Time-reversed adapted-perturbation optical focusing onto dynamic objects inside scattering media

Determination of optimal phase offset. Digital phase-shifting holography measures the relative phase of light at different pixels; the absolute phase values are unknown, and an unavoidable phase offset exists between the two measured fields. For example, a phase offset can be induced by a drift of the optical path length difference between the sample and reference arms due to environmental instabilities. Here, we develop a method to optimally find the phase offset that yields the best focusing quality. The analysis is based on the simplest situation, in which the absorption and refractive index of a single target are perturbed. For multiple or moving targets, extension of the analysis reaches the same conclusion.