Quantitative phase imaging in dual-wavelength interferometry using a single wavelength illumination and deep learning

On the use of deep learning for phase recovery

Phase recovery (PR) refers to calculating the phase of the light field from its intensity measurements. As exemplified from quantitative phase imaging and coherent diffraction imaging to adaptive optics, PR is essential for reconstructing the refractive index distribution or topography of an object and correcting the aberration of an imaging system. In recent years, deep learning (DL), often implemented through deep neural networks, has provided unprecedented support for computational imaging, leading to more efficient solutions for various PR problems. In this review, we first briefly introduce conventional methods for PR. Then, we review how DL provides support for PR from the following three stages, namely, pre-processing, in-processing, and post-processing. We also review how DL is used in phase image processing. Finally, we summarize the work in DL for PR and provide an outlook on how to better use DL to improve the reliability and efficiency of PR. Furthermore, we present a live-updating resource ( https://github.com/kqwang/phase-recovery ) for readers to learn more about PR.

Dynamic X-ray speckle-tracking imaging with high-accuracy phase retrieval based on deep learning

Speckle-tracking X-ray imaging is an attractive candidate for dynamic X-ray imaging owing to its flexible setup and simultaneous yields of phase, transmission and scattering images. However, traditional speckle-tracking imaging methods suffer from phase distortion at locations with abrupt changes in density, which is always the case for real samples, limiting the applications of the speckle-tracking X-ray imaging method. In this paper, we report a deep-learning based method which can achieve dynamic X-ray speckle-tracking imaging with high-accuracy phase retrieval. The calibration results of a phantom show that the profile of the retrieved phase is highly consistent with the theoretical one. Experiments of polyurethane foaming demonstrated that the proposed method revealed the evolution of the complicated microstructure of the bubbles accurately. The proposed method is a promising solution for dynamic X-ray imaging with high-accuracy phase retrieval, and has extensive applications in metrology and quantitative analysis of dynamics in material science, physics, chemistry and biomedicine.

Two-step orthogonalization phase demodulation method based on a single differential interferogram

To reduce the acquisition time of interferogram and provide a dynamic phase retrieval method with arbitrary phase shift using a dual-channel simultaneous polarization phase-shifting system, a two-step orthogonalization phase demodulation method (TOPD) based on a single differential interferogram is proposed in this paper. In this method, the differential interferogram obtained by subtracting two phase-shifting interferograms and one of the Gaussian filtered based-interferograms are used to normalize and orthogonalize, and then the phase related parameters are solved by the Lissajous ellipse fitting method. Finally, the measured phase is obtained with high accuracy. The proposed method further reduces the deviation caused by the filtering operation performed in the two-step phase demodulation method. At the same time, combined it with the Lissajou ellipse fitting method reduces the limitation associated with the approximation conditions of the orthogonalization and normalization method. The experimental and simulation results demonstrate that this method provides a solution with high accuracy, high stability, strong practicability, and few restrictions for phase extraction in quantitative phase imaging.

Deep learning in optical metrology: a review

With the advances in scientific foundations and technological implementations, optical metrology has become versatile problem-solving backbones in manufacturing, fundamental research, and engineering applications, such as quality control, nondestructive testing, experimental mechanics, and biomedicine. In recent years, deep learning, a subfield of machine learning, is emerging as a powerful tool to address problems by learning from data, largely driven by the availability of massive datasets, enhanced computational power, fast data storage, and novel training algorithms for the deep neural network. It is currently promoting increased interests and gaining extensive attention for its utilization in the field of optical metrology. Unlike the traditional "physics-based" approach, deep-learning-enabled optical metrology is a kind of "data-driven" approach, which has already provided numerous alternative solutions to many challenging problems in this field with better performances. In this review, we present an overview of the current status and the latest progress of deep-learning technologies in the field of optical metrology. We first briefly introduce both traditional image-processing algorithms in optical metrology and the basic concepts of deep learning, followed by a comprehensive review of its applications in various optical metrology tasks, such as fringe denoising, phase retrieval, phase unwrapping, subset correlation, and error compensation. The open challenges faced by the current deep-learning approach in optical metrology are then discussed. Finally, the directions for future research are outlined.

Computational multi-wavelength phase synthesis using convolutional neural networks [Invited]

Multi-wavelength digital holographic microscopy (MWDHM) provides indirect measurements of the refractive index for non-dispersive samples. Successive-shot MWDHM is not appropriate for dynamic samples and single-shot MWDHM significantly increases the complexity of the optical setup due to the need for multiple lasers or a wavelength tunable source. Here we consider deep learning convolutional neural networks for computational phase synthesis to obtain high-speed simultaneous phase estimates on different wavelengths and thus single-shot estimates of the integral refractive index without increased experimental complexity. This novel, to the best of our knowledge, computational concept is validated using cell phantoms consisting of internal refractive index variations representing cytoplasm and membrane-bound organelles, respectively, and a simulation of a realistic holographic recording process. Specifically, in this work we employed data-driven computational techniques to perform accurate dual-wavelength hologram synthesis (hologram-to-hologram prediction), dual-wavelength phase synthesis (unwrapped phase-to-phase prediction), direct phase-to-index prediction using a single wavelength, hologram-to-phase prediction, and 2D phase unwrapping with sharp discontinuities (wrapped-to-unwrapped phase prediction).

Automated phase unwrapping in digital holography with deep learning

Digital holography can provide quantitative phase images related to the morphology and content of biological samples. After the numerical image reconstruction, the phase values are limited between -π and π; thus, discontinuity may occur due to the modulo 2π operation. We propose a new deep learning model that can automatically reconstruct unwrapped focused-phase images by combining digital holography and a Pix2Pix generative adversarial network (GAN) for image-to-image translation. Compared with numerical phase unwrapping methods, the proposed GAN model overcomes the difficulty of accurate phase unwrapping due to abrupt phase changes and can perform phase unwrapping at a twice faster rate. We show that the proposed model can generalize well to different types of cell images and has high performance compared to recent U-net models. The proposed method can be useful in observing the morphology and movement of biological cells in real-time applications.

Enhancement of image sharpness and height measurement using a low-speckle light source based on a patterned quantum dot film in dual-wavelength digital holography

A dual-wavelength single light source based on a patterned quantum dot (QD) film was developed with a 405nm LED and bandpass filters to increase color conversion efficiency as well as to decouple the two peaks of dual-wavelength emitted from the QD film. A QD film was patterned laterally with two different sizes of QDs and was combined with bandpass filters to produce a high efficiency and low-speckle dual-wavelength light source. The experimental results showed that the developed dual-wavelength light source can decrease speckle noise to improve the reconstructed image sharpness and the accuracy on height measurement in dual-wavelength digital holography.

Hybrid-net: a two-to-one deep learning framework for three-wavelength phase-shifting interferometry

In this paper, we propose a two-to-one deep learning (DL) framework for three- wavelength phase-shifting interferometry. The interferograms at two different wavelengths are used as the input of the proposed hybrid-net, and the interferogram of the third wavelength is used as the output. Using the advantages of the hybrid learning network, the interferogram of the third wavelength can be obtained accurately. Finally, the three-wavelength phase-shifting interferometry is realized. Compared with the previous DL-based dual-wavelength interferometry (DWI), the proposed method can further improve the measurement range of the sample without changing the DWI system. Especially for the independent step sample, the problem of limited measurement range is solved due to the input of auxiliary information. More importantly, the third wavelength can be set freely according to the measurement requirements, which is no longer limited by the actual laser and can provide more measuring ruler for phase measurement. Both experimental results and simulation analysis demonstrate the proposed method in the feasibility and the performance in improving the measurement range.