In order for the Czerny-Turner spectrometer to be utilized in the imaging spectrometer for far-ultraviolet waveband, we describe the elimination of the principal aberration coma and astigmatism for the arrangement by light-path function analysis. The modified structure is built by a spherical mirror, a toroidal mirror, and a fixed plane grating. Starting with coma and astigmatism corrected by adjusting the incident angle to the collimating mirror and using a toroidal mirror, we obtain the optimized distances between the grating to the focusing mirror and the focusing mirror to the image plane by geometric analysis and first order differential calculation, in order to acquire high imaging quality in broad waveband. The design result shows a simple optical imaging structure that can be used in the ionosphere detection (120 to 180 nm) that is superior and convenient.