Lens Design II. Lecture 8: Special correction features I Herbert Gross. Winter term
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1 Lens Design II Lecture 8: Special correction features I Herbert Gross Winter term
2 Preliminary Schedule Aberrations and optimization Repetition Structural modifications Zero operands, lens splitting, lens addition, lens removal, material selection Aspheres Correction with aspheres, Forbes approach, optimal location of aspheres, several aspheres Freeforms Freeform surfaces Field flattening Astigmatism and field curvature, thick meniscus, plus-minus pairs, field lenses Chromatical correction I Achromatization, axial versus transversal, glass selection rules, burried surfaces Chromatical correction II secondary spectrum, apochromatic correction, spherochromatism Special correction topics I Symmetry, wide field systems,stop position Special correction topics II Anamorphotic lenses, telecentricity Higher order aberrations high NA systems, broken achromates, induced aberrations Further topics Sensitivity, scan systems, eyepieces Mirror systems special aspects, double passes, catadioptric systems Zoom systems mechanical compensation, optical compensation Diffractive elements color correction, ray equivalent model, straylight, third order aberrations, manufacturing Realization aspects Tolerancing, adjustment
3 3 Contents 1. Symmetry 2. Camera lenses 3. Stop position 4. Vignetting
4 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 1 3
5 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 6 Symmetrical Dublet Variable focal length f = 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 f = 15 mm
7 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
8 8 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
9 Photographic Lenses Tessar Distagon Double Gauss Tele system Super Angulon Wide angle Fish-eye
10 Retrofocus Lenses Example lens 2 Distagon
11 Special Designs Compact Camera Plastic Aspheric Lens Mobile Phone camera
12 Handy Phone Objective lenses Examples US L = 4.2 mm, F'=2.8, f = 3.67 mm, 2w=2x34 US L = 6.0 mm, F'=2.8, f = 4.0 mm, 2w=2x31 EP 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
13 Fish-Eye-Lens Nikon 210 Pleon (air reconnaissance)
14 Wide-Angle Lenses Hypergon Strong vignetting 1.0 I(r) 0.5 Topogon Metrogon field 0 angle w
15 Wide-Angle Lenses Hologon Inverse Triplet Pleogon Biogon Super-Angulon
16 Retrofocus Lenses Flektogon Vivitar
17 Fish-Eye-Lens Example lens fisheye y -100% 0 100% a) nm 587 nm 656 nm tan sag ideal [mm -1 ] cyc/mm 20 cyc/mm 40 cyc/mm 60 cyc/mm b) c) solid: tan dashed: sag field angle 100
18 Fish-Eye-Lens Distortion types y' [a.u.] 2 gnomonic stereographic 1.5 f- -projection orthographic y' [mm] 1 aperture related y' = f' tan(w) y' = f' w fisheye lens w [ ] 10 a b w [ ]
19 Fish-Eye-Lens Pupil variation: position and orientation pupil location s ExP [mm] 110 a y' ExP [mm] 150 b w [ ] w [ ]
20 Panoramic Lens 360 viewing azimuth
21 21 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
22 22 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 R j Pleogon Double Gauss Biogon stop z j z j
23 23 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 Fisheye Distagon stop z j
24 24 Influence of Stop Position on Performance Ray path of chief ray depends on stop position stop positions spot
25 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 Aberration: y' 0.5 mm y' 0.5 mm (a) (b) From : H. Zügge
26 26 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
27 27 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
28 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 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 81 % F# 2.8 Ref.: H. Zügge
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