

[0001] The present invention relates to the field of object light wave extraction, and in particular to a digital holographic object light wave extraction method based on machine learning. Background Art

[0002] Current methods for extracting light waves using phase-shifting interferometry digital holography involve using a phase shifter to introduce a phase shift into the optical path of a reference light wave. Multiple interference patterns are recorded before and after the phase shift. Algorithms are then used to calculate the corresponding pixel values ​​in these patterns to derive the phase distribution of the object's light wave. This phase distribution contains valuable information about the object under test, and once quantitatively determined, various measurement applications can be performed.

[0003] Phase-shift interferometry offers high measurement accuracy and is a key technique in optical interferometry precision measurement, with widespread applications in optical measurement and detection. However, traditional phase-shift interferometry requires specific or equal phase shift values, precise calibration and control of the phase-shifting device, and is sensitive to mechanical vibration and ambient air disturbances. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a digital holographic object light wave extraction method based on machine learning, complete holographic recording and reproduction simulation on MATLAB, and be used to produce the training set, verification set, and test set required for training the neural network. The network is built, trained, and verified based on the ResU-Net neural network architecture. The trained model will be verified using the test set; the phase shift value is extracted using the verified neural network, and then the original object light wave is reconstructed based on the phase shift value and the interference pattern according to the phase shift algorithm, and finally the reconstruction quality is analyzed.

[0005] The present invention adopts the following technical solutions to achieve the invention objectives:

[0006] A method for extracting digital holographic object light waves based on machine learning, characterized by comprising the following steps:

[0007] Step 1: Create a training set;

[0008] Step 1: Construct a curved surface as the object input of the holographic system, and the reference light is plane light;

[0009] Step 1 and 2: Obtain the phase distribution and complex amplitude distribution of the light wave on the object surface;

[0010] Step 13: Through formula (1):

[0011] R(x, y, θ) = A O e iθ (1)

[0012] A rectangular coordinate system is established with the center of the surface as the origin, with the Z axis pointing vertically upward and the X axis pointing horizontally to the right, and the X, Y, and Z axes forming a right-handed spiral relationship;

[0013] Where: R(x, y, θ) represents the complex amplitude of the reference light, x, y represent the X-axis and Y-axis coordinates, θ represents the phase of the reference light, and A O represents the real amplitude of the reference light, and i represents the imaginary unit.

[0014] By continuously changing the phase θ of the reference light wave, setting θ = 0.005 × k, where k is the number of recordings, k interference patterns with a phase shift value θ from the original interference pattern can be obtained.

[0015] Step 2: Neural network construction: Use ResUNET to build a neural network. After training, the neural network will return the model loss on the training set and the validation set to evaluate the accuracy of the model.

[0016] Step 3: Phase reconstruction;

[0017] Step 31: Phase-shift hologram generation and reconstruction;

[0018] Step 32: Data analysis;

[0019] Step 33: Error analysis.

[0020] As a further limitation of the present technical solution, in step 2, after the model training is completed, the performance of the trained neural network is evaluated by the Pearson linear correlation coefficient;

[0021] The expression of Pearson linear correlation coefficient is as follows:

[0022]

[0023] Where: Cov(x,y) is the covariance of x and y, Var[x] is the variance of x, and Var[y] is the variance of y.

[0024] As a further limitation of the present technical solution, a four-step phase shift method is adopted in step 31.

[0025] The four-step phase shifting algorithm refers to using a phase shifter to take four phase shift values ​​for the reference light when recording a hologram of a certain measurement state of an object. The intensity distributions of the four recorded images are:

[0026]

[0027]

[0028] Among them: A O represents the real amplitude of the object light wave, A Rrepresents the real amplitude of the reference light wave, and the two are measured values. represents the phase of the object light wave, which is to be measured and can be calculated by the following formula.

[0029] Using the four-step phase shift algorithm, the complex amplitude distribution of the object wave at the holographic surface can be obtained as:

[0030]

[0031] Generalized phase-shifting digital holographic interferometry, based on a four-step phase-shifting algorithm, allows the phase shift value, which originally required strictly equal step length, to be arbitrary, or even unknown. Through complex calculations, the unknown phase shift value is extracted from the phase-shift interferogram, the object light wave is reconstructed, and a holographic reconstruction simulation system is built.

