Design and Correction of Optical Systems

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1 Design and Correction of Optical Systems Lecture 12: Optical system classification Herbert Gross Summer term

2 2 Preliminary Schedule - DCS Basics Materials and Components Paraxial Optics Optical Systems Geometrical Aberrations Wave Aberrations PSF and Transfer function Further Performance Criteria Optimization and Correction Correction Principles I Correction Principles II Optical System Classification Law of refraction, Fresnel formulas, optical system model, raytrace, calculation approaches Dispersion, anormal dispersion, glass map, liquids and plastics, lenses, mirrors, aspheres, diffractive elements Paraxial approximation, basic notations, imaging equation, multi-component systems, matrix calculation, Lagrange invariant, phase space visualization Pupil, ray sets and sampling, aperture and vignetting, telecentricity, symmetry, photometry Longitudinal and transverse aberrations, spot diagram, polynomial expansion, primary aberrations, chromatical aberrations, Seidels surface contributions Fermat principle and Eikonal, wave aberrations, expansion and higher orders, Zernike polynomials, measurement of system quality Diffraction, point spread function, PSF with aberrations, optical transfer function, Fourier imaging model Rayleigh and Marechal criteria, Strehl definition, 2-point resolution, MTF-based criteria, further options Principles of optimization, initial setups, constraints, sensitivity, optimization of optical systems, global approaches Symmetry, lens bending, lens splitting, special options for spherical aberration, astigmatism, coma and distortion, aspheres Field flattening and Petzval theorem, chromatical correction, achromate, apochromate, sensitivity analysis, diffractive elements Overview, photographic lenses, microscopic objectives, lithographic systems, eyepieces, scan systems, telescopes, endoscopes Special System Examples Zoom systems, confocal systems

3 3 Contents 1. Overview 2. Achromates and apochromates 3. Collimators 4. Relay systems 5. Miscellaneous 6. Photographic lenses 7. Scan lenses 8. Lithographic lenses 9. Telescopes 10. Microscopic lenses

4 4 Field-Aperture-Diagram Classification of systems with field and aperture size Scheme is related to size, correction goals and etendue of the systems w Biogon Triplet photographic lithography Braat Distagon Aperture dominated: Disk lenses, microscopy, Collimator Sonnar Field dominated: Projection lenses, camera lenses, Photographic lenses Spectral widthz as a correction requirement is missed in this chart split triplet projection Gauss projection double Gauss achromat Petzval projection micro 10x0.4 diode collimator micro 40x0.6 disc lithography 2003 micro 100x0.9 constant etendue microscopy collimator focussing NA

5 5 Classification: l-l w -Diagram Throughput as fieldaperture product l Photography Microscopy Additional dimension: spectral bandwidth Astronomy Interferometer lens metrology lens Lithography L w

6 6 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 < only very small field corrected Crown in front Flint in front solution 1 solution 2

7 7 Achromate Achromate Longitudinal aberration Transverse aberration Spot diagram y' 486 nm 587 nm 656 nm l = 486 nm axis 1 r p l = 587 nm l = 656 nm sinu' nm 587 nm 656 nm s' [mm] 2

8 8 Axial Colour : Apochromate 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 (1)+(2) T N-KZFS11 (3) 656nm 588nm 0,54 (1) 90 N-FK nm -0.2mm z -0.2mm 436nm 0 1mm z

9 9 New Achromate Conventional achromate: strong bending of image shell, typical R ptz 1.3 f ' Petzval shell mean image shell y' Special selection of glasses: 1. achromatization F F2 2. Petzval flattening Residual field curvature: 1 Combined condition R ptz 1 But usually no spherical correction possible 1 F n n n n F ' n1 n 2 f n f R P selected crown glass perfect image plane line of solution for flint glass

10 10 Collimation Collimating source radiation: Finite divergence angle is reality Geometrical part due to finite size : Diffraction part: Defocussing contribution to divergence G D D f l D 2 z sin u f divergence G /2 D source u f

11 11 Collimator Optics Monochromatic doublet Correction only spherical and coma: Seidel surface contributions Limiting : astigmatism and curvature spherical coma astigmatism Enlarged aperture : meniscus added curvature distortion sum

12 12 Relay Systems: Achromate Large residual aberrations: 1. Astigmatism 2. Field curvature a) spherical aberration b) astigmatic field curves c) distortion y p / y pmax nm 546 nm 486 nm 435 nm tan sag y' / y' max 1.0 y' / y' max z [mm] z [mm] [%]

13 13 Relay Systems: Achromate with Field Lens Correction comparable Better fit of pupil a) spherical aberration y p / y pmax nm 546 nm 486 nm 435 nm b) astigmatic field curves y' tan sag / y' max 1.0 c) distortion y' / y' max z [mm] z [mm] [%] a) spherical aberration b) astigmatic field curves c) distortion y p / y pmax nm 546 nm 486 nm 435 nm tan sag y' / y' max 1.0 y' / y' max z [mm] z [mm] [%]

