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LDII16 Lens Design II

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LDII16 Lens Design II Lens Design II Lecture 8: Special correction features I 2016-12-07 Herbert Gross Winter term 2016 www.iap.uni-jena.de 2 Preliminary Schedule 1 19.10. Aberrations and optimization Repetition Zero operands, lens splitting, lens addition, lens removal, 2 26.10. Structural modifications material selection Correction with aspheres, Forbes approach, optimal location 3 02.11. Aspheres of aspheres, several aspheres 4 09.11. Freeforms Freeform surfaces Astigmatism and field curvature, thick meniscus, plus-minus 5 16.11. Field flattening pairs, field lenses Achromatization, axial versus transversal, glass selection 6 23.11. Chromatical correction I rules, burried surfaces secondary spectrum, apochromatic correction, 7 30.11. Chromatical correction II spherochromatism 8 07.12. Special correction topics I Symmetry, wide field systems,stop position 9 14.12. Special correction topics II Anamorphotic lenses, telecentricity 10 21.12. Higher order aberrations high NA systems, broken achromates, induced aberrations 11 04.01. Further topics Sensitivity, scan systems, eyepieces 12 11.01. Mirror systems special aspects, double passes, catadioptric systems 13 18.01. Zoom systems mechanical compensation, optical compensation color correction, ray equivalent model, straylight, third order 14 25.01. Diffractive elements aberrations, manufacturing 15 01.02. Realization aspects Tolerancing, adjustment 3 Contents 1. Symmetry 2. Camera lenses 3. Stop position 4. Vignetting 4 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 3 1 5 Symmetrical Systems Ideal symmetrical systems: . Vanishing coma, distortion, lateral color aberration . Remaining residual aberrations: 1. spherical aberration 2. astigmatism 3. field curvature 4. axial chromatical aberration 5. skew spherical aberration skew spherical aberration 6 Symmetrical Dublet . Variable focal length f = 200 mm f = 15 ...200 mm f = 100 mm . Invariant: object size y = 10 mm numerical aperture NA = 0.1 f = 50 mm . Type of system changes: - dominant spherical for large f - dominant field for small f f = 20 mm . Data: focal Length spherical field astigma- No length [mm] c curvature c tism c [mm] 9 4 5 1 200 808 3.37 -2.01 -2.27 f = 15 mm 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 Classification Special Extrem Wide Angle Quasi-Symmetrical Angle Topogon Telecentric I Fish Eye Metrogon Telecentric II Compact . Families of photographic lenses Pleon Super-Angulon Hypergon Telephoto Catadioptric . Long history Panoramic Lens . Not unique Wide Angle Retrofocus Pleogon Hologon Plastic Plastic Aspheric Retrofocus SLR Aspheric I II IR Camera Lens UV Lens Flektogon Biogon Distagon Triplets Retrofocus II Vivitar Triplet Pentac Singlets Heliar Hektor Less Symmetrical Achromatic Landscape Landscape Ernostar Ernostar II Inverse Triplet Sonnar Petzval Symmetrical Doublets Petzval, Portrait Petzval Dagor Rapid Projection Rectilinear Aplanat Quadruplets Petzval,Portrait flat R-Biotar Double Gauss Ultran Dagor Biotar / Planar reversed Periskop Double Gauss II Quasi-Symmetrical Doublets Noctilux Orthostigmatic Tessar Protar Plasmat Celor Kino-Plasmat Unar Antiplanet Angulon 8 Symmetry Principle . Application of symmetry principle: photographic lenses . Especially field dominant aberrations can be corrected . Also approximate fulfillment of symmetry condition helps Triplet Double Gauss (6 elements) significantly: quasi symmetry . Realization of quasi- symmetric setups in nearly all photographic systems 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 US 7643225 US 6844989 . Examples L = 4.2 mm , F'=2.8 , f = 3.67 mm , 2w=2x34° L = 6.0 mm , F'=2.8 , f = 4.0 mm , 2w=2x31° EP 1357414 Olympus 2 L = 5.37 mm , F'=2.88 , f = 3.32 mm , 2w=2x33.9° 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 I(r) . Hypergon 1.0 Strong vignetting 0.5 field 0 angle w 0 13° 26° 39° 52° 65° . Topogon Metrogon Wide-Angle Lenses . Hologon Inverse Triplet . Pleogon . Biogon . Super-Angulon Retrofocus Lenses . Flektogon . Vivitar Fish-Eye-Lens . Example lens 486 nm 587 nm 656 nm a) 1 tan b) fisheye sag 0.8 0° y ideal 0.6 0° 50° 0.4 71° 100° 50° 0.2 -1 0 [mm ] 0 20 40 60 80 100 1 10 cyc/mm 40 cyc/mm c) 20 cyc/mm 60 cyc/mm 71° 0.8 100% -100% 0 solid: 0.6 tan dashed: 0.4 sag 100° 0.2 field angle 0 0 50° 100° Fish-Eye-Lens y' [a.u.] . Distortion types gnomonic stereographic 2 f--projection 1.5 orthographic aperture 1 related y' [mm] 25 y' = f' tan(w) y' = f' w 0.5 fisheye 20 lens w 0 0 10 20 30 40 50 60 70 80 90 [°] 15 a b 10 5 0 w [°] 0 20 40 60 80 100 120 Fish-Eye-Lens . Pupil variation: position and orientation y' sExP ExP pupil [mm] a [mm] b location 110 150 100 90 80 100 70 60 50 50 40 30 20 0 0 20 40 60 80 100 0 20 40 60 80 100 w [°] w [°] Panoramic Lens . 360° viewing azimuth 21 Photographic lens Photographic lens . Incidence angles for chief and marginal ray . Field dominant system marginal . Primary goal is to control and correct ray field related aberrations: chief ray coma, astigmatism, field curvature, lateral color incidence angle 60 40 20 0 20 40 60 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 22 Wide Angle Lenses - Symmetrical . Radii of curvature of wide angle camera lenses - symmetrical setups . Mostly radii 'concentric' towards the stop losition . Locations zj of surfaces normalized for comparison . Nearly linear trend, some exceptions near to the pupil . Stop position centered Rj 250 200 150 100 Pleogon 50 0 -50 -100 -150 zj Double Gauss -200 Biogon -250 zj -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 stop 23 Wide Angle Lenses - Asymmetrical . Radii of curvature of wide angle camera lenses - asymmetrical setups . No clear trend . Locations zj of surfaces normalized for comparison . Stop position in the rear part Rj Flektogon 300 200 100 0 Fisheye -100 -200 Distagon -300 zj -1 -0.8 -0.6 -0.4 -0.2 0 0.2 stop 24 Influence of Stop Position on Performance . Ray path of chief ray depends on stop position stop positions spot 25 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 y' y' Aberration: 0.5 mm 0.5 mm (a) (b) From : H. Zügge 26 Coma Correction: Stop Position and Aspheres . Combined effect, aspherical case prevent correction Sagittal Sagittal Plano-convex element coma Spherical aberration corrected coma exhibits spherical aberration y' with aspheric surface y' 0.5 mm 0.5 mm aspheric aspheric aspheric Ref : H. Zügge 27 Effect of Stop Position stop . Example photographic lens . Small axial shift of stop changes tranverse aberrations . In particular coma is strongly influenced Ref: H.Zügge 28 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 29 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 F# 2.8 81 % Ref.: H. Zügge .
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