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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 µm are obtained for speeds as high as f/2.5 and a wavelength range of 0.4–1.0 µm. A design example is presented using a free interactive optical design tool.

In this study, we aimed to measure material dispersion in fused silica using a low coherence interferometric method. The measurement was carried out quickly and efficiently in a wide spectral range using this method. The refractive index and group index of fused silica were determined by capturing a few interferograms. The material dispersion was modeled using a Sellmeier equation with three resonances. Three different fits were investigated; the most appropriate fit was the one that used both the measured refractive and group indexes to model the dispersion. Second-order dispersion was also quantified, and zero-dispersion wavelength was determined.