The generalized optical memory effect (1705.01373v1)

Abstract: The optical memory effect is a well-known type of wave correlation that is observed in coherent fields that scatter through thin and diffusive materials, like biological tissue. It is a fundamental physical property of scattering media that can be harnessed for deep-tissue microscopy or 'through-the-wall' imaging applications. Here we show that the optical memory effect is a special case of a far more general class of wave correlation. Our new theoretical framework explains how waves remain correlated over both space and angle when they are jointly shifted and tilted inside scattering media of arbitrary geometry. We experimentally demonstrate the existence of such coupled correlations and describe how they can be used to optimize the scanning range in adaptive optics microscopes.

Generalized Optical Memory Effect

The paper "The Generalized Optical Memory Effect" presents an advanced theoretical framework that extends the conventional understanding of the optical memory effect, widely recognized within the field of imaging through scattering media. This research broadens the scope of the optical memory effect, positing it as a specific example within a more extensive and general class of wave correlations. The paper establishes both theoretical predictions and experimental validation, exhibiting that waves exhibit coupled correlations over space and angle and remain coherent when jointly shifted and tilted in scattering media of arbitrary geometry.

Theoretical Framework

The generalized optical memory effect model introduced in this paper provides a comprehensive description of first-order spatial correlations for coherent waves passing through scattering media. This model effectively integrates two foundational concepts: the tilt memory effect and the shift memory effect. The tilt memory effect indicates that when a scattered wavefront is tilted, it maintains its shape, as primarily seen in surfaces like thin isotropic scattering screens. Conversely, the shift memory effect permits the spatial shifting of a focal spot within anisotropic scattering media. This paper suggests that these effects are manifestations of a broader class of correlations, expressed mathematically through equations that leverage a Wigner distribution function—representing optical fields as joint phase-space functions.

Experimental Validation

Experiments conducted include measurements of both average light field transmission and generalized correlation functions. The paper utilizes finely tuned optical setups to examine samples of silica microspheres suspended in gel with distinct thicknesses. Results demonstrate coherent wave correlations across the samples, validating the theoretical model. The experimental findings align closely with the predictions derived from a Fokker-Planck model, which is employed to represent forward scattering scenarios in the paper.

Implications and Future Directions

The implications of these findings are profound for adaptive optics and biomedical imaging, providing a theoretical basis for optimizing scanning ranges in adaptive optics microscopes. The generalized model suggests that instead of utilizing solely tilt or shift-based corrections in adaptive optics systems, an optimized combination of tilt and shift—found by effectively conjugating correction planes—can significantly extend the isoplanatic patch in imaging applications. This enhances the ability to focus on images from deeper tissue layers and scattering media.

In terms of theoretical development, the model opens up avenues for further exploration into higher-order correlations, analogous to $C_2$ and $C_3$ correlations in intensity. These correlations might offer further enhancements in imaging clarity and focus control in complex scattering environments.

This paper serves as a foundational piece, providing a robust framework for understanding and manipulating wavefront propagation through disordered media. It suggests that leveraging generalized correlations potentiate advancements in optical imaging technologies, particularly in scenarios requiring penetration through opaque materials.

By delineating the generalized optical memory effect and verifying it through experimental rigor, this paper contributes a critical theoretical and practical tool for researchers in optics and imaging disciplines, potentially guiding future developments in having better control and precision over imaging through complex scattering media.