Optical Design with Zemax for PhD

Transcription

1 Optical Design with Zemax for PhD Lecture 3: Tolerancing I Herbert Gross Winter term 25 / Summer term 26

2 2 Preliminary Schedule No Date Subject Detailed content.. Introduction Zemax interface, menus, system description, editors,, coordinate systems, aperture, field, wavelength, layouts, raytrace, stop and pupil, solves, ray fans, paraxial optics Basic Zemax handling surface types, quick focus, catalogs, vignetting, footprints, system insertion, scaling, component reversal 3 aspheres, gradient media, gratings and diffractive surfaces, special types of 9.2. Properties of optical systems surfaces, telecentricity, ray aiming, afocal systems Aberrations I Aberrations II PSF, MTF, ESF representations, spot, Seidel, transverse aberration curves, Zernike wave aberrations Optimization I algorithms, merit function, variables, pick up s Optimization II methodology, correction process, special requirements, examples Advanced handling Correction I simple and medium examples.2. Correction II advanced examples slider, universal plot, I/O of data, material index fit, multi configuration, macro language 2.3. Illumination simple illumination calculations, non-sequential option Physical optical modelling Gaussian beams, POP propagation Tolerancing I Sensitivities, Tolerancing Tolerancing II Adjustment, thermal loading Coatings Scattering

3 3 Content. Introduction 2. Tolerances general aspects 3. Statistics and compensators 4. Form tolerances 5. Material tolerances 6. Centering tolerances 7. Mechanical design and mountings 8. Tolerancing in Zemax

4 Introduction to Tolerancing Specifications are usually defined for the as-built system Optical designer has to develop an error budget that cover all influences on performance degradation as - design imperfections - manufacturing imperfections - integration and adjustment - environmental influences No optical system can be manufactured perfectly (as designed) - Surface quality, scratches, digs, micro roughness - Surface figure (radius, asphericity, slope error, astigamtic contributions, waviness) - Thickness (glass thickness and air distances) - Refractive index (n-value, n-homogeneity, birefringence) - Abbe number - Homogeneity of material (bubbles and inclusions) - Centering (orientation of components, wedge of lenses, angles of prisms, position of components) - Size of components (diameter of lenses, length of prism sides) - Special: gradient media deviations, diffractive elements, segmented surfaces,... Tolerancing and development of alignment concepts are essential parts of the optical design process Ref: K. Uhlendorf 4

5 Sensitivity of a System Sensitivity/relaxation: Average of weighted surface contributions of all aberrations Sp h Sph -3 Correctability: Average of all total aberration values Total refractive power Kom a Coma k F F F j j j2 Important weighting factor: ratio of marginal ray heights Ast Ast j h j h CH L CHL Inz- Wi 3 2 incidence angle

6 Sensitivity of a System Quantitative measure for relaxation with normalization A k j j A j j F j F h j h F j F Non-relaxed surfaces:. Large incidence angles 2. Large ray bending 3. Large surface contributions of aberrations 4. Significant occurence of higher aberration orders 5. Large sensitivity for centering Internal relaxation can not be easily recognized in the total performance Large sensitivities can be avoided by incorporating surface contribution of aberrations into merit function during optimization

7 Sum Sensitivity of a System Double Gauss.4/ Representation of wave Seidel coefficients [l] , ,8 5,6-5,4 -, surfaces Ref: H.Zügge Verz Sph Koma Ast Petz Verz

8 Tolerances: Standards Standard ISO- ISO -2 ISO -3 ISO -4 ISO -5 ISO -6 ISO -7 ISO -8 ISO -9 Material imperfections stress birefringence Material imperfections bubbles and inclusions Material imperfections inhomogeneity and striae Surface-form tolerances Centering tolerances Surface-imperfection tolerances Surface texture Surface treatment and coating Ref.: M. Peschka

