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

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1 Lens Design I Lecture : Optimization II 5-6- Herbert Gross Summer term 5

2 Preliminary Schedule 3.. Basics.. Properties of optical systrems I Properties of optical systrems II Properties of optical systrems III 5.5. Advanced handling I Aberrations I 7.6. Aberrations II Wave aberrations, Zernike polynomials 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 Add fold mirror, scale system, slider, multiconfiguration, universal plot, diameter types, lens catalogs Representation of geometrical aberrations, Spot diagram, Transverse aberration diagrams, Aberration expansions, Primary aberrations Aberrations III Point spread function, Optical transfer function Optimization I Principles of nonlinear optimization, Optimization in optical design, Global optimization methods, Solves and pickups, variables, Sensitivity of variables in optical systems.6. Optimization II Systematic methods and optimization process, Starting points, Optimization in Zemax 9.6. Imaging Fundamentals of Fourier optics, Physical optical image formation, Imaging in Zemax 6.7. Correction I Correction II Symmetry principle, Lens bending, Correcting spherical aberration, Coma, stop position, Astigmatism, Field flattening, Chromatical correction, Retrofocus and telephoto setup, Design method Field lenses, Stop position influence, Aspheres and higher orders, Principles of glass selection, Sensitivity of a system correction

3 3 Contents. Initial systems. Systematic optimization process 3. Sensitivity of variables in optical systems. Miscellaneous

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

5 5 System Design Phases. 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. 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. Check of higher order aberrations 5. Final correction, fine tuning of compromise 6. Tolerancing, manufactability, cost, sensitivity, adjustment concepts

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. Distortion correction according to Berek 3. Tri-chromatical correction Secondary spectrum s n M M m M m M m M m m P N m n M m m N m n N n N pm n N pm n n N P m n

7 7 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

8 8 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.. 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.

9 9 Structural Changes for Correction Lens bending Lens splitting Power combinations (a) (b) (c) (d) (e) Distances (a) (b) Ref : H. Zügge

10 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 3 CHL Inz- Wi 3 incidence angle

11 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. 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

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

13 3 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

14 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

15 Struc Special Surfaces Action Material Lens Parameters Spherical Aberration Coma Astigmatism Petzval Curvature Distortion 5th Order Spherical Axial Color Lateral Color Secondary Spectrum Spherochromatism 5 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

16 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 Diffraction limited systems with different field size and aperture diameter of field [mm] 6 8 lenses Number of elements numerical aperture

Color correction: index n large dispersion difference desired positive lens field

17 7 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

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 8-6- Herbert Gross Summer term 8 www.iap.uni-jena.de Preliminary Schedule - Lens Design I 8.4. Basics 9.4. Properties of optical systems I 3 6.4. Properties of optical