Design method of optical system of improved Czerny-Turner imaging spectrometer

Astigmatism is the main aberration that limits the spatial resolution of Czerny-Turner imaging spectrometer. Focal power is introduced to calculate astigmatism, and formulas are deduced to correct it. The method of computing the distance between grating and collimator is given, which is able to correct the aberration of the edge of field of view. The computing method of tilt angle of imaging plane, which is helpful to correct the aberration at all wavelengths. And an imaging spectrometer based on such structure working in 115~200 nm is designed, with f'=48 mm, F number is 5.0 and image size is 8 mm×7 mm. The designed imaging spectrometer can get spectral resolution δλ=0.22 nm and modulation transimission function (MTF) is 0.7 at all wavelengths and full field of view. The design method can be applied to other imaging spectrometers of different structures.