Focal length and slit size calculation method for grating spectrometer optical system

The invention discloses a focal length and slit size calculation method for a grating spectrometer optical system. The method comprises the following steps: building an optical system of the detectiongrating spectrometer of a space astronomical point source, and enabling the image quality of the optical system to reach a diffraction limit; obtaining the full width at half maximum (FWHM) of a starpoint image PSF at the slit according to the maximum wavelength lambdamax of the detection spectrum and the entrance pupil diameter D of the optical system; obtaining the focal length f' of the optical system according to the full width at half maximum FWHM of the star point image PSF at the slit, the spectral sampling rate n and the spectral direction pixel spacing p of the detector; obtaining the size of a first dark ring of an Airy spot according to the maximum wavelength lambdamax of the detection spectrum and the entrance pupil diameter D of the optical system; and obtaining the width Wsof the slit according to t