Generalized Fresnel
This surface represents a generalization of the Fresnel surface described in "Fresnel". The basic concept of a Fresnel surface, as far as ray tracing is concerned, is that the overall shape of the surface substrate is independent of the local slope. The generalized Fresnel uses a polynomial aspheric substrate model, identical to the Even Aspheric surface described in "Even Asphere". The sag of the surface is given by the following expression:
where the terms are identical to those in the even asphere surface model. See that section for a complete discussion.
Once the ray has intercepted the surface, the ray reflects or refracts as if the surface had a shape described by a polynomial expansion of the form:
where N is the number of polynomial coefficients in the series, and Ai is the coefficient on the ith extended polynomial term. The polynomial terms are identical to those described in "Extended Polynomial". It is the gradient of the extended polynomial terms alone that determines the reflective or refractive properties of the surface, not the surface substrate shape.
One application for this surface type is modeling faceted surfaces. For example, a flat substrate may consist of a series of small faceted planes, which would reflect or refract the light as though the surface was tilted. This can be simulated using a flat substrate and a linear x or y tilt term in the polynomial coefficients.
Because there is no reliable way to compute the phase through a Fresnel surface which is not a plane, any calculation that requires OPD data, such as OPD fans, MTF, and Zernike coefficients, will not be supported if a non-plane substrate Fresnel surface is present in the lens description.
Note that the coefficients have units. The coefficients are entered in the corresponding parameter columns, as shown in the following table.
PARAMETER DEFINITIONS FOR GENERALIZED FRESNEL SURFACES
| Parameter # | Definition |
| 1 - 8 | α1 - α8 |
| 13 | Maximum term number (up to 230) |
| 14 | Normalization radius. All ray-intercept points are divided by this number to determine the x and y coordinates for polynomial evaluation. |
| 15-244 | Polynomial terms. |
The "Maximum term number" is used to specify the maximum polynomial term to be used in calculating the surface sag. This number is provided to speed the ray tracing calculation, as terms beyond this number are ignored.
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