High étendue Fourier transform spectroscopy by quadratic off-axis path difference error cancellation

Abstract

Instrumentation design for Fourier transform spectroscopy has until now been hindered by a seemingly fundamental tradeoff between the étendue of the analyzed light source on one hand and the spectral resolution on the other. For example, if a freespace scanning Michelson interferometer is to achieve a spectral resolution of 4 per centimeter, it can have a maximum angular field of view of roughly 1 degree for wavelengths in the neighborhood of 800 nm, where the general tradeoff for this instrument is that the quotient \theta_m^2 / \Delta k of the square of the angular field of view \theta_m and the minimum resolvable wavenumber difference \Delta k is a constant. This paper demonstrates a method to increase the angular field of view allowable for a given resolution by a full order of magnitude, and thus to increasethe étendue and, with it, the potential power gathered from an extended source and potential measurement signalto-noise ratio, by two orders of magnitude relative to the performance of a freespace Michelson interferometer. Generalizing this example, we argue that there may be no fundamental thermodynamic grounds for the tradeoff and that a scanning Fourier transform spectrometer can accept an arbitrarily high étendue field and still, in theory, achieve an arbitrarily narrowspectral resolution.