CN113743579B - Three-wavelength phase unwrapping method, system, equipment and medium based on deep learning - Google Patents
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Abstract
The invention relates to the field of optical interferometry or digital holographic measurement, in particular to a three-wavelength phase unwrapping method, a system, equipment and a medium based on deep learning, wherein the method comprises the following steps: sample at wavelength lambda 1 The interferogram is input into a deep learning neural network to obtain the sample at the wavelength lambda 2 And lambda (lambda) 3 An interferogram under the deep learning neural network for obtaining a correlation between the three wavelength interferograms at a wavelength lambda from the sample 1 From the interferograms below, the sample is obtained simultaneously at two other different wavelengths lambda 2 And lambda (lambda) 3 An interference pattern below; calculating the wavelength lambda of the sample 1 、λ 2 And lambda (lambda) 3 The lower wrap phase distribution; calculating the wavelength lambda of the sample according to the calculated wrapping phase distribution 1 、λ 2 、λ 3 The unwrapped phase below. The invention greatly simplifies the interferometry device, reduces measurement errors, effectively improves the phase measurement range, solves the problem of phase noise amplification, and improves the measurement precision.
Description
Technical Field
The invention relates to the field of optical interferometry or digital holographic measurement, in particular to a three-wavelength phase unwrapping method, a system, equipment and a medium based on deep learning.
Background
Optical interferometry is a technique for obtaining phase modulation information of an object by using light waves as an information carrier and by using the principle of interference or diffraction of light. The method realizes the measurement of the phase information of the object by recording and analyzing the interference pattern with the phase information of the object to be measured, has the advantages of full field, rapidness, no contact, high precision and the like, and has been widely used in biological microscopic imaging and high-precision quantitative measurement. The optical interferometric phase measurement technique then uses the basic principle of trigonometric functions to achieve phase reconstruction, with the extracted phase distributed between (-pi, pi). When the optical path difference of the sample to be measured changes by more than one wavelength, the phase of the object is also wrapped between (-pi, pi). In order to obtain the real phase information of the sample, a phase unwrapping method is indispensable.
Along with the continuous development of science and technology, various phase unpacking methods are proposed, but the unpacking methods proposed in the prior art all have different kinds of defects.
Among them, single Wavelength Interferometry (SWI), due to the limitation of illumination wavelength, usually employs a phase unwrapping method to recover the true phase of the sample. A number of numerical phase unwrapping methods (such as a branch cut method, a least squares unwrapping method, a quality map analysis method, etc.) are proposed, and these methods can effectively reduce the influence of noise on the phase unwrapping precision. However, in practical applications, unwrapping algorithms are long, and they are ineffective for step-like or refractive index changing measurement samples.
The dual-wavelength interferometry unpacking method introduces two wavelengths to realize dual-wavelength interferometry, and the range of wavelength limitation is obviously increased by synthesizing an equivalent wavelength longer than a single wavelength. In dual wavelength depacketizing, it is often necessary to extract the wrapping phase of a single wavelength. The more common scheme is a dual wavelength interferometry-single wavelength phase shift measurement (SWPS-DWI) and simultaneous dual wavelength interferometry acquisition. However, the main problem with existing DWIs the amplification of the inherent noise, resulting in a measurement accuracy that is far lower than SWI. In summary, the improvement of the phase recovery accuracy is still an important research direction of DWI. In order to solve this problem, many efforts have been made to reduce noise and improve accuracy. The dual-wavelength method based on special algorithm (immune algorithm, linear regression, total variation regularization) and the utilization of shorter synthetic wavelength can further improve the accuracy of DWI, but the expansion range is limited, the calculation is complex, and some specific conditions need to be met in advance.
Then, with the development of the unpacking technology, a three-wavelength unpacking method is proposed. The influence of noise on the accuracy of the dual-wavelength phase unwrapping method can be further reduced by introducing three wavelengths. Three wrapping phase diagrams with gradually reduced synthetic wavelengths can be generated by utilizing the interference diagram of the third wavelength, and then the true phase of the object is calculated by utilizing a layered optical phase unwrapping method. However, the acquisition process of the three-wavelength interference-single-wavelength phase-shifting unpacking method is easy to be interfered by vibration and takes a long time. Meanwhile, the anti-interference capability and the acquisition efficiency can be improved to a certain extent by adopting the three-wavelength interference acquisition method, but the experimental system is complex due to the introduction of three wavelengths, which is not beneficial to practical application.
Disclosure of Invention
The invention aims to overcome at least one defect (deficiency) of the prior art, and provides a three-wavelength phase unwrapping method, a system, equipment and a medium based on deep learning, which are used for solving the problems of complex experimental system and larger error in the process of phase unwrapping of a sample.
The technical scheme adopted by the invention is that the three-wavelength phase unwrapping method based on deep learning specifically comprises the following steps:
sample at wavelength lambda 1 The interferogram is input into a deep learning neural network to obtain the sample at the wavelength lambda 2 And lambda (lambda) 3 An interferogram under the deep learning neural network for obtaining a correlation between the three wavelength interferograms at a wavelength lambda from the sample 1 Simultaneously deriving the sample at two other different wavelengths lambda 2 And lambda (lambda) 3 An interference pattern below;
according to the wavelength lambda of the sample 1 The interference pattern below and the resulting sample at wavelength lambda 2 And lambda (lambda) 3 Lower interferogram, meterCalculating the wavelength lambda of the sample 1 、λ 2 And lambda (lambda) 3 The lower wrap phase distribution;
calculating the wavelength lambda of the sample according to the calculated wrapping phase distribution 1 The unwrapped phase below.