[0032] Assume that the phase of the plane reference light of the first interference pattern is 0, the phase shift of the plane reference light from the first to the second interference pattern is α1, the phase shift from the second to the third is α2, and the phase shift from the third to the fourth is α3. Then, the intensity expressions of the four interference patterns can be deduced from formula (3):

[0033]

[0034] Subtract I3 from I1, and I4 from I2, and we get

[0035]

[0036]

[0037] The light field distribution on the CCD recording surface is O(x, y);

[0038] Combining (6) and (7) we can get the imaginary part of the complex amplitude of the physical light: and real part

[0039]

[0040] Further substituting the imaginary and real parts of the complex amplitude of the object light into the formula for recovering the complex amplitude of the object light wave is:

[0041]

[0042] As a further limitation of this technical solution, the specific process of step 31 is as follows:

[0043] Step 3: Input the four holograms into the neural network and extract the phase shift between them;

[0044] Step 3-2: Reconstruct the original object light wave and extract the wrapped phase using the obtained phase shift value and the recorded phase shift interferogram;

[0045] Step 313: Unwrap the recovered phase using a correlation algorithm.

[0046] Compared with the prior art, the advantages and positive effects of the present invention are:

[0047] 1. Optical holography simulations are performed using MATLAB to obtain a large amount of hologram data. This data is used as a training set to train the machine learning system. When the data of any two phase-shifted holograms are input, the phase difference (phase shift value) between the reference light waves in the two adjacent holograms can be obtained. The object light wave is reconstructed using the phase-shifting algorithm, thereby recovering the amplitude and phase of the object light wave to be measured.

[0048] 2. The method proposed in this patent does not require the phase shift value to be set in advance. Instead, the phase shift value is directly extracted from the interference pattern through machine learning methods. These phase shift values ​​can be arbitrarily unknown (generally between 0 and π) and can be unequal. The object light wave to be measured is then obtained through the corresponding object light wave reconstruction algorithm. Therefore, the calibration and control accuracy requirements for the phase shifter are reduced, the influence of environmental factors and other factors are reduced, the error immunity and ease of use are improved, the application field of digital holography technology is greatly broadened, and the cost of the instrument system is reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a three-dimensional drawing of the object surface of the present invention.

[0050] Figure 2 It is the reference light wave of the present invention.

[0051] Figure 3 This is the phase distribution and complex amplitude distribution of the present invention.

[0052] Figure 4 This is the holographic interference pattern before phase shifting of the present invention.

[0053] Figure 5 This is the interference pattern of the present invention.

[0054] Figure 6 This is a schematic diagram of the object plane phase of the training set of the present invention.

[0055] Figure 7 It is the model loss of the present invention.

[0056] Figure 8 These are the predicted data and target data of the present invention.

[0057] Figure 9 is the amplitude distribution of the input image of the present invention.

[0058] Figure 10 This is the Lena phase-shift interferogram of the present invention.

[0059] Figure 11is the restored image amplitude of the present invention.

[0060] Figure 12 is the unwrapped recovered image phase of the present invention.

[0061] Figure 13 This is the restored image phase of the present invention.

[0062] Figure 14 This is the superposition of two phase images of the present invention.

[0063] Figure 15 This is the amplitude image contrast of the present invention. DETAILED DESCRIPTION

[0064] A specific embodiment of the present invention is described in detail below with reference to the accompanying drawings, but it should be understood that the protection scope of the present invention is not limited by the specific embodiment.

[0065] like Figures 1-15 As shown, the present invention includes the following steps:

[0066] Step 1: Create a training set.

[0067] Step 1: Perform a holographic recording simulation in MATLAB, constructing an object plane (input plane) and a recording plane with a size of 128 pixels × 128 pixels. The recording and reconstruction distance of the hologram is 21.6540 mm, and the laser light source wavelength is 532 nm green light.

[0068] Construct a surface as the object surface input of the holographic system and use MATLAB to draw the object surface image, such as Figure 1 As shown: The reference light is a plane light, drawn using MATLAB, as shown Figure 2 shown.

[0069] Step 1 and 2: Obtain the phase distribution and complex amplitude distribution of the light wave on the object surface. Figure 3 As shown, the left is the phase distribution and the right is the complex amplitude distribution.

