Quantitative phase microscopy via optimized inversion of the phase optical transfer function

Abstract

Although the field of quantitative phase imaging (QPI) has wide-ranging biomedical applicability, many QPI methods are not well-suited for such applications due to their reliance on coherent illumination and specialized hardware. By contrast, methods utilizing partially coherent illumination have the potential to promote the widespread adoption of QPI due to their compatibility with microscopy, which is ubiquitous in the biomedical community. Described herein is a new defocus-based reconstruction method that utilizes a small number of efficiently sampled micrographs to optimally invert the partially coherent phase optical transfer function under assumptions of weak absorption and slowly varying phase. Simulation results are provided that compare the performance of this method with similar algorithms and demonstrate compatibility with large phase objects. The accuracy of the method is validated experimentally using a microlens array as a test phase object. Lastly, time-lapse images of live adherent cells are obtained with an off-the-shelf microscope, thus demonstrating the new method's potential for extending QPI capability widely in the biomedical community.

Revealing architectural order with quantitative label-free imaging and deep learning

“…Assuming a specimen with weak absorption, the intensity variations in a Z-stack encode the phase information via the transport of intensity (TIE) equation (7). In the following, we leverage weak object transfer function (WOTF) formalism (17)(18)(19)(20)(21)(22) to retrieve 2D and 3D phase from this TIE phase contrast and describe the corresponding inverse algorithm.…”

“…Phase can be converted into intensity modulation by propagation of light (5,6), by interfering the light scattered by the specimen with another beam whose phase is controlled (7)(8)(9)(10), and by illuminating the specimen from diverse angles (11)(12)(13). Recent advances in computational microscopy show that robust retrieval of phase from throughfocus series is possible via weak object transfer function model of image formation (14)(15)(16)(17)(18)(19). Polarization can be converted into intensity modulation using optical components that selectively transmit and change polarization (20)(21)(22).…”

“…Among these approaches, reconstruction of phase from propagation of light is experimentally the simplest approach, since the data can be acquired on any microscope with motorized focus drive. The weak object transfer function model of image formation (17)(18)(19)(20)(21)(22) allows for robust reconstruction of phase from a stack of intensities measured in transmission.…”

Three-dimensional quantitative phase imaging via tomographic deconvolution phase microscopy

“…If the sample is rotated by 180°, for example, the symmetries of H A ρ and H P ρ allow Pr to be recovered uniquely by subtraction of their respective 3D image stacks relative to a single reference coordinate system because the absorption contrast is an even function about each scatterer. This is analogous to phase recovery using 2D WOTF theory based on subtraction of images on either side of the focus [42]. Another benefit of subtracting the through-focal series obtained from opposing perspectives is the ability to recover stronger pure phase objects because the second-order term, as well as all even-ordered terms, in the Taylor series expansion of Eq.…”

“…Since it needs to operate on partially coherent intensity data, an algorithm is selected which can easily model partial coherence, such as TIE phase recovery [45] or methods based on inversion of the 2D WOTF [46]. In this work, a recent phase reconstruction method referred to as POTF recovery [42] was utilized. This method is the 2D analog of TDPM and results in phase recovery from multiple defocused planes which is optimal in the sense of minimized noise in the final phase image.…”