Toroidal Hologram (non-sequential geometry objects)
A Toroidal Hologram consists of a rectangular, circular, or elliptical lens with possibly aspheric toroidal surfaces on the front and back faces and an optically fabricated hologram on the front face. 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 hologram on the front face is defined in a manner similar to the Hologram 1 and Hologram 2 sequential surfaces.
This object can also be used as a volume hologram by setting the Volume Hologram? parameter to 1. This does not affect the deviation of rays but it is used in the calculation of efficiency. Similarly, the Hologram Thickness parameter of the object does not effect the geometric shape of the object, only the efficiency. For a full description of non-sequential volume hologram objects, see Hologram Lens.
The Toroidal Hologram is defined by the following parameters (Par 34-41 are only available when Par 33= 1):
| Parameter # | Description | Face Name | Face # |
| 1 | Radial Height of the lens in the y direction. | NA | NA |
| 2 | 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 of the lens along the local Z axis. | Side | 0 |
| 4-5 | Unused. | NA | NA |
| 6, 7, 8 | The radius of rotation, radius of curvature, and conic constant for the front face. | Front | 1 |
| 9-14 | The coefficients on the powers of y for the front face. | Front | 1 |
| 15, 16, 17 | The radius of rotation, radius of curvature, and conic constant for the back face. | Back | 2 |
| 18-23 | The coefficients on the powers of y for the back face. | Back | 2 |
| 24 | Holo Type: 1 if both sources converging/diverging, 2 if one source is converging and one is diverging. For more information, see Hologram 1 and Hologram 2. | Front | 1 |
| 25 | Diffraction Order: Multiple orders may be specified in Object Properties Diffraction tab, see Diffraction from NSC Objects. | Front | 1 |
| 26 | Construction Wavelength: The wavelength in micrometers used to fabricate the hologram. | Front | 1 |
| 27-32 | The X, Y, and Z coordinates in lens units of the construction points relative to the vertex of the front face of the Hologram. | Front | 1 |
| 33 | Volume Hologram?: 0 for false, 1 for true. | Front | 1 |
| 34 | Hologram Thickness: only used for efficiency calculations, not ray-tracing. | Front | 1 |
| 35 | Refractive index seen by construction beam 1 outside hologram, n1. | Front | 1 |
| 36 | Refractive index seen by construction beam 2 outside hologram, n2. | Front | 1 |
| 37 | Average refractive index of the hologram emulsion, n. | Front | 1 |
| 38 | Modulation of the refractive index, dn. | Front | 1 |
| 39 | Shrinkage: 0 for no shrinkage, else scale of thickness e.g. 0.98 is 2% shrinkage. | Front | 1 |
| 40 | Index Shift: change of average refractive index after developing. | Front | 1 |
| 41 | Consider Fresnel?: 0 for false, 1 for true. | Front | 1 |
To make any of the 4 radii flat; use a value of zero. Note a cylinder lens results if the radius of rotation is set to zero. If the order is zero or if the ray totally internally reflects at the hologram boundary, no hologram diffraction is computed.
For important information on diffractive objects, see Diffraction from NSC objects .
The reference coordinate is the center of the front face. Face Numbers: Front face Face 1, back face Face 2, all other faces Face 0.
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