Medical Photonics Lecture Optical Engineering

Transcription

1 Medical Photonics Lecture Optical Engineering Lecture 11: Optical Design Herbert Gross Winter term

2 2 Schedule Optical Engineering 2017 No Subject Ref Date Detailed Content 1 Introduction Gross Materials, dispersion, ray picture, geometrical approach, paraxial approximation 2 Geometrical optics Gross Ray tracing, matrix approach, aberrations, imaging, Lagrange invariant 3 Diffraction Gross Basic phenomena, wave optics, interference, diffraction calculation, point spread function, transfer function 4 Components Kempe Lenses, micro-optics, mirrors, prisms, gratings 5 Optical systems Gross Field, aperture, pupil, magnification, infinity cases, lens makers formula, etendue, vignetting 6 Aberrations Gross Introduction, primary aberrations, miscellaneous 7 Image quality Gross Spot, ray aberration curves, PSF and MTF, criteria 8 Instruments I Kempe Human eye, loupe, eyepieces, photographic lenses, zoom lenses, telescopes 9 Instruments II Kempe Microscopic systems, micro objectives, illumination, scanning microscopes, contrasts 10 Instruments III Kempe Medical optical systems, endoscopes, ophthalmic devices, surgical microscopes 11 Optic design Gross Aberration correction, system layouts, optimization, realization aspects 12 Photometry Gross Notations, fundamental laws, Lambert source, radiative transfer, photometry of optical systems, color theory 13 Illumination systems Gross Light sources, basic systems, quality criteria, nonsequential raytrace 14 Metrology Gross Measurement of basic parameters, quality measurements

3 3 Modelling of Optical Systems Principal purpose of calculations: 1. Solving the direct problem of understanding the properties: analysis System, data of the structure (radii, distances, indices,...) 2. Solving the inverse problem: Finding the concret system data for a required functionality: synthesis Analysis imaging aberration theory Synthesis lens design inverse problem Function, data of properties, quality performance (spot diameter, MTF, Strehl ratio,...) Ref: W. Richter

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 Optical System Examples Fraunhofer IOF 5 Microscopic lens Telescope Camera lens Interferometer Endoscope

6 Optical System Examples Fraunhofer IOF 6 Lithographic lens stop reticle mask Fisheye lens Eyepiece

7 Optical System Examples Fraunhofer IOF 7 Microscope Spectrometer Scan lens

8 Optical System Examples Fraunhofer IOF 8 Zoom system Line generator Auto focus sensor

9 Historical Instruments Ref: University Arizona Museum

10 Historical Instruments Ref: University Arizona Museum

11 Miniature Systems Fiber coupler Variable endoscope Endoscope with prism Mobile phone camera Microscopic lens Spectrometer Ref: IOF, Jena Ref: Leica Ref: GrinTech, Jena Monolithic Miniature- Spectrometer 11 Ref: IMTEK

12 Complete Lithographic Maschine Photomaske (Reticle) Beleuchtungssystem Excimer Laser Reticle Laderoboter Strahlführung Projektionsobjektiv Wafertisch Wafer Laderoboter

13 Lithographic Lens in Reality Ref: Carl Zeiss AG

14 Lithographic Optics EUV a-tool 2008

15 15 Early Data sheets and Calculation of Abbe First Apochromate of Abbe 1886 Data sheet for prototyp production Diffraction theory and meaning of the numerical aperture Ref: B. Dörband / H. Müller

16 16 Speed of Raytrace in Optical Design Development of technological support for raytrace calculations Ref: V. Blahnik

17 17 Surface Contributions: Example 200 Seidel aberrations: representation as sum of surface contributions possible Gives information on correction of a system Example: photographic lens Retrofocus F/2.8 Field: w= S I Spherical Aberratio S II Coma S III Astigmatism S IV Petzval field curvatu S V Distortion C I Axial color Surface Sum C II Lateral color

18 18 Basic Idea of Optimization Topology of the merit function in 2 dimensions Iterative down climbing in the topology topology of meritfunction F start iteration path x 1 x 2

19 19 Nonlinear Optimization Mathematical description of the problem: n variable parameters m target values Jacobi system matrix of derivatives, Influence of a parameter change on the various target values, sensitivity function Scalar merit function Gradient vector of topology x f (x) J i j f x m F( x) w g j i 1 F x j i j i y f ( x) 2 i Hesse matrix of 2nd derivatives H jk 2 F x x j k

20 20 Optimization Merit Function in Optical Design Goal of optimization: Find the system layout which meets the required performance targets according of the specification Formulation of performance criteria must be done for: - Apertur rays - Field points - Wavelengths - Optional several zoom or scan positions Selection of performance criteria depends on the application: - Ray aberrations - Spot diameter - Wavefornt description by Zernike coefficients, rms value - Strehl ratio, Point spread function - Contrast values for selected spatial frequencies - Uniformity of illumination Usual scenario: Number of requirements and targets quite larger than degrees od freedom, Therefore only solution with compromize possible

