Optical Design with Zemax for PhD - Advanced Seminar 8 : Tolerancing II 2015-01-28 Herbert Gross Winter term 2014 www.iap.uni-jena.de 2 Preliminary Schedule No Date Subject Detailed content 1 12.11. Repetition Correction, handling, multi-configuration 2 19.11. Illumination I Simple illumination problems 3 26.11. Illumination II Non-sequential raytrace 4 03.12. Physical modeling I Gaussian beams, physical propagation 5 10.12. Physical modeling II Polarization 6 07.01. Physical modeling III Coatings 7 14.01. Physical modeling IV Scattering 8 21.01. Tolerancing I Sensitivity, practical procedure 9 28.01. Tolerancing II Adjustment, thermal loading, ghosts Adaptive optics, stock lens matching, index fit, Macro language, 10 04.02. Additional topics coupling Zemax-Matlab 3 Content 1. Adjustment 2. Ghosts 3. Thermal loading 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 Adjustment of Objective Lenses t . Adjustment of air gaps to t2 t4 t6 8 optimize spherical aberration . Reduced optimization setup c c c c j , j 2,4,6,8 j jo j k1,4 tk . Compensates residual aberrations due to tolerances (radii, thicknesses, refractive indices) d2 d4 d6 d8 c20 c40 c60 c80 Wrms nominal 0.77300 0.17000 3.2200 2.0500 0.00527 -0.0718 0.00232 0.01290 0.0324 d2 varied 0.77320 0.17000 3.2200 2.0500 0.04144 -0.07586 0.00277 0.12854 d4 varied 0.77300 0.17050 3.2200 2.0500 0.03003 -0.07461 0.00264 0.01286 d6 varied 0.77300 0.17000 3.2250 2.0500 0.00728 -0.07367 0.00275 0.01284 d8 varied 0.77300 0.17000 3.2200 2.0550 0.005551 -0.0717 0.00235 0.01290 optimized 0.77297 0.16942 3.12670 3.2110 0.000414 0.00046 0.00030 0.01390 0.00468 Adjustment of Objective Lenses . Significant improvement for one wavelength on axis . Possible decreased performance in the field Wrms in 0.3 480 nm solid lines : nominal 546 nm dashed lines : adjusted 644 nm 0.15 improve- ment y/y 0 max 0 0.5 1 7 Adjustment and Compensation . Example Microscopic lens . Adjusting: 1. Axial shifting lens : focus 2. Clocking: astigmatism 3. Lateral shifting lens: coma . Ideal : Strehl DS = 99.62 % With tolerances : DS = 0.1 % After adjusting : DS = 99.3 % Ref.: M. Peschka 8 Adjustment and Compensation . Sucessive steps of improvements Ref.: M. Peschka 9 Glare and Polarization . Filtering of polarized glare light Straylight and Ghost Images What is Stray light? . Diffraction at aperture diffraction-limited PSF, blurred image . Ghosts specular reflections from imperfectly coated refractive surfaces . Unwanted diffraction orders imperfect diffracting surfaces generate spurious images (e.g. Unintentional gratings from diamond turning process) Ref: K. Uhlendorf 11 What is Stray light? . Scatter from structures . Scatter from optical surfaces contamination and sub-wavelength surface defects . Thermal emission from optical and mechanical surfaces Ref: K. Uhlendorf 12 Ghost Images Ghost image in photographic lenses: Reflex film / surface Ref: K. Uhlendorf, D. Gängler Straylight and Ghost Images 3 4 . Calculation of reflected light 5 6 sequence 6 - 4 sequence 5 - 3 . Colour effects due to coatings 15 - 11 14 - 11 sequence 13 - 4 sequence 13 - 5 sequence 20 - 18 20 - 18 6 - 4 5 - 3 9 - 3 sequence 7 - 2 sequence 6 - 4 7 - 2 Heating of Optical Systems . Rise of temperature: 1. Scaling of components in size 2. Stress and strain (birefringence), especially at the glass-metal interface 3. Change of refractive indices with temperature (mostly dominant effect) . Reasons for changes in temperature: - environmental changes - absorption of light in components Problem: depends on actual power level . Homogeneous increase in temperature: usually not critical, can be compensated by focussing . Temperature gradients inside the lenses: - very critical, if transverse oriented - chnages of wavefront accross the pupil . Boundary conditions in optical systems: - heat conduction via mountings (dominant) - air convection - T4 radiation Thermo-mechanical Modellierung . Physical modelling: 2T 1T 2T Q - heat conduction equation 2 2 0 - thermal loading by radiation absorption r r r z K - stress-strain by elasticity equations dP(r, z) . Iterative calculation: Q(r, z) I(r, z) thermal effects influences beam profiles dV . Practice: boundary conditions only poorly known absorption of effects on optical radiation system: 1. n-profil thermal analysis 2. Deformations mechanical geometrical analysis analysis 3. Birefringence thermal boundary conditions mechanical boundary conditions Heating of Lens Systems . Homogeneous rise of temperature: typical not very critical, compensated by defocussing . Heating by absorption and internal heating by the signal light 2T 1T 2T Q - Heat equation 0 r 2 r r z 2 K dP(r, z) - source term Q(r, z) I(r, z) dV - gradients are the problem: lensing effects . Boundary conditions badly defined: - heat flow and cooling by mechanical parts - cooling by air turbulence . Totally three different effects: 1. geometric expansion 2. index gradients due to dn/dT 3. material stress and birefringence Heated Lens . Example: heated lens . Calculated by finite elements Temperature Deformation axial Deformation radial T(r,z) u(r,z) v(r,z) r r r 10 10 10 5 5 5 0 z 0 z 0 z 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Temperature Effects . FE calculation of temperature degradation of a microscopic lens . Especially hot spot in the object space due to oil-parameters and high energy density . Example: 1. Distribution of temperature 2. Cold and hot Psf Ref: S. Förster Thermal Loading case c) : . Thermal loading inside the radial parabolic objective lens due to absorption gradient case a) : T of . Parabolic profile of temperature immersion and refractive index . Special effects in the immersion liquid: Strehl ratio drops down . Compensation by refocusing is possible D DS S 1 1 refocused 0.8 without refocusing 0.95 0.6 0.4 0.9 0.2 T 0 T [grd] 0.85 0 5 10 15 20 -5 0 5 [grd] Material Data Expansion Young modul E Type Material in 10-6 m/grd in 103 N /mm2 Glass BK7 7.1 81 KzFSN4 4.5 60 LF5 9.1 59 LaK9 6.3 110 PK51A 12.7 73 Plastics Polycarbonat 69 CR 39 100 Crystals Quartz 0.55 72 Zerodur 0.05 91 Diamond 0.8 1050 ZnSe 7.1 70 Metals Aluminium 24 6800 Invar 1.0 141 Steel 14.7 193 Athermalization . Change of focal length 1 dn Coefficient f f T Material n 1dT in 10-6 m/grd . Opto-thermal coefficient TiF6 20.94 1 dn BK1 3.28 n 1 dT LaKN9 0.32 BAK4 -0.23 KzFS1 -2.89 . System with focal powers Fj : ZnSe -28.24 Fj j silica -64.1 j Fges . Homogeneous heating of complete Germanium -85.19 system: - only defocussing - mechanical expansion compensates change of focal length - special optimization of materials, mechanical design and materials necessary .