Fourier-transform spectral imaging: retrieval of source information from three-dimensional spatial coherence

Abstract

A method is described for efficiently obtaining the comprehensive information of a polychromatic radiator. Under certain conditions both the spatial and spectral details of the radiative object can be recovered simultaneously from the three-dimensional spatial coherence function in the diffraction region. The recovery of object information is based on a Fourier-transform relationship derived from the basic formula [E. Wolf and W. H. Carter, J. Opt. Soc. Am. 68, 953-964 (1978)] describing the field correlation function in terms of the source correlation function. A new type of interferometer is proposed for the efficient collection of the spatial coherence data. Experimental results of the spectral-image recovery are also presented.

Fully interferometric three-dimensional imaging spectrometry using hyperbolic-type volume interferogram

“…The principle of our method is based on the measurement of a five-dimensional (5D) spatial coherence function and signal processing including a synthetic aperture technique. Reports of other passive interferometry include techniques to obtain a set of spectral components of two-dimensional (2D) images [24,25], various techniques to obtain 3D monochromatic images [26][27][28][29][30], and spectral tomography based on spatial coherence measurements by a rotational shear interferometer and a four-dimensional (4D) Fourier transform of the coherence function [31].…”

Interferometry following adaptive optics

“…They tend to measure the interference in the pupil plane, where the gain in integration volume is direct 10,11 . Folding, lateral, and rotational shear interferometers (Figure 3) are well established 12,13,14,15,16,17 .…”

High-Resolution Direction Finding and Scan-Free Spectrum Estimation with Rotational-Shear Interferometric Sensor Arrays

“…It has previously been applied in hyperspectral and spatial imaging systems. [3][4][5][6][7][8] If a prism is rotated by θ 2 with respect to the vertical axis, then it will rotate the field in the observation plane by θ. Consider the special case in which the prisms in the two interferometer arms are rotated by shear angle ∓ θ 2 .…”