Optical Design with Zemax

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1 Optical Design with Zemax Lecture : Correction I Herbert Gross Summer term 202

2 Preliminary time schedule Introduction Introduction, Zemax interface, menues, file handling, preferences, Editors, updates, windows, Coordinate systems and notations, System description, Component reversal, system insertion, scaling, 3D geometry, aperture, field, wavelength Properties of optical systems I Properties of optical systems II Aberrations I Diameters, stop and pupil, vignetting, Layouts, Materials, Glass catalogs, Raytrace, Ray fans and sampling, Footprints Types of surfaces, Aspheres, Gratings and diffractive surfaces, Gradient media, Cardinal elements, Lens properties, Imaging, magnification, paraxial approximation and modelling Representation of geometrical aberrations, Spot diagram, Transverse aberration diagrams, Aberration expansions, Primary aberrations, Aberrations II Wave aberrations, Zernike polynomials, Point spread function, Optical transfer function Advanced handling 7.2. Optimization I Telecentricity, infinity object distance and afocal image, Local/global coordinates, Add fold mirror, Vignetting, Diameter types, Ray aiming, Material index fit, Universal plot, Slider,IO of data, Multiconfiguration, Macro language, Lens catalogs Principles of nonlinear optimization, Optimization in optical design, Global optimization methods, Solves and pickups, variables, Sensitivity of variables in optical systems Optimization II Systematic methods and optimization process, Starting points, Optimization in Zemax Imaging Fundamentals of Fourier optics, Physical optical image formation, Imaging in Zemax Illumination Correction I Correction II Introduction in illumination, Simple photometry of optical systems, Non-sequential raytrace, Illumination in Zemax Symmetry principle, Lens bending, Correcting spherical aberration, Coma, stop position, Astigmatism, Field flattening, Chromatical correction, Retrofocus and telephoto setup, Design method Field lenses, Stop position influence, Aspheres and higher orders, Principles of glass selection, Sensitivity of a system correction, Microscopic objective lens, Zoom system Physical optical modelling Gaussian beams, POP propagation, polarization raytrace, coatings

3 Contents 3. Symmetry principle 2. Lens bending 3. Correcting spherical aberration 4. Coma, stop position 5. Astigmatism 6. Field flattening 7. Chromatical correction 8. Retrofocus and telephoto setup 9. Design method 0. Starting points

4 Principle of Symmetry 4 Perfect symmetrical system: magnification m = - Stop in centre of symmetry Symmetrical contributions of wave aberrations are doubled (spherical) Asymmetrical contributions of wave aberration vanishes W(-x) = -W(x) Easy correction of: coma, distortion, chromatical change of magnification front part rear part 2 3

5 Symmetrical Systems 5 Ideal symmetrical systems: Vanishing coma, distortion, lateral color aberration Remaining residual aberrations:. spherical aberration 2. astigmatism 3. field curvature 4. axial chromatical aberration 5. skew spherical aberration skew spherical aberration

6 Symmetry Principle 6 Application of symmetry principle: photographic lenses Especially field dominant aberrations can be corrected Also approximate fulfillment of symmetry condition helps Triplet significantly: quasi symmetry Realization of quasisymmetric setups in nearly all photographic systems Double Gauss (6 elements) Biogon Double Gauss (7 elements) Ref : H. Zügge

7 Spherical Aberration: Lens Bending 7 Effect of bending a lens on spherical aberration Optimal bending: Minimize spherical aberration Dashed: thin lens theory Solid : think real lenses Vanishing SPH for n=.5 only for virtual imaging Correction of spherical aberration possible for:. Larger values of the magnification parameter M 2. Higher refractive indices Spherical Aberration (a) (b) (c) (d) M=0 M=-3 M=3 M=-6 M=6 X Ref : H. Zügge