Further, the deep learning neural network is a multi-wavelength deep learning neural network MW-Net network, and the MW-Net network is trained by adopting the following steps:
constructing a MW-Net network of a multi-wavelength deep learning neural network;
collecting the sample at wavelength lambda 1 Several interferogram samples below and at two other different wavelengths lambda 2 And lambda (lambda) 3 The lower interferogram sample is used as a training data set to train the MW-Net network.
Further, the MW-Net network comprises a downsampling section, a first upsampling section and a second upsampling section; the downsampling section comprises a plurality of feature embedded blocks which are sequentially connected, each feature embedded block comprises a convolution layer, an activation function layer connected with the input end of the convolution layer, the feature embedded blocks connected between the first feature embedded block and the last feature embedded block, an activation function layer connected with the input end of the convolution layer and a normalization layer connected with the output end of the convolution layer; the first up-sampling section and the second up-sampling section comprise a plurality of feature coding blocks which are sequentially connected, and each feature coding block comprises a deconvolution layer, a normalization layer connected to the input end of the deconvolution layer and an activation function layer connected to the input end of the normalization layer;
sample at wavelength lambda 1 The interferogram is input into a deep learning neural network to obtain the sample at the wavelength lambda 2 And lambda (lambda) 3 The following interferograms specifically include:
sample at wavelength lambda 1 The lower interferogram is input into the downsampling section, and the sample is at wavelength lambda 2 The lower interferogram is output through the first up-sampling segment, the sample is at wavelength lambda 3 The lower interferogram is output through the second upsampling segment.
Further, the feature encoding blocks connected to the first three further include a dropout layer connected to the output of the deconvolution layer.
Furthermore, a plurality of jump connection layers are arranged between the downsampling section and the first upsampling section, and between the downsampling section and the second upsampling section.
In the invention, the MW-Net network learns the mapping relation among different wavelengths in an end-to-end mode, wherein the downsampling section is used for completing the characteristic downsampling process of an input interferogram, and the first upsampling section and the second upsampling section are used for realizing the interferogram output of different wavelengths in an upsampling mode. In addition, the setting of activation function layer and normalization layer in the neural network is favorable to making neural network training more stable, and the setting of dropout layer is favorable to avoiding neural network to cross the fit, and the setting of jump link layer has fused the characteristic of characteristic embedded block and characteristic coding block in downsampling section and the upsampling section, is favorable to improving neural network's training speed.
Further, training the MW-Net network specifically includes:
optimizing the weight and bias of the MW-Net network by using an Adam optimizer, and taking the minimum absolute deviation loss function as the loss function of the MW-Net network after optimization;
the loss function formula is as follows:
wherein,and->Respectively representing the wavelength lambda of the sample passing through the MW-Net network 2 And lambda (lambda) 3 Loss of->Indicating that the sample is at wavelength lambda 2 Lower interferogram sample, < ->Representing the interference pattern generated by said sample through said MW-Net network, < >>Indicating that the sample is at wavelength lambda 3 Lower interferogram sample, < ->Representing an interferogram generated by the sample in the MW-Net network, L total Representing a weighted sum of losses, i.e. the total loss, where v 1 And v 2 The weighted value is 50%, and N represents the number of pixel points in the interference image.
After the MW-Net network training is completed, the sample is at wavelength lambda 1 The interferogram is input into a deep learning neural network to obtain the sample at the wavelength lambda 2 And lambda (lambda) 3 The interference pattern below can then be calculated at the wavelength lambda of the sample by a phase shift phase recovery algorithm, such as a four-step phase shift, AIA algorithm, or the like 1 、λ 2 And lambda (lambda) 3 The lower wrap phase profile. Wherein the phase obtained is inversely proportional to the wavelength, satisfying the following requirements:
wherein,and h (x, y) is the phase and height of the sample and λ is the wavelength. The interferograms of different wavelengths satisfy the following relationship:
wherein A (x, y) and B (x, y) are the background and amplitude of the interferogram,and delta λ1,n (x, y) represents the sample at wavelength lambda 1 Phase distribution at wavelength lambda 1 The phase shift of the lower interferogram, delta λ2,n (x, y) and delta λ3,n (x, y) represents that the sample is at wavelength lambda 2 And lambda (lambda) 3 Phase shift amount of the lower interferogram. n=1, 2,3 … is the sequence of interferograms.
Further, calculating the wavelength lambda of the sample according to the calculated wrapping phase distribution 1 、λ 2 、λ 3 The following unwrapping phase comprises the following specific steps:
the composite wavelength is calculated according to the following formula:
wherein, lambda 1-2 Is of wavelength lambda 1 And lambda (lambda) 2 Λ of the composite wavelength of (a) 2-3 Is of wavelength lambda 2 And lambda (lambda) 3 Λ of the composite wavelength of (a) 1-3 Is of wavelength lambda 1 And lambda (lambda) 3 The composite wavelength of (a) and the wavelength size Λ 1-2 >Λ 2-3 >Λ 1-3 >λ 1 >λ 2 >λ 3 ；
The sample at the composite wavelength Λ is calculated according to the following formula 1-2 Lower unwrapped phase
Indicating that the sample is at wavelength lambda 1 Lower phase distribution>Indicating that the sample is at wavelength lambda 2 The lower phase distribution;
will lambda 1-2 、Λ 2-3 、Λ 1-3 、λ 1 、λ 2 、λ 3 Sequentially denoted as lambda i ，i＝1，2，3，4，5，6；
By means of the wavelength lambda of the previous order i Is a unwrapped phase of the next-order wavelength lambda i+1 Continuously iterating the wrapping phase of the sample, and calculating the wavelength lambda of the sample 1 、λ 2 、λ 3 The following unwrapped phases are iterated as follows:
wherein,indicating that the sample is at wavelength lambda i Lower unwrapped phase,/>Indicating that the sample is at wavelength lambda i+1 Lower unwrapped phase,/>Indicating that the sample is at wavelength lambda i+1 The lower wrapping phase, floor function is a downward rounding function, and K is an iteration intermediate coefficient.
