Partially coherent contrast-transfer-function approximation

Three-dimensional contrast-transfer-function approach in phase-contrast tomography

A new method is developed for 3D reconstruction of multimaterial objects using propagation-based x-ray phase-contrast tomography (PB-CT) with phase retrieval via contrast-transfer-function (CTF) formalism. The approach differs from conventional PB-CT algorithms, which apply phase retrieval to individual 2D projections. Instead, this method involves performing phase retrieval to the CT-reconstructed volume in 3D. The CTF formalism is further extended to the cases of partially coherent illumination and strongly absorbing samples. Simulated results demonstrate that the proposed post-reconstruction CTF method provides fast and stable phase retrieval, producing results equivalent to conventional pre-reconstruction 2D CTF phase retrieval. Moreover, it is shown that application can be highly localized to isolated objects of interest, without a significant loss of quality, thus leading to increased computational efficiency. Combined with the extended validity of the CTF to greater propagation distances, this method provides additional advantages over approaches based on the transport-of-intensity equation.

Deep learning for label-free nuclei detection from implicit phase information of mesenchymal stem cells

Monitoring of adherent cells in culture is routinely performed in biological and clinical laboratories, and it is crucial for large-scale manufacturing of cells needed in cell-based clinical trials and therapies. However, the lack of reliable and easily implementable label-free techniques makes this task laborious and prone to human subjectivity. We present a deep-learning-based processing pipeline that locates and characterizes mesenchymal stem cell nuclei from a few bright-field images captured at various levels of defocus under collimated illumination. Our approach builds upon phase-from-defocus methods in the optics literature and is easily applicable without the need for special microscopy hardware, for example, phase contrast objectives, or explicit phase reconstruction methods that rely on potentially bias-inducing priors. Experiments show that this label-free method can produce accurate cell counts as well as nuclei shape statistics without the need for invasive staining or ultraviolet radiation. We also provide detailed information on how the deep-learning pipeline was designed, built and validated, making it straightforward to adapt our methodology to different types of cells. Finally, we discuss the limitations of our technique and potential future avenues for exploration.

Simultaneous measurement and reconstruction tailoring for quantitative phase imaging

We propose simultaneous measurement and reconstruction tailoring (SMaRT) for quantitative phase imaging; it is a joint optimization approach to inverse problems wherein minimizing the expected end-to-end error yields optimal design parameters for both the measurement and reconstruction processes. Using simulated and experimentally-collected data for a specific scenario, we demonstrate that optimizing the design of the two processes together reduces phase reconstruction error over past techniques that consider these two design problems separately. Our results suggest at times surprising design principles, and our approach can potentially inspire improved solution methods for other inverse problems in optics as well as the natural sciences.

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.

Source diversity for transport of intensity phase imaging

The transport of intensity equation (TIE) is a phase retrieval method that relies on measurements of the intensity of a paraxial field under propagation between two or more closely spaced planes. A limitation of TIE is its susceptibility to low frequency noise artifacts in the reconstructed phase. Under Köhler illumination, when both illumination power and exposure time are limited, the use of larger sources can improve low-frequency performance although it introduces blurring. Appropriately combining intensity measurements taken with a diversity of source sizes can improve both low- and high-frequency performance in phase reconstruction.

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.

Quantitative phase imaging of weakly scattering objects using partially coherent illumination

In this paper, we extend our recent work on partially coherent quantitative phase imaging (pcQPI) from two-dimensional (2D) to three-dimensional (3D) imaging of weakly scattering samples. Due to the mathematical complexity, most theoretical modeling of quantitative phase image formation under partial coherence has focused on thin, well-focused samples. It is unclear how these abberations are affected by defocusing. Also, as 3D QPI techniques continue to develop, a better model needs to be developed to understand and quantify these aberrations when imaging thicker samples. Here, using the first order Born's approximation, we derived a mathematical framework that provides an intuitive model of image formation under varying degrees of coherence. Our description provides a clear connection between the halo effect and phase underestimation, defocusing and the 3D structure of the sample under investigation. Our results agree very well with the experiments and show that the microscope objective defines the sectioning ability of the imaging system while the condenser lens is responsible for the halo effect.