Quantitative phase imaging of weakly scattering objects using partially coherent illumination

Quantitative phase microscopies: accuracy comparison

Quantitative phase microscopies (QPMs) play a pivotal role in bio-imaging, offering unique insights that complement fluorescence imaging. They provide essential data on mass distribution and transport, inaccessible to fluorescence techniques. Additionally, QPMs are label-free, eliminating concerns of photobleaching and phototoxicity. However, navigating through the array of available QPM techniques can be complex, making it challenging to select the most suitable one for a particular application. This tutorial review presents a thorough comparison of the main QPM techniques, focusing on their accuracy in terms of measurement precision and trueness. We focus on 8 techniques, namely digital holographic microscopy (DHM), cross-grating wavefront microscopy (CGM), which is based on QLSI (quadriwave lateral shearing interferometry), diffraction phase microscopy (DPM), differential phase-contrast (DPC) microscopy, phase-shifting interferometry (PSI) imaging, Fourier phase microscopy (FPM), spatial light interference microscopy (SLIM), and transport-of-intensity equation (TIE) imaging. For this purpose, we used a home-made numerical toolbox based on discrete dipole approximation (IF-DDA). This toolbox is designed to compute the electromagnetic field at the sample plane of a microscope, irrespective of the object's complexity or the illumination conditions. We upgraded this toolbox to enable it to model any type of QPM, and to take into account shot noise. In a nutshell, the results show that DHM and PSI are inherently free from artefacts and rather suffer from coherent noise; In CGM, DPC, DPM and TIE, there is a trade-off between precision and trueness, which can be balanced by varying one experimental parameter; FPM and SLIM suffer from inherent artefacts that cannot be discarded experimentally in most cases, making the techniques not quantitative especially for large objects covering a large part of the field of view, such as eukaryotic cells.

Spatial light interference microscopy: principle and applications to biomedicine

In this paper, we review spatial light interference microscopy (SLIM), a common-path, phase-shifting interferometer, built onto a phase-contrast microscope, with white-light illumination. As one of the most sensitive quantitative phase imaging (QPI) methods, SLIM allows for speckle-free phase reconstruction with sub-nanometer path-length stability. We first review image formation in QPI, scattering, and full-field methods. Then, we outline SLIM imaging from theory and instrumentation to diffraction tomography. Zernike's phase-contrast microscopy, phase retrieval in SLIM, and halo removal algorithms are discussed. Next, we discuss the requirements for operation, with a focus on software developed in-house for SLIM that enables high-throughput acquisition, whole slide scanning, mosaic tile registration, and imaging with a color camera. We introduce two methods for solving the inverse problem using SLIM, white-light tomography, and Wolf phase tomography. Lastly, we review the applications of SLIM in basic science and clinical studies. SLIM can study cell dynamics, cell growth and proliferation, cell migration, mass transport, etc. In clinical settings, SLIM can assist with cancer studies, reproductive technology, blood testing, etc. Finally, we review an emerging trend, where SLIM imaging in conjunction with artificial intelligence brings computational specificity and, in turn, offers new solutions to outstanding challenges in cell biology and pathology.

Analytical phase optical transfer function for Gaussian illumination and the optimized illumination profiles

The imaging performance of tomographic deconvolution phase microscopy can be described in terms of the phase optical transfer function (POTF) which, in turn, depends on the illumination profile. To facilitate the optimization of the illumination profile, an analytical calculation method based on polynomial fitting is developed to describe the POTF for general nonuniform axially symmetric illumination. This is then applied to Gaussian and related profiles. Compared to numerical integration methods that integrate over a series of annuli, the present analytical method is much faster and is equally accurate. Further, a "balanced distribution" criterion for the POTF and a least-squares minimization are presented to optimize the uniformity of the POTF. An optimum general profile is found analytically by relaxed optimal search, and an optimum Gaussian profile is found through a tree search. Numerical simulations confirm the performance of these optimum profiles and support the balanced distribution criterion introduced.