According to the three-wavelength unpacking method, the MW-Net network of the multi-wavelength deep learning neural network with single-wavelength illumination is utilized, and two interference patterns with different wavelengths can be obtained from the interference pattern with a certain wavelength simultaneously by learning the relation between the interference patterns with different wavelengths, so that compared with the three-wavelength interference phase unpacking method in the prior art, the method can be realized by only acquiring the phase-shift interference pattern with a single wavelength, and the interferometry device is greatly simplified. Meanwhile, the invention combines a three-wavelength phase unwrapping method, utilizes the synthesized wavelength to replace a single wavelength, can effectively improve the phase measurement range, solves the problem of phase noise amplification of the synthesized wavelength, and improves the measurement precision.
On the other hand, the invention also provides a three-wavelength phase unwrapping system based on deep learning, which specifically comprises the following steps:
an interferogram acquisition module for acquiring a sample at wavelength lambda 1 The interferogram is input into a deep learning neural network to obtain the sample at the wavelength lambda 2 And lambda (lambda) 3 The following interferograms are used for learning by deep learning neural networkThe relationship between the three wavelength interferograms is learned from one wavelength lambda 1 Simultaneously deriving two other different wavelengths lambda from the interferograms of (a) 2 And lambda (lambda) 3 Is a pattern of interference of (a);
a wrapped phase calculation module for calculating a wrapped phase of the sample at a wavelength lambda 1 The interference pattern below and the resulting sample at wavelength lambda 2 And lambda (lambda) 3 The interference pattern of the sample at wavelength lambda is calculated 1 、λ 2 And lambda (lambda) 3 The lower wrap phase distribution;
an unwrapped phase calculation module for calculating the wavelength λ of the sample according to the wrapped phase distribution calculated by the wrapped phase module 1 、λ 2 、λ 3 The unwrapped phase below.
On the other hand, the invention also provides computer equipment, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the steps of the three-wavelength phase unwrapping method based on deep learning when executing the computer program.
In another aspect, the present invention further provides a storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the three-wavelength phase unwrapping method based on deep learning described above.
Compared with the prior art, the invention has the beneficial effects that: according to the invention, based on a multi-wavelength deep learning neural network MW-Net network, by learning the relation among interference patterns of three different wavelengths, interference patterns of two other different wavelengths are obtained from the interference patterns of a sample at one wavelength, and only the phase shift interference patterns of the sample at a single wavelength are required to be collected in the measurement process, so that the interferometry device is greatly simplified; meanwhile, in the unpacking process, the single wavelength is replaced by the synthetic wavelength, so that the phase measurement range is effectively improved, the problem of phase noise amplification is solved, and the measurement accuracy is improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a diagram of a MW-Net network architecture in accordance with the present invention.
FIG. 3 is a graph showing the experimental results of Jurkat cells as a sample to be measured in example 1 of the present invention.
Fig. 4 is a system configuration diagram in embodiment 2 of the present invention.
Description of the drawings: the interferogram acquisition module 100, the wrapping phase calculation module 200, and the unwrapping phase calculation module 300.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the invention. For better illustration of the following embodiments, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the actual product dimensions; it will be appreciated by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
Example 1
As shown in fig. 1, the implementation provides a three-wavelength phase unwrapping method based on deep learning, which specifically includes the following steps:
s1: sample at wavelength lambda 1 The interferogram is input into a deep learning neural network to obtain the sample at the wavelength lambda 2 And lambda (lambda) 3 An interferogram under the deep learning neural network for obtaining a correlation between the three wavelength interferograms at a wavelength lambda from the sample 1 Simultaneously deriving the sample at two other different wavelengths lambda 2 And lambda (lambda) 3 An interference pattern below;
s2: according to the wavelength lambda of the sample 1 The interference pattern below and the resulting sample at wavelength lambda 2 And lambda (lambda) 3 The interference pattern of the sample at wavelength lambda is calculated 1 、λ 2 And lambda (lambda) 3 The lower wrap phase distribution;
s3: calculating the wavelength lambda of the sample according to the calculated wrapping phase distribution 1 、λ 2 、λ 3 The unwrapped phase below.
Specifically, in the present embodiment, λ 1 Specifically set at 632.8nm lambda 2 Specifically set to 532nm lambda 3 Specifically set at 457nm, the input sample is at wavelength lambda 1 The specific size of the interferogram below is 256 x 256 pixels.
Further, the deep learning neural network is a multi-wavelength deep learning neural network MW-Net network, and the MW-Net network is trained by adopting the following steps:
s01: constructing a MW-Net network of a multi-wavelength deep learning neural network;
s02: collecting the sample at wavelength lambda 1 Several interferogram samples below and at two other different wavelengths lambda 2 And lambda (lambda) 3 The lower interferogram sample is used as a training data set to train the MW-Net network.
Specifically, in this embodiment, 16200 interferogram samples of samples at a wavelength of 632.8nm and corresponding interferogram samples of samples at a wavelength of 532nm and 457nm may be collected as training data sets to train the MW-Net network. The training data set can also be obtained by carrying out arithmetic operation on Gaussian functions and shape functions with different mean values and variances. In addition, to make the training data more similar to experimental data, different degrees of gaussian noise may be added to the training data set. Meanwhile, all the network training environments in the embodiment are implemented based on Pytoch 1.0 of Python 3.7, and nvidiaaeforcetegtx 1080ti GPU can be used for accelerating computation.
