Connecting Mueller and Jones tensors for describing nonlinear optical conversion of unpolarized light

Abstract

A method is demonstrated enabling polarization analysis of second harmonic generation (SHG) and two-photon excited fluorescence (TPEF) measurements of tissue samples driven by partially or wholly depolarized light. Partial depolarization routinely arises in tissue imaging, but is incompatible with standard Jones tensor formulations for polarization analysis of SHG. A more general Mueller tensor mathematical framework supports compatibility with partially or wholly depolarized incident light, but at the expense of significant increase in unknown parameter and additional mathematical complexity. In this work, the Mueller tensor can be cast in terms of the simpler and more intuitive Jones tensor, greatly reducing the number of potentially unique parameters (from 64 in the general Mueller tensor to as few as 2 in SHG of collagen). Using this architecture, local-frame tensor elements in thick, partially depolarizing tissues were recoverable with no substantial increase in mathematical complexity relative to conventional polarizationdependent nonlinear optical imaging. These results provide a relatively simple but mathematically rigorous framework for integrating partial depolarization effects in biological imaging, supporting polarization analyses in broad classes of samples that were otherwise limited to thin tissue sections.