Cylinder Fresnel

The Cylinder Fresnel surface has a polynomial aspheric cylindrical substrate with an independent polynomial aspheric cylindrical function defining the Fresnel lens properties. The surface substrate sag is given by:

The previous expression is used to compute the ray-surface intercept. Once the intercept is found, the refraction (or reflection) of the surface is determined by the local slope of the Fresnel facets. The Fresnel facet shape is described by an identical expression, with independent coefficients:

Note that the curvature (symbol c), the conic constant (symbol k), and all of the polynomial coefficients are independent for the substrate sag and Fresnel portions of the surface. The refraction at the surface accounts for only the Fresnel sag, while the ray-surface intercept depends only upon the substrate sag.

The substrate sag radius, conic, and polynomial terms are all specified in the Lens Data Editor. The Fresnel sag terms are specified as extra data values in an extra data file (see the Import section of the Surface Properties). However, the extra data file uses curvature (the reciprocal of radius) rather than radius for the Fresnel sag. The Parameter and Extra Data Values used are summarized in the following tables.

PARAMETER DEFINITIONS FOR CYLINDER FRESNEL SURFACES

Parameter #	Definition
1 - 8	α1 - α8
13	Maximum aspheric polynomial term number, n. The maximum is 8.
14	The Y direction curvature (NOT RADIUS) of the Fresnel surface. This parameter will effect the refraction of the surface, but not the shape of the substrate.
15	The Y direction conic constant of the Fresnel surface. This parameter will effect the refraction of the surface, but not the shape of the substrate.
16	Coefficient on y^2
17	Coefficient on y^4
...	...
23	Coefficient on y^16

The "Maximum aspheric polynomial term number" is used to specify the maximum polynomial term to be used in calculating the Fresnel sag. This number is provided to speed the ray tracing calculation, as terms beyond this number are ignored. As with any complex surface model, extreme care should be taken to evaluate the accuracy and appropriateness of this model, especially where fabrication decisions are concerned.

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.

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• Data (sequential surfaces, lens data editor)