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- How to Perform a Tolerance Analysis
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- How to Perform a Tolerance Analysis
How to Perform a Tolerance Analysis
- By Mark Nicholson
- Published 7 May 2007
- Tolerancing , First Time Users
-
Rating:
The First Tolerancing Run
As we chose to overlay Monte-Carlo graphics, and had an opern OPD plot on the desktop, the resulting OPDs of the 20 Monte-Carlo files can be clearly seen: we are a long way from our target performance of 0.05 waves RMS (l/20)!
During Sensitivity Analysis, ZEMAX measured the tolerancing criterion of the nominal system, and then takes the first tolerance, puts it to the minimum value and adjusts compensators, and reports the tolerancing criterion value. It does this again for the tolerance set to its maximum value. It then steps through each tolerance in turn, computing the sensitivity of the tolerancing criterion to each tolerance. It gives a report like so:
Now the nominal system has a tolerace criterion of 0.0025, or l/400. We require l/20, or 0.05 waves in production. However some tolerances produce more than this by themselves: the refractive index tolerance of the second lens alone causes the wavefront error to degrade to 0.07 waves after adjustment of the compensator.
After all the individual tolerances are computed, ZEMAX then computes a variety of statistics, the most important of which is the estimated change in the criterion and associated estimated performance. ZEMAX uses a Root Sum Square (RSS) assumption for computing the estimated changes in the performance.
For each tolerance, the change in performance from the nominal is squared and then averaged between the min and max tolerance values. The average of the min and max squared change is taken because the min and the max tolerance cannot both occur simultaneously, and so summing the squares would result in an overly pessimistic prediction. The final predicted, as-built performance is then computed.
For this system, the RSS calculation predicts a system performance of 0.079 waves compared to our specification of 0.05.
The Monte-Carlo analysis is in broad agreement:
although with only 20 samples, this is a crude assessment. The estimated yield of lenses below 0.05 RMS wavefront error is less than 50%:
Clearly some tolerances need to be tightened if the yield is to be improved. We can do this by hand, and re-run the sensitivity analysis if desired, or we can ask ZEMAX to automatically tighten the tolerances for us, in a process called Inverse Sensitivity Tolerancing.
During Sensitivity Analysis, ZEMAX measured the tolerancing criterion of the nominal system, and then takes the first tolerance, puts it to the minimum value and adjusts compensators, and reports the tolerancing criterion value. It does this again for the tolerance set to its maximum value. It then steps through each tolerance in turn, computing the sensitivity of the tolerancing criterion to each tolerance. It gives a report like so:
Now the nominal system has a tolerace criterion of 0.0025, or l/400. We require l/20, or 0.05 waves in production. However some tolerances produce more than this by themselves: the refractive index tolerance of the second lens alone causes the wavefront error to degrade to 0.07 waves after adjustment of the compensator.
After all the individual tolerances are computed, ZEMAX then computes a variety of statistics, the most important of which is the estimated change in the criterion and associated estimated performance. ZEMAX uses a Root Sum Square (RSS) assumption for computing the estimated changes in the performance.
For each tolerance, the change in performance from the nominal is squared and then averaged between the min and max tolerance values. The average of the min and max squared change is taken because the min and the max tolerance cannot both occur simultaneously, and so summing the squares would result in an overly pessimistic prediction. The final predicted, as-built performance is then computed.
For this system, the RSS calculation predicts a system performance of 0.079 waves compared to our specification of 0.05.
The Monte-Carlo analysis is in broad agreement:
although with only 20 samples, this is a crude assessment. The estimated yield of lenses below 0.05 RMS wavefront error is less than 50%:
Clearly some tolerances need to be tightened if the yield is to be improved. We can do this by hand, and re-run the sensitivity analysis if desired, or we can ask ZEMAX to automatically tighten the tolerances for us, in a process called Inverse Sensitivity Tolerancing.