[0070] The Fresnel diffraction is calculated using the convolution method, and the impulse response of the Fresnel diffraction is given. The Fresnel diffraction field of the object light wave on the recording surface is obtained. The diffraction field of the object light wave on the recording surface interferes with the reference light wave to form a holographic interference pattern, such as Figure 4 As shown:

[0071] Step 13: Through formula (1):

[0072] R(x, y, θ) = A O e iθ (1)

[0073] A rectangular coordinate system is established with the center of the surface as the origin, with the Z axis pointing vertically upward and the X axis pointing horizontally to the right, and the X, Y, and Z axes forming a right-handed spiral relationship;

[0074] Where: R(x, y, θ) represents the complex amplitude of the reference light, x, y represent the X-axis and Y-axis coordinates, θ represents the phase of the reference light, and A O represents the real amplitude of the reference light, and i represents the imaginary unit.

[0075] By continuously changing the phase θ of the reference light wave, setting θ = 0.005×k, where k is the number of recordings, k interference patterns with a phase shift value θ from the original interference pattern can be obtained.

[0076] The original image with a phase shift value of 0 and the interference image after the first phase shift are used as the input pair of the neural network, and the phase shift value between the two interference images is used as the output of the neural network. The input pair is shown as follows Figure 5 As shown, the left side is θ=0 and the right side is θ=2.2.

[0077] When actually generating the training set, in order to prevent the training set from being too single, causing the training model to overfit and affecting the experimental results, in addition to irregular surfaces, many three-dimensional surfaces are also simulated to enhance the diversity of the training set.

[0078] Finally, 1000 pairs of interference patterns were generated as data sets by MATLAB simulation. The 1000 pairs of interference patterns were divided into training set: verification set: test set in a ratio of 6:2:2, and sent to the neural network respectively. The training set and verification set were used for model training and verification during the training process, and the test set was used for testing and performance verification after the model training was completed.

[0079] Step 2: Neural network construction; Use ResUNET to build a neural network. After training, the neural network will return the model's loss on the training set and the validation set to evaluate the accuracy of the model.

[0080] ResUNET was selected for the neural network architecture. The development environment was the TensorFlow2-GPU deep learning framework based on Python3.6.2. The computer configuration was CPU (i7-8750HCPU@2.20GHz), GPU (NvidiaGeForceGTX1050ti, 3GB video memory, CUDA11.2), and 16GB memory.

[0081] ResUNET is a combination of the deep residual neural network (ResNET) and U-NET, and makes good use of the advantages of these two neural networks: the addition of the residual module effectively suppresses the gradient vanishing or gradient exploding while reducing the number of parameters and computation; the U-shaped network structure, the training strategy of downsampling first and then upsampling, adds a small number of parameters in exchange for increased network depth.

[0082] ResUNet consists of three parts: encoding unit, bridge unit, and decoding unit.

[0083] In the encoding unit, instead of using pooling operations to downsample the feature map size, a stride of 2 is applied to the first convolutional block to reduce the amount of feature map data by half.

[0084] Before each decoding unit, the lower-level feature maps are upsampled and concatenated with the feature maps from the corresponding encoding path.

[0085] The original network structure applies 1x1 convolution with Sigmoid activation to obtain a two-dimensional output. However, the model trained in this article outputs one-dimensional data, namely phase shift values. Therefore, it is necessary to add a two-dimensional average pooling layer and a fully connected layer after the convolution block, and set the activation function to Linear.

[0086] The loss function is defined as the mean square error (MSE), and certain settings are made for the network hyperparameters. The specific network model training hyperparameters are shown in Table 1.

[0087] Table 1 Hyperparameter settings

[0088]

[0089] After training, the neural network will return the loss of the model on the training set and the validation set to evaluate the accuracy of the model, such as Figure 7 As shown in the figure, the loss of the model continues to converge with the increase in the number of training times, that is, the model works well on the verification set and can be evaluated on the test set.

[0090] After the model training is completed, 200 pairs of validation data are used to evaluate its performance. The 200 pairs of images are shuffled and input into the neural network for prediction. The predicted values ​​are compared with the original values ​​(such as Figure 8 The performance of the trained neural network was evaluated by the Pearson linear correlation coefficient.

