# 8 Tolerancing - Tolerancing Optical Systems Why are...

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Introductory Optomechanics J. H. Burge 1 Tolerancing Optical Systems • Why are tolerances important? – Somebody is going to make it (hopefully) – It must meet some performance requirement – Cost (and schedule) are always important • Why is it difficult? – Involves complex relationships across disciplines • System engineering • Optical design and analysis • Optical fabrication • Opto-mechanical design • Mechanical fabrication • If you can tolerance effectively, then you can be a good designer, otherwise you are not.

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Introductory Optomechanics J. H. Burge 2 Process of optical system tolerancing 1. Define quantitative figures of merit for requirements 2. Estimate component tolerances 3. Define assembly/alignment procedure and estimate tolerances 4. Calculate sensitivities 5. Estimate performance 6. Adjust tolerances, balance cost and schedule with performance 7. Iterate with system engineer, fabricators, management
Introductory Optomechanics J. H. Burge 3 System Figure of Merit • Keep this as simple as possible • Must propagate all performance specs through assembly • Typical requirements RMSWE (root mean square wavefront error) MTF at particular spatial frequencies Distortion Fractional encircled energy Beam divergence Geometric RMS image size Dimensional limits Boresight

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Introductory Optomechanics J. H. Burge 4 Parameters to tolerance Allowable errors are called tolerances. What needs to be toleranced? • General parts (usually machined metal) • Physical dimensions of optical elements • Optical surfaces • Material imperfections for optics • Optical assembly
Introductory Optomechanics J. H. Burge 5 Estimate system performance For a merit function that uses RSS to combine independent contributions: Φ 0 is from design residual – simulation of system with no manufacturing errors ΔΦ i is effect from a single parameter having an error equal to its tolerance () ( ) ... 2 2 2 1 2 0 + ΔΦ + ΔΦ + Φ = Φ

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Introductory Optomechanics J. H. Burge 6 Calculate sensitivities Define merit function Φ Make list of parameters to tolerance, x 1 , x 2 , x 3 , … all of the things that will go wrong. Use simulation to calculate the effect of each of these on the system performance. –For each x i , use perturbation to find sensitivity So the contribution from a tolerance Δ x i on parameter x i is ii x x ∂Φ ΔΦ ∂Δ i x x ∂Φ ΔΦ = Δ = (change in merit function) / (change in parameter) = (sensitivity) * (tolerance)
Introductory Optomechanics J. H. Burge 7 If the nominal merit function Φ 0 is small (residual aberrations) calculate sensitivity directly Δ x i is perturbation (by the expected tolerance) Φ ( x i + Δ x i ) is the system merit function of the perturbed system To include the nominal merit function Φ 0 This can be tricky Evaluate Φ 0 and Φ ( x i + Δ x i ) – If Φ 0 << Φ ( x i + Δ x i ) then ΔΦ = Φ ( x i + Δ x i ) as above – If Φ 0 is correlated with Φ ( x i + Δ x i ) then ΔΦ = Φ ( x i + Δ x i ) - Φ 0 –E lse Φ 0 and ΔΦ combine in RSS, so Sensitivity calculation () 2

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8 Tolerancing - Tolerancing Optical Systems Why are...

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