Further, as shown in fig. 2, the MW-Net network includes a downsampling section, a first upsampling section, and a second upsampling section; the downsampling section comprises a plurality of feature embedded blocks connected in sequence, each feature embedded block comprises a convolutional layer Conv, the last feature embedded block connected with the last feature embedded block further comprises an activating function layer LRelu connected with the input end of the convolutional layer Conv, and the feature embedded block connected between the first feature embedded block and the last feature embedded block further comprises an activating function layer LRelu connected with the input end of the convolutional layer Conv and a normalization layer BN connected with the output end of the convolutional layer Conv; the first up-sampling section and the second up-sampling section comprise a plurality of feature coding blocks which are sequentially connected, and each feature coding block comprises a deconvolution layer DeConv, a normalization layer BN connected to the input end of the deconvolution layer DeConv and an activation function layer LRelu connected to the input end of the normalization layer BN;
sample at wavelength lambda 1 The interferogram is input into a deep learning neural network to obtain the sample at the wavelength lambda 2 And lambda (lambda) 3 The following interferograms specifically include:
sample at wavelength lambda 1 The lower interferogram is input into the downsampling section, and the sample is at wavelength lambda 2 The lower interferogram is output through the first up-sampling segment, the sample is at wavelength lambda 3 The lower interferogram is output through the second upsampling segment.
Specifically, in this embodiment, the downsampling section includes 7 feature embedded blocks FEB1-FEB7 connected in sequence, the convolution kernel size of the convolution layer Conv included in the feature embedded blocks FEB1-FEB7 is 4*4, the convolution step size is 2, the first upsampling section and the second upsampling section include 7 symmetric feature coding blocks FDB1-FDB7 connected in sequence, the convolution kernel size of the feature coding blocks FDB1-FDB7 in the deconvolution layer DeConv included is 4*4, and the convolution step size is 2.
Further, the feature encoding blocks connected to the first three further comprise a dropout layer connected to the deconvolution layer DeConv output terminal.
Furthermore, a plurality of jump connection layers are arranged between the downsampling section and the first upsampling section, and between the downsampling section and the second upsampling section. Specifically, in this embodiment, the number of jump connection layers between the downsampling section and the first upsampling section, and between the downsampling section and the second upsampling section is set to 6 (as shown by the dashed line in fig. 2).
In this embodiment, the MW-Net network learns the mapping relationship between different wavelengths in an end-to-end manner, where the downsampling section is used to complete a feature downsampling process of an input interferogram, and the first upsampling section and the second upsampling section are used to implement interferogram output of different wavelengths in an upsampling manner. In addition, the setting of activation function layer and normalization layer in the neural network is favorable to making neural network training more stable, and the setting of dropout layer is favorable to avoiding neural network to cross the fit, and the setting of jump link layer has fused the characteristic of characteristic embedded block and characteristic coding block in downsampling section and the upsampling section, is favorable to improving neural network's training speed.
Further, training the MW-Net network specifically includes:
optimizing the weight and bias of the MW-Net network by using an Adam optimizer, and taking the minimum absolute deviation loss function as the loss function of the MW-Net network after optimization;
the loss function formula is as follows:
wherein,and->Respectively representing the wavelength lambda of the sample passing through the MW-Net network 2 And lambda (lambda) 3 Loss of->Indicating that the sample is at wavelength lambda 2 Lower interferogram sample, < ->Representing the interference pattern generated by said sample through said MW-Net network, < >>Indicating that the sample is at wavelength lambda 3 Lower interferogram sample, < ->Representing an interferogram generated by the sample in the MW-Net network, L total Representing a weighted sum of losses, i.e. the total loss, where v 1 And v 2 The weighted value is 50%, and N represents the number of pixel points in the interference image.
Specifically, in this embodiment, an Adam optimizer with a learning rate of 0.01 is used to optimize the weight and bias of the MW-Net. The training step length is 10000 steps, the learning rate is reduced by 1 time every 3000 steps, and the attenuation rate is 0.8.
After the MW-Net network training is completed, the sample is at wavelength lambda 1 The interferogram is input into a deep learning neural network to obtain the sample at the wavelength lambda 2 And lambda (lambda) 3 The interference pattern below can then be calculated at the wavelength lambda of the sample by a phase shift phase recovery algorithm, such as a four-step phase shift, AIA algorithm, or the like 1 、λ 2 And lambda (lambda) 3 The lower wrap phase profile. Wherein the phase obtained is inversely proportional to the wavelength, satisfying the following requirements:
wherein,and h (x, y) is the phase and height of the sample and λ is the wavelength. The interferograms of different wavelengths satisfy the following relationship:
wherein A (x, y) and B (x, y) are the background and amplitude of the interferogram,and delta λ1,n (x, y) represents the sample at wavelength lambda 1 Phase distribution at wavelength lambda 1 The phase shift of the lower interferogram, delta λ2,n (x, y) and delta λ3,n (x, y) represents that the sample is at wavelength lambda 2 And lambda (lambda) 3 Phase shift amount of the lower interferogram. n=1, 2,3 … is the sequence of interferograms.