9 Specification of Data Data for mechanical design, development and manufacturing: Dat a sheet with standard data/numbersof system and tolerances Additional support data (optional) :. Prisms, plano comopnents, test procedures 2. Adjustment and system integration 3. Centering for cementing 4. Centering for mechanics 5. Coatings 6. Geometrical dimensions / folding mirrors 7. Test procedures and necessary accuracies 8. Auxiliary optics for testing 9. Combination of tolerances.zoom curves and dependencies.adaptive control data 2.Interface to connected systems

10 Data Sheet

11 Tolerances Surface quality, scratches, digs, micro roughness Surface figure radius, asphericity, slope error, astigamtic contributions, waviness Thickness glass thickness and air distances Refractive index n-value, n-homogeneity, birefringence Abbe number Homogeneity of material bubles and inclusions Centering: orientation of components, wedge of lenses, angles of prisms, position of components Size of components diameter of lenses, length of prism sides Special: gradient media deviations, diffractive elements, segmented surfaces,...

12 Tolerances: Typical Values Diameter Tolerance Unit < mm mm mm Center thickness mm Centering Tilt angle sek Decenter/offset m Roughness nm 5 Spherical/radius spherical rings astigmatism rings.5 Asphericity Global deviation m.2.5 Global asphericity m Local deviation m Slope error rad.5.5.5

13 Tolerance Analysis by Sensitivities Systematic finding of tolerances Optical system design Set of assigned tolerances Redesign of optical system Sensitivity analysis (evaluation of performance measure changes for each tolerance. Optionally with adjustment) Adjustment steps and compensators Estimation of overall performance degradation and tolerance cost Define/change adjustment steps and compensators Change assigned tolerances Performance degradation acceptable? NO YES System too sensitive? NO and / or Cost acceptable? NO YES Ref.: M. Peschka YES Further performance simulations with assigned tolerances

14 Tolerance Analysis Selection of the performance criterion, spot size, rms wavefront, MTF, Strehl,... Choice of the allowed degradation of performance, limiting maximum value of the criterion Definition of compensators for the adjustments image location, intermediate air distances, centering lenses, tilt mirrors,... Calculation of the sensitivities of all tolerances: influence of all tolerances on all performance numbers Starting the tolerance balancing with proper default values, alternatively inverse sensitivity: largest amount of deviation for the accepted degradation Tolerance balancing: calculating all tolerances individually to keep the overall performance with technical realistic accuracies of the parameter Ref: C. Menke

15 Error Budget Sources of errors: - materials - manufacturing - integration/adjustment/mounting - enviromental influences - residual design aberrations Performance evaluation: selection of proper criterion fixation of allowed performance level calculation of sensitivity of individual tolerances and combined effects (groups, dependent errors) balancing of overall tolerance limits for complete system Performance criteria (spot size, RMS, Strehl, MTF, ) Design Manufacturing Integration Environment savety adding Ref: C. Menke

16 Tolerances and Cost Impact Typical behavior of the cost function: additive cost Exponential growth of cost with decreased tolerance width The slope and the reference value depends on type of tolerance and technology of manufacturing Special aspects: - new manufacturing technologies - jumps of cost 3 % relative cost 25 % 2 % C C a N rings 5 % % reference 5 % Log N rings

17 Tolerances and Additional Cost Diameter tolerance in mm % % 3 % 5 % 5 % Thickness tolerance in mm % 5 % 5 % 5 % 3 % Centering tolerance in minutes 6' 3' 2' ' 3" 5" % 3 % 8 % 5 % 4 % 2 % Shape tolerance as ring number in l 7 5 % 5 / 2 5 % 3 / 2 % 2 /.5 4 % 2 / % /.2 3 % ratio diameter vs thickness % 2 % 5 % 2 % 3 % 5 % Scratches and dots 8 / 5 6 / 4 4 / 3 2 / 7 5 ( MIL-Norm ) % % 25 % 75 % 35 % Coating without Layer 3 Layer Multilay. % 5 % 5 % < 5 %

