Lens Design I Lecture 4: Properties of optical systems III 018-05-03 Herbert Gross Summer term 018 www.iap.uni-jena.de
Preliminary Schedule - Lens Design I 018 1 1.04. Basics 19.04. Properties of optical systems I 3 6.04. Properties of optical systems II 4 03.05. 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 5 17.05. Advanced handling I Miscellaneous, fold mirror, universal plot, slider, multiconfiguration, lens catalogs 6 4.05. Aberrations I Representation of geometrical aberrations, Spot diagram, Transverse aberration diagrams, Aberration expansions, Primary aberrations 7 31.05. Aberrations II Wave aberrations, Zernike polynomials, measurement of quality 8 07.06. Aberrations III Point spread function, Optical transfer function 9 14.06. Optimization I 10 1.06. Optimization II (subs/shift) 11 8.06. 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 1 05.07. Correction I 13 1.07. 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 Contents Lecture 1. Solves. System changes 3. Aspheres 4. Gratings and diffractive surfaces 5. Gradient media
4 Modifications and System Setups System changes: Tilt/Decenter Elements Reverse Elements Scale Lens Make Focal Add Fold Mirror Delete Double Pass Local to Global Global to Local Convert Semi-Diameters to Circular Apertures Convert Semi-Diameters to Floating Apertures Convert Semi-Diameters to Maximum Apertures Remove All Apertures Replace Vignetting With Apertures
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
Solves Examples for solves: 1. last radius forces given image aperture. 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
Solves Open different menus with a click in the corresponding editor cell Solves can be chosen individually Individual data for every surface in this menu
8 Aspherical Correction Correction of spherical aberration by an asphere a) spherical lens refraction too strong b) aspherical lens asphere reduces power Ref: A. Herkommer
9 Conic sections Explicite surface equation, resolved to z Parameters: curvature c = 1 / R conic parameter Influence of on the surface shape cx y 1 c x z 1 1 y Parameter Surface shape = - 1 paraboloid < - 1 hyperboloid = 0 sphere > 0 oblate ellipsoid (disc) 0 > > - 1 prolate ellipsoid (cigar ) Relations with axis lengths a,b of conic sections a b 1 c b a b 1 c 1 a c 1 1
Aspherical shape of conic sections Conic aspherical surface Variation of the conical parameter z cy 1 c 1 1 y 1 0.8 0.6 0.4 z 0. 0-1 -0.8-0.6-0.4-0. 0 0. 0.4 0.6 0.8 1 y
Parabolic mirror Equation c : curvature 1/R s : eccentricity ( = -1 ) z cy 1 1 (1 ) y c y y C F z ray R sag vertex circle sagittal circle of curvature tangential circle of curvature R tan vertex circle R s parabolic mirror F y z x R radii of curvature : tan Rs 1 y R s parabolic mirror R tan Rs 1 R s y R s f 3
Ellipsoid mirror Equation c: curvature 1/R : Eccentricity e z cy 1 1 (1 ) y c b oblate vertex radius Rso F prolate vertex radius R sp a F' ellipsoid
Sag of a surface Sag z at height y for a spherical surface: y parabola z r r Paraxial approximation: quadratic term y z p r y height y z p = y /(r) z sag sphere axis z
Polynomial Aspherical Surface Standard rotational-symmetric description 14 Basic form of a conic section superimposed by a Taylor expansion of z cr z(r) 1 1 1 cr M m0 a r r... radial distance to optical axis r x y m m4 z(r) r 4 r 6 r 8 r 10 r 1 r 14 r 16 c a m curvature conic constant aapherical coefficients r Ref: K. Uhlendorf
Surface properties and settings Setting of surface properties
16 Important Surface Types Special surface types Data in Lens Data Editor or in Extra Data Editor Gradient media are descriped as 'special surfaces' Diffractive / micro structured surfaces described by simple ray tracing model in one order Standard Even asphere Paraxial Paraxial XY Coordinate break Diffraction grating Gradient 1 Toroidal Zernike Fringe sag Extended polynomial Black Box Lens ABCD spherical and conic sections classical asphere ideal lens ideal toric lens change of coordinate system line grating gradient medium cylindrical lens surface as superposition of Zernike functions generalized asphere hidden system, from vendors paraxial segment
17 Surface Analysis in Zemax Analysis of surfaces
18 Surface Analysis in Zemax Analysis of surface sag
19 Surface Analysis in Zemax Analysis of surface curvature
0 Surface Analysis in Zemax Analysis of freeform surfaces
Grating Diffraction Maximum intensity: constructive interference of the contributions of all periods grating Grating equation g sin sin m o grating constant g in-phase + 1. diffraction order s = incident light
Ideale diffraction grating Ideal diffraction grating: monochromatic incident collimated beam is decomposed into discrete sharp diffraction orders Constructive interference of the contributions of all periodic cells grating +4. +3. diffraction orders +. Only two orders for sinusoidal +1. incident collimated light 0. -1. -. g = 1 / s grating constant -3. -4.
