Abstract

An advanced optical design for a low $f$-number, high resolution, astigmatism-free, and broadband Czerny–Turner spectrometer is proposed. A hemispherical lens is added between the entrance slit and collimating mirror, which can correct astigmatism and increase numerical aperture at the same time. The theory and method for the aberration correction are analyzed in detail. An example of a design with the $f$-number as 3 working in 350–750 nm has been presented by the optimized theory. The comparison of the improved Czerny–Turner spectrometer with the conventional Czerny–Turner spectrometer is also thoroughly described in the paper. The ray-tracing results show that the RMS spot radius of the improved Czerny–Turner spectrometer decreases from over 200 µm to less than 18 µm compared with the traditional Czerny–Turner spectrometer.

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