Computationally efficient spectrum-recovery methods which compensate for static and dynamic nonidealities in electrooptic masks used in Hadamard-transform spectrometry

A Hadamard-transform spectrometer having no moving parts can be implemented by placing a stationary electrooptic mask in the optical path of a dispersive monochromator. However, two kinds of nonidealities-static and dynamic-associated with the electrooptic mask can cause distortions in the recovered spectrum-estimates. Two system models and corresponding recovery schemes have been developed previously that incorporate the effects of both types of nonidealities. This paper focuses on representing the dynamic nonidealities of the mask by a right-cyclic matrix T_D, obtaining T_D in practice, and computing T_D^-1 by computationally efficient moans, thus completing the development of fast implementations of the two previously reported recovery schemes. These computationally efficient recovery schemes were applied to simulated and experimental data, with examples of results presented and discussed