Compact and lightweight optical designs achieving visually acceptable image quality, field of view, eye clearance, eye
box diameter and operating across the visible spectrum, are the key to the success of next generation head-worn displays.
There have been several approaches in the design of head-worn displays including holographic optical elements and
laser scanner systems. For example, Minolta has pursued a monochromatic display (green) with a 3 mm exit pupil
realized by a 3.4 mm thick light guide with a holographic optical element to achieve an eyeglass form-factor head-worn
display . Our approach in this paper is to investigate the field of view, eyebox diameter, and the performance limit of
a single element magnifier comprised of freeform surfaces. The surface shape is a major variable in such a constrained
system with respect to the optimization degrees of freedom.
Typical optical surfaces are functions mapping vectors in R<sup>2</sup> to real numbers representing the sag of the surface. A
majority of optical designs to-date have relied on conic sections to which are added polynomials as the functions of
choice. The choice of conic sections is easily justified, since conic sections are stigmatic surfaces under certain imaging
geometries. The choice of polynomials from an image quality analysis point of view is understood since the wavefront
aberration function is typically expanded in terms of polynomials. Therefore, a polynomial surface description may link
a designer's understanding of the wavefront aberrations and the surface shape. However, from the point of view of shape
optimization and representation, polynomial shape descriptions can be challenged. In Section 2, we briefly describe the
radial basis function approach to represent freeform optical surfaces. In Section 3, we apply the RBF to design a single
element see-through compatible head-worn display.