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

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