Epi-illumination gradient light interference microscopy for imaging opaque structures

Multiple scattering and absorption limit the depth at which biological tissues can be imaged with light. In thick unlabeled specimens, multiple scattering randomizes the phase of the field and absorption attenuates light that travels long optical paths. These obstacles limit the performance of transmission imaging. To mitigate these challenges, we developed an epi-illumination gradient light interference microscope (epi-GLIM) as a label-free phase imaging modality applicable to bulk or opaque samples. Epi-GLIM enables studying turbid structures that are hundreds of microns thick and otherwise opaque to transmitted light. We demonstrate this approach with a variety of man-made and biological samples that are incompatible with imaging in a transmission geometry: semiconductors wafers, specimens on opaque and birefringent substrates, cells in microplates, and bulk tissues. We demonstrate that the epi-GLIM data can be used to solve the inverse scattering problem and reconstruct the tomography of single cells and model organisms.

Novel computer-generated hologram encoding method based on partially temporal coherent light

Partially temporal coherent light (PTCL) has been applied to holographic reconstruction to reduce speckle noise in display systems, while the encoding methods of computer-generated hologram (CGH), based on PTCL, have not been reported. We propose a novel method to encoding CGH, in which a PTCL with a broadband continuous spectrum is used to illuminate the object image. The continuous spectrum is discretized into different wavelengths and a weight value associated with PTCL power spectrum is assigned to each wavelength. The diffractive transmission is based on Fresnel diffraction theory. The phase distribution of the encoded CGH is obtained using the sum of multiplying the different CGH phase distributions of corresponding discrete wavelengths by the corresponding weight values. The modulation results without iteration are performed to verify the feasibility of the proposed method and the iterative algorithm is introduced to improve the quality of the modulation. The reconstructed images from the proposed encoding method exhibit high quality as compared with that obtained from the encoding method based on ideal temporal coherent light. Numerical simulations and optical experiments are good consistent with each other. The proposed method can provide a reference for various wave-front modulations.

A gradient-based, GPU-accelerated, high-precision contour-segmentation algorithm with application to cell membrane fluctuation spectroscopy

We present a novel intensity-gradient based algorithm specifically designed for nanometer-segmentation of cell membrane contours obtained with high-resolution optical microscopy combined with high-velocity digital imaging. The algorithm relies on the image oversampling performance and computational power of graphical processing units (GPUs). Both, synthetic and experimental data are used to quantify the sub-pixel precision of the algorithm, whose analytic performance results comparatively higher than in previous methods. Results from the synthetic data indicate that the spatial precision of the presented algorithm is only limited by the signal-to-noise ratio (SNR) of the contour image. We emphasize on the application of the new algorithm to membrane fluctuations (flickering) in eukaryotic cells, bacteria and giant vesicle models. The method shows promising applicability in several fields of cellular biology and medical imaging for nanometer-precise boundary-determination and mechanical fingerprinting of cellular membranes in optical microscopy images. Our implementation of this high-precision flicker spectroscopy contour tracking algorithm (HiPFSTA) is provided as open-source at www.github.com/michaelmell/hipfsta.

Isotropic differential phase contrast microscopy for quantitative phase bio-imaging

Quantitative phase imaging (QPI) has been investigated to retrieve optical phase information of an object and applied to biological microscopy and related medical studies. In recent examples, differential phase contrast (DPC) microscopy can recover phase image of thin sample under multi-axis intensity measurements in wide-field scheme. Unlike conventional DPC, based on theoretical approach under partially coherent condition, we propose a new method to achieve isotropic differential phase contrast (iDPC) with high accuracy and stability for phase recovery in simple and high-speed fashion. The iDPC is simply implemented with a partially coherent microscopy and a programmable thin-film transistor (TFT) shield to digitally modulate structured illumination patterns for QPI. In this article, simulation results show consistency of our theoretical approach for iDPC under partial coherence. In addition, we further demonstrate experiments of quantitative phase images of a standard micro-lens array, as well as label-free live human cell samples.