18 Models and Statistics in Tolerancing Evaluation of the complete system: additive effect of all tolerances, taking partial compensations due to sign and statistics into acount Worst case superposition: - adding all absolute amounts of degradations - usually gives to costly and tight tolerances - no compensations considered, to pessimistic f j f j Rms mean superposition: - approach with ideal statistics and quadratic summation - compensations are taken into account approximately - real world statistics is more complicated probability - deterministic effects of adjustments are not considered f 2 j f j Calculation of Monte Carlo statistics with deterministic adjustment steps - best practice approach - statistical distribution can be adapted to experience - problems with small number manufacturing yield 9% nominal value real values

19 Tolerance Distributions Gaussian p Truncated Gaussian ( tt 2 ( t) e 2 2 ) 2 Uniform p( t), t t t 2 Ping-pong p( t) a ( t t ) b ( t t a b ) Ref.: M. Peschka

20 Tolerances and Statistics Statistics of refractive index tolerances: nearly normal distributed probability Tolerances of lens thickness: - biased statistical istribution with mean at.3 d - less pronounced offset for small intervals of tolerance - width of the distribution depends on the hardness of the material n o - n nominal value n o probability probability HK = 55 d =. Knoop hardness tolerance range HK = 45 d =.2 HK = 35 d =. <d>-d o d d o - d.275 d o + d

21 Compensators Compensators: - changeable system parameter to partly compensate the influence of tolerances - compensators are costly due to an adjustment step in the production - usually the tolerances can be enlarged, which lowers the cost of components - clever balance of cost and performance between tolerances and adjustment Adjustment steps should be modelled to lear about their benefit, observation of criterias, moving width,... Special case: image position compensates for tolerances of radii, indices, thickness Centeriung lenses: lateral shift of one lens to get a circular symmetric point spread function on axis Adjustment of air distances between lenses to adjust for spherical aberration, afocal image position,... centering lens

22 Thickness Tolerance Tolerances of thickness or distances in case of glass thickness: effect of tolerance depends on the mounting setup, the difference usually is added or subtracted in the neighboring air distance usually, the overall length of the system remains constant the thickness tolerance is far less sensitive as curvature errors Ref: C. Menke

23 Surface Shape Tolerance Tolerance of the surface shape: specification in fringes interferometric measurement irregularity: deviation from spherical shape typical specification: 5() menas: 5 ring spherical deviation ring asymmetry/astigmatism R R' Ref: C. Menke

24 Tolerances of Aspheres Conventional tolerance:. error of radii, can be compensated by defocussing 2. irregularity, astigmatism 3. higher order spherical errors like 4th order edge errors Slope errors:. relevant error from viewpoint of optical influence 2. reverence basis length necessary for specification to fix spatial frequency 3. diversification by tolerancing different diameter ranges Sag error of the real surface. not propriate tolerance without specification of the basis length (spatial frequency) 2. rms number more significant than pv value Micro roughness:. high frequent errors due to manufacturing, causes wide angle scattering 2. specification as rms tolerance 3. influences contrast

25 Tolerances of Aspheres Typical errors of aspherical surfaces. long range figure errors 2. high frequency micro roughness Application Figure error Rms [nm] Micro roughness Rms [nm] Eye glassesr 2 Illumination systems 3 2 Digital projection 3 Photographic lenses, cameras, comsumer Satellite systems 2.5 DUV Lithography lenses 2.3 EUV Lithography lenses..

