Gradient 1

This surface has the same shape as the Standard surface, with media whose index of refraction is described by

where r2 = x2 + y2 . Four parameters are required: the maximum step size, Δt , the base index, n0, the radial quadratic index, nr2 , and the radial linear index, nr1 . Note that nr2 and nr1 have units.

Discussion on maximum step size for GRIN surfaces

The maximum step size is measured in lens units along the local z-axis and determines the increments in which the gradient index is recalculated.  For example, if Δt = 0.1 and the system units are millimeters, then the index of refraction will be recalculated every 0.1 mm along the z-axis.  Therefore, a ray passing through this gradient surface will refract every 0.1 mm.

The maximum step size Δt determines the trade-off between ray tracing speed and accuracy. The exact value required depends upon the numerical aperture of the system and the magnitude of the coefficients. To determine a suitable step size, start at a large value (on the order of the thickness of the surface), and then perform a spot diagram. Note the RMS spot radius. Now decrease the step size by a factor of two. If the RMS spot radius changes by less than a few percent, the new step size is probably small enough. Otherwise, decrease the step again. For the final design phase, you may want to decrease the step size again. Using too small a step size needlessly slows the ray tracing speed without enhancement of accuracy. OPD tracing generally converges more slowly than ray tracing, so you may want to repeat the above procedure while inspecting the OPD fan. Occasionally check to ensure that the step size is appropriate as the design progresses.

Restrictions on surfaces following GRIN surfaces

The ray trace through a gradient index media requires iteration to determine the point of intersection of the ray with the surface following the gradient index surface. Because of this, not all surface types are allowed to follow gradient index surface types. If the type of the surface after a gradient index surface is not supported, a message will be presented indicating the error.

PARAMETER DEFINITIONS FOR GRADIENT 1 SURFACES

Parameter # Definition
1 Δt
2 n0
3 nr2
4 nr1

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