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Fourier analysis of a four-dimensional imaging spectrometer with a fiber optic dimension transform element

A four-dimensional imaging spectrometer with a fiber optic dimension transform element has the ability to capture all four dimensions of data (2D spatial, spectral and temporal) with a single, radiometrically calibrated sensor at a single exposure, which satisfies the need to record transient events and fast changing phenomena of interest. In order to analyze the corresponding relation between the input light intensity and the output light intensity of a four-dimensional imaging spectrometer with a fiber optic dimension transform element, this paper utilizes the Fourier optics theory and complex Gaussian functions expansion method to derive and analyze the transmission characteristics of the imaging spectrometer optical system. This paper introduces the light intensity distribution formula when the detector is fixed on the negative first order spectral image plane and establishes and simulates the corresponding relation between the light intensity distribution of the detector and the spatial/spectral information on the target space. The research results show that the target information can be extracted and analyzed directly according to the corresponding relation.