Numerical analysis of the imaging properties of nonlinear microscopy in highly scattering media

Abstract

Analysis ofthe imaging properties of optical microscopes is a necessary procedure that aid in the improvement of resolution, as well as investigation of the limitations of the system at various operating conditions. Optical microscopy has been recently applied to image through a scattering medium particularly of turbid biological samples because of its applications in biomedical research. Under worse scattering conditions and mismatches in refractive index, the imaging properties at various sample thicknesses should be analyzed in order to establish the limitations at which a valid image is observed. Attenuation of light in both illumination and detected light and its effect on the three-dimensional imaging properties are certain issues to resolve in the analysis of light microscopy in turbid media.
Scattering of light have been studied extensively using classical electromagnetic theory by Mie. The analysis, however, was limited only to independent and single scattering primarily because of the complications brought about by the solution of the higher order terms in the Born series. In 1989, Flock et al. proposed a Monte Carlo model of photon transport that is composed of a pencil of rays that is multiply scattered by randomly distributed particles in a medium. It provides promising results as it agrees with Diffusion theory in commonly set operating conditions. This model was later applied to confocal microscopy by Schmitt et al. and further implemented in the analysis of the imaging properties of linear and non-linear microscopy.
Although this approach, which allows photons to scatter like particles, provide a good approximation on the three-dimensional intensity distribution near the focus of the lens, it neglects the effect of interference and distortion ofthe point spread function (PSF). In nonlinear microscopy applications, the region of concern is within the diffraction limited focal volume of the excitation source as well as the preservation of temporal coherence at the focus. In this work, we modify the Monte Carlo based photon transport model to a semi-complete quantum mechanical realization that incorporates phase on the propagating photons. Such an approach enables a diffraction-limited analysis of a focused and pulsed beam that are essential factors for non-linear microscopy.