Lens Design II Lecture 8: Special correction topics 2018-12-12 Herbert Gross Winter term 2018 www.iap.uni-jena.de
2 Preliminary Schedule Lens Design II 2018 1 17.10. Aberrations and optimization Repetition 2 24.10. Structural modifications Zero operands, lens splitting, lens addition, lens removal, material selection 3 07.11. Aspheres Correction with aspheres, Forbes approach, optimal location of aspheres, several aspheres 4 14.11. Freeforms Freeform surfaces, general aspects, surface description, quality assessment, initial systems 5 21.11. Field flattening Astigmatism and field curvature, thick meniscus, plus-minus pairs, field lenses 6 28.11. Chromatical correction I Achromatization, axial versus transversal, glass selection rules, burried surfaces 7 05.12. Chromatical correction II Secondary spectrum, apochromatic correction, aplanatic achromates, spherochromatism 8 12.12. Special correction topics I Symmetry, wide field systems, stop position, vignetting 9 19.12. Special correction topics II Telecentricity, monocentric systems, anamorphotic lenses, Scheimpflug systems 10 09.01. Higher order aberrations High NA systems, broken achromates, induced aberrations 11 16.01. Further topics Sensitivity, scan systems, eyepieces 12 23.01. Mirror systems special aspects, double passes, catadioptric systems 13 30.01. Zoom systems Mechanical compensation, optical compensation 14 06.01. Diffractive elements Color correction, ray equivalent model, straylight, third order aberrations, manufacturing
3 Contents 1. Symmetry 2. Camera lenses 3. Stop position 4. Vignetting
4 Even Aberrations in Symmetrical Systems Aberrations with even symmetry are doubled Spherical aberration, Astigmatism, field curvature, axial chromatical aberration spherical aberration in an symmetrical system W c4 Z4 c9 Z9 W c4 Z4 c9 Z9 doubled values W 2c Z 2c Z 4 4 9 9 Ref: M. Seesselberg
5 Odd Aberrations in Symmetrical Systems Aberrations with odd symmetry are vanishing Coma, distortion, transverse chromatical aberration coma in an symmetrical system W c8 Z8 c15 Z15 W c8 Z8 c15 Z15 vanishing values Ref: M. Seesselberg W 0
6 Photographic lens Incidence angles for chief and marginal ray Photographic lens Field dominant system Primary goal is to control and correct field related aberrations: coma, astigmatism, field curvature, lateral color chief ray 60 incidence angle marginal ray 40 20 0 20 40 60 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
7 Principle of Symmetry Perfect symmetrical system: magnification m = -1 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 1 3
8 Symmetrical Dublet Variable focal length f = 15...200 mm Invariant: object size y = 10 mm numerical aperture NA = 0.1 Type of system changes: - dominant spherical for large f - dominant field for small f Data: f = 200 mm f = 100 mm f = 50 mm f = 20 mm No focal length [mm] Length [mm] spherical c 9 field curvature c 4 astigmatism c 5 1 200 808 3.37-2.01-2.27 2 100 408 1.65 1.19-4.50 3 50 206 1.74 3.45-7.34 4 20 75 0.98 3.93 2.31 5 15 59 0.20 16.7-5.33 f = 15 mm
9 Wide Angle Lenses - Symmetrical Radii of curvature of wide angle camera lenses - symmetrical setups Mostly radii 'concentric' towards the stop losition Locations z j of surfaces normalized for comparison Nearly linear trend, some exceptions near to the pupil Stop position centered 250 200 150 R j 100 50 Pleogon 0-50 -100-150 -200-250 Double Gauss Biogon -0.5-0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 0.5 stop z j z j
10 Wide Angle Lenses - Asymmetrical Radii of curvature of wide angle camera lenses - asymmetrical setups No clear trend Locations z j of surfaces normalized for comparison Stop position in the rear part R j 300 Flektogon 200 100 0-100 Fisheye -200-300 Distagon -1-0.8-0.6-0.4-0.2 0 0.2 stop z j
11 Coma Correction: Symmetry Principle Perfect coma correction in the case of symmetry But magnification m = -1 not useful in most practical cases Image height: y = 19 mm Symmetry principle Pupil section: meridional sagittal Transverse Aberration: y' 0.5 mm y' 0.5 mm (a) (b) From : H. Zügge
12 Coma Correction: Stop Position and Aspheres 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
