To demonstrate, consider a single element for which you would like to know how the RMS Spot Radius changes for a tilt tolerance about the X axis.

FILE:  Single Element Lens.ZMX (attached to last page of article)

TETX is the operand for tolerance on element tilt about the X axis.  In this case, the single element has a tilt tolerance of +/- 0.5 degrees.



Running the tolerance with the following settings (note that Paraxial Focus is set as the compensator):



In the Sensitivity Analysis of the tolerance output, we can see the criteria value as well as the change in criteria as a function of our TETX tolerance. 



In this case, the tilt did not affect the RMS Spot Radius very much, but we can review what ZEMAX has done more closely by saving the file ZEMAX internally constructed to perform this perturbation. 

In the Tolerance Data Editor, under the TETX line, insert a SAVE tolerance control operand.



The SAVE command allows you to save the previous tolerance to a ZEMAX Lens File with the specified “File #.”  A file will be saved for both the maximum and minimum tolerance.  The file names will be TSAV_MIN_xxxx.ZMX and TSAV_MAX_xxxx.ZMX for the min and max tolerance analysis, respectively, where xxxx is the integer number specified in the Int1 column.  In this case, the integer number is 5, so the minimum tolerance file will be TSAV_MIN_0005.ZMX.  Note that the saved file is saved into the same directory as the current lens file.

Run the tolerance analysis once more with the SAVE operand in place (use the same tolerance settings).

Once the analysis is complete, open the TSAV_MIN_0005.ZMX file from the appropriate directory.  Note the modifications made to the Lens Data Editor.  To tilt the element about the X axis, ZEMAX inserted a pair of Coordinate Break Surfaces with the appropriate solves and values.  ZEMAX even places text in the Comment column to indicate which tolerance each surface represents.  Also note the marginal ray height solve on surface 6.  Remember, we chose to have Paraxial Focus as our compensator when performing the tolerance analysis!





With this capability, we can clearly review what ZEMAX has done to ensure any given tolerance is performed the way we expect.  Most importantly, we can thoroughly investigate any tolerance which we find to produce curious results.

In the saved file, it is also possible to review the merit function which ZEMAX constructed to evaluate the RMS Spot Radius criteria.  The Merit Function Value is equivalent to the criteria value reported in the tolerance output: