Sensitivity Analysis
For the sensitivity analysis, each tolerance is evaluated independently using the following algorithm:
The temporary lens is restored.
The parameter whose tolerance is being evaluated is adjusted to the extreme minimum value. For example, if the tolerance being evaluated is TRAD, and the nominal value is 100 mm, with a minimum tolerance of -0.1 mm, the radius is set to 99.9. If the tolerance is an element tilt or decenter tolerance, dummy coordinate breaks are inserted as required to model the perturbation. For surface tilts and decenters, such as TSDX, TSDY, TSTX, TSTY, TIRX, or TIRY, the Irregular surface type is used if the surface is initially of type Standard.
The compensators are adjusted.
The resulting criterion are printed on the report.
The procedure is repeated for the maximum tolerance.
This basic algorithm is repeated for each tolerance operand.
The value of the sensitivity analysis is that the tolerances which are too loose will, in general, have greater contributions to the increase in the criterion than other tolerances. This technique allows the designer to identify surfaces which are highly sensitive to certain errors, such as tilts or decenters. Different surfaces also will, in general, have very different sensitivities to the various errors. The sensitivity analysis aids in identification of which tolerances need to be tightened, and which might be loosened. It is also valuable for finding the optimum (and minimum) number of compensators, and the required range of adjustment. There are in fact many more applications for this feature; for example, designing lens mounts to maximize compensation leverage.
The sensitivity analysis aids in identification of which tolerances need to be tightened, and which might be loosened.
The amount of output can be overwhelming, especially for lenses with many elements and a corresponding large number of tolerances. Often, the sensitivity to the tolerances varies widely over all the possible tolerances. The "Show worst" control is extremely useful for summarizing the worst offenders, because it sorts the tolerances by contribution to the criterion and then prints them in descending order. The "Hide all but worst" control turns off the bulk of the printing if only the worst offenders are of interest.
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