The light collection power and the relative aperture of weak-light spectrometers, such as Raman and hyperspectral spectrometers, are expected as high or big as possible, in order to improve their signal-to-noise ratio (SNR). Littrow-Offner spectroscopic mount has the advantages of both Offner and Littrow mounts, including its simplicity and compactness, concentricity of all spherical elements, low inherent aberration, realizable big relative aperture and high light collection. Such combined mount structure and principle are briefly introduced and then its imaging performance is investigated. Its astigmatic characteristic then is investigated, through application of the sagittal and meridian imaging formulas of spherical mirror and diffractive grating. The means to eliminate astigmatism in the wavelength range is suggested. Furthermore, the inherent astigmatism is corrected by introducing a meniscus singlet with negative astigmatism. In the case of Raman spectrometer, a compact spectroscopic optics with big relative aperture and resolution and excellent imaging quality is optimally designed.