Further, calculating the wavelength lambda of the sample according to the calculated wrapping phase distribution 1 、λ 2 、λ 3 The following unwrapping phase comprises the following specific steps:
the composite wavelength is calculated according to the following formula:
wherein, lambda 1-2 Is of wavelength lambda 1 And lambda (lambda) 2 Λ of the composite wavelength of (a) 2-3 Is of wavelength lambda 2 And lambda (lambda) 3 Λ of the composite wavelength of (a) 1-3 Is of wavelength lambda 1 And lambda (lambda) 3 The composite wavelength of (a) and the wavelength size Λ 1-2 >Λ 2-3 >Λ 1-3 >λ 1 >λ 2 >λ 3 ；
The sample at the composite wavelength Λ is calculated according to the following formula 1-2 Lower unwrapped phase
Indicating that the sample is at wavelength lambda 1 Lower phase distribution>Indicating that the sample is at wavelength lambda 2 The lower phase distribution;
will lambda 1-2 、Λ 2-3 、Λ 1-3 、λ 1 、λ 2 、λ 3 Sequentially denoted as lambda i ，i＝1，2，3，4，5，6；
By means of the wavelength lambda of the previous order i Is a unwrapped phase of the next-order wavelength lambda i+1 Continuously iterating the wrapping phase of the sample, and calculating the wavelength lambda of the sample 1 、λ 2 、λ 3 The following unwrapped phases are iterated as follows:
wherein,indicating that the sample is at wavelength lambda i Lower unwrapped phase,/>Indicating that the sample is inWavelength lambda i+1 Lower unwrapped phase,/>Indicating that the sample is at wavelength lambda i+1 The lower wrapping phase, floor function is a downward rounding function, and K is an iteration intermediate coefficient.
According to the three-wavelength phase unwrapping method provided by the embodiment, based on a single-wavelength illumination multi-wavelength deep learning neural network MW-Net network, two interference patterns with different wavelengths can be obtained from the interference patterns of a sample under one wavelength at the same time by learning the relation among the interference patterns with the three different wavelengths, and the measurement process can be realized by only collecting the phase shift interference patterns under the single wavelength, so that the interferometry device is greatly simplified; meanwhile, in the unpacking process of the embodiment, the single wavelength is replaced by the synthesized wavelength, so that the phase measurement range is effectively improved, the problem of phase noise amplification is solved, and the measurement accuracy is improved.
In addition, as shown in fig. 3, in this embodiment, jurkat cells are also included as a sample to be measured, and fig. 3 is a graph of specific experimental results of various types through an experiment of the unpacking method in this embodiment, where fig. 3 (a) shows an interferogram (MW-Net network input) of the sample at a wavelength of 632.8 nm; panel (b) shows an interferogram of a sample generated by a MW-Net network at 532nm wavelength (MW-Net network output result); FIG. (c) shows an interferogram at a wavelength of 457nm for a sample generated by a MW-Net network (MW-Net network output results); graph (d) shows the phase result (lambda) calculated by the conventional unpacking method of single wavelength interferometry 1 =632.8 nm); graph (e) shows the composite wavelength (Λ 1-2 =3.34 um); graph (f) shows the composite wavelength (Λ 2-3 =3.24 um); fig. (g) shows a phase distribution calculated by the unpacking method in the present embodiment.
Example 2
As shown in fig. 4, the embodiment provides a three-wavelength phase unwrapping system based on deep learning, which specifically includes:
an interferogram acquisition module 100 for acquiring a sample at a wavelength λ 1 The lower interferogram is input into a deep learning neural network,obtaining the sample at wavelength lambda 2 And lambda (lambda) 3 An interferogram under the deep learning neural network for learning the relationship between the three wavelength interferograms from one wavelength lambda 1 Simultaneously deriving two other different wavelengths lambda from the interferograms of (a) 2 And lambda (lambda) 3 Is a pattern of interference of (a);
a wrapping phase calculation module 200 for calculating a wrapping phase of the sample at a wavelength lambda 1 The interference pattern below and the resulting sample at wavelength lambda 2 And lambda (lambda) 3 The interference pattern of the sample at wavelength lambda is calculated 1 、λ 2 And lambda (lambda) 3 The lower wrap phase distribution;
an unwrapped phase calculation module 300 for calculating the wavelength λ of the sample according to the wrapped phase distribution calculated by the wrapped phase module 1 、λ 2 、λ 3 The unwrapped phase below.
Specifically, in the present embodiment, λ 1 Specifically set at 632.8nm lambda 2 Specifically set to 532nm lambda 3 Specifically set at 457nm, the input sample is at wavelength lambda 1 The specific size of the interferogram below is 256 x 256 pixels.
Further, the deep learning neural network is a multi-wavelength deep learning neural network MW-Net network, and the MW-Net network is trained by adopting the following steps:
constructing a MW-Net network of a multi-wavelength deep learning neural network;
collecting the sample at wavelength lambda 1 Several interferogram samples below and at two other different wavelengths lambda 2 And lambda (lambda) 3 The lower interferogram sample is used as a training data set to train the MW-Net network.
Specifically, in this embodiment, 16200 interferogram samples of samples at a wavelength of 632.8nm and corresponding interferogram samples of samples at a wavelength of 532nm and 457nm may be collected as training data sets to train the MW-Net network. The training data set can also be obtained by carrying out arithmetic operation on Gaussian functions and shape functions with different mean values and variances. In addition, to make the training data more similar to experimental data, different degrees of gaussian noise may be added to the training data set. Meanwhile, all the network training environments in the embodiment are implemented based on Pytoch 1.0 of Python 3.7, and nvidiaaeforcetegtx 1080ti GPU can be used for accelerating computation.
