Abstract Optical vignetting of a Schmidt reflector is caused mainly by the spherical primary mirror not being big enough and by the effective light-collecting area of the corrector, which depends on the direction of the star light. Calculations of the vignetting of LAMOST, a special reflecting Schmidt telescope, are made by ray-tracing methods. The results show various features due to LAMOST's structure and observing modes. The un-vignetted field is small compared with its field of view. In the outmost portions of the field vignetting increases rapidly with the distance to the field center. The vignetting at a general position within the field of view is a function of both its distance to the field center and its position angle. Vignetting varies when the telescope points at different declinations and during observations. There is difference in vignetting between direct imaging and multi-fiber spectroscopy. Vignetting distorts the relative intensity of celestial objects at different positions in a field and also affects accurate sky-estimation and sky-subtraction. The determined vignetting functions may be used to correct the vignetting effect; alternatively flat-fielding may be adopted for the calibration. The effective apertures, which affect the signal-to-noise ratio of the observations, depend on the different declinations the telescope is pointing at and also different positions within a field due to vignetting.
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