Interferometric Phase Microscopy of Biological Cells using New Phase Unwrapping Strategies

Imaging biological cells in vitro is useful for both medical diagnosis and biological research. However, isolated cells in vitro are mostly transparent, and therefore cannot be imaged with sufficient contrast via standard bright-field microscopy. Quantitative interferometric phase microscopy enables imaging of isolated cells in vitro without using cell staining, by measuring how much the light is delayed when passing through the sample. However, the measured phase is inherently encoded inside a complex exponent, such that the phase obtained is wrapped, meaning that it is a modulo 2π function of the actual phase, where the quotient is unknown. As long as the local spatial gradient in the true phase profile does not exceed an absolute value of π radians, so that there is no aliasing, the 2-D phase profile can be found in a satisfactory manner by various phase unwrapping algorithms, which are typically based either on path following methods or minimum norm methods. Nevertheless, these methods might fail when the phase gradients are steep, such that they exceed π radians in all boundaries of the object. We propose two different
approaches to tackle this problem.

The first approach is using the information present in additional dimensions; In Ref. [1], we suggested to use the angular dimension, in order to earn information helpful for phase unwrapping of optically thick objects that cannot be reconstructed by conventional 2-D phase unwrapping algorithms but are thin enough at certain viewing angle. In this approach, we reconstruct the object phase for the angular view from which it is optically thick by utilizing multiple interferometric projections acquired from consecutive angles in small angular increments, containing at least one viewing angle where the object is optically thin. This approach is specifically useful for tomographic phase microscopy, where multiple angular phase maps are acquired for 3-D refractive-index map reconstruction, enabling the reconstruction of quantitative phase projections even from the thick angular views. This concept can be further generalized to acquiring this angular information over time, enabling incorporating temporal and angular phase
unwrapping in order to properly unwrap the phase maps. Therefore, in Ref. [2], we used four dimensions: two spatial dimensions of the projection (x and y), illumination angle, and time. This algorithm is suitable even for time points where the second condition of a thin angular view is not met, given that it is met at least once during the recording of the dynamic object, and that the time or angular steps between acquisitions are sufficiently small.

The second approach is using state-of-the-art deep learning tools for phase unwrapping. Artificial neural networks have the potential to yield a robust solution to the phase unwrapping problem, since they can learn the characteristics of the input data, and if trained properly, use this information to unwrap the phase more accurately based on the characteristic gradients while ignoring noise. We explored two inherently different deep-learning concepts for approaching the 2-D phase unwrapping problem; either observing it as an inverse problem, where the output image is composed of continuous values, or as a semantic segmentation problem, where the output image is composed of integers. We then compared the two methods, to determine the favorable deep-leaning approach for 2-D phase unwrapping when imaging biological cells in vitro.