Finite width of real grating orders Interference function of a finite number N of periods Finite width of every order depends on N Sharp order direction only in the limit of g N sin sin I g sin sin sin 1 / 4g N N N = 5 N = 15 N = 50 1 1 1 0.9 0.9 0.9 0.8 0.8 0.8 0.7 0.7 0.7 0.6 0.6 0.6 0.5 0.5 0.5 0.4 0.4 0.4 0.3 0.3 0.3 0. 0. 0. 0.1 0.1 0.1 0-30 -0-10 0 10 0 30 0-30 -0-10 0 10 0 30 0-30 -0-10 0 10 0 30
Diffractive Elements Original lens height profile h(x) Wrapping of the lens profile: h red (x) reduction on maximal height h Digitalization of the reduced profile: h q (x) z h 3 h h h(x) : continuous profile 1 h h red (x) : wrapped reduced profile h q (x) : quantized profile
5 Diffracting surfaces Surface with grating structure: new ray direction follows the grating equation Local approximation in the case of space-varying grating width s' n s n' mg gˆ e n' d Raytrace only into one desired diffraction order Notations: g : unit vector perpendicular to grooves d : local grating width m : diffraction order e : unit normal vector of surface s e g p p grooves s Applications: - diffractive elements - line gratings d - holographic components
6 Diffracting surfaces Local micro-structured surface Location of ray bending : macroscopic carrier surface Direction of ray bending : local grating micro-structure Independent degrees of freedom: 1. shape of substrate determines the point of the ray bending. local grating constant determines the direction of the bended ray lens local grating g(x,y) thin layer bending angle macroscopic surface curvature m-th order
7 Diffractive Surfaces in Zemax Diffraction grating Classical grating with straight lines Parameters: LP/mm, diffraction order Substrate can be curved, lines are straight in the local coordinate system on the surface Elliptical grating 1: Similar, but grooves can be curved for projection onto x-y-plane, Substrate can be aspheric Elliptical grating : Similar to 1, but curved lines defined by intersection of planes with asphere Binary1 Substrate rotational symmetric asphere Phase of binary element: extended polynomial, scaled on normalization radius in radiant
8 Diffractive Surfaces in Zemax Binary Similare to 1, but phase only circular symmetric Binary3 Substrate and phase circular symmetric Two different data sets on two ring zones Binary4 Similar to 3, but several zones possible
9 Diffractive Surfaces in Zemax Diffraction grating Classical grating with straight lines Parameters: LP/mm, diffraction order Substrate can be curved, lines are straight in the local coordinate system on the surface Elliptical grating 1: Similar, but grooves can be curved for projection onto x-y-plane, Substrate can be aspheric Elliptical grating : Similar to 1, but curved lines defined by intersection of planes with asphere Binary1 Substrate rotational symmetric asphere Phase of binary element: extended polynomial, scaled on normalization radius in radiant
30 Diffractive Surfaces in Zemax Radial grating Grating with circular symmetry and a line spacing, which changes over the radius Variable line space grating Straight lines but unevenly separated Hologram 1 Hologram Toroidal hologram Optically fabricated hologram Defined by corresponding lens systems to generate the interference with residual aberrations Toroidal grating Cylindrical surface with usual line grating structure Extended toroidal grating
31 Raytracing in GRIN media Ray: in general curved line Numerical solution of Eikonal equation Step-based Runge-Kutta algorithm 4th order expansion, adaptive step width Large computational times necessary for high accuracy d r dt n n D n n x n n y n n z y x Brechzahl : n(x,y,z) b b y' c s c s x' Strahl
3 Description of GRIN media Analytical description of grin media by Taylor expansions of the function n(x,y,z) Separation of coordinates nn c o, c 1 hc 10 xc h 11 x c 3 c Circular symmetry, nested expansion with mixed terms nn c o, z Circular symmetry only radial 1 h 1 4 c x 3 4 h c 6 13 c 5 yc h 14 8 c y 6 c zc 4 6 8 4 6 8 ch c3h c4h zc5c 6h c7h c8h c9h 4 6 8 3 4 6 8 c c h c h c h c h z c c h c h c h c h h 10 11 1 13 4 6 8 n n o, 1 c ( c 1 h) c 3 ( c 1 h) c 4 ( c 1 h) c 5 ( c 1 h) c 6 ( c 1 h) 14 15 16 15 y 7 3 z 17 c 8 z 3 c 18 9 z 4 19 10 Only axial gradients 4 6 n n o, 1 c ( c 1 z ) c 3 ( c 1 z ) c 4 ( c 1 z ) c 5 ( c 1 z ) 8 Circular symmetry, separated, wavelength dependent 4 6 8 nn c h c h c h c h c z c z c z o, 1,, 3, 4, 5, 6, 7, 3
Gradient Lens Types Curved ray path in inhomogeneous media Different types of profiles y n entrance (y) n exit (y) radial gradient rod lens axial gradient rod lens radial and axial gradient rod lens n i n o z n(x,y,z) radial gradient lens axial gradient lens radial and axial gradient lens
Collecting radial selfoc lens F L F' Thick Wood lens with parabolic index profile Principal planes at 1/3 and /3 of thickness P P' L n( r) n n r 0 n > 0 : collecting lens n < 0 : negative lens F' P P'
Gradient Lenses y marginal Types of lenses with parabolic profile n( r) n 0 n 0 n 1 r 1 n Ar 0 1 n r r y coma Pitch length 0.5 Pitch Object at infinity p n0 n n r 0.50 Pitch Object at front surface 0.75 Pitch Object at infinity 1.0 Pitch Object at front surface Pitch 0.5 0.50 0.75 1.0
36 Description of Grin Media in Zemax Gradient 1 Gradient Gradient 3 Gradient 4 Gradient 5 Gradient 6 with dispersion Gradient 7 spherical shells
37 Description of Grin Media in Zemax GRADIUM Gradient 9 iso-index lines as z-surfaces Gradient 10 Grid gradient
38 Description of Grin Media in Zemax Gradient 1 Gradient Gradient 3 Gradient 4 Gradient 5 Gradient 6 with dispersion Gradient 7 spherical shells
39 Description of Grin Media in Zemax GRADIUM Gradient 9 iso-index lines as z-surfaces Gradient 10 Grid gradient