Optical Array Aspects of Computed Spectroscopy

Computed spectroscopytrade (CS) is a new approach to hyperspectral imaging recently introduced by the authors (R.T. Hoctor et al., 2006). The CS technique uses an adjustable optical array, which can be considered to be a form of delay-and-sum passive beamformer. Adopting this point of view, such an array can be analyzed using the (difference) coarray (R.T. Hoctor and S.A. Kassam, 1990), and a previous publication by the present authors (R.T. Hoctor et al., 2006) features a brief coarray-based analysis. In the present paper we review the computed spectroscopy method, give a coarray-based analysis of the approach, show how numerical problems arise in the reconstruction of wavenumber spectra at low spatial frequencies and give a method for addressing these problems in the computation. Additionally, we discuss an improved approach to discretization of the image formation model