14 14 Relay Systems: More Complicated Systems Improved performance with more lenses In particular better color correction a) spherical aberration y p / y pmax 1.0 b) astigmatic field curves y' / y' max nm 546 nm 486 nm 0.5 solid: tan dashed: sag Magnification m = z [mm] z [mm] a) spherical aberration b) field curvature c) distortion y p / y pmax 1.0 T S y/y max T S T S y/y max nm 587 nm 656 nm z [mm] s' [mm] [%]

15 15 Relay Systems: 4f-Systems Double telecentric: magnification f f 2 1 Wave transport: phase is invariant use in phase imaging Use in Fourier-optical setups or pupil transfer systems 1 x y E '( x, y) E, starting plane final plane d f 1 f 1 f 2 f 2 d'

16 16 Relay Systems: 4f-Systems Basic system with achromates a) spherical aberration y p / y pmax nm 546 nm 486 nm 435 nm b) astigmatic field curves y' / y' max 1.0 sag tan c) distortion y' / y' max z [mm] z [mm] [%] Split achromates a) spherical aberration b) astigmatic field curves c) distortion y p / y pmax nm 546 nm 486 nm 435 nm sag y' / y' max 1.0 tan y' / y' max z [mm] z [mm] [%]

17 17 Relay Systems: Endoscopes Different subsystems: Differences in performance, complexity, distance, weight

18 18 Relay Systems: Endoscopes Transport over large distances Combination of several relay subsystems Large field-angle objective lens Applications: Technical or medical objective 1. relay 2. relay 3. relay Different subsystems: W rms [l] nm 587 nm 656 nm diffraction limit y' [mm]

19 19 Relay Systems: Periscope Major parts: 1. Eyepiece 2. Relay system, several stages 3. Objective 4. Turnable prism objective field lens 1. relay system 1. image 2. relay system 2. image 3. relay system eyepiece

20 20 Beam Guiding Systems Transport of laser light over large distances Adaptation of beam diameter Solutions : Telescopes of Kepler or Galilei type a) = 5 b) = 5 c) = 4 d) = 50 e) = 4 adjustment

21 21 Interferometer Collimator Lens Example lens Aperture NA = 0.5 Spherical correction with one surface sph coma surfaces lenses L1 L2 L3 L4 W rms [l] 0.1 sum possible surfaces under test diffraction limit w [ ]

22 22 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

23 23 Photographic Lenses Tessar Distagon Double Gauss Tele system Super Angulon Wide angle Fish-eye

24 24 Retrofocus Lenses Example lens 2 Distagon

25 25 Fish-Eye-Lens Nikon 210 Pleon (air reconnaissance)

26 Zoom Lens 26 Zoom lens Three moving groups group 1 group 2 group 3 e) f' = 203 mm w = 5.64 F# = 16.6 d) f' = 160 mm w = 7.13 F# = 13.7 c) f' = 120 mm w = 9.46 F# = 10.9 b) f' = 85 mm w = F# = 8.5 a) f' = 72 mm w = F# = 7.7

27 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.

27 27 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

28 28 Scan Systems: Introduction Basic setup lens 1 lens 2 chief ray due to scan angle point source virtual source point for scan angle scan angle s scan mirror t D s' marginal ray L field size Scan-magnification m = d m d Virtual source point on curved line: special flattening formula Requirements: - Duty cycle - Point resolution - Speed - Accuracy - Linearity - Cost

29 29 Scan Systems: Introduction Scan resolution: Number of resolvable points in the field of view corresponds to angle resolution N L D Airy 2 DExP l max Information capacity: 1. Resolvable points 2. Speed of scanning log angle resolution holographic scanner polygon mirror growing scan capacity resonant galvo scanner galvo scanner acoustic optical modulator electro optical modulator scan speed log v

30 30 Scan System Non-telecentric Scan angle 2x30 a) standard distortion y/y max 1 b) f- -distortion y/y max 1 c) wave aberration W rms [l] 0.1 Monochromatic 0.08 F- -corrected % 0 10% -0.2% 0 0.2%

31 31 Scan Systems: Introduction Deflecting components allows a field scan Mostly rotating mirrors Pre-objective scanning rotating scan mirror scan angle scan objective lens image plane y y Post-objective scanning image surface scan lens scan mirror

32 32 Deflecting Components: Polygon Mirrors Rotating mirror with plane facets Pyramidal pyramidal polygon objective lens scan line Prismatic prismatic polygon scan line objective lens

