Local slope tolerance model for optical surfaces with distortion as the evaluation criterion.

Ultra-precision imaging systems support cutting-edge scientific exploration and technological innovation. The continuous development of optical freeform and aspheric surface technology offers new possibilities for high-performance optical systems but also presents significant manufacturing challenges. In this paper, we derive and discuss in detail the impact of surface manufacturing errors on the image point positions of optical systems. The analysis reveals that among the manufacturing errors, the surface slope error is the primary factor driving positional changes in image points. Based on these insights, a local slope tolerance model using distortion as the evaluation criterion is proposed. This model specifies the slope error requirements at each point on the surface, ensuring the optical system's distortion meets the acceptable threshold during manufacturing. The model's effectiveness is validated through an off-axis three-mirror freeform optical system and a Cassegrain aspheric optical system.