26 Tolerancing of Free Form Surfaces Today there is only insufficient experience for the tolerancing of free shaped surfaces Specification and tolerancing are not standardized Possible options are:. rms value 2. global maximum deviation z (peak valley) 3. Slope error, in components, in various area ranges of the surface 4. Sinusoidal perturbations with specified intervals, amplitudes to cover the mid-frequency range 5. Limiting straight line or accepted thresholds in a logarithmic power spetrum representation

27 Spatial Frequency Ranges of Surface Errors Spatial frequency domain discussion of surface errors Power spectral density describes the power in the Fourier components Low frequency range: - figure error - loss in resolution - classical aberrations, description by Zernikes - interferometric measurement - spatial frequency n < 2/D Midfrequency range: - ripple due to manufacturing - spatial frequency n < 2/D...4/D - reason mostly mechanical perturbations in manufacturing log A 2 Four oscillation of the polishing machine limiting line slope m = High frequency range: - micro roughness with high spatial frequencies - causes wide angle scattering and straylight - reasons are problems with polishing long range low frequency figure Zernike loss of resolution mid frequency /D 2/D 4/D micro roughness loss of contrast /l n

28 Diamond Turning of Plastic Surfaces Structured surface with ripple Ref: A. Rohrbach

29 29 Spatial Midfrequency Errors Surface with diamond turning shaping Surface and PSD before and after polishing Ref.: Zhang et. al.

30 Tolerances of Glass Discrete tolerance steps Rectangulare tolerance areas in n-n- plane Grade (tolerance step) n n / n +/.2 +/.2% 2 +/.3 +/.3% 3 +/.5 +/.5% 4 +/. +/.8% Ref.: M. Peschka

31 Index Homogeneity of Glasses Different classes of homogeneity of glasses Class ISO n in the sample H H H H Ref.: M. Peschka

32 Definition of Striae Standard not sufficient Appearance: like wood in transmission shadow image 6 mm 5 mm

33 Measurement with Shadowgraphy Advantages:. Fast, cheap 2. Simple setup 3. Small requirements on sample surface quality shadow image Disadvantage:. no quantitatve calibration until now observation camera screen quasi point-like Hg light source sample rotatable desk desk

34 Centering Wedge Error Wedge error: - tilt of a single surface relative to the optical or mechanical axis. - Specification as tilt error of total indicator runout (TIR) in [mm] - angle value in rad: TIR / D (D diameter) TIR = A - B The optical axis is the straight line through the two centers of curvature of the two spherical surfaces A Mechanical axis: defined by the cylindrical boundary of the lens C Usually the optical and the mechanical axes do no coincide C 2 A wedge error must be specified only for one of the surfaces B Ref: C. Menke

35 Centering of Spherical Surfaces Equivalence of decenter (offset) and tilt angle v sin r Small change in sag (vertex position) in 2nd order surface decentered z r cos C surface axis r v decenter/offset S vertex tilt angle optical axis z sag change

36 Rotation of a Spherical Surface Shift of center of rotation to D: relation sin r v z Conversion of units form radiant in minutes k optical axis v S r surface decentered z C center of rotation D surface axis

37 Rotation of a Group of Surfaces Rigid coupled sequence of surfaces Tilt with arbitrary location of center of rotation v e j d k k j sin Model for tilt error in mounted lens groups Effect on performance shows compensations Gr surface Nr j S j C Gr v j d j e

38 optisches Element bzw. der darauf folgende Luftraum Centering Tolerances OLaF-Diagramm "T-Schalenkippung" Centering tolerances in photographic lenses: L F S Rollen my Quer my Kipp my F.8. System layout L2 S F 2 L3 2.8 S F.7 L4. S F - KG 2. S..2. F L7.5 S Tilt of image plane due to - tilt (yellow) - roll (green dark) - decenter (green bright) of lenses KG2 L L F S6..8 F Asphäre F S T-Schale in my From: D. Gängler

39 Centering of Aspheres Asphere : The location of the center of curvature moves with the radial surface position Conventional reflex light measurement in autocollimation is not possible aspherical surface moving center of curvature C edge C zone C inner optical axis

40 Centering Errors of Lenses Lens. Radial offset 2. Shearing 3. Wedge Lens group. Group tilt 2. Group offset Ref.: M. Peschka

