# Heterodyne detection of scattered light: Application to mapping and tomography of optically inhomogeneous media

## TL;DR

This paper presents a heterodyne detection method for scattered light to map and reconstruct the refractive index in inhomogeneous media, enabling spatial characterization of internal structures.

## Contribution

It introduces an analytical model for heterodyne detection in scattering, facilitating the mapping and tomography of optically inhomogeneous objects.

## Key findings

- Signal depends only on the overlap region of the beams.
- Method allows reconstruction of the refractive-index relief.
- Proposed spatial mapping estimates inhomogeneity size and magnitude.

## Abstract

The signal registered by a plane photodetector placed behind an optically inhomogeneous object irradiated by two coherent Gaussian beams intersecting inside the object at small angle to each other is calculated in the single-scattering approximation. In the considered arrangement, only one of the beams hits the detector and serves as local oscillator for heterodyning the field scattered by the other beam (not hitting the detector). The results of analytical calculation show that the signal detected in this way is contributed only by the region of the inhomogeneous object where the two beams overlap. By moving the scatterer with respect to the overlap region and monitoring the heterodyned signal, with the aid of the derived expression, one can reconstruct the refractive-index relief of the scatterer. We also propose a simple method of spatial mapping of the sample that allows one to estimate the magnitude and characteristic dimensions of the inhomogeneities.