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 $4\;{{\rm cm}^{- {1}}}$, it can have a maximum angular field of view of roughly 1° for wavelengths in the neighborhood of $\lambda = 800\;{\rm 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 increase the étendue and, with it, the potential power gathered from an extended source and potential measurement signal-to-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 narrow spectral resolution.

© 2020 Optical Society of America

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