This paper presents a derivation of the response of a simple grating spectrometer to a plane wave that is modulated in both phase and amplitude by arbitrary functions. The spectrometer is characterized by its familiar frequency-domain response and by its less familiar time-domain response. It is found that the time-domain characterization is a useful form for studying the response of a spectrometer to a modulated plane wave. The quasi-static response for low modulation rates is clearly revealed by the time-domain characterization. Furthermore, the response of the first moment of the light intensity in the focal plane of the spectrometer can be derived easily from the time-domain characterization.
The technique described here is used to compute the time-domain response of a spectrometer to a plane wave with a linearly sweeping frequency.
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