View Full Document

Meshfree Approximation Methods for Free-Form Surface



View the full content.
View Full Document
View Full Document

2 views

Unformatted text preview:

Invited Paper Meshfree Approximation Methods for Free Form Surface Representation in Optical Design with Applications to Head Worn Displays Ozan Cakmakci1 Gregory E Fasshauer2 Hassan Foroosh3 Kevin P Thompson4 and Jannick P Rolland1 3 1 CREOL The College of Optics and Photonics University of Central Florida Orlando Florida 2 Department of Applied Mathematics Illinois Institute of Technology Chicago Illinois 3 School of Computer Science University of Central Florida Orlando Florida 4 Optical Research Associates Pasadena California ABSTRACT In this paper we summarize our initial experiences in designing head worn displays with free form optical surfaces Typical optical surfaces implemented in raytrace codes today are functions mapping two dimensional vectors to real numbers The majority of optical designs to date have relied on conic sections and polynomials as the functions of choice The choice of conic sections is justified since conic sections are stigmatic surfaces under certain imaging geometries The choice of polynomials from the point of view of surface description can be challenged The advantage of using polynomials is that the wavefront aberration function is typically expanded in polynomials Therefore a polynomial surface description may link a designer s understanding of wavefront aberrations and the surface description The limitations of using multivariate polynomials are described by a theorem due to Mairhuber and Curtis from approximation theory In our recent work we proposed and applied radial basis functions to represent optical surfaces as an alternative to multivariate polynomials We compare the polynomial descriptions to radial basis functions using the MTF criteria The benefits of using radial basis functions for surface description are summarized in the context of specific magnifier systems i e head worn displays They include for example the performance increase measured by the MTF or the ability to increase the field of view or pupil size Full



Access the best Study Guides, Lecture Notes and Practice Exams

Loading Unlocking...
Login

Join to view Meshfree Approximation Methods for Free-Form Surface and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Meshfree Approximation Methods for Free-Form Surface and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?