Tolerancing is a vital stage that comes after the design phase, critical enough to warrant a re-design. It is a statistical evaluation balancing quality, cost and end-user satisfaction. The purpose of tolerancing is to determine the maximum manufacturing errors, for both optical and optomechanical components, that still produce a system with acceptable performance. Here I discuss two tolerancing techniques, Inverse Limit and Sensitivity.
As an example, I will use a telescopic system of four lenses, first and fourth being identical, as well as second and third. The below Ray Fan demonstrates its design specifications at axis, at 0.7x aperture radius (2.1 ° HFOV) and at edge (3 ° HFOV). In cases like this, where identical lenses are used again elsewhere in the system, all lenses must have the same tightest tolerances even where not necessary, since in practice it would be impossible to keep identical lenses made with different tolerances separated.
Inverse Limit technique calculates the error limits in such a way that all manufacturing instances would produce design specifications to all manufactured units. Inverse Limit also would produce a plead from the manufacturing engineer to loosen the tolerances because it cannot be realized, and a call from Finances saying that the project went over the budget by a factor of gazillion.
From the above Ray Fan one sees that the system at it's worst is still somewhat OK. However, as the manufacturing engineer the latest will point out, one lens radius has a manufacturing error of ±2.5µm. So yeah, that's not doable.
The tight tolerances do not necessarily mean the design is a failure, as there are always other considerations to be made, and those are easier to implement with Sensitivity analysis.
Sensitivity analysis lets the designer to control all the error limits. This is not as daunting as it sounds, as manufacturing industry has their parameter guidelines which are easily enough inserted as starting values. When error limits are set to 'Precision' category (catalogued in SPIE Field Guide to Optomechanical Design and Analysis, ISBN: 9780819491619), the Sensitivity analysis will predict 50% manufacturing success, where success is defined (arbitrarily for the purposes of this article) as diffraction-limited performance up until 0.7x radius.
The first Sensitivity analysis run is not the end of the line, if the performance is still not acceptable. The analysis will also describe the worst offenders, or the limits which have the most weight in the outcome. These (and only these) limits may be moved up to industry category 'High Precision' and the analysis run again. By tightening only the selected limits one can up the above defined success to 70%.
Luckily, the new tolerance analysis described the next set of Worst Offenders, which also can be tightened. The third tightening Sensitivity round resulted in 88% success (which was diffraction-limited center up to 0.7 radius), which is a very good result. The Sensitivity analysis revealed that only three lens radii needs industry standard 'High Precision', and the mechanical machining workshop should have special tools to achieve ±20µm accuracy for the optomechanics. This is still the same design that previously required ±2.5µm error tolerances.
As a further discussion, there are several ways to remove variables from the tolerancing analysis. Most tightest decentering/tilt dimensions may be removed with an adjusting screw mechanism. This would require more from the assembly crew, but it would remove the tightest tolerance requirements (screws having adjusting range as small as 10µm) and also loosen tolerances elsewhere. Component spacing tolerances can be loosened by inserting adjustable lens tube, where a mere 1° twist corresponds to a 20µm shift (with 0.7mm screw pitch). Basically, the tolerance analysis and troubleshooting is the window to the art of mechanical design for the optical designer. Also, in this stage, communication between everyone is literally worth it's weight in gold, since one problem is never equal to another.