In recent years, tremendous efforts have been spent on deep tissue imaging using phase conjugation, a technique used to undo the effects of light scattering in a thick tissue. Despite the early debates between Yariv and Wolf, it is still not well understood physically how deep can a field propagate into biological tissue and still be phase conjugated. In order to answer this question, we developed a light scattering theory to describe the evolution of the phase associated with a field scattered by a thick tissue block. The multiple scattering through the sample is simplified to a series of single scattering through consecutive thin tissue slices. With this theory, we identify the limits of the phase conjugation operation and recover the previous results by Yariv and Wolf, which asserts that phase conjugation is rooted in small angle approximation. Importantly, we discover the fundamental principle that rules phase conjugation: the mean axial wavenumber of a field progressively decreases to zero as it scatters multiple times. At this point, phase becomes a spatially random variable and phase conjugation becomes impossible. This result describes a fundamental phenomenon: the interaction between a deterministic object and a deterministic field can result in a random scattered field. We show that this phenomenon is rooted into Heisenberg’s uncertainty principle.
Renjie Zhou, Taewoo Kim, and Gabriel Popescu, "Reversibility of scattered fields
(Conference Presentation)," Proc. SPIE 9718, Quantitative Phase Imaging II, 97180E (Presented at SPIE BiOS: February 14, 2016; Published: 27 April 2016); https://doi.org/10.1117/12.2216388.4848767810001.
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