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# Class Note for OPTI 696D at UA

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Date Created: 02/06/15

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 Optomechanical design Mechanical fabrication If you can tolerance effectively then you can be a good designer othenNise you are not Practical Optics J i H Burge Practical Optics J i H Burge Process of optical system tolerancing Define quantitative figures of merit for requirements Estimate component tolerances Define assemblyalignment procedure and estimate tolerances Calculate sensitivities estimate performance Adjust tolerances keeping cost and schedule in mind Iterate with system engineer fabricators management Make drawings with tolerances verify them 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 HMS image size Dimensional limits Boresight Practical Optics J l H Burge Parameters t0 tolerance General parts usually machined metal Physical dimensions of optical elements Optical surfaces Material imperfections for optics Optical assembly Practical Optics J l H Burgc Estimate system performance For a merit function that uses RSS to combine independent contributions c1gt c1gt AC1312 AC1322 CDC is from design residual simulation of system with no manufacturing errors ACIDi is effect from a single parameter having an error equal to its tolerance Practical Optics J r H Burge Combining multiple sources of error There are usually many things that can go wrong that will affect system performance To calculate the combined effect If the causes are independent Combine the effects as a rootsumsquare For example 10 urad pointing from element 1 15 urad pointing from element 2 5 urad pointing from element 3 Combined effect 102 152 52 J100 225 25 x 350 187 Practical Optics J l H Burge Some interesting things about RSS combination 1 The RSS is dominated by the biggest contributors 2 The smallest contributors are negligible 3 For Nequal contributions the RSS is equal to W times an individual contribution Examples 1 compute RSS 0f 10 1 2 1 1 3 Compute RSS for N equal contributions of x sqrt100l4ll 103 RSSx2x2x2x2Ntimes not much different from 10 lle2l 2 Compute RSS of 10 ll 10 sqrt100121100 N 39x 179 Now add another term of 2 rss 2 sqrt100121100 4 2180 Not much different from 17 9 Practical Optics 7 J r H Burge Calculate sensitivities Define merit function CI Make list of parameters to tolerance x1 x2 x3 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 find sensitivity by perturbation acp ltIxi Axi2 413 8x Ax l l 0 is for unperturbed system assume uncorrelated with perturbation Ax is perturbation by the expected tolerance Practical Optics J r H Burge Using compensators For most optical systems a final focus adjustment will be made after the system is assembled The tolerance analysis must take this into account When calculating the effect of each perturbation you simulate this adjustment simulate sensing the error adjust the appropriate parameter This can be used for other degrees of freedom Always make the simulation follow the complete procedure Practical Optics J l H Burge Combining different effects Calculate system merit function from sensitivities using RSS acp 2 acp 2 CI 133 o391 o392 8x1 8x2 a is now the tolerance for X which could be adjusted Put the sensitivities into a spreadsheet to allow easy calculation of the system errors With all effects Practical Optics 1 0 If H Burge Practical Optics J i H Burge Spreadsheet for combining tolerances You can change the tolerance value i Sensitivities do not change Parameter Tolerance Sensitivity Effect on merit function XI 02 92 2 0132 8x1 8x1 X2 0392 81 81 02 8x2 axz X3 0393 82 Z 0 3 8x3 3x3 i Root Sum Square sqrtsumsqD1D23 Automatically recalculate effect from each term and RSS 1 Example From perturbation analysis j value tolerance RMS spot rad perturbation RMS spotrad Lens 1 Radius 1 mm 622 02 0000730 01 0000365 Surface 1 powirreg over TP 5 25 0001089 5 25 0001089 thickness mm 45 01 0000600 005 0000300 Radius 2 mm 813 03 0000743 01 0000248 Surface 2 wavescm 0025 0000757 0025 0000757 wedgeum 50 0000670 25 0000335 tilt um 50 0000245 50 0000245 decenter mm 01 0000300 01 0000300 r Tolerance 6i Effect of Perturb ltIgtx Ax2 ltIgt3 Effect of tolerance 0 Ach choc Ax2 dgt3 A l Perturbation Axi i many more terms R33 at the end 12 Practical Optics J H Burge Practical Optics J l H Burge Assigning initial tolerances Start with rational easy to achieve