To obtain satisfactory performance in characterizing optical freeform surfaces with local features, this paper proposes a model of a radial basis function with slope-based shape factor and distribution (RBF-SSD). Compared to previous RBF-slope models with only slope-based shape factors, the RBF-SSD model relates both shape factors and distribution with the surface slope, ensuring greater fitting ability can be achieved when fitting a surface with local features. Fitting experiments for two different surfaces demonstrated the fitting ability of the RBF-SSD model. An off-axis three-mirror system with 3 ° × 3.6 ° field of view was designed as an example to show the optical design efficacy of our model.
It is of great importance to utilize a model to characterize the surfaces while designing an optical imaging system with freeform surfaces. For this purpose, a model with radial basis function based on surface slope (RBF-slope) for optical freeform surfaces was investigated by establishing the relationship between the shape factor and local surface slope, and improving the distributions of the basis functions for circular apertures. We performed the fitting experiment for “bumpy” paraboloids; the results demonstrated that the RBF-slope model has stronger fitting ability than conventional RBF model. A prototype of single mirror magnifier for head-worn display was designed and fabricated, in which the freeform mirror was described and characterized using the RBF-slope model. It can be proved by the design results that the RBF-slope model for optical freeform surfaces has obvious advantages in aberration balancing over conventional model. The primary experiments showed that the freeform surface was well fabricated and expected image display can be achieved.
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