41 Wedge Angle of a Thin Lens Thin lens with wedeg error v ( n ) f optical axis C C 2 v 2 v shape axis (edge cylinder) v 2 r r 2 v 2

42 Tolerances: Centering Methods Axially fixed Chuck Pressing Chuck Mechanical Ray in transmission Chuck Direction of lens motion Red surface centered Deflected laser beam Incoming laser beam Green surface after lens rotation by Rays in reflection Chuck Red surface centered Green surface after lens rotation by Reflected laser beam Incoming laser beam Incoming laser beam Reflected laser beam Ref.: M. Peschka

43 Centering of a Lens with Interferogram Measurement of the centering of lens by inspection of the interferogram of front and rear surface r r 2 source point Z 2 Z D

44 Centering in Bonding Process Centering carrier lens Light source Cross-hair Rotating chuck Surface being centered Collimator Eyepiece Eye / detector Adjustable test optics Beam splitter Reading scale Image of Cross-hair Adjusting second lens Centering motion of lens Light source Rotating chuck Centering motion of lens Surface being centered Cross-hair Collimator Eyepiece Adjustable test optics Beam splitter Reading scale Image of Cross-hair Eye / detector Ref.: M. Peschka

45 Tolerances and Mechanical Interface Coupling optics mechanics Interface glass metal clearance r Mechanical design of mountings and housing Typical options:. Filling cylinder with fixating screw 2. Cementing, later centering 3. Lace / bordering Critical: - Centering tolerances - reference surfaces - analysis of complete geometry (kinematic) D s fixating screw tilt angle axis of mounting axis of lens mounting

46 Mechanicl Mounting Geometry Filling of lenses into mounting cylinder with spacers Accumulation of centering errors by transportation of reference Definition of lens positions by:. mechanical play inside mounting 2. fixating ring screw 3. planarity of spacers fixating screw mounting cylinder spacer

47 Tolerances of Mounting Assembly Mechanical Play Wedge errors Ref.: M. Peschka

48 High Precision Mountings Adjustment turning Adjustment glueing Ref.: M. Peschka

49 On-Axis Astigmatism On-axis astigmatism due to cylindrical irregularity Vectorial addition of astigmatism in systems Ref.: M. Peschka

50 Correcting Astigmatism by Clocking Rotating of lenses around the optical axis Vectorial addition of individual astigmatism components Ref.: M. Peschka

51 Adjustment of Objective Lenses Adjustment of air gaps to optimize spherical aberration Reduced optimization setup t 2 t 4 t 6 t 8 c j c jo k,4 c j c t k j, j 2,4,6,8 Compensates residual aberrations due to tolerances (radii, thicknesses, refractive indices) d 2 d 4 d 6 d 8 c 2 c 4 c 6 c 8 W rms nominal d 2 varied d 4 varied d 6 varied d 8 varied optimized

52 Adjustment of Objective Lenses Significant improvement for one wavelength on axis Possible decreased performance in the field W rms in l.3 48 nm 546 nm 644 nm solid lines : nominal dashed lines : adjusted.5 improvement.5 y/y max

53 Mechanical Design of Mountings Photographic lens: Digiprime 7 Ref.: M. Peschka

54 Drawing of Microscopic Lens with Housing

55 Mechanical Design of Photographic Lens

56 Tolerancing in Zemax Tolerance editor

57 Tolerancing in Zemax Specification of tolerances: Operators : TRAD Radius TFRN Number of rings TTHI Thickness TEDX Element decenter x TETX Element tilt x TSDX Flächen decenter x TIRX Flächen tilt x TIRR Surface irregularity TIND Refractive index TABB Abbe number...

58 Tolerancing in Zemax Specifying options: - statistics - model mode - criteria - compensators -...

59 Tolerancing in Zemax Results Sensitivity and total performance

60 Tolerancing in Zemax Graphical overlay of tolerance influence