Further, as shown in fig. 2, the MW-Net network in this embodiment includes a downsampling section, a first upsampling section, and a second upsampling section: the downsampling section comprises a plurality of feature embedded blocks connected in sequence, each feature embedded block comprises a convolutional layer Conv, the last feature embedded block connected with the last feature embedded block further comprises an activating function layer LRelu connected with the input end of the convolutional layer Conv, and the feature embedded block connected between the first feature embedded block and the last feature embedded block further comprises an activating function layer LRelu connected with the input end of the convolutional layer Conv and a normalization layer BN connected with the output end of the convolutional layer Conv; the first up-sampling section and the second up-sampling section comprise a plurality of feature coding blocks which are sequentially connected, and each feature coding block comprises a deconvolution layer DeConv, a normalization layer BN connected to the input end of the deconvolution layer DeConv and an activation function layer LRelu connected to the input end of the normalization layer BN;
the interferogram acquisition module 100 acquires the sample at wavelength λ 1 The interferogram is input into a deep learning neural network to obtain the sample at the wavelength lambda 2 And lambda (lambda) 3 The following interferograms specifically include:
the interferogram acquisition module 100 acquires the sample at wavelength λ 1 The lower interferogram is input into the downsampling section, and the sample is at wavelength lambda 2 The lower interferogram is output through the first up-sampling segment, the sample is at wavelength lambda 3 The lower interferogram is output through the second upsampling segment.
Specifically, in this embodiment, the downsampling section includes 7 feature embedded blocks FEB1-FEB7 connected in sequence, the convolution kernel size of the convolution layer Conv included in the feature embedded blocks FEB1-FEB7 is 4*4, the convolution step size is 2, the first upsampling section and the second upsampling section include 7 symmetric feature coding blocks FDB1-FDB7 connected in sequence, the convolution kernel size of the feature coding blocks FDB1-FDB7 in the deconvolution layer DeConv included is 4*4, and the convolution step size is 2.
Further, the feature encoding blocks connected to the first three further comprise a dropout layer connected to the deconvolution layer DeConv output terminal.
Furthermore, a plurality of jump connection layers are arranged between the downsampling section and the first upsampling section, and between the downsampling section and the second upsampling section. Specifically, in this embodiment, the number of jump connection layers between the downsampling section and the first upsampling section, and between the downsampling section and the second upsampling section is set to 6 (as shown by the dashed line in fig. 2).
In this embodiment, the MW-Net network learns the mapping relationship between different wavelengths in an end-to-end manner, where the downsampling section is used to complete a feature downsampling process of an input interferogram, and the first upsampling section and the second upsampling section are used to implement interferogram output of different wavelengths in an upsampling manner. In addition, the setting of activation function layer and normalization layer in the neural network is favorable to making neural network training more stable, and the setting of dropout layer is favorable to avoiding neural network to cross the fit, and the setting of jump link layer has fused the characteristic of characteristic embedded block and characteristic coding block in downsampling section and the upsampling section, is favorable to improving neural network's training speed.
Further, training the MW-Net network specifically includes:
optimizing the weight and bias of the MW-Net network by using an Adam optimizer, and taking the minimum absolute deviation loss function as the loss function of the MW-Net network after optimization;
the loss function formula is as follows:
wherein,and->Respectively representing the wavelength lambda of the sample passing through the MW-Net network 2 And lambda (lambda) 3 Loss of->Indicating that the sample is at wavelength lambda 2 Lower interferogram sample, < ->Representing the interference pattern generated by said sample through said MW-Net network, < >>Indicating that the sample is at wavelength lambda 3 Lower interferogram sample, < ->Representing an interferogram generated by the sample in the MW-Net network, L total Representing a weighted sum of losses, i.e. the total loss, where v 1 And v 2 The weighted value is 50%, and N represents the number of pixel points in the interference image.
Specifically, in this embodiment, an Adam optimizer with a learning rate of 0.01 is used to optimize the weight and bias of the MW-Net. The training step length is 10000 steps, the learning rate is reduced by 1 time every 3000 steps, and the attenuation rate is 0.8.
After the MW-Net network training is completed, the interferogram acquisition module 100 samples at wavelength λ 1 The interferogram is input into a deep learning neural network to obtain the sample at the wavelength lambda 2 And lambda (lambda) 3 The lower interferogram, then wrapped around the phase computation module 200 may be shifted in phasePhase recovery algorithms, such as four-step phase shift, AIA algorithm, etc., calculate the sample at wavelength λ 1 、λ 2 And lambda (lambda) 3 The lower wrap phase profile. Wherein the phase obtained is inversely proportional to the wavelength, satisfying the following requirements:
wherein,and h (x, y) is the phase and height of the sample and λ is the wavelength. The interferograms of different wavelengths satisfy the following relationship:
wherein A (x, y) and B (x, y) are the background and amplitude of the interferogram,and delta λ1,n (x, y) represents the sample at wavelength lambda 1 Phase distribution at wavelength lambda 1 The phase shift of the lower interferogram, delta λ2,n (x, y) and delta λ3,n (x, y) represents that the sample is at wavelength lambda 2 And lambda (lambda) 3 Phase shift amount of the lower interferogram. n=1, 2,3 … is the sequence of interferograms.
