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| The spectral and spatial distortions, known as "smile" and "keystone", introduced by dispersive prisms in dispersive imaging spectrometers usually are nuisance for the accurate reconstruction of spectra and images. In addition to the software correction of distortion, the system designs, such as direct-vision compound prism, is also critical to reduce those distortions before corrections. In this paper, using vector ray tracing method, distortions and dispersive lengths are derived analytically for three-element or two-element compound prisms. The distortions are found to be the complex functions of the apex angles, the refractive indices and the incident vector on the first surface of the prisms, and relate to the focal length of imaging lens in the dispersive imaging spectrometer. The merit functions to optimize apex angles for the selected glasses at the fixed focal length over incident vectors are proposed. The presented method is useful for the designs of compound prisms in the dispersive imaging spectrometers with high accuracy. |
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| Keywords:optical design; imaging spectrometer; direct-vision prism; dispersion; distortion |
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