8 Correcting Spherical Aberration: Lens Splitting 8 Transverse aberration Correction of spherical aberration: Splitting of lenses (a) 5 mm Distribution of ray bending on several surfaces: - smaller incidence angles reduces the effect of nonlinearity - decreasing of contributions at every surface, but same sign Last example (e): one surface with compensating effect (b) (c) 5 mm 5 mm Improvement (a)à(b) : /4 Improvement (b)à(c) : /2 5 mm (d) Improvement (c)à(d) : / mm (e) Improvement (d)à(e) : /75 Ref : H. Zügge

9 Correcting Spherical Aberration: Cementing 9 Correcting spherical aberration by cemented doublet: Strong bended inner surface compensates Solid state setups reduces problems of centering sensitivity In total 4 possible configurations:. Flint in front / crown in front 2. bi-convex outer surfaces / meniscus shape Residual zone error, spherical aberration corrected for outer marginal ray.0 mm 0.25 mm Crown in front (a) (b) Filnt in front (c) 0.25 mm (d) 0.25 mm Ref : H. Zügge

10 Correcting Spherical Aberration: Refractive Index 0 Better correction for higher index Shape of lens / best bending changes from. nearly plane convex for n=.5 2. meniscus shape for n > 2 Δs best shape plano-convex 4.0 n best shape n =.5 n =.7 n =.9 n = 4.0 plano-convex Ref : H. Zügge

11 Correcting Spherical Aberration: Refractive Index Better correction for high index also for meltiple lens systems Example: 3-lens setup with one surface for compensation Residual aberrations is quite better for higher index n =.5 n =.8 S I () Surface sum 0.5 mm n = mm n =.8 Ref : H. Zügge

12 Coma Correction: Symmetry Principle 2 Perfect coma correction in the case of symmetry But magnification m = - not useful in most practical cases Image height: y = 9 mm Symmetry principle Pupil section: meridional sagittal Transverse Aberration: y' 0.5 mm y' 0.5 mm (a) (b) From : H. Zügge

13 Coma Correction: Stop Position and Aspheres 3 Combined effect, aspherical case prevent correction Plano-convex element exhibits spherical aberration Sagittal coma y' 0.5 mm Spherical aberration corrected with aspheric surface aspheric Sagittal coma y' 0.5 mm aspheric aspheric Ref : H. Zügge

14 Distortion and Stop Position 4 Sign of distortion for single lens: depends on stop position and sign of focal power Ray bending of chief ray defines distortion Stop position changes chief ray heigth at the lens Lens Stop location Distortion Examples positive rear V > 0 tele photo lens negative in front V > 0 loupe positive in front V < 0 retrofocus lens negative rear V < 0 reversed binocular positive negative Ref: H.Zügge

15 Astigmatism: Lens Bending 5 Bending effects astigmatism For a single lens 2 bending with zero astigmatism, but remaining field curvature Astigmatism Seidel coefficients in [] Surface 2 Sum Surface Curvature of surface T S T S S T ST T S Ref : H. Zügge

16 Petzval Theorem for Field Curvature 6 Petzval theorem for field curvature:. formulation for surfaces 2. formulation for thin lenses (in air) Important: no dependence on bending R ptz R ptz n m ' k n f j j nk ' nk n n ' r j k k k Natural behavior: image curved towards system object plane Problem: collecting systems with f > 0: If only positive lenses: R ptz always negative R optical system real image shell ideal image plane

17 Petzval Theorem for Field Curvature 7 Goal: vanishing Petzval curvature and positive total refractive power for multi-component systems R f ptz n f j h h j f j j j Solution: General principle for correction of curvature of image field:. Positive lenses with: - high refractive index - large marginal ray heights - gives large contribution to power and low weighting in Petzval sum 2. Negative lenses with: - low refractive index - samll marginal ray heights - gives small negative contribution to power and high weighting in Petzval sum

