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We present the analytical design of an imaging spectrometer based on the three-concentric-mirror (Offner) configuration. The approach presented allows for the rapid design of this class of system. Likewise, high-optical-quality spectrometers are obtained without the use of aberration-corrected gratings, even for high speeds. Our approach is based on the calculation of both the meridional and the sagittal images of an off-axis object point. Thus, the meridional and sagittal curves are obtained in the whole spectral range. Making these curves tangent to each other for a given wavelength results in a significant decrease in astigmatism, which is the dominant residual aberration.RMS spot radii less than 5 mm are obtained for speeds as high as f/2.5 and a wavelength range of 0.4-1.0 microm. A design example is presented using a free interactive optical design tool.
Prieto-Blanco et al. (2006) studied this question.