Further, the unwrapped phase calculation module 300 calculates the wavelength λ of the sample according to the calculated wrapped phase distribution 1 、λ 2 、λ 3 The following unwrapping phase comprises the following specific steps of：
The composite wavelength is calculated according to the following formula:
wherein, lambda 1-2 Is of wavelength lambda 1 And lambda (lambda) 2 Λ of the composite wavelength of (a) 2-3 Is of wavelength lambda 2 And lambda (lambda) 3 Λ of the composite wavelength of (a) 1-3 Is of wavelength lambda 1 And lambda (lambda) 3 The composite wavelength of (a) and the wavelength size Λ 1-2 >Λ 2-3 >Λ 1-3 >λ 1 >λ 2 >λ 3 ；
The sample at the composite wavelength Λ is calculated according to the following formula 1-2 Lower unwrapped phase
Indicating that the sample is at wavelength lambda 1 Lower phase distribution>Indicating that the sample is at wavelength lambda 2 The lower phase distribution;
will lambda 1-2 、Λ 2-3 、Λ 1-3 、λ 1 、λ 2 、λ 3 Sequentially denoted as lambda i ，i＝1，2，3，4，5，6；
By means of the wavelength lambda of the previous order i Is a unwrapped phase of the next-order wavelength lambda i+1 Continuously iterating the wrapping phase of the sample, and calculating the wavelength lambda of the sample 1 、λ 2 、λ 3 The following unwrapped phases are iterated as follows:
wherein,indicating that the sample is at wavelength lambda i Lower unwrapped phase,/>Indicating that the sample is at wavelength lambda i+1 Lower unwrapped phase,/>Indicating that the sample is at wavelength lambda i+1 The lower wrapping phase, floor function is a downward rounding function, and K is an iteration intermediate coefficient.
According to the three-wavelength phase unwrapping system provided by the embodiment, based on a single-wavelength illumination multi-wavelength deep learning neural network MW-Net network, two interference patterns with different wavelengths can be obtained from the interference patterns of a sample with one wavelength at the same time by learning the relation among the interference patterns with three different wavelengths, and the measurement process can be realized by only collecting the phase shift interference patterns with the single wavelength, so that the interferometry device is greatly simplified; meanwhile, in the unpacking process of the embodiment, the single wavelength is replaced by the synthesized wavelength, so that the phase measurement range is effectively improved, the problem of phase noise amplification is solved, and the measurement accuracy is improved.
Example 3
The present embodiment provides a computer device, including a memory and a processor, where the memory stores a computer program, and the processor implements the steps of the three-wavelength phase unwrapping method based on deep learning in the foregoing embodiment 1 when executing the computer program.
Example 4
The present embodiment provides a storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the three-wavelength phase unwrapping method based on deep learning in the above embodiment 1.
It should be understood that the foregoing examples of the present invention are merely illustrative of the present invention and are not intended to limit the present invention to the specific embodiments thereof. Any modification, equivalent replacement, improvement, etc. that comes within the spirit and principle of the claims of the present invention should be included in the protection scope of the claims of the present invention.
Claims (9)
1. The three-wavelength phase unwrapping method based on deep learning is characterized by comprising the following steps of:
sample at wavelength lambda 1 The interferogram is input into a deep learning neural network to obtain the sample at the wavelength lambda 2 And lambda (lambda) 3 An interferogram under the deep learning neural network for obtaining a correlation between the three wavelength interferograms at a wavelength lambda from the sample 1 From the interferograms below, the sample is obtained simultaneously at two other different wavelengths lambda 2 And lambda (lambda) 3 An interference pattern below;
according to the wavelength lambda of the sample 1 The interference pattern below and the resulting sample at wavelength lambda 2 And lambda (lambda) 3 The interference pattern of the sample at wavelength lambda is calculated 1 、λ 2 And lambda (lambda) 3 The lower wrap phase distribution;
calculating the wavelength lambda of the sample according to the calculated wrapping phase distribution 1 、λ 2 、λ 3 Lower unwrapped phase；
Calculating the wavelength lambda of the sample according to the calculated wrapping phase distribution 1 、λ 2 、λ 3 The following unwrapping phase comprises the following specific steps:
the composite wavelength is calculated according to the following formula:
wherein, lambda 1-2 Is of wavelength lambda 1 And lambda (lambda) 2 Λ of the composite wavelength of (a) 2-3 Is of wavelength lambda 2 And lambda (lambda) 3 Λ of the composite wavelength of (a) 1-3 Is of wavelength lambda 1 And lambda (lambda) 3 The composite wavelength of (a) and the wavelength size Λ 1-2 ＞Λ 2-3 ＞Λ 1-3 ＞λ 1 ＞λ 2 ＞λ 3 ；
The sample at the composite wavelength Λ is calculated according to the following formula 1-2 Lower unwrapped phase
Indicating that the sample is at wavelength lambda 1 Lower phase distribution>Indicating that the sample is at wavelength lambda 2 A lower phase distribution, h (x, y) is the height of the sample;
will lambda 1-2 、Λ 2-3 、Λ 1-3 、λ 1 、λ 2 、λ 3 Sequentially denoted as lambda i ，i＝1，2，3，4，5，6；
By means of the wavelength lambda of the previous order i Is a unwrapped phase of the next-order wavelength lambda i+1 Continuously iterating the wrapping phase of the sample, and calculating the wavelength lambda of the sample 1 、λ 2 、λ 3 The following unwrapped phases are iterated as follows:
wherein,indicating that the sample is at wavelength lambda i Lower unwrapped phase,/>Indicating that the sample is at wavelength lambda i+1 Lower unwrapped phase,/>Indicating that the sample is at wavelength lambda i+1 The lower wrapping phase, floor function is a downward rounding function, and K is an iteration intermediate coefficient.
2. The three-wavelength phase unwrapping method based on deep learning of claim 1, wherein the deep learning neural network is a multi-wavelength deep learning neural network MW-Net network, and the MW-Net network is trained by:
constructing a MW-Net network of a multi-wavelength deep learning neural network;
collecting the sample at wavelength lambda 1 Several interferogram samples below and at two other different wavelengths lambda 2 And lambda (lambda) 3 The lower interferogram sample is used as a training data set to train the MW-Net network.
