For tolerancing, we will consider the effects of tilting and decentering the lens.  Normally, the built in element tolerances, such as TEDX, TEDY, TETX, TETY, could be used to automate the perturbations of an element.  However, in a double pass system, tolerancing of these effects requires some additional modification to the LDE.  The reason for this is ZEMAX has no way of knowing that the lens defined in the second pass is supposed to be the same physical component as the lens defined in the first pass.  As a result, coordinate breaks describing the tilts/decenters need to be manually entered into the Lens Data Editor, and the tolerances on the parameters of the coordinate breaks may be performed via user-defined tolerance operands: TUDX, TUDY, TUTX, TUTY, and TUTZ.  These operands will be discussed and used in more detail later on in the article.

So why is this necessary?  Well, given the fact that ZEMAX has no way of knowing that the lenses in each pass define the same physical lens, each element would be treated individually with the built-in element decenter/tilt operands.  So for the purposes of a Sensitivity Analysis, the lens in the first pass may be perturbed, but not mirrored in the return path.  Therefore, the rays traced in the return will refract with an untilted lens. 

In the Monte Carlo simulation, both lens elements may be tilted by different amounts, or even by different signs.  Consequently, the criteria value reported for each Monte Carlo simulation will not be representative of the true, physical perturbation of that element.

To begin, each occurrence of the lens will need to be wrapped with coordinate breaks.  The front vertex of the lens will be assumed to be the pivot axis.  As such, any tilt must be restored at this location.  On the second pass, the pivot should be initialized in the same location. 

To setup the double pass system for tolerancing, we must first insert and arrange the coordinate breaks.  These may be setup manually, or the Tilt/Decenter tool may be utilized.  For the details in how to tilt and decenter elements, as well as a complete discussion of how coordinate breaks work, please refer to the article, “How to Tilt and Decenter a Sequential Optical Component.”

• Highlight surfaces 1 & 2 and choose the Tilt/Decenter Element Tool (Tools > Coordinates > Tilt/Decenter Elements).  The tilt values will remain zero for the time being, since we are just using the tool to setup the coordinate breaks for us.

At this point, the Lens Data Editor should look as follows:





and the layout looks the same as before: