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.

中文翻译：

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通过二次离轴路径差误差消除实现的高étendue傅里叶变换光谱

迄今为止，一方面在被分析光源的光衰率与另一方面在光谱分辨率之间存在看似基本的权衡关系，阻碍了傅里叶变换光谱仪的仪器设计。例如，如果自由空间扫描迈克尔逊干涉仪要实现$ 4 \; {{\ rm cm} ^ {-{1}}} $的光谱分辨率，则对于波长，它的最大视角范围大约为1°在$ \ lambda = 800 \; {\ rm nm} $附近，这里仪器的一般权衡是视场角场平方的商$ \ theta _m ^ 2 / \ Delta k $ {\ theta _m} $和最小可分辨波数差$ \ Delta k $是一个常数。本文演示了一种方法，该方法可以将给定分辨率所允许的视场角增加整个数量级，从而增加光度，并由此增加从扩展源收集到的势能以及可能的信号对相对于自由空间迈克尔逊干涉仪的性能，噪声比降低了两个数量级。概括这个例子，我们认为可能没有折衷的基本热力学依据，而扫描傅立叶变换光谱仪可以接受任意高的埃登场，并且在理论上仍可以达到较窄的光谱分辨率。