18 Flattening Meniscus Lenses 8 Possible lenses / lens groups for correcting field curvature Interesting candidates: thick mensiscus shaped lenses r 2 nk ' nk n n ' r Rptz k k k k n f n n 2 d r r 2 r d. Hoeghs mensicus: identical radii - Petzval sum zero - remaining positive refractive power F' ( n ) nr 2 2 d 2. Concentric meniscus, - Petzval sum negative - weak negative focal length - refractive power for thickness d: r 2 R ptz r d ( n ) d n r r d ( n ) d F' nr ( r d) 3. Thick meniscus without refractive power Relation between radii r r d n 2 n R ptz n r 2 ( n ) d nr d ( n ) 0

19 Correcting Petzval Curvature 9 Group of meniscus lenses n n d collimated r r 2 Effect of distance and refractive indices /R pet [/mm] 0 - K5 / d=25 mm 0-2 K5 / d=5 mm SF66 / d=5 mm r [mm] From : H. Zügge

20 Field Curvature 20 Correction of Petzval field curvature in lithographic lens for flat wafer R j F n j j Positive lenses: Green h j large Negative lenses : Blue h j small F j h h j F j Correction principle: certain number of bulges

21 Flattening Field Lens 2 Effect of a field lens for flattening the image surface. Without field lens 2. With field lens curved image surface image plane image shell flat image field lens

22 Axial Colour: Achromate 22 Compensation of axial colour by appropriate glass choice (a) (b) Chromatical variation of the spherical aberrations: spherochromatism (Gaussian aberration) Therefore perfect axial color correction (on axis) are often not feasable BK7 n =.568 = 64.7 F= BK7 F2 n = = F = n = = F = r p r p 486 nm 588 nm 656 nm z z -00 Ref : H. Zügge

23 Achromate Achromate: - Axial colour correction by cementing two different glasses - Bending: correction of spherical aberration at the full aperture - Aplanatic coma correction possible be clever choice of materials Four possible solutions: - Crown in front, two different bendings - Flint in front, two different bendings Typical: - Correction for object in infinity - spherical correction at center wavelength with zone - diffraction limited for NA < 0. - only very small field corrected Crown in front Flint in front solution solution 2

24 Achromate: Realization Versions Advantage of cementing: solid state setup is stable at sensitive middle surface with large curvature Disadvantage: loss of one degree of freedom a) flint in front Different possible realization forms in practice edge contact cemented b) crown in front edge contact cemented contact on axis broken, Gaussian setup

25 Achromate : Basic Formulas Idea:. Two thin lenses close together with different materials 2. Total power F F F 2 3. Achromatic correction condition F F2 0 2 Individual power values F F F2 F 2 2 Properties:. One positive and one negative lens necessary 2. Two different sequences of plus (crown) / minus (flint) 3. Large -difference relaxes the bendings 4. Achromatic correction indipendent from bending 5. Bending corrects spherical aberration at the margin 6. Aplanatic coma correction for special glass choices 7. Further optimization of materials reduces the spherical zonal aberration

26 Achromate: Correction Cemented achromate: 6 degrees of freedom: 3 radii, 2 indices, ratio / 2 Correction of spherical aberration: diverging cemented surface with positive spherical contribution for n neg > n pos Choice of glass: possible goals. aplanatic coma correction 2. minimization of spherochromatism 3. minimization of secondary spectrum s' rim case with 2 solutions Bending has no impact on chromatical correction: is used to correct spherical aberration at the edge Three solution regions for bending. no spherical correction 2. two equivalent solutions 3. one aplanatic solution, very stable case without solution, only sperical minimum R case with one solution and coma correction

27 Achomatic solutions in the Glass Diagram crown positive lens flint negative lens Achromat

28 Achromate Achromate Longitudinal aberration Transverse aberration Spot diagram y' 486 nm 587 nm 656 nm = 486 nm axis r p = 587 nm = 656 nm sinu' nm 587 nm 656 nm s' [mm] 2