21 21 Optimization in Optical Design Merit function: Weighted sum of deviations from target values Formulation of target values: 1. fixed numbers 2. one-sided interval (e.g. maximum value) 3. interval g f ist j j f j 1, m soll j 2 Problems: 1. linear dependence of variables 2. internal contradiction of requirements 3. initail value far off from final solution Types of constraints: 1. exact condition (hard requirements) 2. soft constraints: weighted target Finding initial system setup: 1. modification of similar known solution 2. Literature and patents 3. Intuition and experience

22 22 Parameter of Optical Systems Characterization and description of the system delivers free variable parameters of the system: - Radii - Thickness of lenses, air distances - Tilt and decenter - Free diameter of components - Material parameter, refractive indices and dispersion - Aspherical coefficients - Parameter of diffractive components - Coefficients of gradient media General experience: - Radii as parameter very effective - Benefit of thickness and distances only weak - Material parameter can only be changes discrete

23 23 Constraints in Optical Systems Constraints in the optimization of optical systems: 1. Discrete standardized radii (tools, metrology) 2. Total track 3. Discrete choice of glasses 4. Edge thickness of lenses (handling) 5. Center thickness of lenses(stability) 6. Coupling of distances (zoom systems, forced symmetry,...) 7. Focal length, magnification, workling distance 8. Image location, pupil location 9. Avoiding ghost images (no concentric surfaces) 10. Use of given components (vendor catalog, availability, costs)

24 24 Lack of Constraints in Optimization Illustration of not usefull results due to non-sufficient constraints negative edge thickness negative air distance lens thickness to large lens stability to small air space to small

25 25 Boundary Conditions and Constraints Types of constraints 1. Equation, rigid coupling, pick up 2. One-sided limitation, inequality 3. Double-sided limitation, interval Numerical realizations : 1. Lagrange multiplier 2. Penalty function 3. Barriere function 4. Regular variable, soft-constraint F(x) F(x) penalty function P(x) p large barrier function B(x) p large F 0 (x) p small F 0 (x) p small x x x min permitted domain x max permitted domain

26 26 Optimization Landscape of an Achromate Typical merit function of an achromate Three solutions, only two are useful r 2 aperture reduced r 1 good solution

27 27 System Design Phases 1. 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

28 Number of Lenses Approximate number of spots over the field as a function of the number of lenses Linear for small number of lenses. Depends on mono-/polychromatic design and aspherics. Number of spots monochromatic aspherical monochromatic polychromatic Diffraction limited systems with different field size and aperture diameter of field [mm] lenses 14 Number of elements numerical aperture

29 29 Optimization: Starting Point 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 1 f 2 f 3 f 4 f 5 Approach of Shafer AC-surfaces, monochromatic, buried surfaces, aspherics Expert system Experience and genius

30 30 Optimization and Starting Point The initial starting point determines the final result p 2 Only the next located solution without hill-climbing is found D' A' C' B' A B p 1

31 Struc Special Surfaces Action Material Lens Parameters Spherical Aberration Coma Astigmatism Petzval Curvature Distortion 5th Order Spherical Axial Color Lateral Color Secondary Spectrum Spherochromatism 31 Correction Effectiveness Effectiveness of correction features on aberration types Aberration Primary Aberration 5th Chromatic Lens Bending (a) (c) e (f) Makes a good impact. Makes a smaller impact. Makes a negligible impact. Zero influence. Power Splitting Power Combination a c f i j (k) Distances (e) k Stop Position Refractive Index (b) (d) (g) (h) Dispersion (i) (j) (l) Relative Partial Disp. GRIN Cemented Surface b d g h i j l Aplanatic Surface Aspherical Surface Mirror Diffractive Surface Symmetry Principle Field Lens Ref : H. Zügge

32 32 Spherical Aberration: Lens Bending 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=1.5 only for virtual imaging Correction of spherical aberration possible for: 1. 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

33 33 Correcting Spherical Aberration: Lens Splitting 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) : 1/4 Improvement (b)à(c) : 1/2 5 mm (d) Improvement (c)à(d) : 1/ mm (e) Improvement (d)à(e) : 1/75 Ref : H. Zügge

34 34 Sensitivity of a System Representation of wave Seidel coefficients [l] Double Gauss 1.4/50 Ref: H.Zügge surfaces

35 35 Structural Changes for Correction Lens bending Lens splitting Power combinations (a) (b) (c) (d) (e) Distances (a) (b) Ref : H. Zügge

36 36 Lens Removal Removal of a lens by vanishinh of the optical effect For single lens and cemented component Problem of vanishinh index: Generation of higher orders of aberrations a) Geometrical changes: radius and thickness 1) adapt second radius of curvature 2) shrink thickness to zero b) Physical changes: index

