Application of radial basis functions to shape description in a dual-element off-axis magnifier

Abstract

We previously demonstrated that radial basis functions may be preferred as a descriptor of free-form shape for a single mirror magnifier when compared to other conventional descriptions such as polynomials [Opt. Express 16, 1583 (2008)]. A key contribution is the application of radial basis functions to describe and optimize the shape of a free-form mirror in a dual-element magnifier with the specific goal of optimizing the pupil size given a 20 degrees field of view. We demonstrate a 12 mm exit pupil, 20 degrees diagonal full field of view, 15.5 mm eye clearance, 1.5 arc min resolution catadioptric dual-element magnifier design operating across the photopic visual regime. A second contribution is the explanation of why it is possible to approximate any optical mirror shape using radial basis functions.

Review of optical freeform surface representation technique and its application

“…Cakmakci and Rolland 26 designed a dual-element off-axis near-eye optical magnifier by combining a freeform reflector represented by XY polynomials and a diffractive lens. Furthermore, Cakmakci et al 27 applied the radial basis function, instead of XY polynomials, to characterize the freeform reflector, which could increase the exit pupil diameter from 8 to 12 mm. Cheng et al 7 reported a freeform prism-based head-worn display characterized by XY polynomials, which had the advantages of a fast focal ratio, large field of view, and see-through properties.…”

“…Thus, the radial basis function is multicentric. Cakmakci et al 27 designed a head-worn display using a Gaussian radial basis function freeform surface, which was integrated into optical design software by applying the "user-defined surface" feature. Moreover, the local feature of the freeform surface can be controlled by the radial basis function.…”

Application of radial basis functions to represent optical freeform surfaces

“…We have been able to extend the field of view from 20 degrees full-field to 25 degrees full-field replacing the x-y polynomial terms of the mirror with RBFs [4]. We also extended the pupil size from 8 mm to 12 mm in the dual-element catadioptric magnifier by using an RBF description on the freeform mirror [5].…”

Application of radial basis functions to shape description in a dual‐element off‐axis eyewear display: Field‐of‐view limit

“…In our previous work, we estimated the pupil-size limit of the dual-element magnifier design form to be 12 mm, given a 20°field of view and a 15-mm eye clearance. 15 The main approach of this paper is to describe the free-form mirror using radial basis functions in a dualelement magnifier to establish the field-of-view limit given a >15-mm eye clearance and an 8-mm exit pupil. The design form presented in this paper is an off-axis magnifier that folds the optical axis around a human head while providing the necessary mechanical clearances.…”