29 Coma Correction: Achromate Bending of an achromate - optimal choice: small residual spherical aberration - remaining coma for finite field size Splitting achromate: additional degree of freedom: - better total correction possible - high sensitivity of thin air space Aplanatic glass choice: vanishing coma Cases: a) simple achromate, sph corrected, with coma b) simple achromate, coma corrected by bending, with sph c) other glass choice: sph better, coma reversed d) splitted achromate: all corrected e) aplanatic glass choice: all corrected (a) (b) (c) (d) (e) Achromat bending Achromat, splitting Achromat, aplanatic glass choice Image height: y = 0 mm y = 2 mm Pupil section: meridional meridional sagittal Transverse y' y' y' Aberration: 0.05 mm 0.05 mm 0.05 mm Wave length: Ref : H. Zügge

30 Achromate Residual aberrations of an achromate Clearly seen:. Distortion 2. Chromatical magnification 3. Astigmatism

31 Spherochromatism: Achromate 3 Residual spherochromatism of an achromate Representation as function of apeture or wavelength r p longitudinal aberration 656 defocus variation pupil height : 587 r p = r p = r p = 0.4 r p = nm 587 nm nm z z

Axial Colour: Achromate and Apochromate 32 Effect of different materials Axial chromatical aberration changes with wavelength Different levels of correction:.

32 Axial Colour: Achromate and Apochromate 32 Effect of different materials Axial chromatical aberration changes with wavelength Different levels of correction:.no correction: lens, one zero crossing point 2.Achromatic correction: - coincidence of outer colors - remaining error for center wavelength - two zero crossing points 3. Apochromatic correction: - coincidence of at least three colors - small residual aberrations - at least 3 zero crossing points - special choice of glass types with anomalous partial dispertion necessery apochromate singlet C' residual error apochromate e residual error achromate achromate F' s' lens

33 Axial Colour: Apochromate 33 Anormal partial dispersion and normal line P g,f N-FK5 N-PK52 normal line GG375G34 N-BAF52 N-BAF3 N-BAF5 K5G20 N-BAK4 N-BAF0 N-SK2 N-SK8 N-LAF3 SK0G0 N-BALF5 N-LLF6 BAKG2 N-SSK8 SK4G3 N-BALF4 N-SK5 SSK5G06 N-SK4 N-SSK5 N-K5 SK5 N-BAK2 N-KF9 K7 N-SK N-PK5 N-SK5 N-PSK53 N-PSK57 N-PSK58 BK7G25 N-PSK3 N-FK5 N-BK0 BK7G8 N-BK7 N-LAK7 N-LAK2 N-ZK7 N-SK6 N-PSK3 N-SK4 SK5G06 N-LLF N-LAF N-BAF4 BASF5 F5 N-BAK N-LAK4 SF5 N-LAF7 N-SF64 N-SF8 N-SF5 N-SF9 N-LASF40 N-LF5 N-BASF2 N-F2 F2G2 N-LAK33 N-LAK2 N-LAK9 N-LAK22 LAKL2 N-SK0 N-SF N-SF0 N-SF5 SF0 N-LAK8 SF2 SF5 N-LASF45 N-LASF36 F2 LAFN7 N-KZFS2 N-BASF64 LF5G5 LF5 KZFSN5 N-LASF43 N-LASF3 N-LAF2 LLF N-LASF4 N-LAF33 N-KZFS KZFSN4 KZFS4G20 N-LASF30 N-LASF44 N-KZFS4 N-LAF2 N-LAF32 LAK9G5 K0 N-LAK34 N-KZFS2 N-SF4 N-SF6 SF4 N-SF57 N-LAF35 N-LAF28 N-LAF34 N-LAK0 N-SSK2 LAKN3 SF66 SFL57 SF57 SF SF N-SF56 SF6G05 SF6 SF56A SF4 N-LASF35 SF8G07 N-LASF46 LASFN9 SF5G0

