Toroidal Lens
A toroidal lens consists of a rectangular, circular, or elliptical lens with possibly aspheric toroidal surfaces on the front and back faces. A toroidal surface is defined by a curve in the YZ plane which is then rotated about an axis parallel to the Y axis but displaced by a distance R; the radius of rotation. The curve in the YZ plane is defined by:
where c is the reciprocal of the radius of curvature in YZ plane.
The toroidal lens is defined by 23 parameters:
| Parameter # | Description | Face Name | Face # |
| 1 | The Radial Height of the lens in the Y-direction | NA | NA |
| 2 | The X-Half Width. If this parameter is zero, then the outer boundary of the lens will be a circle with a radial size equal to the Radial Height. If this parameter is positive, the outer boundary of the lens will be rectangular. If this parameter is negative, the outer boundary of the lens will be elliptical. | NA | NA |
| 3 | Thickness | Side | 0 |
| 4-5 | Unused. | NA | NA |
| 6, 7, 8 | The radius of rotation, radius of curvature, and conic for the front surface. | Front | 1 |
| 9-14 | The coefficients on the powers of y for the front surface. | Front | 1 |
| 15, 16, 17 | The radius of rotation, radius of curvature, and conic for the back surface. | Back | 2 |
| 18-25 | The coefficients on the powers of y for the back surface. | Back | 2 |
To make either the radius of rotation or radius of curvature flat; use a value of zero. Note a cylindrical surface results if the radius of rotation is set to zero.
The reference coordinate is the center of the front face. Face Numbers: Face Numbers: Front face Face 1, back face Face 2, Side faces Face 0.
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