[0091] The expression of Pearson linear correlation coefficient is as follows:

[0092]

[0093] Where: Cov(x,y) is the covariance of x and y; Var[x] is the variance of x; Var[y] is the variance of y.

[0094] After calculation, the correlation coefficient between the 200 pairs of predicted values ​​and original values ​​is:

[0095] r(target, predict)=0.980088768

[0096] Step 3: Phase reconstruction.

[0097] A phase-shifted holographic interferogram reconstruction system was established in MATLAB. The hologram was reconstructed by inputting four phase-shifted holograms generated by the holographic recording simulation system and the phase shift values ​​predicted by the neural network.

[0098] Step 31: Phase-shift hologram generation and reconstruction;

[0099] The specific process of step 31 is as follows:

[0100] A Lena image with a resolution of 512 pixels x 512 pixels is used as the amplitude input of the object, and a circular paraboloid is used as the phase input of the object to be recorded. A four-step phase shift method is used, with phase shift values ​​of 0, 0.1, 0.4, and 0.9 (for comparison and verification only; the actual value can be unknown).

[0101] like Figure 9 As shown, the left side is the amplitude distribution and the right side is the phase distribution.

[0102] Step 3: Input the four holograms into the neural network and extract the phase shift values ​​between them.

[0103] Since the neural network is trained on a 128-pixel × 128-pixel hologram, the hologram needs to be divided into 16 parts of 128 pixels × 128 pixels for input, and the extracted phase shift values ​​are averaged.

[0104] The phase shift values ​​finally predicted by the neural network are: α1 = 0.0998384 between (I) and (II), α2 = 0.4001463 between (II) and (III), and α3 = 0.9086141 between (III) and (IV).

[0105] Step 3.1.2: Input the obtained phase shift value and phase shift interferogram into MATLAB for reconstruction, as shown in Figure 11 and Figure 12 shown.

[0106] Step 3: Unwrap the phase of the restored image using MATLAB related algorithms, such as Figure 13 shown.

[0107] Step 32: Data analysis.

[0108] In order to more intuitively see the relationship between the original phase and the reconstructed phase, we can use X=256 as a cross section to compare the difference between the two phases.

[0109] like Figure 14 As shown, it can be seen that the red line (original phase) and the blue line (recovered phase) almost completely overlap, and the four-step phase-shifting coaxial holography can achieve higher-quality phase reconstruction through the phase shift value predicted by the neural network.

[0110] Through the amplitude image, Figure 15 The comparison shown here shows the original image on the left and the restored image on the right. It can be seen that there is subtle wavy noise in the restored image. The structural similarity (SSIM) of the two images calculated using MATLAB is 0.9511, indicating acceptable overall image quality.

[0111] Step 33: Error analysis.

[0112] In the experiments conducted by the present invention, the system error is the deviation between the predicted value of the neural network and the true value. The error can be reduced by further increasing the network depth and optimizing the network algorithm, but it cannot be completely avoided.

[0113] In step 31, a four-step phase shift method is adopted;

[0114] The four-step phase shifting algorithm refers to using a phase shifter to take four different phase shift values ​​for the reference light when recording a hologram of a certain measurement state of an object. The intensity distributions of the four recorded images are:

[0115]

[0116] Among them: A O represents the real amplitude of the object light wave, A R represents the real amplitude of the reference light wave, and the two are measured values. represents the phase of the object light wave, which is to be measured and can be calculated by the following formula.

[0117] Using the four-step phase shift algorithm, the complex amplitude distribution of the object light wave at the holographic surface can be obtained as follows:

[0118]

[0119] Generalized phase-shifting digital holographic interferometry, based on a four-step phase-shifting algorithm, allows the phase shift value, which originally required strictly equal step length, to be arbitrary, or even unknown. Through complex calculations, the unknown phase shift value is extracted from the phase-shift interferogram, the object light wave is reconstructed, and a holographic reconstruction simulation system is built.

