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A unique method to design a high-throughput and high-resolution ultrathin Czerny–Turner (UTCT) spectrometer is proposed. This paper reveals an infrequent design process of spectrometers based on Coddington’s equations, which will lead us to develop a high-performance spectrometer from scratch. The spectrometer is composed of cylindrical elements except a planar grating. In the simulation design, spot radius is sub-pixel size, which means that almost all of the energy is collected by the detector. The spectral resolution is 0.4 nm at central wavelength and 0.75 nm at edge wavelength when the width of slit is chosen to be 25 μm and the groove density is 900 lines/mm.

A modified optical design for a broadband, high resolution, astigmatism-free Czerny-Turner spectrometer is proposed. Astigmatism is corrected by using cylindrical mirrors over a broad spectral range. The theory and method for astigmatism correction are thoroughly analyzed. The comparison between the modified Czerny-Turner spectrometer and the traditional Czerny-Turner spectrometer is also described in detail. The ray-tracing results show that the RMS spot radius has decreased to 4.2 μm at the central wavelength and 17 μm at the wedge wavelength.

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