In this paper various factors influencing the image quality of plane grating spectrometer are discussed in detail. By means of vector elgebra a general formula is given for the form of the spectral lines in relation to the form of the entrance slit. A formula describing the angular dispersion of the spectral line resulting from a circular slit is also given. Investigation on the optical performance of the Ebert-Fastie grating spectrometer shows that among various residual optical aberrations, due to unsymmetrical disposition of the incident and diffracting beams with respect to the grating surface, coma is the most serious image defect. This can however be corrected by changing the focal length of one of its reflecting mirrors and placing it at a definite distance from the other mirror. It is also shown that residual aberrations can be well eliminated by placing an aspherical correcting plate near the grating surface. By the latter means there is the potentiality of greatly improving the performance of the instrument; either the volume of the instrument may be greatly reduced where shorter focal length optical systems can be used, or much better light gathering capacity can be achieved without sacrificing its monochrometicity when the spectrometer is used as a monochrometor.