Classification Extrem Wide Angle Fish Eye Quasi-Symmetrical Angle Topogon Metrogon Special Telecentric I Families of photographic lenses Long history Not unique Panoramic Lens Pleon Wide Angle Retrofocus Retrofocus SLR Super-Angulon Pleogon Hypergon Hologon Telephoto Plastic Aspheric I Telecentric II Compact Catadioptric Plastic Aspheric II Flektogon Distagon Biogon IR Camera Lens UV Lens Triplets Retrofocus II Vivitar Triplet Pentac Ernostar Less Symmetrical Ernostar II Landscape Singlets Achromatic Landscape Heliar Hektor Inverse Triplet Sonnar Double Gauss Biotar / Planar Quadruplets Ultran Petzval, Portrait Petzval Petzval,Portrait flat Petzval Projection R-Biotar Symmetrical Doublets Dagor Dagor reversed Rapid Rectilinear Aplanat Periskop Double Gauss II Noctilux Quasi-Symmetrical Doublets Tessar Protar Orthostigmatic Plasmat Kino-Plasmat Celor Unar Antiplanet Angulon
14 Symmetry Principle 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
Photographic Lenses Tessar Distagon Double Gauss Tele system Super Angulon Wide angle Fish-eye
Retrofocus Lenses Example lens 2 Distagon
Special Designs Compact Camera Plastic Aspheric Lens Mobile Phone camera
Handy Phone Objective lenses Examples US 7643225 L = 4.2 mm, F'=2.8, f = 3.67 mm, 2w=2x34 US 6844989 L = 6.0 mm, F'=2.8, f = 4.0 mm, 2w=2x31 EP 1357414 L = 5.37 mm, F'=2.88, f = 3.32 mm, 2w=2x33.9 Olympus 2 L = 7.5 mm, F'=2.8, f = 4.57 mm, 2w=2x33 Ref: T. Steinich
Fish-Eye-Lens Nikon 210 Pleon (air reconnaissance)
Wide-Angle Lenses Hypergon Strong vignetting 1.0 I(r) 0.5 Topogon Metrogon field 0 angle w 0 13 26 39 52 65
Wide-Angle Lenses Hologon Inverse Triplet Pleogon Biogon Super-Angulon
Retrofocus Lenses Flektogon Vivitar
Fish-Eye-Lens Example lens fisheye y -100% 0 100% a) 0 50 71 486 nm 587 nm 656 nm 1 0.8 tan sag ideal 0.6 0 50 0.4 71 100 0.2 0 [mm -1 ] 0 20 40 60 80 100 1 0.8 0.6 0.4 10 cyc/mm 20 cyc/mm 40 cyc/mm 60 cyc/mm b) c) solid: tan dashed: sag 100 0.2 0 0 50 field angle 100
Fish-Eye-Lens Pupil variation: position and orientation pupil location s ExP [mm] 110 a y' ExP [mm] 150 b 100 90 80 100 70 60 50 50 40 30 20 0 20 40 60 80 100 w [ ] 0 0 20 40 60 80 100 w [ ]
Fish-Eye-Lens Distortion types y' [a.u.] 2 gnomonic stereographic 1.5 f- -projection orthographic y' [mm] 1 aperture related 25 20 15 y' = f' tan(w) y' = f' w fisheye lens 0.5 0 0 10 20 30 40 50 60 70 80 90 w [ ] 10 a b 5 0 0 20 40 60 80 100 120 w [ ]
26 Optimization of the Stop Position Change of stop position changes the path of the ray bundle for the field points through the system Aberrations changes Vignetting occur for extrem pupil positions
27 Stop Shift Formula exit pupil semi diameter h E T T h H field height h E εh H ρ ε Normalized field height Normalized pupil height Stop shift parameter T old exit pupil T new exit pupil image plane Taylor series expansion using stop shift parameter: Examples: W spherical aberration W new ρ; H = W old ρ x, ρ y + εh; H = W old ρ; H + εh ρy W old ρ; H + ε2 2 H2 2 ρy W old ρ; H + constant spherical aberration linear coma quadratic astigmatism & curvature W coma linear coma quadratic astigmatism & curvature cubic distortion Ref: D. Ochse
28 Optimization of the Stop Position Relay system Change of stop size and position without re-optimization: 1. Vignetting occurs 2. Performance drops spot size in mm relative illumination NA optimized point NA optimized point z-enp z-enp
29 Optimization of the Stop Position Relay system Change of stop position with re-optimization: 1. Vignetting occurs 2. Performance drops In case of vignetting: spot size grows more slowly Optimal stop position inside the system due to averaged chief ray heights D spot in mm 7 6 5 4 3 2 1 0 50 100 150 200 250 300 350 400 transmission 1 no vignetting without vignetting z-pupil 0.8 0.6 0.4 0.2 0 50 100 150 200 250 300 350 400 z-pupil
30 Influence of Stop Position on Performance Ray path of chief ray depends on stop position stop positions spot
31 Stop Position Relative stop position in wide angle camera lenses: - symmetric / asymmetric concepts - angle ratio incoming / outgoing balanced - relative chief ray heights balanced / diameters - chief ray correction - special case aspheres Fisheye lens w inc = 85 w out = 7 Super Angulon w inc = 45 w out = 48 Handy lens II aspheres w inc = 34 w out = 22 Flektogon w inc = 45 w out = 25 Pleogon w inc = 45 w out = 46 Handy lens I aspheres w inc = 33 w out = 34 Distagon I w inc = 37 w out = 21 Distagon I w inc = 27 w out = -3
32 Effect of Stop Position Example photographic lens stop Small axial shift of stop changes tranverse aberrations In particular coma is strongly influenced Ref: H.Zügge
33 Aberrations Limited by Vignetting Clipping of outer coma rays by vignetting Consequences: - reduced brightness - anisotropic resolution without vignettierung with vignettierung tangential / sagittal Ref: H.Zügge
34 Vignetting Double Gauss Lens 1.4 / 50 Improved performance Reduced uniformity of brightness a) no vignetting:weight 251 g relative illumination b) vignetted: weight 90 g 81 % F# 2.8 Ref.: H. Zügge