Spectral tomography from spatial coherence measurements

We describe the use of non-focal interferometric cameras for reconstruction of the four-dimensional power spectral density of incoherent sources. We develop a 4D version of the generalized van Cittert-Zernike theorem to establish the Fourier transform relationship between the mutual coherence function and the power spectral density. We present experimental demonstrations of 4D imaging using a rotational shearing interferometer. We discuss limitations of interferometric imaging systems and consider how sensor systems might evolve to combine the stability of focal systems with the algorithmic sophistication and multidimensional capacity of interferometry.