Endoscopic diffraction phase microscopy

In this Letter, we present, to our knowledge, the first endoscopic diffraction phase microscopy (eDPM) system. This instrument consists of a gradient-index-lens-based endoscope probe followed by a DPM module, which enables single-shot phase imaging at a single-cell-level resolution. Using the phase information provided by eDPM, we show that the geometric aberrations associated with the endoscope can be reduced by digitally applying a spectral phase filter to the raw data. The filter function is a linear combination of polynomials with weighting optimized to improve resolution. We validate the principle of the proposed method using reflective semiconductor samples and blood cells. This research extends the current scope of quantitative phase imaging applications, and proves its potential for future in vivo studies.

Efficient quantitative phase microscopy using programmable annular LED illumination

In this work, we present an efficient quantitative phase imaging (QPI) approach using programmable annular LED illumination. As a new type of coded light source, the LED array provides flexible illumination control for noninterferometric QPI based on a traditional microscopic configurations. The proposed method modulates the transfer function of system by changing the LED illumination pattern, which provides noise-robust response of transfer function and achieves twice resolution limit of objective NA. The quantitative phase can be recovered from slightly defocused intensity images through inversion of transfer function. Moreover, the weak object transfer function (WOTF) of axis-symmetric oblique source is derived, and the noise-free and noisy simulation results validate the predicted theory. Finally, we experimentally confirm accurate and repeatable performance of our method by imaging calibrated phase samples and cellular specimens with different NA objectives.

Double-channel angular-multiplexing polarization holography with common-path and off-axis configuration

We propose a double-channel angular-multiplexing polarization holographic imaging system with common-path and off-axis configurations. In the system, its input plane is spatially divided into three windows: an object window and two reference windows, and two orthogonal linear polarizers are attached, respectively, on the two reference windows; a two-dimensional cross grating is inserted between the input and output planes of the system. Thus the object beam passing through the object window and the two orthogonal polarized reference beams passing through the two reference windows can overlap each other at the output plane of the system and form a double-channel angular-multiplexing polarization hologram (DC-AM-PH). Using this system, the complex amplitude distributions of two orthogonal polarized components from an object can be recorded and reconstructed by one single-shot DC-AM-PH at the same time. Theoretical analysis and experimental results demonstrated that the system can be used to measure the Jones matrix parameters of polarization-sensitive or birefringent materials.

High-resolution transport-of-intensity quantitative phase microscopy with annular illumination

For quantitative phase imaging (QPI) based on transport-of-intensity equation (TIE), partially coherent illumination provides speckle-free imaging, compatibility with brightfield microscopy, and transverse resolution beyond coherent diffraction limit. Unfortunately, in a conventional microscope with circular illumination aperture, partial coherence tends to diminish the phase contrast, exacerbating the inherent noise-to-resolution tradeoff in TIE imaging, resulting in strong low-frequency artifacts and compromised imaging resolution. Here, we demonstrate how these issues can be effectively addressed by replacing the conventional circular illumination aperture with an annular one. The matched annular illumination not only strongly boosts the phase contrast for low spatial frequencies, but significantly improves the practical imaging resolution to near the incoherent diffraction limit. By incorporating high-numerical aperture (NA) illumination as well as high-NA objective, it is shown, for the first time, that TIE phase imaging can achieve a transverse resolution up to 208 nm, corresponding to an effective NA of 2.66. Time-lapse imaging of in vitro Hela cells revealing cellular morphology and subcellular dynamics during cells mitosis and apoptosis is exemplified. Given its capability for high-resolution QPI as well as the compatibility with widely available brightfield microscopy hardware, the proposed approach is expected to be adopted by the wider biology and medicine community.

3D differential phase contrast microscopy

We demonstrate 3D phase and absorption recovery from partially coherent intensity images captured with a programmable LED array source. Images are captured through-focus with four different illumination patterns. Using first Born and weak object approximations (WOA), a linear 3D differential phase contrast (DPC) model is derived. The partially coherent transfer functions relate the sample's complex refractive index distribution to intensity measurements at varying defocus. Volumetric reconstruction is achieved by a global FFT-based method, without an intermediate 2D phase retrieval step. Because the illumination is spatially partially coherent, the transverse resolution of the reconstructed field achieves twice the NA of coherent systems and improved axial resolution.