33 33 Fundamental System Groups Principal layout of a lithographic system rema relay lens homogenizer integrator rod laser reticle projection lens pupil shaping diffuser diameter adaptation axicon zoom wafer beam guiding beam steering mirror

34 34 Moores Law Historical development of shrinking feature size Moores law: factor 2 every two years resolution [mm] g-line 436 i-line 365 Processors: Intel Mhz Pentium Mhz Pentium II 300 Mhz KrF 248 ArF 193 ArF 193 immersion Pentium III 600 Mhz Pentium IV 1-2 Ghz 3 Ghz Future Processors 4-10 Ghz EUV year

35 35 Development of Stepper Lenses Ref: W. Kaiser

36 36 Lithographic Lens in Reality Ref: Carl Zeiss AG

37 M 2 M 1 M 6 M 5 37 Development of Lithographic Lenses a) Early systems d) Catadioptric cube systems M 2 M 1 g) EUV mirror systems M 3 M 4 b) Refractive spherical systems e) Multi-axis catadioptric systems M 1 M 8 M 4 M 3 c) Refractive with aspheres and immersion f) Uni-axis catadioptric systems M 2 M 3 M 6 M 4 M 6 M 5

38 38 Lithographic Optics H-Design

39 39 Lithographic Optics I-Design

40 40 Lithographic Optics X-Design

41 41 Field Flatness one waist two waists Principle of multi-bulges to reduce Petzval sum 1 1 n' r n f p k k k Seidel contributions show principle Petz Petz 1. bulge 1. waist 2. bulge 2. waist 3. bulge

42 42 Resolution Lateral resolution (CD) k 1 = Axial resolution l0 x k1 NA z k 2 n l0 2 NA High NA : z k 2 n l NA Influence: Wavelength and NA 1 ( NA/ n) 2 2 z [mm] 10 0 Diagram : k 1 = 0.36, k 2 = l = = NA x [mm]

43 43 Evolution of Projection lenses Growing NA and field of view: Increasing size of objective lenses Problems with correction, homogeneity, material cost, thermal effects Technological steps: aspherical surfaces, immersion, catadioptric designs Volume [a.u.] n = 1 n H2O (193 nm) Volume [a.u.] 1 n = 1 n H20 (193nm) design progress HI expectation hyper-na refractive HI folded catadioptric inline catadioptric NA pure spherical aspherical strong aspheres immersion catadioptric high index hypothetical NA

44 44 Size Reduction by Aspheres Considerable reduction of length and diameter by aspherical surfaces a) NA = 0.7 spherical b) NA = 0.8 spherical c) NA = 0.8 aspherical d) NA = 0.9 aspherical -9% -13%

45 45 Projection Processing Modes Different process modes: 1. Full field 2. Scanning 3. Step and repeat a) Full wafer projection b) Full wafer scanning c) Step and repeat d) Step and scan Reticle Reticle Reticle Reticle Lens Lens Lens Lens Wafer Wafer Wafer Wafer

46 46 Lithographic Optics EUV a-tool 2008

47 47 Basic Refractive Telescopes Kepler typ: - internal focus - longer total track - > 0 Telescope pupil intermediate focus a) Kepler/Fraunhofer Eyepiece Eye pupil Galilei typ: - no internal focus - shorter total track Telescope pupil telescope focal length f T eyepiece focal length f E b) Galilei - < 0 Eye pupil telescope focal length f T eyepiece focal length f E

48 48 Catadioptric Telescopes Maksutov compact L1 M1 M2 L2 L3 L4, L5 Klevtsov M1 M2 L1, L2

49 49 Astronomical Telescope Primary and secondary mirror

50 50 Four-Mirror Schiefspiegler Telescopes Solution Variants A B D E F G H

51 51 Catadioptric Telescopes Schmidt Telescope - Aspherical corrector plate - Residual chromatical aberrations - Achromatic corrector plate possible y corrector plate r field focus a marginal rays primary mirror Primary mirror M 1 M1 Stop Stop N-F2 N-BK7 Corrector plate Image focal plane (curved) r = 2f f

52 52 Evolution of Eyepiece Designs Huygens Loupe Monocentric Ramsden Von-Hofe Plössl Kellner Kerber Erfle Bertele König Erfle type Erfle diffractive Bertele Nagler 1 Erfle type (Zeiss) Aspheric Nagler 2 Scidmore Bertele Wild Dilworth

53 53 Eyepiece: Notations Field lens reduces chief ray height Eye lens adapts pupil diameter instrument pupil stop intermediate image eye lens f 1 eye pupil Matching of 1. Field of view 2. Pupil diameter 3. Pupil location field lens f 2 F' Eye relief : s' - distance between last lens surface and eye cornea x' z' e x - required : 15 mm - with eyeglasses : 20 mm Pupil size: 2-8 mm

