“Budgeting” of Optical Systems A Tutorial on Optomechanical Tolerancing and a Synopsis of the Economics Involved Ezra Milby OPTI 521 – Optomechanical Engineering Fall 2009 – Prof. J.H. Burge

Overview Defining a System Performance Characteristic Defining the Variable Parameters of the System Creating a Tolerance Budget Analyze Production Costs Iterate the Design Process for Optimization 22 September 2018 E. Milby - OPTI521 - Intro to Optomech Eng

Performance Characteristics Image Quality Physical Parameter MTF Resolution Energy Distribution Spot Size Wavefront Error Beam Divergence Geometrical Aberrations PSF Bore sight Shift Effective Focal Length Back Focal Length Distortion Image Plane Displacement Test 22 September 2018 E. Milby - OPTI521 - Intro to Optomech Eng

MTF WRT Defocus Error 22 September 2018 Source: Smith (1985) 22 September 2018 E. Milby - OPTI521 - Intro to Optomech Eng 4

Primary Parameters Sag (A) Spacer Thickness (B) Contact Diameter (C) A variable parameter that is independent of adjustments in other parameters. Sag (A) Spacer Thickness (B) Contact Diameter (C) Surface Radii (R) Airspace Source: Magarill (1999) 22 September 2018 E. Milby - OPTI521 - Intro to Optomech Eng

Primary Parameters Center Thickness Surface Sag Index of Refraction Contact Diameter Axial Seat Position Clearance Wedge Seat Tilt Contact Diameter Eccentricity Surface to Surface Displacement Base Diameter Eccentricity Second Barrel Clearance 22 September 2018 E. Milby - OPTI521 - Intro to Optomech Eng Source: Magarill (1999)

Common Variable Parameters Optics Assembly Index of Refraction Radius Irregularity Thickness Sag Diameter Wedge Surface Roughness Airspace Decenter – Axially Decenter – Laterally Tilt Lens Roll 22 September 2018 E. Milby - OPTI521 - Intro to Optomech Eng

Assign Tolerances Base Cost

Tolerance Budget Assign a Tolerance Determine Sensitivity Error Type Units Tolerance Tolerance Value Sensitivity WF Error Φ (λ) L1 Tilt deg +/- 0.10 0.1 0.132 0.011 L1 Decenter mm +/- 0.09 0.09 0.187 0.019 Airspace 1.1 0.016 0.003 L2 Tilt 0.192 0.018 L2 Decenter 0.186 RSS 0.036 Assign a Tolerance Determine Sensitivity Determine Performance Degrade Adjust as Needed

Cost Assign a cost sensitivity in tolerance budget C = P·T + B Adjust tolerances to minimize cost in the same way Source: Willey (1984) 22 September 2018 E. Milby - OPTI521 - Intro to Optomech Eng

Glass Costs Source: Willey (1992) 22 September 2018 E. Milby - OPTI521 - Intro to Optomech Eng

The Cost of Computing Engineering Salary Cost Savings Mass Production Source: Willey (1983) Mass Production High Cost Materials 22 September 2018 E. Milby - OPTI521 - Intro to Optomech Eng

The Iterative Tolerancing Process 22 September 2018 Source: Ginsberg (1981) E. Milby - OPTI521 - Intro to Optomech Eng

Sources Burge, J. (2009). System LOS, RSS combination - Class Notes OPTI521. Ginsberg, R. H. (March/April 1981). Outline of tolerancing (from performance specification to toleranced drawings). Optical Enginerering , 175-180. Lagger, J. P. (1982). Cost-Effective Design --- A Prudent Approach to the Design of Optics. Photnics Spectra , 65-68. Magarill, S. (1999). Optomenchanical sensitvity and tolerancing. SPIE Conference on Optomechanical Design and Engineering, (pp. 220-228). Denver, Colorado. Smith, W. J. (1985). Fundamentals of Establishing an Optical Tolerance Budget. Proc. of SPIE Vol. 0531, Geometriucal Optics, ed. Fischer, Price, Smith . Willey, R. (1983). Economics in optical design, analysis, and production. Optical System Design, Analysis, and Production, SPIE Vol. 399 , 106-111. Willey, R. (1992). Maximizing production yeild and performance in optical instruments through effective design and tolerancing. Critical Review Vol. CR43, Optomechanical Design . Willey, R. (1983). Minimized cost through optimization tolerance distibution in optical assemblies. Proc. of SPIE Vol. 0389, Optical Systems Engineering III , 12-17. Willey, R. R. (1984). The Impact of Tight Tolerance and Other Factors on the Cost of Optical Components. Proc. of SPIE Vol. 0518, Optical Systems Engineering IV, ed. P.R> Yoder Jr. , (pp. 106-111). 22 September 2018 E. Milby - OPTI521 - Intro to Optomech Eng