tolerances Only tighten these as your analysis requires Rules of thumb for element tolerances Rules of thumb for assembly tolerances Best know what the fabrication and alignment processes you plan to use will give 13 Practical Optics J i H Burge Develop complete set of tolerances Start with tolerances that make sense Use experience Rules of thumb Check overall magnitudes of the terms Terms with small effects loosen tolerances Terms with big effects may need to tighten tolerances Revise fabrication alignment plans as needed the goal is 1 Meet performance specifications 2 Minimize cost or pain 14 Practical Optics J H Burge Using optical design codes Much of the above work can be done entirely within the optical design code You can specify tolerances and the software will calculate sensitivities and derive an RSS Be careful with this It is easy to get this wrong The optical design codes also include a useful Monte Carlo type tolerance analysis This creates numerous simulations of your system with all of the degrees of freedom perturbed by random amounts 15 Dimensional tolerances for lenses Diameter tolerance of 25 i 01 mm means that the lens must have diameter between 249 and 251 mm Lens thickness is almost always defined as the center thickness Typical tolerances for small 1 O 50 mm optics Diameter OO1 mm Thickness i 02 mm Clear aperture is defined as the area of the surface that must meet the specifications For small optics this is usually 90 of the diameter 16 Practical Optics J l H Burge Tolerance for radius of curvature Surface can be made spherical with the wrong radius Tolerance this several ways 1 Tolerance on R in mm or 2 Tolerance on focal length combines surfaces and refractive index 3 Tolerance on surface sag in pm or rings W sa 2 g 2R D2 Asa AR g 8R2 1 ring M2 sag difference between part and test glass Practical Optics 1 7 If H Burge Practical Optics J H Burge Tolerancing surface figure Specifications are based on measurement Inspection with test plate Typical spec 05 fringe Measurement with phase shift interferometer Typical spec 005 7 rms For most diffraction limited systems rms surface gives good figure of merit Special systems require PSD spec Geometric systems really need a slope spec but this is uncommon Typically you assume the surface irregularities follow low order forms and simulate them using Zernike polynomials 18 Understanding wedge in a lens wedge in a lens refers to an asymmetry between The mechanical axis defined by the outer edge And the optical axis defined by the optical surfaces Lens wedge deviates the light which can cause aberrations in the system Practical Optics J l H Burge Optical vs Mechanical Axis Opucoi ClxiS deimec uz c ui cs 7 7 gto Eerier m 2mm m Swims 39 Decenter is the difference between the mechanical and optical axes may not be well defined my Way Pmucai Op cs 20 i H Burg Effect of lens wedge rm D k rnaanln D x ETD D 5 xn 1 mamal Optics J H Burge Parks Practical Optics J H Burge Tilt and decenter of lens elements Optical Axis 8 Axis of Edge Cylinder m m FIG 633 Centered element Axis of Edge Cylinder l f m m 4 2 l 4M1 4 FIG 63b Displaced decentered element XAxis ol Edge Cylinder Optical Axis Centre Sumt 2 Centre Surl 1 FIG 63c Tilted element Axis cl Edge Cylinder Optical Axis Centre Sun 2 Centre Surl 1 FIG 63d Element with tilted surface 22 Lens wedge specified as centration An equivalent specification of centration is sometimes used This is defined as the difference between the mechanical and optical axes lt f gt Optical axis I Mechanical decenter S devzatzon 6 S 5 7 5 s Wedge on n 1 f n 1 Practical Optics I Hi Burge Mechanical tolerancing This is a huge important subject for optomechanical engineers Basic types of tolerances for optical systems General position tolerances lens spacing and alignment Surface texture comes from fabrication process Level of constraint overconstrain for stiffness clearance for motion interference or clearance for optic mounts Practical Optics J l H Burge Dimensional tolerances for machined parts Depends on fabrication methods and equipment so discuss these with your fabricator Rules of thumb for machined parts Practical Optics J H Burge i 1 mm for coarse dimensions that are not important i 025 mm for typical machining without difficulty i 0025 mm precision machining readily accessible lt i 0002 mm highprecision requires special tooling 25 Fabrication of mechanical components Most of the small lt1 m parts for optics are