A method of designing a compact pushbroom imaging spectrometer includes explicit consideration and minimization of nonuniformity of spatial and spectral response. It appears that prior to the development of this method, the issue of nonuniformity of response was addressed haphazardly. The major advantage afforded by the present method is that it enables systematic optimization of the smallest possible pushbroom spectrometer within a given class of spectrometer designs.

A pushbroom spectrometer includes a rectangular photodetector array with pixels arranged in columns (parallel to a spatial axis defined by a straight slit) and rows (parallel to the spectral axis). Light enters the spectrometer through the slit. Each point or pixel along the slit corresponds to a point or pixel along one spatial axis in the scene under observation. Thus, each row of pixels gives a readout of the spectrum for one point or pixel on a columnar line that crosses the scene. The term "pushbroom" arises because in an action reminiscent of a pushbroom sweeping a floor, the field of view is swept through the scene, along a line perpendicular to the slit, to acquire spectral readouts from all pixels in the scene.

A Compact Dyson Spectrometer has been designed to cover the wavelength range of 1,000 to 2,500 nm. Version 1 has been optimized with respect to distortion and image quality only. Version 2 has been optimized with respect to uniformity of response in addition to distortion and image quality. The two versions are similar, except that the distance from the lens to the grating is about 10 percent greater in version 2. In version 1, the variation of the spectral and spatial response functions shown negates the high degree of distortion correction achieved in the design and becomes the dominant source of spectral artifacts. In version 2, the spectral and spatial response function variation has been reduced to a very low level, compatible with the high degree of distortion correction achieved by the design.

Heretofore, designers of pushbroom spectrometers have been concerned with optimizing spot sizes and minimizing distortions. While satisfaction of these design requirements is necessary, it is not sufficient. Even though spectral and spatial distortions might be minimized, there can remain variations in the spectral and spatial response functions that exert detrimental effects similar to those of spectral and spatial distortions. For complete optimization of design, it is necessary to seek a proper balance among all relevant measures of performance, including variations in spectral and spatial responses in addition to the customary measures of spot energy inside a pixel and spectral and spatial distortions.

The present method provides for optimizing design in the sense of choosing design parameters that yield an arbitrarily specified balance among all of the aforementioned measures of performance. The method is based partly on the theoretical observation that spectral and spatial response functions can be controlled through the spectrometer modulation transfer function (MTF) in their respective directions. (In the case of a spectrometer used to view the Earth from above the atmosphere, the effect of the atmosphere can be included, at least in an average way, by inclusion of an atmospheric MTF as mere multiplicative factor of the spectrometer MTF.)

In this method, an optimization (merit) function is constructed for use with an appropriate previously or subsequently developed optical-design computer program. The merit function contains specific spectral- and spatial-distortion components, spectral- and spatial-uniformity components, and spot-size components with appropriate weights between them. The optimization for uniform spectral response is based on equalization of the MTF along the spectral axis, independent of field location. The optimization for uniform spatial response is based on either (1) equalization of the MTF along the spatial direction, independent of wavelength, or (2) achieving specified ratios among MTF values at various wavelengths.

In applications of the method to two generic spectrometer designs with only a few degrees of freedom, it was shown that optimally balanced specific designs can be obtained, even though the designs cannot be fully optimized to satisfy all requirements. In practice, one trades spot size to gain uniformity of response. This trade is demonstrated in the figure by comparison between two versions of one of these spectrometers.

This work was done by Pantazis Mouroulis, Robert Green, and Thomas Chrien of Caltech for NASA's Jet Propulsion Laboratory.


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Designing For Optimum Response in a Pushbroom Spectrometer

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This article first appeared in the January, 2001 issue of Photonics Tech Briefs Magazine.

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