Radial Grating
The radial grating surface is similar to the diffraction grating surface (see "Diffraction Grating"), except the grating lines have radial symmetry, the grating line spacing is variable over the surface, and the substrate is an even aspheric surface shape (see "Even Asphere"). For a plane grating, rays traced to the grating are refracted according to the equation
where d is the grating spacing (always in micrometers), θ2 is the refracted angle, θ1 is the incident angle, M is the diffraction order, λ is the wavelength (always in micrometers), and n1 and n2 are the indices of refraction before and after the grating. The radial grating surface allows d to vary over the surface according to the equation:
where the Ai coefficients all have units of micrometers, and p is the normalized radial coordinate defined by
where r is the radial coordinate on the surface in lens units and R is the user defined normalization radius. The grating spacing d can be interpreted in two different ways. The normal OpticStudio convention is to measure d along the projection of the grating on the XY plane, ignoring any sag or curvature of the underlying surface. The Radial Grating surface supports an additional "Grating Mode", where d is interpreted as being measured along the local surface tangent. The Grating Mode can be set to 0 or 1 in parameter 9 in the Lens Data Editor.
Note that the sign convention for M is arbitrary. The grating surface can be plane, spherical, conical, or even aspheric, and the medium before the grating, as well as the grating itself, can be air, glass, "MIRROR" or any other valid glass type. OpticStudio only models gratings to the extent of deviating ray paths. Other properties, such as efficiency, and relative transmission are not supported. If the grating spacing is too small to satisfy the grating relation, then a "Ray missed surface" error will be reported.
PARAMETER DEFINITIONS FOR RADIAL GRATING SURFACES
| Parameter # | Definition |
| 0 | Diffraction Order |
| 1-8 | Even aspheric coefficients α1 –α8 |
| 9 | Grating Mode |
| 13 | Maximum number of terms |
| 14 | Normalization Radius |
| 15 | Coefficient on p^0 |
| 16 | Coefficient on p^1 |
| n | Coefficient on p^(n-15) |
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