3. The deep learning based three-wavelength phase unwrapping method of claim 2, wherein the MW-Net network includes a downsampling stage, a first upsampling stage, and a second upsampling stage;
the downsampling section comprises a plurality of characteristic embedded blocks which are connected in sequence, and each characteristic embedded block comprises a convolution layer; the characteristic embedded block connected to the last one further comprises an activation function layer connected to the input end of the convolution layer; the feature embedded block connected between the first feature embedded block and the last feature embedded block further comprises an activation function layer connected with the input end of the convolution layer and a normalization layer connected with the output end of the convolution layer;
the first up-sampling section and the second up-sampling section comprise a plurality of feature coding blocks which are sequentially connected, and each feature coding block comprises a deconvolution layer, a normalization layer connected to the input end of the deconvolution layer and an activation function layer connected to the input end of the normalization layer;
sample at wavelength lambda 1 The interferogram is input into a deep learning neural network to obtain the sample at the wavelength lambda 2 And lambda (lambda) 3 The following interferograms specifically include:
sample at wavelength lambda 1 The lower interferogram is input into the downsampling section, and the sample is at wavelength lambda 2 The lower interferogram is output through the first up-sampling segment, the sample is at wavelength lambda 3 The lower interferogram is output through the second upsampling segment.
4. A three-wavelength phase unwrapping method based on deep learning as in claim 3, wherein the signature encoding blocks coupled to the first three further comprise a dropout layer coupled to the deconvolution layer output.
5. The deep learning-based three-wavelength phase unwrapping method of claim 4, further comprising a plurality of skip connection layers between the downsampling section and the first upsampling section, and between the downsampling section and the second upsampling section.
6. The three-wavelength phase unwrapping method based on deep learning as in claim 2, wherein training the MW-Net network specifically comprises:
optimizing the weight and bias of the MW-Net network by using an Adam optimizer, and taking the minimum absolute deviation loss function as the loss function of the MW-Net network after optimization;
the loss function formula is as follows:
wherein,and->Respectively representThe sample is at wavelength lambda through the MW-Net network 2 And lambda (lambda) 3 Loss of->Indicating that the sample is at wavelength lambda 2 Lower interferogram sample, < ->Representing the interference pattern generated by said sample through said MW-Net network, < >>Indicating that the sample is at wavelength lambda 3 Lower interferogram sample, < ->Representing an interferogram generated by the sample in the MW-Net network, L total Representing a weighted sum of losses, i.e. the total loss, where v 1 And v 2 The weighted value is 50%, and N represents the number of pixel points in the interference image.
7. The three-wavelength phase unwrapping system based on deep learning is characterized by comprising the following specific steps:
an interferogram acquisition module for acquiring a sample at a wavelength lambda 1 The interferogram is input into a deep learning neural network to obtain the sample at the wavelength lambda 2 And lambda (lambda) 3 An interferogram under the deep learning neural network for learning the relationship between the three wavelength interferograms from one wavelength lambda 1 Simultaneously deriving two other different wavelengths lambda from the interferograms of (a) 2 And lambda (lambda) 3 Is a pattern of interference of (a);
a wrapping phase calculation module for calculating the phase of the sample at wavelength lambda 1 The interference pattern below and the resulting sample at wavelength lambda 2 And lambda (lambda) 3 The interference pattern of the sample at wavelength lambda is calculated 1 、λ 2 And lambda (lambda) 3 The lower wrap phase distribution;
an unwrapped phase calculation module for calculating the wavelength lambda of the sample according to the wrapped phase distribution calculated by the wrapped phase module 1 、λ 2 、λ 3 The unwrapped phase below;
calculating the wavelength lambda of the sample according to the calculated wrapping phase distribution 1 、λ 2 、λ 3 The following unwrapping phase comprises the following specific steps:
the composite wavelength is calculated according to the following formula:
wherein, lambda 1-2 Is of wavelength lambda 1 And lambda (lambda) 2 Λ of the composite wavelength of (a) 2-3 Is of wavelength lambda 2 And lambda (lambda) 3 Λ of the composite wavelength of (a) 1-3 Is of wavelength lambda 1 And lambda (lambda) 3 The composite wavelength of (a) and the wavelength size Λ 1-2 ＞Λ 2-3 ＞Λ 1-3 ＞λ 1 ＞λ 2 ＞λ 3 ；
The sample at the composite wavelength Λ is calculated according to the following formula 1-2 Lower unwrapped phase
Indicating that the sample is at wavelength lambda 1 Lower phase distribution>Indicating that the sample is at wavelength lambda 2 A lower phase distribution, h (x, y) is the height of the sample;
will lambda 1-2 、Λ 2-3 、Λ 1-3 、λ 1 、λ 2 、λ 3 Sequentially denoted as lambda i ，i＝1，2，3，4，5，6；
By means of the wavelength lambda of the previous order i Is a unwrapped phase of the next-order wavelength lambda i+1 Continuously iterating the wrapping phase of the sample, and calculating the wavelength lambda of the sample 1 、λ 2 、λ 3 The following unwrapped phases are iterated as follows:
wherein,indicating that the sample is at wavelength lambda i Lower unwrapped phase,/>Indicating that the sample is at wavelength lambda i+1 Lower unwrapped phase,/>Indicating that the sample is at wavelength lambda i+1 The lower wrapping phase, floor function is a downward rounding function, K is an iterative intermediate coefficient。
8. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor implements the steps of the method of any of claims 1 to 6 when the computer program is executed.
9. A storage medium having stored thereon a computer program, which when executed by a processor, implements the steps of the method of any of claims 1 to 6.
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