Visualization 1: Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy

The evolution of the amplitude reconstructions of an USAF resolution target with an adaptive step-size. Originally published in Optics Express on 05 September 2016 (oe-24-18-20724

Resolution analysis in a lens-free on-chip digital holographic microscope

Lens-free on-chip digital holographic microscopy (LFOCDHM) is a modern imaging technique whereby the sample is placed directly onto or very close to the digital sensor, and illuminated by a partially coherent source located far above it. The scattered object wave interferes with the reference (unscattered) wave at the plane where a digital sensor is situated, producing a digital hologram that can be processed in several ways to extract and numerically reconstruct an in-focus image using the back propagation algorithm. Without requiring any lenses and other intermediate optical components, the LFOCDHM has unique advantages of offering a large effective numerical aperture (NA) close to unity across the native wide field-of-view (FOV) of the imaging sensor in a cost-effective and compact design. However, unlike conventional coherent diffraction limited imaging systems, where the limiting aperture is used to define the system performance, typical lens-free microscopes only produce compromised imaging resolution that far below the ideal coherent diffraction limit. At least five major factors may contribute to this limitation, namely, the sample-to-sensor distance, spatial and temporal coherence of the illumination, finite size of the equally spaced sensor pixels, and finite extent of the image sub-FOV used for the reconstruction, which have not been systematically and rigorously explored until now. In this work, we derive five transfer function models that account for all these physical effects and interactions of these models on the imaging resolution of LFOCDHM. We also examine how our theoretical models can be utilized to optimize the optical design or predict the theoretical resolution limit of a given LFOCDHM system. We present a series of simulations and experiments to confirm the validity of our theoretical models

Visualization 1. Large SBP phase video of unstained HeLa cells in vitro recovered by using SFPM .

Visualization 1 shows Large SBP phase video recovered by using SFPM with single-shot acquisition speed (50 Hz) for tracking dynamic subcellular features of unstained HeLa cells in vitro

On a universal solution to the transport-of-intensity equation

Transport-of-intensity equation (TIE) is one of the most well-known approaches for phase retrieval and quantitative phase imaging. It directly recovers the quantitative phase distribution of an optical field by through-focus intensity measurements in a noninterferometic, deterministic manner. Nevertheless, the accuracy and validity of state-of-the-art TIE solvers depend on restrictive preknowledge or assumptions, including appropriate boundary conditions, a well-defined closed region, and quasi-uniform in-focus intensity distribution, which, however, cannot be strictly satisfied simultaneously under practical experimental conditions. In this Letter, we propose a universal solution to TIE with the advantages of high accuracy, convergence guarantee, applicability to arbitrarily-shaped regions, and simplified implementation and computation. With the "maximum intensity assumption", we firstly simplified TIE as a standard Possion equation to get an initial guess of the solution. Then the initial solution is further refined iteratively by solving the same Possion equation, and thus, the instability associated with the division by zero/small intensity values and large intensity variations can be effectively bypassed. Simulations and experiments with arbitrary phase, arbitrary aperture shapes, and nonuniform intensity distributions verify the effectiveness and universality of the proposed method

Video_1_Quantitative Phase Imaging Camera With a Weak Diffuser.MP4

We introduce the quantitative phase imaging camera with a weak diffuser (QPICWD) as an effective scheme of quantitative phase imaging (QPI) based on normal microscope platforms. The QPICWD is an independent compact camera measuring object induced phase delay under low-coherence quasi-monochromatic illumination by examining the deformation of the speckle intensity pattern. By interpreting the speckle deformation with an ensemble average of the geometric flow, we can obtain the high-resolution distortion field via the transport of intensity equation (TIE). Since the phase measured by TIE is the generalized phase of the partially coherent image, rather than the phase of the measured object, we analyze the effect of illumination coherence and imaging numerical aperture (NA) on the accuracy of phase retrieval, revealing that the sample's phase can be reliably reconstructed under the conditions that the coherence parameter (the ratio of illumination NA to objective NA) of the Köhler illumination is between 0.3 and 0.5. We present some applications for the proposed design involving nondestructive optical testing of microlens array with nanometric thickness and imaging of fixed and live unstained HeLa cells. Since the designed QPI camera does not require any modification of the widely available bright-field microscope or additional accessories for its use, it is expected to be applied by the broader communities of biology and medicine.</p

Media 2: Lensless phase microscopy and diffraction tomography with multi-angle and multi-wavelength illuminations using a LED matrix

