Optical Design with Zemax for PhD

Size: px

Start display at page:

Download "Optical Design with Zemax for PhD"

Loraine Mathews
5 years ago
Views:

1 Optical Design with Zemax for PhD Lecture 7: Optimization II Herbert Gross Winter term 25

2 2 Preliminary Schedule No Date Subject Detailed content.. Introduction Basic Zemax handling Properties of optical systems Aberrations I Aberrations II PSF, MTF, ESF Zemax interface, menus, file handling, system description, editors, preferences, updates, system reports, coordinate systems, aperture, field, wavelength, layouts, raytrace, diameters, stop and pupil, solves, ray fans, paraxial optics surface types, quick focus, catalogs, vignetting, footprints, system insertion, scaling, component reversal aspheres, gradient media, gratings and diffractive surfaces, special types of surfaces, telecentricity, ray aiming, afocal systems representations, spot, Seidel, transverse aberration curves, Zernike wave aberrations Optimization I algorithms, merit function, variables, pick up s Optimization II methodology, correction process, special requirements, examples Advanced handling Imaging Fourier imaging, geometrical images.2. Correction I simple and medium examples 7.2. Correction II advanced examples slider, universal plot, I/O of data, material index fit, multi configuration, macro language Illumination simple illumination calculations, non-sequential option Physical optical modelling Gaussian beams, POP propagation Tolerancing Sensitivities, Tolerancing, Adjustment

3 3 Contents. Basic principles and strategy 2. Structural changes 3. Bending and splitting 4. Symmetry principle 5. Miscellaneous

4 4 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 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

5 5 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

6 6 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 if the potential of the setup seems to by not improvable, enlarge the number of degrees of freedom

7 7 Strategy of Correction and Optimization If the potential of the setup seems to by not improvable, enlarge the number of degrees of freedom by structural changes of the system Possible options are: add a lens split a lens by distribution of nearly equal ray bending split a lens by decomposing it by a positive and negative part split a lens by decomposing it with two different materials add especially a field lens break a cemented component insert a burried surface make a surface aspherical make a surface free shaped insert a mirror replace a lens by a mirror implement a diffractive surface remove a lens cement two lenses make an asphere spherical

8 Struc Special Surfaces Action Material Lens Parameters Spherical Aberration Coma Astigmatism Petzval Curvature Distortion 5th Order Spherical Axial Color Lateral Color Secondary Spectrum Spherochromatism 8 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

9 9 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 2 f 3 f 4 f 5 Approach of Shafer AC-surfaces, monochromatic, buried surfaces, aspherics Expert system Experience and genius

10 Initial Conditions Valid for object in infinity: Relative height of marginal ray. Total refractive power 2. Correction of Seidel aberrations 2. Dichromatic correction of marginal ray axial achromatical 2.2 Dichromatic correction of chief ray achromatical lateral magnification 2.3 Field flattening Petzval 2.4 Distortion correction according to Berek 3. Tri-chromatical correction Secondary spectrum s j F' F' F' F' n M h h M m M m M m m M m F' P ( MR) j ( MR) N m n M m m F' nm N 2 F' nm m n nm N n N pm n N pm n F' n nm nm F' nm F' nm nm N 2 PnmF' nm m n nm

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 j2 Important weighting factor: ratio of marginal ray heights Ast Ast j h j h CH L CHL Inz- Wi 3 2 incidence angle

12 Relaxed System Example: achromate with cemented/splitted setup Equivalent performance Inner surfaces of splitted version more sensitive a ) Cemented achromate f = mm, NA = surface index Seidel coefficient spherical aberration spot enlargement for.2 surface tilt b ) Splitted achromate f = mm, NA = surface index - -5 Ref: H. Zügge

13 3 As Built Performance Comparison of performance with / without tolerances relaxed / stressed a) cemented Seidel / Dy - wave surface contribution surface 3: tilt.2 b) splitted achromate surface 3: tilt.2 Ref.: H. Zügge

14 4 Zero-Operations Operationen with zero changes in first approximation:. 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.. Removing a lens without refractive power.. Splitting an element into two lenses which are very close together but with the same total refractive power. 2. 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.

15 5 Structural and Smooth Changes for Correction Smooth changes Lens bending Distances Structural changes: Lens splitting (a) (b) Power combinations Ref : H. Zügge (a) (b) (c) (d) (e)

16 6 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 ) adapt second radius of curvature 2) shrink thickness to zero b) Physical changes: index

17 7 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) : /4 Improvement (b)à(c) : /2 5 mm (d) Improvement (c)à(d) : /4.5 mm (e) Improvement (d)à(e) : /75 Ref : H. Zügge

18 8 Principle of Symmetry Perfect symmetrical system: magnification m = - 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 2 3

19 9 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

2 Symmetrical Dublet Variable focal length f = 5.

Type of system changes: - dominant spherical for large f - dominant field for small f Data: f = 2 mm f =

20 2 Symmetrical Dublet Variable focal length f = mm Invariant: object size y = mm numerical aperture NA =. Type of system changes: - dominant spherical for large f - dominant field for small f Data: f = 2 mm f = mm f = 5 mm f = 2 mm No focal length [mm] Length [mm] spherical c 9 field curvature c 4 astigmatism c f = 5 mm

21 2 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=.5 only for virtual imaging Correction of spherical aberration possible for:. Larger values of the magnification parameter M 2. Higher refractive indices Spherical Aberration (a) (b) (c) (d) M= M=-3 M=3 M=-6 M=6 X Ref : H. Zügge

22 22 Correcting Spherical Aberration: Refractive Index Better correction for higher index Shape of lens / best bending changes from. nearly plane convex for n=.5 2. meniscus shape for n > 2 Δs best shape plano-convex 4. n best shape n =.5 n =.7 n =.9 n = 4. plano-convex Ref : H. Zügge

23 23 Astigmatism: Lens Bending Bending effects astigmatism For a single lens 2 bending with zero astigmatism, but remaining field curvature 2 5 Astigmatism Seidel coefficients in [] Surface 2 Sum 5-5 Surface Curvature of surface T S T S S T ST T S Ref : H. Zügge

24 24 Influence of Stop Position on Performance Ray path of chief ray depends on stop position stop positions spot

25 Basic Principles of Glass Selection Positive lenses with anomalous partial dispersion and high : PK5, FK5, FK52, FK54 For monochromatic correction disadvantageous Negative lenses with anomalous partial dispersion andf low : 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

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