Super-resolution microscopy for biological specimens: lensless phase retrieval in noisy conditions

Quantitative phase imaging techniques for measuring scattering properties of cells and tissues: a review-part I

Significance

Quantitative phase imaging (QPI) techniques offer intrinsic information about the sample of interest in a label-free, noninvasive manner and have an enormous potential for wide biomedical applications with negligible perturbations to the natural state of the sample in vitro.

Aim

We aim to present an in-depth review of the scattering formulation of light-matter interactions as applied to biological samples such as cells and tissues, discuss the relevant quantitative phase measurement techniques, and present a summary of various reported applications.

Approach

We start with scattering theory and scattering properties of biological samples followed by an exploration of various microscopy configurations for 2D QPI for measurement of structure and dynamics.

Results

We reviewed 157 publications and presented a range of QPI techniques and discussed suitable applications for each. We also presented the theoretical frameworks for phase reconstruction associated with the discussed techniques and highlighted their domains of validity.

Conclusions

We provide detailed theoretical as well as system-level information for a wide range of QPI techniques. Our study can serve as a guideline for new researchers looking for an exhaustive literature review of QPI methods and relevant applications.

Pixel Super-Resolution Phase Retrieval for Lensless On-Chip Microscopy via Accelerated Wirtinger Flow

Empowered by pixel super-resolution (PSR) and phase retrieval techniques, lensless on-chip microscopy opens up new possibilities for high-throughput biomedical imaging. However, the current PSR phase retrieval approaches are time consuming in terms of both the measurement and reconstruction procedures. In this work, we present a novel computational framework for PSR phase retrieval to address these concerns. Specifically, a sparsity-promoting regularizer is introduced to enhance the well posedness of the nonconvex problem under limited measurements, and Nesterov’s momentum is used to accelerate the iterations. The resulting algorithm, termed accelerated Wirtinger flow (AWF), achieves at least an order of magnitude faster rate of convergence and allows a twofold reduction in the measurement number while maintaining competitive reconstruction quality. Furthermore, we provide general guidance for step size selection based on theoretical analyses, facilitating simple implementation without the need for complicated parameter tuning. The proposed AWF algorithm is compatible with most of the existing lensless on-chip microscopes and could help achieve label-free rapid whole slide imaging of dynamic biological activities at subpixel resolution.

Phase retrieval of a Kolmogorov phase screen from very sparse data using four binary masks

We investigate experimentally the phase retrieval of a Kolmogorov phase screen from very sparse data by modulating its amplitude with four binary masks and compare the retrieved phase screen to the ground truth measured with a surface profiler. Previously, we have shown in simulations that this kind of modulation can be successfully used for the phase retrieval of a Kolmogorov phase screen. After subtracting the ground truth from the retrieved phase screen, the root-mean-square error decreased from 0.14 µm to 0.10 µm. We conclude that a Kolmogorov phase screen can be recovered using simple modulation and very sparse data.

Phase Recovery Guarantees from Designed Coded Diffraction Patterns in Optical Imaging

Phase retrieval is an inverse problem that consists in estimating a scene from diffraction intensities. This problem appears in optical imaging, which has three main diffraction zones where the measurements can be acquired, i.e., near, middle and far. Recent works have theoretically solved this inverse problem for the far zone, creating redundancy in the measurement process by including a coded aperture, which allows to modulate the scene and acquire coded diffraction patterns (CDP). However, in the state-of-the-art, the PR problem has not been theoretically studied for CDP at the near and middle zones. Moreover, the structure of the coded aperture is selected at random, leading to suboptimal estimations. Indeed, some of the coding elements employed in the literature are unfeasible because they increase the power of the scene in the modulation process. This paper provides theoretical guarantees for the recovery of a scene from CDP acquired at the three diffraction zones using admissible modulations. Based on the theoretical results, it is established that the image reconstruction quality directly depends on the coded aperture structure; therefore, a design strategy is proposed. In fact, when the scene can be sparsely represented in some basis, its support can be better estimated for a suitable choice of the coding elements in the modulation process. Experimental results show that the scene is successfully recovered by using designed coded apertures with up to 40% less measurements compared to non-designed ensembles.

Single exposure lensless subpixel phase imaging: optical system design, modelling, and experimental study

Design and optimization of lensless phase-retrieval optical system with phase modulation of free-space propagation wavefront is proposed for subpixel imaging to achieve super-resolution reconstruction. Contrary to the traditional super-resolution phase-retrieval, the method in this paper requires a single observation only and uses the advanced Super-Resolution Sparse Phase Amplitude Retrieval (SR-SPAR) iterative technique which contains optimized sparsity based filters and multi-scale filters. The successful object imaging relies on modulation of the object wavefront with a random phase-mask, which generates coded diffracted intensity pattern, allowing us to extract subpixel information. The system's noise-robustness was investigated and verified. The super-resolution phase-imaging is demonstrated by simulations and physical experiments. The simulations included high quality reconstructions with super-resolution factor of 5, and acceptable at factor up to 9. By physical experiments 3 μm details were resolved, which are 2.3 times smaller than the resolution following from the Nyquist-Shannon sampling theorem.

Image restoration and color fusion of digital microscopes

Traditional microscopes do not meet a wide field of view and high resolution at the same time. We propose a method for image restoration and color fusion of digital microscopes. It combines a single high-resolution gray scale hologram with a low-resolution color image to obtain a high-resolution color image. Specifically, the high-resolution gray scale image is obtained by reconstructing three different height holograms using a wavelet-based method, and the color information is obtained using a portable cell phone microscope. The subsequent calibration and blending of colors ultimately results in a high-resolution, wide-field color map that can be of great help in the study of pathology or biomedicine. This method breaks the rule that the large field of view and high resolution of a traditional microscope cannot be simultaneously satisfied, which can realize a more comprehensive observation of the shape and details of the slice.