54 20 arcmin 54 Kellner Eyepiece Corresponds to Ramsden type Field lens moved Eye lens achromatized LONGITUDINAL SPHERICAl ABER. ASTIGMATIC FIELD CURVES DISTORTION DIOPTER DIOPTER Distortion (%) 0 tan sag

55 20 arcmin 55 Abbe Orthoscopic Eyepiece Distortion corrected General problems with eyepieces: - remote eye pupil - typical eye relief 22 mm LONGITUDINAL SPHERICAl ABER. ASTIGMATIC FIELD CURVES DISTORTION DIOPTER DIOPTER Distortion (%) 0 tan sag

toxicology,... Micro system technology geology polymer chemistry Pathology clinical routine forensic,.

56 56 Application Fields of Microscopy Microscopy Research Routine applications Biomedical basic research Material research Medical routine Industrial routine Cell biology biological development toxicology,... Micro system technology geology polymer chemistry Pathology clinical routine forensic,... Microscopic surgery ophthalmology Pharmacy semiconductor inspection semiconductor manufacturing Ref: M. Kempe

57 57 Image Planes and Pupils Principal setup of a classical optical microscope Upper row : image planes Lower row : pupil planes Köhler setup collector condenser objective tube lens eyepiece eye field stop aperture stop exit pupil objective eye pupil source object intermediate image image

58 58 Microscope with Infinite Image Setup Basic microscopic system with infinite image location and tube lens Magnification of the first stage: Magnification of the complete setup Exit pupil size m m D obj micro ExP f f tube obj f f 2 tube obj f obj 250mm f eye NA' 2 f obj m NA obj objective lens pupil tube lens intermediate image eyepiece eye pupil eye object h marginal ray w' w h' chief ray f obj s 1 tube length t f eye

59 59 Upright-Microscope Sub-systems: film plane 1. Detection / Imaging path 1.1 objective lens 1.2 tube with tube lens and eyepiece photo camera binocular beam splitter 1.3 eyepieces 1.4 optional equipment for photo-detection intermediate image binocular beamsplitter tube lens lamp 2. Illumination collector 2.1 lamps with collector and filters 2.2 field aperture 2.3 condenser with aperture stop objective lens object condensor collector lamp

60 60 Microscope Stands Stereo microscopes Upright microscopes Inverse microscopes Routine microscopes From M. Kempe

61 61 Microscope Objective Lens: Performance Classes Classification: 1. performance in colour correction 2. correction in field flattening Division is rough Notation of quality classes depends on vendors (Neofluar, achro-plane, semi-apochromate,...) improved colour correction no Achromate Fluorite Apochromat improved field flatness Plan Planachromat Plan- Fluorite Plan- Apochromat

62 62 Microscope Objective Lens: Structure Typical parts of lens structure for high NA-objective lenses Separation of the lens setup in 3 major sections a front part : 1. spherical aberration : only small 2. coma : only small 3. astigmatism : only small 4. curvature : only small b middle part : 1. spherical aberration : correction 2. color : correction 3. coma : correction c rear part : 1. curvature : correction 2. astigmatism : correction 3. color : correction

63 63 Microscope Objective Lens Types Medium magnification system 40x0.65 High NA system 100x0.9 without field flattening High NA system 100x0.9 with flat field Large-working distance objective lens 40x0.65

64 64 Microscope Objective Lens: Correcting lens Floating element to adjust and correct spherical aberration air distance cover slide 0 mm 4.46 mm floating element Applications: 1. different thickness values of cover glass 2. index mismatch at 0.7 mm 3.99 mm mm the sample 3.66 mm mm 1.2 mm 3.32 mm mm 1.7 mm

65 65 Microscope Objective Lens: Pupil Object space telecentric Real rear stop is not object plane objective lens rear stop exit pupil defining the pupil marginal ray Collimated outgoing beam Exit pupil usually telecentric, entrance pupil infinity u y' p chief ray not accessible f' f' object plane pupil exit pupil rear stop chief ray

66 66 Illumination Optics: Overview Instrumental realizations a) incident illumination bright field b) incident illumination dark field c) transmitted illumination bright field d) transmitted illumination dark field observation observation ring mirror observation observation illumination illumination objective lens object plane object plane ring mirror object plane condenser object plane ring condenser illumination illumination

67 67 Stereo Microscope Telescopic setup : common main objective lens View along the axis left imaging channel right imaging channel eye eyepiece tube system zoom system common objective lens stereo angle object plane possible illumination channels common axis

Design and Correction of Optical Systems

Design and Correction of Optical Systems Lecture 12: Optical system classification 2015-07-01 Herbert Gross Summer term 2015 www.iap.uni-jena.de 2 Preliminary Schedule 1 15.04. Basics 2 22.04. Materials