There are many fabrication and mounting errors to consider when tolerancing an optical system.  ZEMAX’s tolerancing capabilities can model a number of different tolerances, including tolerance on radius, thickness, tilts and decenters of surfaces or elements, surface irregularity, and much more.  Each of these is supported via their own tolerance operand in ZEMAX.

Sometimes, it is desirable to tolerance for machined optical glass errors, such as the spatial inhomogeneity of the refractive index of a material.  As there is not a built-in tolerance operand for inhomogeneity, this article is designed to cover the alterative and superior approach to tolerancing for such fabrication errors.

Accurately modeling the inhomogeneity of a material is not as “standard” as you might expect.  Think of it this way:  Inhomogeneity basically means NOT homogeneous.  In other words, there are an infinite number of solutions to modeling a non-homogenous medium.  Which one do you pick, and how do you know for certain that this assumption is accurately representing your particular blank of glass?

If we know the exact profile of how the index varies over the aperture and thickness of the lens, then we can mathematically model the varying refractive index using ZEMAX’s GRIN capabilities.  However, it is not often that a manufacturer will provide the index profile for you.

Instead, the inhomogeneity of a glass is often expressed as a grade, which corresponds to some maximum refractive index variation of the cut glass.  For example, the ISO 10110 part 4 homogeneity grades range from 0 to 5, while SCHOTT denotes their grades using the symbols below (S0, S1, and H1 through H5) [1]:



Table courtesy of SCHOTT glass.  Please see Reference [1].