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Medical Photonics Lecture Optical Engineering Medical Photonics Lecture Optical Engineering Lecture 11: Optical Design 2017-01-12 Herbert Gross Winter term 2016 www.iap.uni-jena.de 2 Contents No Subject Ref Date Detailed Content Materials, dispersion, ray picture, geometrical approach, paraxial 1 Introduction Gross 20.10. approximation Ray tracing, matrix approach, aberrations, imaging, Lagrange 2 Geometrical optics Gross 03.11. invariant 3 Components Kempe 10.11. Lenses, micro-optics, mirrors, prisms, gratings Field, aperture, pupil, magnification, infinity cases, lens makers 4 Optical systems Gross 17.11. formula, etendue, vignetting 5 Aberrations Gross 24.11. Introduction, primary aberrations, miscellaneous Basic phenomena, wave optics, interference, diffraction 6 Diffraction Gross 01.12. calculation, point spread function, transfer function 7 Image quality Gross 08.12. Spot, ray aberration curves, PSF and MTF, criteria Human eye, loupe, eyepieces, photographic lenses, zoom lenses, 8 Instruments I Kempe 15.12. telescopes Microscopic systems, micro objectives, illumination, scanning 9 Instruments II Kempe 22.12. microscopes, contrasts Medical optical systems, endoscopes, ophthalmic devices, 10 Instruments III Kempe 05.01. surgical microscopes Aberration correction, system layouts, optimization, realization 11 Optic design Gross 12.01. aspects Notations, fundamental laws, Lambert source, radiative transfer, 12 Photometry Gross 19.01. photometry of optical systems, color theory Light sources, basic systems, quality criteria, nonsequential 13 Illumination systems Gross 26.01. raytrace 14 Metrology Gross 02.02. Measurement of basic parameters, quality measurements 3 Modelling of Optical Systems . Principal purpose of calculations: . Imaging model with levels of refinement Paraxial model System, data of the structure (focal length, magnification, aperture,..) (radii, distances, indices,...) linear approximation Analysis imaging aberration Synthesis Analytical approximation and classification theorie lens design (aberrations,..) Taylor Function, data of properties, expansion quality performance (spot diameter, MTF, Strehl ratio,...) Geometrical optics (transverse aberrations, wave aberration, distortion,...) with approximation diffraction --> 0 Wave optics (point spread function, OTF,...) Ref: W. Richter Classification in Field and Aperture Size . Overview and sorting Log w 100° . Different types of systems Fisheye . Diagram of W. Smith: objective Retrofocus aperture vs field size 50° objective . Spectral properties not concidered Tessar 20° Double- landscape Gauss objective Cooke-triplet objective 10° Petzval- objective Schmidt- 5.0° Cassegrain telescope Schmidt 3-mirror telescope telescope 2.0° Ritchey-Cretien telescope Microscope 1.0° Cassegrain objective telescope 0.5° Paraboloid Diskobjective Achromate telescope 0.2° 0.02 0.05 0.10 0.20 0.50 1.0 Log NA Field-Aperture-Diagram w . Classification of systems with photographic Biogon field and aperture size 40° lithography Braat 1987 36° . Scheme is related to size, correction goals and etendue 32° of the systems Triplet 28° Distagon . Aperture dominated: 24° Disk lenses, microscopy, Sonnar Collimator 20° projection 16° . Field dominated: split double triplet Gauss lithography Projection lenses, 12° 2003 projection camera lenses, projection constant Gauss Petzval etendue 8° Photographic lenses micro micro micro micros- 100x0.9 10x0.4 40x0.6 copy 4° . Spectral widthz as a correction achromat diode collimator disc collimator focussing requirement is missed in this chart 0° 0 0.2 0.4 0.6 0.8 NA Classification: -Lw-Diagram . Throughput as field- Photography aperture product Microscopy . Additional dimension: spectral bandwidth Astronomy Interferometer metrology lens lens Lithography Lw 7 Surface Contributions: Example 200 SI 0 . Seidel aberrations: Spherical Aberration -200 representation as sum of 1000 surface contributions possible SII . Gives information on correction 0 Coma of a system -1000 . Example: photographic lens 2000 SIII 0 Astigmatism -2000 1000 SIV 0 Retrofocus F/2.8 Petzval field curvature Field: w=37° -1000 6000 SV 0 Distortion -6000 5 10 150 3 4 2 CI 1 6 7 8 9 0 Axial color -100 600 CII 0 Lateral color -400 Surface 1 2 3 4 5 6 7 8 9 10 Sum 8 Basic Idea of Optimization . Topology of the merit function in 2 dimensions . Iterative down climbing in the topology start topology of meritfunction F iteration path x1 x2 9 Nonlinear Optimization Mathematical description of the problem: . n variable parameters x . m target values f (x) f . Jacobi system matrix of derivatives, J i Influence of a parameter change on the i j x various target values, j sensitivity function m 2 . Scalar merit function F(x) wi yi f (x) i1 F . Gradient vector of topology g j x j 2 F . Hesse matrix of 2nd derivatives H jk x j x k 10 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) p large penalty p large barrier function function P(x) B(x) p small F (x) F0(x) p 0 small x x permitted domain permitted domain xmin xmax 11 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 12 Optimization in Optical Design . Merit function: 2 Weighted sum of deviations from target values ist soll g j f j f j j1,m . Formulation of target values: 1. fixed numbers 2. one-sided interval (e.g. maximum value) 3. interval . 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 13 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 14 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) 15 Lack of Constraints in Optimization negative edge negative air thickness distance Illustration of not usefull results due to non-sufficient constraints lens stability air space lens thickness to large to small to small 16 Optimization Landscape of an Achromate . Typical merit function of an achromate . Three solutions, only two are useful r2 aperture 2 reduced 3 1 good solution r1 17 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 Number of Lenses . Approximate number of spots Number of spots monochromatic aspherical 12000 over the field as a function of mono- chromatic the number of lenses 10000 poly- Linear for small number of lenses. chromatic 8000 Depends on mono-/polychromatic design and aspherics. 6000 4000 2000 Number of 0 0 2 4 6 8 elements . Diffraction limited systems diameter of field with different field size and [mm] lenses aperture 8 10 12 14 6 8 2 4 6 4 2 numerical 0 aperture 0 0.2 0.4 0.6 0.8 1 19 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 f f f f 1 2 3 4 5 . Approach of Shafer AC-surfaces, monochromatic, buried surfaces, aspherics . Expert system . Experience and genius 20 Optimization and Starting
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