34 Axial Colour : Apochromate 34 Choice of at least one special glass P gf Correction of secondary spectrum: anomalous partial dispersion 0,62 0,60 N-FS6 (2) At least one glass should deviate significantly form the normal glass line 0,58 0,56 ()+(2) T N-KZFS (3) 656nm 588nm 0,54 () 90 N-FK nm -0.2mm z -0.2mm 436nm 0 mm z

35 Buried Surface 35 Cemented surface with perfect refrcative index match No impact on monochromatic aberrations Only influence on chromatical aberrations Especially 3-fold cemented components are advantages Can serve as a starting setup for chromatical correction with fulfilled monochromatic correction Special glass combinations with nearly perfect parameters Nr Glas n d n d d d SK F SK LF SSK F SK BaF d d 2 d 3

36 8 Correction II Telephoto Systems Combination of a positiv and a negative lens: Shift of the first principal plane in front of the system The intersection length is smaller than the focal length: reduction factor k Typical values: k = Focal lengths: f f a b Overall length f ' d f ' ( k) d f dkf ' d a f a kf ' P' y a a y b b L k f ' Free intersection length f ' s ' sf k f ' d d k f '

37 8 Correction II Retrofocal System Combination of a negative and a positive lens: Shift of the second principal plane behind the system The intersection length is larger than the focal length Application: systems for large free working distance Corresponds to an inverse telephoto system P' f ' s '

38 8 Correction II Telephoto and inverse Telephoto Principle Retrofocus system results form a telephoto system by inversion principal plane P' telephoto system image plane retrofocus system inverse telephoto focal length f

39 System Design Phases 39. Paraxial layout: - specification data, magnification, aperture, pupil position, image location - distribution of refractive powers - locations of components - system size diameter / length - mechanical constraints - choice of materials for correcting color and field curvature 2. Correction/consideration of Seidel primary aberrations of 3rd order for ideal thin lenses, fixation of number of lenses 3. Insertion of finite thickness of components with remaining ray directions 4. Check of higher order aberrations 5. Final correction, fine tuning of compromise 6. Tolerancing, manufactability, cost, sensitivity, adjustment concepts

40 Optimization: Starting Point 40 Existing solution modified Literature and patent collections Principal layout with ideal lenses successive insertion of thin lenses and equivalent thick lenses with correction control object pupil intermediate image image f f 2 f 3 f 4 f 5 Approach of Shafer AC-surfaces, monochromatic, buried surfaces, aspherics Expert system Experience and genius

41 Strategy of Correction and Optimization 4 Usefull options for accelerating a stagnated optimization: split a lens increase refractive index of positive lenses lower refractive index of negative lenses make surface with large spherical surface contribution aspherical break cemented components use glasses with anomalous partial dispersion

42 Correction Methods 42 Lens bending Lens splitting Power combinations (a) (b) (c) (d) (e) Distances (a) (b) Ref : H. Zügge

43 Zero-Operations 43 Operationen with zero changes in first approximation:. Bending a lens. 2. Flipping a lens into reverse orientation. 3. Flipping a lens group into reverse order. 4. Adding a field lens near the image plane. 5. Inserting a powerless thin or thick meniscus lens. 6. Introducing a thin aspheric plate. 7. Making a surface aspheric with negligible expansion constants. 8. Moving the stop position. 9. Inserting a buried surface for color correction, which does not affect the main wavelength. 0. Removing a lens without refractive power.. Splitting an element into two lenses which are very close together but with the same total refractive power. 2. Replacing a thick lens by two thin lenses, which have the same power as the two refracting surfaces. 3. Cementing two lenses a very small distance apart and with nearly equal radii.

Optical Design with Zemax for PhD

Optical Design with Zemax for PhD Lecture 7: Optimization II 26--2 Herbert Gross Winter term 25 www.iap.uni-jena.de 2 Preliminary Schedule No Date Subject Detailed content.. Introduction 2 2.2. Basic Zemax