Tolerance/Sensitivity Analysis

Since no lens assembly can be fabricated or system built without knowing what the machining tolerances are, this process is of paramount importance. Many designers skip this step or else attempt fabrication on a “best effort” basis.

Many times a system is ready for fabrication, but no tolerance analysis has been done. Other times a system specification is known, but it hasn’t been broken down into components. Other times there is a specification for the system and components, but they don’t match. Andorra has seen all these scenarios and thus has developed expertise in understanding how to tolerance complex systems for cost effective fabrication.

The determination of fabrication tolerances is typically done one of two ways depending on the circumstances. One way is to take the final error budget, subtract out the design residuals, and run a hard analysis to determine the allowable tolerances, making changes in weighting as needed. The other method is to simply put typical and reasonable shop tolerances (especially if known) into the program, add them up in an RSS fashion and see if final system performance is met. In both cases, it is usually better to do a sensitivity analysis first. This involves making small changes in a parameter, such as decenter, and calculating the change in performance parameter. This allows one to determine which tolerances are most sensitive and thus need to be tightened, allowing the loosening of others.

The simplified block diagram of performance error budgeting looks like this:

Although RMS wavefront error is used as an example here, other performance measures can be toleranced such as MTF or encircled energy. Of course, each block of high level errors must be broken down further.