Routley Selene Amy, Flynn Jamie, Martin Antony, Palmer William
J Opt Soc Am A Opt Image Sci Vis. 2020 Nov 1;37(11):1767-1777. doi: 10.1364/JOSAA.396748.
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, it can have a maximum angular field of view of roughly 1° for wavelengths in the neighborhood of =800, where the general tradeoff for this instrument is that the quotient 2/ of the square of the angular field of view and the minimum resolvable wavenumber difference 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.
到目前为止，傅里叶变换光谱仪的仪器设计一直受到一种看似基本的权衡的阻碍，一方面是被分析光源的 étendue，另一方面是光谱分辨率。例如，如果一个自由空间扫描迈克尔逊干涉仪要实现 4 的光谱分辨率，对于波长在 =800 附近的光，它的最大角视场约为 1°，对于该仪器的一般权衡是角视场 的平方与最小可分辨波数差 的商 2/ 是一个常数。本文展示了一种方法，可将给定分辨率下允许的角视场提高整整一个数量级，从而将 étendue 提高两个数量级，随之也将从扩展光源收集的潜在功率以及潜在测量信噪比相对于自由空间迈克尔逊干涉仪的性能提高两个数量级。推广这个例子，我们认为这种权衡可能没有基本的热力学依据，并且扫描傅里叶变换光谱仪可以接受任意高的 étendue 场，并且在理论上仍然可以实现任意窄的光谱分辨率。
