Advanced Lens Design

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1 Advanced Lens Design Lecture 4: Optimization III Herbert Gross Winter term

2 2 Preliminary Schedule Introduction Paraxial optics, ideal lenses, optical systems, raytrace, Zemax handling Optimization I Basic principles, paraxial layout, thin lenses, transition to thick lenses, scaling, Delano diagram, bending Optimization II merit function requirements, effectiveness of variables Optimization III complex formulations, solves, hard and soft constraints Structural modifications zero operands, lens splitting, aspherization, cementing, lens addition, lens removal Aberrations and performance Geometrical aberrations, wave aberrations, PSF, OTF, sine condition, aplanatism, isoplanatism Aspheres and freeforms spherical correction with aspheres, Forbes approach, distortion correction, freeform surfaces, optimal location of aspheres, several aspheres Field flattening thick meniscus, plus-minus pairs, field lenses Chromatical correction Achromatization, apochromatic correction, dialyt, Schupman principle, axial versus transversal, glass selection rules, burried surfaces Special topics symmetry, sensitivity, anamorphotic lenses Higher order aberrations high NA systems, broken achromates, Merte surfaces, AC meniscus lenses Advanced optimization local optimization, control of iteration, global approaches, strategies growing requirements, AC-approach of Shafer Mirror systems special aspects, bending of ray paths, catadioptric systems Diffractive elements color correction, straylight suppression, third order aberrations Tolerancing and adjustment tolerances, procedure, adjustment, compensators

3 3 Contents 1. Strategy of correction 2. Glass selection 3. Solves 4. Constraints in optimization

4 4 Strategy of Correction and Optimization Usefull options for accelerating a stagnated optimization: split a lens increase refractive index of positive lenses lower refractive index of negative lenses make surface with large spherical surface contribution aspherical break cemented components use glasses with anomalous partial dispersion kick, if the optimization is captured in a local minimum In general: it is preferred to preserve the achieved (good) result and perform small changes to let the optimization run again, change the weightings if the potential of the setup seems to by not improvable, enlarge the number of degrees of freedom

5 5 Zero-Operations Operationen with zero changes in first approximation: 1. Bending a lens. 2. Flipping a lens into reverse orientation. 3. Flipping a lens group into reverse order. 4. Adding a field lens near the image plane. 5. Inserting a powerless thin or thick meniscus lens. 6. Introducing a thin aspheric plate. 7. Making a surface aspheric with negligible expansion constants. 8. Moving the stop position. 9. Inserting a buried surface for color correction, which does not affect the main wavelength. 10. Removing a lens without refractive power. 11. Splitting an element into two lenses which are very close together but with the same total refractive power. 12. Replacing a thick lens by two thin lenses, which have the same power as the two refracting surfaces. 13. Cementing two lenses a very small distance apart and with nearly equal radii.

6 6 Optimization: Discrete Materials Special problem in glass optimization: finite area of definition with discrete parameters n, n n Restricted permitted area as one possible contraint Model glass with continuous values of n, n in a pre-phase of glass selection, freezing to the next adjacend glass area of permitted glasses in optimization area of available glasses n

7 Basic Principles of Glass Selection Positive lenses with anomalous partial dispersion and high n: PK51, FK51, FK52, FK54 For monochromatic correction disadvantageous Negative lenses with anomalous partial dispersion andf low n: KzFS-glasses High indices for monochromatic correction: LaK, LaSF, LaF expensive, hard to manufacture, disadvantageous for color correction Low refracting glasses for field flattening in negative lenses: TiF, TiSAF expensive, hard to manufacture, disadvantageous for color correction

8 Buried Surface 8 Cemented surface with perfect refrcative index match No impact on monochromatic aberrations Only influence on chromatical aberrations Especially 3-fold cemented components are advantages Can serve as a starting setup for chromatical correction with fulfilled monochromatic correction Special glass combinations with nearly perfect parameters Nr Glas n d n d n d n d 1 SK F SK LF SSK F SK BaF d 1 d 2 d 3

9 9 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

10 10 Glasses in Zemax Selection of glass catalogs in GENERAL / GLASS CATALOGS Viewing of dispersion curves ANALYSIS / GLASS AND GRADIENT Viewing of glass map

11 Glasses in Zemax Selection of glass catalogs in GENERAL / GLASS CATALOGS use your own catalog Viewing of glass properties in ANALYSIS / GLASS AND GRADIENT glass map (zoom in) Ref.: B. Böhme 11

Establish own glass catalogs with additional glasses

12 Glasses in Zemax For optimization Definition of a glass as a variable point in the glass map model glass Establish own glass catalogs with additional glasses preferred choices as an individual library Ref.: B. Böhme 12

Variable Glass in Zemax Modell glass: characterized by index, Abbe number and relative dispersion Individual choice of variables Glass moves in Glass map Restriction of useful area in glass map is

13 Variable Glass in Zemax Modell glass: characterized by index, Abbe number and relative dispersion Individual choice of variables Glass moves in Glass map Restriction of useful area in glass map is desirable (RGLA = regular glass area) Re-substitution of real glass: next neighbor in n-n-diagram Choice of allowed glass catalogs can be controlled in General-menu Other possibility to reset real glasses: direct substitution 13

14 Solves Value of the parameter dependents on other requirement Pickup of radius/thickness: linear dependence on other system parameter Determined to have fixed: - marginal ray height - chief ray angle - marginal ray normal - chief ray normal - aplanatic surface - element power - concentric surface - concentric radius - F number - marginal ray height - chief ray height - edge thickness - optical path difference - position - compensator - center of curvature - pupil position

15 Solves Examples for solves: 1. last radius forces given image aperture 2. get symmetry of system parts 3. multiple used system parts 4. moving lenses with constant system length 5. bending of a lens with constant focal length 6. non-negative edge thickness of a lens 7. bending angle of a mirror (i'=i) 8. decenter/tilt of a component with return

16 Solves Open different menus with a right-mouse-click in the corresponding editor cell Solves can be chosen individually Individual data for every surface in this menu

17 17 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)

18 18 Effect of Constraints on Optimization Effect of constraints x 1 path without constraint 0 local minimum path with constraint constraint x 1 < 0 global minimum initial point x 2

19 Optimization: Constraints x 2 Forbidden solution areas, Restricted range of data Special care at boundaries Selection of solutions F ( x ) h ( x) P j boundary curve h(x) search directions contour of merit function F(x) F ( x) region of constraint g(x) < 0 forbidden area optimum h ( x) x 1 constraint function g(x) feasible range merit function F(x) local minimum solution solution without g(x)- constraint x global minimum x min region of constraint x > 0 x max

20 20 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

21 Penalty Function Analytical function with existing derivative 2 e 2 y y y y 2e y y max max e e Formulation for left- and righthanded case Typical parameter for transition region: e = Advantage: nearly linear in the penalty region gives good convergence P(x) upper limit x max boundary with tolerance intervals lower limit x min e e x-x max/min x max/min

22 22 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

23 23 Constraints Constraints on thickness values and distances maximum center thickness of air MXCA minimum center thickness of air MNCA minimum edge thickness of air MNCA maximum center thickness of glass MXCG minimum center thickness of glass MNCG minimum edge thickness of glass MNCG

Lens Design II. Lecture 2: Structural modifications Herbert Gross. Winter term

Lens Design II. Lecture 2: Structural modifications Herbert Gross. Winter term Lens Design II Lecture 2: Structural modifications 26--26 Herbert Gross Winter term 26 www.iap.uni-jena.de 2 Preliminary Schedule 9.. Aberrations and optimization Repetition 2 26.. Structural modifications