[0120] Assume that the phase of the plane reference light of the first interference pattern is 0, the phase shift of the plane reference light from the first to the second interference pattern is α1, the phase shift from the second to the third is α2, and the phase shift from the third to the fourth is α3. Then, the intensity expressions of the four interference patterns can be deduced from formula (3):

[0121]

[0122] Subtract I3 from I1, and I4 from I2, and we get

[0123]

[0124]

[0125] The light field distribution on the CCD recording surface is O(x, y);

[0126] Combining (6) and (7) we can get the imaginary part of the complex amplitude of the physical light: and real part

[0127]

[0128] Further substituting the imaginary and real parts of the complex amplitude of the object light into the formula for recovering the complex amplitude of the object light wave is:

[0129]

[0130] The above disclosure is only a specific embodiment of the present invention, but the present invention is not limited thereto. Any changes that can be conceived by those skilled in the art should fall within the scope of protection of the present invention.

Claims

1. A method for extracting digital holographic object light waves based on machine learning, characterized in that: The following steps are involved: Step 1: Create a training set; Step 1: Construct a curved surface as the object input of the holographic system, and the reference light is plane light; Step 1 and 2: Obtain the phase distribution and complex amplitude distribution of the light wave on the object surface; Step 13: Through formula (1): R(x,y,θ)=A O e i i (1) A rectangular coordinate system is established with the center of the surface as the origin, with the Z axis pointing vertically upward and the X axis pointing horizontally to the right. The directions of the X, Y, and Z axes form a right-hand spiral relationship. Where: R(x, y, θ) represents the complex amplitude of the reference light, x, y represent the X-axis and Y-axis coordinates, θ represents the phase of the reference light, A O represents the real amplitude of the reference light, and i represents the imaginary unit; By continuously changing the phase θ of the reference light wave, setting θ = 0.005 × k, where k is the number of recordings, k interference patterns with a phase shift value θ from the original interference pattern can be obtained. Step 2: Neural network construction: Use ResUNET to build a neural network. After training, the neural network will return the model loss on the training set and the validation set to evaluate the accuracy of the model. Step 3: Phase reconstruction; Step 31: Phase-shift hologram generation and reconstruction; Step 32: Data analysis; Step 33: Error analysis; The specific process of step 31 is as follows: Step 3: Input the four holograms into the neural network and extract the phase shift between them; Step 3-2: Reconstruct the original object light wave and extract the wrapped phase using the obtained phase shift value and the recorded phase shift interferogram; Step 313: Unwrap the recovered phase using a correlation algorithm.

2. The method for extracting digital holographic object light waves based on machine learning according to claim 1, characterized in that: In the step 2, after the model training is completed, the performance of the trained neural network is evaluated by the Pearson linear correlation coefficient; The expression of Pearson linear correlation coefficient is as follows: Where: Cov(x, y) is the covariance of x and y; Var[x] is the variance of x; Var[y] is the variance of y.

3. The method for extracting digital holographic object light waves based on machine learning according to claim 1, characterized in that: In step 31, a four-step phase shift method is adopted; The four-step phase shift algorithm refers to the use of a phase shifter to take four phase shift values ​​for the reference light when recording a hologram of a certain state of an object, which are 0, The intensity distributions of the four recorded images are: Among them: A O represents the real amplitude of the object light wave, A R represents the real amplitude of the reference light wave, and the two are measured values. Represents the phase of the object light wave, which is to be measured; Using the four-step phase shift algorithm, the complex amplitude distribution of the object light wave at the holographic surface can be obtained as follows: Generalized phase-shifting digital holographic interferometry, based on a four-step phase-shifting algorithm, allows the phase shift value, which originally required strictly equal step length, to be arbitrary. By extracting the unknown phase shift value from the phase-shift interferogram, the object light wave is reconstructed, and a holographic reconstruction simulation system is built. Assume that the phase of the plane reference light of the first interference pattern is 0, the phase shift of the plane reference light from the first to the second interference pattern is α1, the phase shift from the second to the third is α2, and the phase shift from the third to the fourth is α3. Then, the intensity expressions of the four interference patterns can be deduced from formula (3): Subtract I3 from I1, and I4 from I2, and we get The object light wave distribution on the CCD recording surface is O(x, y); Combining (6) and (7) we can get the imaginary part of the complex amplitude of the physical light: and real part Further substituting the imaginary and real parts of the complex amplitude of the object light wave into the complex amplitude recovery formula of the object light wave is obtained:

Images