Digital holographic wrapped phase aberration compensation method based on deep learning
In a digital holographic wrapped phase aberration compensation method based on deep learning, a random Zernike polynomial coefficient and a corresponding wrapped phase map are generated by a computer and are respectively treated as a learning label and a network to train a neural network model. A digital holographic optical setup is built to record a hologram of a sample to be measured, the wrapped phase map is inputted into the trained neural network model after numerical reconstruction, and the Zernike polynomial coefficient is outputted to reconstruct a phase aberration distribution and to compensate complex amplitude in a spatial domain. Phase filtering and unwrapping are performed on the compensated wrapped phase map, and Zernike polynomial fitting based on background segmentation is performed on the unwrapped phase to compensate for residual aberration.
1 . A digital holographic wrapped phase aberration compensation method based on deep learning, applied to a digital holographic optical measurement system characterized in that, the method comprises two stages comprising a network training stage and a holographic measurement stage, and the method is divided into the following steps:
a. in the network training stage, comprising:
automatically generating, by a computer, simulated wrapped phase map data, wherein the simulated wrapped phase map data are obtained by constructing a microstructure phase aberration distribution using Zernike polynomials and converting the microstructure phase aberration distribution into a wrapped phase; and
inputting, by the computer, the simulated wrapped phase map data into a neural network model for training to obtain a trained neural network model, wherein the neural network model is a deep residual network adopting a ResNet50 architecture and is configured to process wrapped phase data with a value in a range of [−π, π]; and
b. in the holographic measurement stage, comprising:
building a digital holographic optical apparatus to measure a microstructure sample used for holographic imaging, wherein the microstructure sample is a transmission type sample or a reflection-type sample; and
processing, by the trained neural network model, an aberration compensation processing on wrapped phase data of the microstructure sample, and obtaining a three-dimensional profile distribution of the microstructure sample, wherein the aberration compensation processing comprises a pre-compensated step performed before phase unwrapping and a residual compensation step performed after phase unwrapping.
2 . The digital holographic wrapped phase aberration compensation method based on deep learning according to claim 1 , wherein the step for generating the simulated wrapped phase map data in the network training stage comprises:
step one: generating, by the computer, a large number of random Zernike polynomial coefficients A, fitting, by using the Zernike polynomial coefficients A, several continuous two-dimensional surfaces as phase aberrations through Zernike polynomials, and superimposing the phase aberrations on a same type of microstructure phase as the sample to be measured to construct a microstructure phase aberration distribution φ;
step two: converting the microstructure phase aberration distribution φ into a complex exponent and calculating a phase angle of the complex exponent to obtain a simulated wrapped phase map φ with the value in the range of [−π, π];
step three: establishing the neural network model adopting the ResNet50 architecture, training the neural network model by treating the simulated wrapped phase map φ as an input of the neural network model and treating the corresponding Zernike polynomial coefficient A as a label of the neural network model, and obtaining the trained neural network model.
3 . The digital holographic wrapped phase aberration compensation method based on deep learning according to claim 1 , wherein the holographic measurement stage comprises following steps:
S1: building the digital holographic optical apparatus to measure the microstructure sample and record a hologram of the microstructure sample, performing numerical reconstruction based on the hologram to obtain a complex amplitude U of the microstructure sample, calculating a wrapped phase map of the complex amplitude U and inputting the wrapped phase map into the trained neural network model, and outputting a Zernike polynomial coefficient A c by the neural network model;
S2: before phase unwrapping, fitting, by using the Zernike polynomial coefficient A c , phase aberration φ ac and multiplying a conjugate complex exponent exp(−jφ α ) of the phase aberration φ ac by the complex amplitude U to obtain a pre-compensated wrapped phase map with most of the phase aberration being compensated;
S3: performing phase filtering and phase unwrapping on the pre-compensated wrapped phase map to obtain a continuous phase distribution φ c containing only a small part of phase aberration, and performing edge enhancement and local adaptive threshold segmentation on the continuous phase distribution φ c to obtain a binary mask that only represents a background region;
S4: extracting, by using the binary mask, phase data of the background region in continuous phase distribution Pc, constructing a Zernike polynomial equation set based on the phase data of the background region, solving a Zernike polynomial coefficient A r of residual aberration, and performing, by using the Zernike polynomial coefficient A r , Zernike polynomial fitting to obtain a residual aberration phase distribution φ r ; and
S5: subtracting the phase distribution φ r from the continuous phase distribution φ c to recover and obtain a true phase of the microstructure sample, and performing wavelength conversion on the true phase to output and obtaining the three-dimensional profile distribution of the sample to be measured.
4 . The digital holographic wrapped phase aberration compensation method based on deep learning according to claim 3 , wherein in the S1, the digital holographic optical setup is one of a coaxial structure, an off-axis structure, a microscopic imaging structure, a multi-wavelength structure and a super-resolution structure.
5 . The digital holographic wrapped phase aberration compensation method based on deep learning according to claim 3 , wherein in the S1, the numerical reconstruction comprises a first step and a second step performed in sequence, wherein the first step is a phase shifting step or a spatial filtering step, and the second step is a Fresnel diffraction method, a convolution method, an angular spectrum method or a compressed sensing reconstruction step.
6 . The digital holographic wrapped phase aberration compensation method based on deep learning according to claim 3 , wherein in the S3, the edge enhancement is achieved by superimposing gradients of continuous phases and a gradient binarization result, and the local adaptive threshold segmentation is to separately calculate a threshold of each pixel in the continuous phases and perform binarization processing.
7 . The digital holographic wrapped phase aberration compensation method based on deep learning according to claim 1 , wherein the microstructure sample used for holographic imaging is a microstructure suitable for digital holographic imaging, comprising a Microelectromechanical Systems micro-nano structure, and an integrated circuit chip.