Shape specification for axially symmetric optical surfaces.

  title={Shape specification for axially symmetric optical surfaces.},
  author={G. W. Forbes},
  journal={Optics express},
  volume={15 8},
  • G. Forbes
  • Published 16 April 2007
  • Physics
  • Optics express
Advances in fabrication and testing are allowing aspheric optics to have greater impact through their increased prevalence and complexity. The most widely used characterization of surface shape is numerically deficient, however. Furthermore, with regard to tolerancing and to constraints for manufacturability, this representation is poorly suited for design purposes. Effective alternatives are therefore presented for working with rotationally symmetric surfaces that are either (i) strongly… 

Lens design with Forbes aspheres

Lens design is a continually expanding field being driven by applications with increasingly difficult packaging and imaging constraints. In order to meet the challenges posed by current and future

Tolerancing Forbes aspheres: advantages of an orthogonal basis

In this paper tolerancing of aspheric surfaces in orthogonal bases, specifically Forbes aspheres, is covered and the significant advantages of such an Orthogonal representation are highlighted and reinforced with an example.

Manufacturability estimates for optical aspheres.

Effective approximations can be exploited when an asphere's shape is characterized by using a particular orthogonal basis, and are used not only as quick manufacturability estimates at the production end, but more importantly as part of an efficient design process that can boost the resulting optical systems' cost-effectiveness.

Characterizing the shape of freeform optics.

A recently introduced method for characterizing the shape of rotationally symmetric aspheres is generalized here for application to a wide class of freeform optics. New sets of orthogonal polynomials

Effective specification of the surface shape of aspheric optics

For hundreds of years, spherical surfaces have been the norm for optics simply because they are easy to make: randomly rubbing two rocks together while allowing free rotation abrades high points and

Optimizing reflective systems using aspheric and freeform surfaces

The large number of surface types that are manufacturable today provide many available paths to the optical designer. It is not always clear which path provides the optimal balance of merit function

Tolerancing an optical freeform surface: an optical fabricator's perspective

Freeform optical shapes or optical surfaces that are designed with non-symmetric features are gaining popularity with lens designers and optical system integrators. Tolerances on a freeform optical

Designing cost-effective systems that incorporate high-precision aspheric optics

The versatility of production tools for fabricating aspheric optics is growing, but accurate cost-effective metrology systems presently have less extensive aspheric capabilities. It is important,

Applying slope constrained Q-type aspheres to develop higher performance lenses.

Results show that Q-type aspheric surfaces that are optimized with slope constraints are not only more testable, an original motivation, but, they can also lead to solutions that are less sensitive to assembly induced misalignments for lithographic quality lenses.

Degeneracy in freeform surfaces described with orthogonal polynomials.

Orthogonal polynomials offer useful mathematical properties for describing freeform optical surfaces. Their advantages are best leveraged by understanding the interactions between variables such as



Optical design with rotationally symmetric NURBS

  • H. Chase
  • Mathematics
    International Optical Design Conference
  • 2002
The standard aspheric surface, a conic surface figured with a polynomial expansion, provides excellent correction in many optical design problems. But there are problems where this set of basis

Concise formula for the Zernike coefficients of scaled pupils

Modern steppers and scanners have a projection lens whose numerical aperture (NA) can be varied so as to optimize the image performance for certain lithographic features. Thus a variable fraction of

Superconic and subconic surface descriptions in optical design

The superconic surface description has been around since 1986 and more recently implemented in commercial design software. A simpler version dubbed the 'subconic' is proposed and appears to work well

On the coefficients of differentiated expansions and derivatives of Jacobi polynomials

A formula expressing explicitly the derivatives of Jacobi polynomials of any degree and for any order in terms of the Jacobi polynomials themselves is proved. Another explicit formula, which

General ray-tracing procedure

Computing formulas are presented for tracing skew rays through optical systems containing cylindrical and toric surfaces of arbitrary orientation and position. Particular attention is given to the