37 Aplanatic Surfaces 37 Aplanatic surfaces: zero spherical aberration: 1. Ray through vertex 2. concentric 3. Aplanatic Condition for aplanatic surface: r ns n' s' ss' n n ' n n' s s' Virtual image location Applications: 1. Microscopic objective lens 2. Interferometer objective lens s' s 0 s' s und u u' ns n' s' hyperboloid oblate ellipsoid oblate ellipsoid prolate ellipsoid + power series + power series + power series + power series s' vertex sphere concentric sphere aplanatic S

38 38 Principles of Glass Selection in Optimization Design Rules for glass selection Different design goals: 1. Color correction: index n large dispersion difference desired positive lens field flattening Petzval curvature 2. Field flattening: large index difference + + desired negative lens color correction + - availability of glasses - - dispersion n Ref : H. Zügge

39 39 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 l 2 l 1 l 3

40 40 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

41 41 Petzval Theorem for Field Curvature Petzval theorem for field curvature: 1. formulation for surfaces 2. formulation for thin lenses (in air) Important: no dependence on bending 1 R ptz 1 R ptz n m ' k 1 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

42 42 Flattening Meniscus Lenses Possible lenses / lens groups for correcting field curvature Interesting candidates: thick mensiscus shaped lenses r 2 1 nk ' nk n n ' r Rptz k k k k 1 n f 2 n 1 n d r r 1 2 r 1 d 1. Hoeghs mensicus: identical radii - Petzval sum zero - remaining positive refractive power F' ( n 1) n r 2 2 d 2. Concentric meniscus, - Petzval sum negative - weak negative focal length - refractive power for thickness d: r 2 1 R ptz 1 r d ( n 1) d n r r d 1 1 ( n 1) d F' nr ( r d) Thick meniscus without refractive power Relation between radii r r d n n 1 R ptz n r 1 2 ( n 1) d nr d ( n 1) 1 0

43 Field Curvature 43 Correction of Petzval field curvature in lithographic lens for flat wafer 1 R j F n j j Positive lenses: Green h j large Negative lenses : Blue h j small F j h h j 1 F j Correction principle: certain number of bulges

44 44 Influence of Stop Position on Performance Ray path of chief ray depends on stop position stop positions spot

45 45 Field Lenses Field lens: in or near image planes Influences only the chief ray: pupil shifted Critical: conjugation to image plane, surface errors sharply seen marginal ray chief ray field lens in intermediate image plane lens L 1 lens L 2 shifted pupil original pupil

46 46 Field Lens im Endoscope Ref : H. Zügge

47 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

48 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

49 Medium Magnification Microscopic lenses 49

50 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 6 M 2 M 5 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

51 Modified Workflow in Instrument Development Historical: sequential workflow Modern: complex workflow with feedback and relationships Development Optical Design Tolerancing Development Optical design Tolerancing phys-opt Simulation Mechanical Design Mechanical Design Metrology Manufacturing Assembly Adjustment Manufacturing components Researchlab Performance Check Control of buyed components Integration Adjustment Software Tests

52 Introduction to Tolerancing Specifications are usually defined for the as-built system Optical designer has to develop an error budget that cover all influences on performance degradation as - design imperfections - manufacturing imperfections - integration and adjustment - environmental influences No optical system can be manufactured perfectly (as designed) - Surface quality, scratches, digs, micro roughness - Surface figure (radius, asphericity, slope error, astigamtic contributions, waviness) - Thickness (glass thickness and air distances) - Refractive index (n-value, n-homogeneity, birefringence) - Abbe number - Homogeneity of material (bubbles and inclusions) - Centering (orientation of components, wedge of lenses, angles of prisms, position of components) - Size of components (diameter of lenses, length of prism sides) - Special: gradient media deviations, diffractive elements, segmented surfaces,... Tolerancing and development of alignment concepts are essential parts of the optical design process Ref: K. Uhlendorf 52

53 Data Sheet

54 Tolerances: Typical Values Diameter Tolerance Unit <10 mm mm mm Center thickness mm Centering Tilt angle sek Decenter/offset m Roughness nm Spherical/radius spherical rings astigmatism rings Asphericity Global deviation m Global asphericity m Local deviation m Slope error rad

55 55 Adjustment and Compensation Example Microscopic lens Adjusting: 1. Axial shifting lens : focus 2. Clocking: astigmatism 3. Lateral shifting lens: coma Ideal : Strehl D S = % With tolerances : D S = 0.1 % After adjusting : D S = 99.3 % Ref.: M. Peschka

56 56 Adjustment and Compensation Sucessive steps of improvements Ref.: M. Peschka

57 Drawing of Microscopic Lens with Housing