Lens Design I. Lecture 10: Optimization II Herbert Gross. Summer term

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1 Lens Design I Lecture : Optimization II 8-6- Herbert Gross Summer term 8

2 Preliminary Schedule - Lens Design I 8.4. Basics 9.4. Properties of optical systems I Properties of optical systems II Properties of optical systems III Introduction, Zemax interface, menues, file handling, preferences, Editors, updates, windows, coordinates, System description, 3D geometry, aperture, field, wavelength Diameters, stop and pupil, vignetting, Layouts, Materials, Glass catalogs, Raytrace, Ray fans and sampling, Footprints Types of surfaces, cardinal elements, lens properties, Imaging, magnification, paraxial approximation and modelling, telecentricity, infinity object distance and afocal image, local/global coordinates Component reversal, system insertion, scaling of systems, aspheres, gratings and diffractive surfaces, gradient media, solves Advanced handling I Miscellaneous, fold mirror, universal plot, slider, multiconfiguration, lens catalogs Aberrations I Representation of geometrical aberrations, Spot diagram, Transverse aberration diagrams, Aberration expansions, Primary aberrations Aberrations II Wave aberrations, Zernike polynomials, measurement of quality Aberrations III Point spread function, Optical transfer function Optimization I.6. Optimization II (subs/shift) 8.6. Advanced handling II Principles of nonlinear optimization, Optimization in optical design, general process, optimization in Zemax Initial systems, special issues, sensitivity of variables in optical systems, global optimization methods System merging, ray aiming, moving stop, double pass, IO of data, stock lens matching 5.7. Correction I 3.7. Correction II Symmetry principle, lens bending, correcting spherical aberration, coma, astigmatism, field curvature, chromatical correction Field lenses, stop position influence, retrofocus and telephoto setup, aspheres and higher orders, freeform systems, miscellaneous

3 3 Contents. Initial systems. Special issues 3. Sensitivity of variables in optical systems 4. Global methods

4 4 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 3 f 4 f 5 Approach of Shafer AC-surfaces, monochromatic, buried surfaces, aspherics Expert system Experience and genius

5 5 Optimization and Starting Point The initial starting point determines the final result p Only the next located solution without hill-climbing is found D' A' C' B' A B p

6 6 Initial Conditions Valid for object in infinity:. Total refractive power. Correction of Seidel aberrations. Dichromatic correction of marginal ray axial achromatical. Dichromatic correction of chief ray achromatical lateral magnification.3 Field flattening Petzval.4 Distortion correction according to Berek 3. Tri-chromatical correction Secondary spectrum s F' F' F' F' n M M m M m M m M m m F' P N m n M m m F' nm N F' nm m n nm N n N pm n N pm n F' n nm nm F' nm F' nm nm N PnmF' nm m n nm

7 7 Zero-Operations Operationen with zero changes in first approximation:. Bending a lens.. 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.. Removing a lens without refractive power.. Splitting an element into two lenses which are very close together but with the same total refractive power.. Replacing a thick lens by two thin lenses, which have the same power as the two refracting surfaces. 3. Cementing two lenses a very small distance apart and with nearly equal radii.

8 8 Structural Changes for Correction Lens bending Lens splitting Power combinations (a) (b) (c) (d) (e) Distances (a) (b) Ref : H. Zügge

9 9 Optimization: Discrete Materials Special problem in glass optimization: finite area of definition with discrete parameters n, n Restricted permitted area as one possible contraint Model glass with continuous values of n, in a pre-phase of glass selection, freezing to the next adjacend glass area of permitted glasses in optimization area of available glasses

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

11 Sensitivity of a System Sensitivity/relaxation: Average of weighted surface contributions of all aberrations Sp h Sph -3 Correctability: Average of all total aberration values Total refractive power Kom a Coma k F F F j j j Important weighting factor: ratio of marginal ray heights Ast Ast j h j h CH L 4 3 CHL Inz- Wi 3 incidence angle

12 Sensitivity of a System Quantitative measure for relaxation with normalization A k j j A j j F j F h j h F j F Non-relaxed surfaces:. Large incidence angles. Large ray bending 3. Large surface contributions of aberrations 4. Significant occurence of higher aberration orders 5. Large sensitivity for centering Internal relaxation can not be easily recognized in the total performance Large sensitivities can be avoided by incorporating surface contribution of aberrations into merit function during optimization

13 Sum 3 Sensitivity of a System Double Gauss.4/ Representation of wave Seidel coefficients [l] , ,8 5,6-5,4 -, -5 - surfaces Ref: H.Zügge Verz Sph Koma Ast Petz Verz

14 4 Microscopic Objective Lens Incidence angles for chief and marginal ray marginal ray microscope objective lens Aperture dominant system Primary problem is to correct spherical aberration chief ray incidence angle

15 5 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 6 incidence angle marginal ray

16 6 Correction Effectiveness Effectiveness of correction features on aberration types Aberration Primary Aberration 5th Chromatic Spherical Aberration Coma Astigmatism Petzval Curvature Distortion 5th Order Spherical Axial Color Lateral Color Secondary Spectrum Spherochromatism Lens Parameters Lens Bending (a) (c) e (f) Power Splitting Power Combination a c f i j (k) Distances (e) k Stop Position Makes a good impact. Refractive Index (b) (d) (g) (h) Makes a smaller impact. Makes a negligible impact. Action Material Dispersion (i) (j) (l) Relative Partial Disp. GRIN Zero influence. Special Surfaces Cemented Surface b d g h i j l Aplanatic Surface Aspherical Surface Mirror Diffractive Surface Struc Symmetry Principle Field Lens Ref : H. Zügge

17 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 8 6 monochromatic aspherical monochromatic polychromatic 4 Diffraction limited systems with different field size and aperture diameter of field [mm] lenses 4 Number of elements numerical aperture

8 Global Optimization: Escape method of Isshiki Simulated Annealing: temporarily added term to overcome local minimum F merit function with additive term F(x)+F esc F

18 8 Global Optimization: Escape method of Isshiki Simulated Annealing: temporarily added term to overcome local minimum F merit function with additive term F(x)+F esc F esc ( x) F F ( x) F Optimization and adaptation of annealing parameters e conventional path F esc local minimum x loc global minimum x glo merit function F(x) x =. =. =. 5

19 9 Global Optimization No unique solution reference design : F =.95 solution 5 : F =.66 solution : F =.47 Contraints not sufficient fixed: unwanted lens shapes solution 6 : F =.73 solution : F =.5 Many local minima with nearly the same performance solution : F =. solution 7 : F =.96 solution 3 : F =.53 solution : F =.6 solution 8 : F =.3 solution 4 : F =.59 solution 3 : F =. solution 9 : F =.36 solution 5 : F =.6 solution 4 : F =.6 solution : F =.384 solution 6 : F =.737

20 Saddel Point Method Saddel points in the merit function topology Systematic search of adjacend local minima is possible Exploration of the complete network of local minima via saddelpoints M S M F o

21 Saddel Point Method Example Double Gauss lens of system network with saddelpoints

Lens Design I. Lecture 10: Optimization II Herbert Gross. Summer term

Lens Design I. Lecture 10: Optimization II Herbert Gross. Summer term Lens Design I Lecture : Optimization II 5-6- Herbert Gross Summer term 5 www.iap.uni-jena.de Preliminary Schedule 3.. Basics.. Properties of optical systrems I 3 7.5..5. Properties of optical systrems