Biconic Zernike Surface

The Biconic Zernike Surface is either rectangular or elliptical in shape, or may have a shape defined by a user defined aperture. The surface is described by the following sag equation:

Where

and

Rx and Ry are the radius of curvature values in the x and y directions, k_x and k_y are the conic constants in the x and y directions, the α terms are the x aspheric coefficients, the β terms are the y aspheric coefficients, N is the number of Zernike coefficients in the series, A_i is the coefficient on the i^th Zernike Standard polynomial, r is the radial coordinate in lens units, ρ is the normalized radial coordinate, and is the angular coordinate. The Zernike Standard polynomials are defined in the table given in Zernike Standard Coefficients.

This surface also supports optional X and Y decenters on the Biconic and Zernike terms separately. The biconic decenters are applied to the biconic sag and individual x and y aspheric coefficients, while the Zernike decenters are applied only to the Zernike terms.

The following parameters are used to define the Biconic Zernike Surface:

Parameter #	Description	Face Name	Face #
1-2	The X and Y Half-Width in lens units. If either value is less than zero, the aperture shape will be elliptical, otherwise, the aperture is rectangular, unless a user-defined aperture is applied to the surface.	All Faces	0
3-4	The Rx and Ry radii of curvature. Use zero for flat.	All Faces	0
5-6	The Kx and Ky conic constants.	All Faces	0
7-8	The biconic X and Y direction decenters.	All Faces	0
9-10	The Zernike X and Y direction decenters.	All Faces	0
11	The number of Standard Zernike terms.	All Faces	0
12	The normalization radius for the Zernike terms.	All Faces	0
13	Unused.	NA	NA
14-29	The x direction aspheric α coefficients.	All Faces	0
30-45	The y direction aspheric β coefficients.	All Faces	0
46-245	The Zernike Standard coefficients.	All Faces	0

Face Numbers: All faces Face 0.

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