The five tolerance operands, TUDX, TUDY, TUTX, TUTY, and TUTZ, are used for more general user defined tilts and decenters than that of TEDX, TEDY; etc.  The primary difference is that ZEMAX does not automatically insert the required coordinate break surfaces to achieve the specified decenters and tilts in the tolerances.  These user defined tolerances will only work on Coordinate Break surfaces.   So, as we have done over the last couple pages, the coordinate breaks must be entered into the Lens Data Editor by the designer.

Just like any other tolerance operand, the TU** operands may be inserted by typing the appropriate name in the Type column of the Tolerance Data Editor.  For the purposes of demonstrating the user defined tolerances simply type each of the TU** operands in the TDE.  Since we have confirmed that the coordinate breaks have already been properly constructed, we only have to perturb the parameters of the very first coordinate break; all of our pickups and position solves will adjust the rest of the system.  So, for each operand, change the “Surf” parameter to 1, the first coordinate break surface.  In addition, modify the Min and Max tolerances for each operand to -0.2 and 0.2 respectively.





For the purposes of keeping the current demonstration as simple as possible, and to focus on the operation of the user defined tolerance operands, no additional operands or compensators will be defined.  An RMS Spot Size tolerance analysis will be performed, and several Monte Carlo files will be saved so that we can insure the toleranced lens is positioned as we expected.

Run the tolerance analysis (Tools > Tolerancing > Tolerancing) using the following settings:



Click OK.

Upon doing so, ZEMAX will issue a warning:



This error message is issued to warn you that ZEMAX has detected one or more solves present in the Lens Data Editor.  Many solves, such as some curvature solves or ray height solves, are generally not appropriate for tolerancing.  For example, if an F Number solve was placed on the Radius of a particular surface, it would act as a compensator during the tolerance analysis, and adjust the radius of curvature for each perturbation so that a particular F Number constraint is met.

Solve like the pickup and position solves are sometimes valid, and in fact necessary for certain systems.  The designer should always carefully examine the solves in place and determine the consequence of having a particular solve in place. 

We may ignore this error message, as the solves that we have constructed are critical to an accurate tolerance analysis of the double pass system.
 
Take a moment to review some of the saved Monte Carlo files, and observe the values ZEMAX has chosen for the tilts and decenters of the lens.  No matter what combination of values has been chosen, the lens should not differ between passes: