Engineering
Tolerancing & yield
Every real lens is ground slightly wrong. Tolerancing asks the only question that matters commercially: if you build a hundred of these, how many meet spec?
Setting tolerances
Each part gets five manufacturing tolerances. Set tolerances on every part fills in a sensible starting set:
| Tolerance | Represents |
|---|---|
| radius % | How far a ground radius may stray from nominal |
| thickness mm | Centre thickness error |
| decenter mm | The element sitting off-axis in its mount |
| tilt deg | The element tipped in its mount |
| axial mm | Spacing error along the beam |
Running the analysis
| Setting | Means |
|---|---|
| criterion | Which operand decides pass or fail — usually RMS spot on the screen |
| refocus | Judge every perturbed build at its own best focus, as if the screen were refocused during assembly. This is the standard compensator and it matters enormously |
| trials | How many random builds to simulate (300 by default) |
| Uniform / Gaussian | Errors spread evenly within ±tol, or normally with sigma = tol/2 clipped at ±tol |
| spec | The value a build must beat to count as good |
Reading the result
- Nominal — the criterion for the perfect design.
- RSS estimate — the quick root-sum-square prediction from the sensitivity table.
- Monte-Carlo mean and sigma — what actually happened across the trials.
- Percentiles — "50% of builds ≤ x, 90% ≤ y, 98% ≤ z". This is the honest picture of your production run.
- Yield — the share of builds that beat your spec.
- Unbuildable builds — perturbations that made parts collide, and builds where the beam was lost entirely. Both count as failures, because both are.
Worst offenders
The sensitivity table lists every tolerance item with how much the criterion changes at +tol and −tol. Sort by that and you know exactly which surface to specify more tightly — and, just as usefully, which ones you can loosen to save money.