Originally published in Optics Express on 01 June 2015 (oe-23-11-14314

Media 1: Lensless phase microscopy and diffraction tomography with multi-angle and multi-wavelength illuminations using a LED matrix

Originally published in Optics Express on 01 June 2015 (oe-23-11-14314

Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy

Differential phase contrast microscopy (DPC) provides high-resolution quantitative phase distribution of thin transparent samples under multi-axis asymmetric illuminations. Typically, illumination in DPC microscopic systems is designed with 2-axis half-circle amplitude patterns, which, however, result in a non-isotropic phase contrast transfer function (PTF). Efforts have been made to achieve isotropic DPC by replacing the conventional half-circle illumination aperture with radially asymmetric patterns with 3-axis illumination or gradient amplitude patterns with 2-axis illumination. Nevertheless, these illumination apertures were empirically designed based on empirical criteria related to the shape of the PTF, leaving the underlying theoretical mechanisms unexplored. Furthermore, the frequency responses of the PTFs under these engineered illuminations have not been fully optimized, leading to suboptimal phase contrast and signal-to-noise ratio (SNR) for phase reconstruction. In this Letter, we provide a rigorous theoretical analysis about the necessary and sufficient conditions for DPC to achieve perfectly isotropic PTF. In addition, we derive the optimal illumination scheme to maximize the frequency response for both low and high frequencies (from 0 to 2NAobj), and meanwhile achieve perfectly isotropic PTF with only 2-axis intensity measurements. We present the derivation, implementation, simulation and experimental results demonstrating the superiority of our method over state-of-the-arts in both phase reconstruction accuracy and noise-robustness

Optimal illumination pattern for transport-of-intensity quantitative phase microscopy

The transport-of-intensity equation (TIE) is a well-established non-interferometric phase retrieval approach, which enables quantitative phase imaging (QPI) of transparent sample simply by measuring the intensities at multiple axially displaced planes. Nevertheless, it still suffers from two fundamentally limitations. First, it is quite susceptible to low-frequency errors (such as \cloudy" artifacts), which results from the poor contrast of the phase transfer function (PTF) near the zero frequency. Second, the reconstructed phase tends to blur under spatially low-coherent illumination, especially when the defocus distance is beyond the near Fresnel region. Recent studies have shown that the shape of the illumination aperture has a significant impact on the resolution and phase reconstruction quality, and by simply replacing the conventional circular illumination aperture with an annular one, these two limitations can be addressed, or at least significantly alleviated. However, the annular aperture was previously empirically designed based on intuitive criteria related to the shape of PTF, which does not guarantee optimality. In this work, we optimize the illumination pattern to maximize TIE's performance based on a combined quantitative criterion for evaluating the \goodness" of an aperture. In order to make the size of the solution search space tractable, we restrict our attention to binary coded axis-symmetric illumination patterns only, which are easier to implement and can generate isotropic TIE PTFs. We test the obtained optimal illumination by imaging both a phase resolution target and HeLa cells based on a small-pitch LED array, suggesting superior performance over other suboptimal patterns in terms of both signal-to-noise ratio (SNR) and spatial resolution

Quasi-Isotropic High-Resolution Fourier Ptychographic Diffraction Tomography with Opposite Illuminations

Optical diffraction tomography (ODT) is a powerful tool for the study of unlabeled biological cells thanks to its unique capability of measuring the three-dimensional (3D) refractive index (RI) distribution of samples quantitatively and noninvasively. In conventional transmission ODT, however, certain spatial frequency components along the optical axis cannot be measured due to the limited angular coverage of the incident beam, resulting in a poor axial resolution several times worse than the lateral one. In this Letter we propose a new type of ODT method, termed opposite illumination Fourier ptychographic diffraction tomography (OI-FPDT), which produces almost isotropic resolution by combining transmissive angle-scanning and reflective wavelength-scanning. Without resorting to interferometric detection, OI-FPDT requires an intensity-only measurement, and the forward and backward scattered intensity images are synthesized in the Fourier space to recover the 3D RI distribution of samples based on an iterative ptychographic reconstruction algorithm. To the best of our knowledge, this is the first time that near-isotropic resolution (∼ 274 nm) of ODT result is obtained in a non-interferometric and sample motion-free manner. Results of simulated cell phantom, tailor-made fiberglass, and onion epidermal cell samples confirm the validity of the proposed method