made by cutting from oversized stock on a few common machines These can be driven by a skilled operator or by numerical control Milling machine aka mill or Bridgeport Lathe o Drill press Other processes are used as needed Near net shape forming Rolling casting extruding stamping Surfacing bead blasting grinding lapping Welding brazing EDM Electrical discharge machining Precision cutting Laser abrasive water jet Different materials have very different limitations Get to know the guys in the shop Practical Optics J r H Burge Tolerancing optical assemblies Element spacing Tilt of elements Mounting decenter Mounting distortion Include stability and thermal errors Get nominal tolerances from assembly and alignment procedures Work with the mechanical designer Practical Optics J l H Burge 27 Define assembly procedure Determine adjustments that will be made in assembly that can compensate other errors Each of these needs a measurement to know how to set it Consider several things Range of adjustment Resolution required for motion and for measurement Required accuracy of motion and measurement Frequency of adjustment Other dimensions will be set once like lenses in cells Practical Optics J r H Burge Rules of thumb for optical assemblies Parameter Base Precision High precision Spacing 200 um 25 pm 6 pm manual machined bores 0r spacers Spacing 50 um 12 um 25 pm NC machined bores 0r spacers Concentricity 200 pm 100 um 25 pm if part must be removed from chuck between cuts Concentricity 200 um 25 pm 5 u cuts made Without de chucking part Base Typical no cost impact for reducing tolerances beyond this Precision Requires special attention but easily achievable in most shops may cost 25 more High precision Requires special equipment or personnel may cost 100 more Practical Optics J i H Burge 29 Practical Optics J l H Burge Example 2 element null corrector Table 3 Accuracy for null lens fabrication S Quantity Tolerance Lens spacing 50 um Lens thickness 25 or 50 um Radius of curvature Flatness Surface figures Index of refraction Index Inhomogeneity Wedge in lenses Decenter in mounting Tilt in mounting Primary radius of curvature l fringe power or 25 um Whichever is smaller N4 0008 rms interferometer 0015 rms lenses i 00002 Grade A BK7 025 E 6 rms H4 grade 50 um 50 um 50 um 2mm 30 Practical Optics J H Burge Table 4 Tolerances for null lens Spherical Figure Design aberration units value uncertainty nm rms nm rms Interferometer Irregularity rms waves 0008 506 Decenter um 0050 000 003 Airspace mm 103972 005 136 000 Relay Lens Curvature 1 mm 000E00 2E06 022 002 Thickness mm 10386 0025 047 002 Radius 2 mm 41595 0025 026 003 rreguarity1 rms waves 0015 489 Irregularity 2 rms waves 0015 489 Index 151509 2E04 117 002 Inhomogeneity rms 25E7 260 Wedge um 50 000 007 Decenter um 50 000 007 Tilt um 50 000 009 Airspace mm 150418 0050 100 002 Field Lens Radius 1 mm 129681 0050 088 004 Thickness mm 2924 0050 001 002 Curvature 2 mm 000E00 14E06 020 003 rreguarity1 rms waves 0015 489 Irregularity 2 rms waves 0015 489 Index 151509 2E04 089 003 Inhomogeneity rms 25E7 073 Wedge um 50 000 010 Decenter um 50 000 006 Tilt um 50 000 009 Residual Wavefront waves 0000182 0 006 Primary Radius mm 7000 2 052 002 RSS 3 1134 31 Error Tree AMSD 223 nm rms Membrane Operational effects Control system 20394 m rms 70 nm rms 58 nm rms Membrane Optical Coating ROC 3 mm Parasitic forces Actuator Wavefront fabrication Testing Corrections from interface resolution sensor 18 nm rms 5 nm rms 82 nm rms 18 nm rms 64 nm rms 5 nm rms 3 nm rms 7 nm rms support 6 nm rms polishing residual 158 nm rms annealing strains Practical Optics J1 Ht Burge References Earle J H Chap 21 Tolerancing in Engineering Design Graphics AddisonWesley 1983 Foster L W Geometrics Ill The Application of Geometric Tolerancing Techniques AddisonWesley 1994 Parks R E Optical component specifications Proc SPIE 237 455 463 1980 Plummer J L Tolerancing for economics in mass production optics Proc SPIE 181 90111 1979 Thorburn E K Concepts and misconceptions in the design and fabrication of optical assemblies Proc SPIE 250 2 7 1980 Willey and Parks Optical fundamentals in Handbook of Optical Engineering A Ahmad ed CRC Press Boca Raton 1997 Willey R R The impact of tight tolerances and other factors on the cost of optical components Proc SPIE 518 106111 1984 Yoder P OptoMechanical Systems Design Marcel Dekker 1986 33 Practical Optics J H Burge

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