Optical Design with Zemax for PhD

Transcription

1 Optical Design with Zemax for PhD Lecture : Physical Optics Herbert Gross Winter term 05

2 Preliminary Schedule No Date Subject Detailed content.. Introduction 0.. 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 Optimiation I algorithms, merit function, variables, pick up s Optimiation II methodology, correction process, special requirements, examples Advanced handling Correction I simple and medium examples 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 3?? Tolerancing Sensitivities, Tolerancing, Adjustment

3 Content Gaussian beams Gauss-Schell beams Non-fundamental modes Propagation methods Numerical issues POP in Zemax POlariation in Zemax Scattering in Zemax

4 Gaussian Beams, Transverse Beam Profile Transverse beam profile is gaussian Beam radius w at 3.5% intensity I( r) I o e r w I(r) / I r / w

5 Gaussian Beams Expansion of the intensity distribution around the waist I(r,) x w() R() w o o o hyperbolic caustic curve asymptotic lines

6 Geometry of Gaussian Beams 4 r / w o 3 asymptotic far field waist o w() / o intensity 3.5 % -4

7 ), ( o T o w r o T o e w P r I 0 ) ( o T w w w o o Gaussian Beams, Definitions and Parameter Paraxial TEM00 fundamental mode Transverse intensity is gaussian Axial isophotes are hyperbolic Beam radius at 3.5% intensity Only independent beam parameter of the set:. waist radius w o. far field divergence angle o 3. Rayleigh range o 4. Wavelength o Relations

8 Transform of Gaussian Beams Diffraction effects are taken into account Geometrical prediction corrected in the waist region No singulare focal point: waist with finite width Focal shift: waist located towards the system, intra focal shift Transform of paraxial beam propagation ' T T T o f T f geometrical limit o / f = 0 ' T / f o / f = 0. o / f = 0. o / f = 0.5 o / f = o / f = T / f

9 Transform of Gaussian Beam Transfer of a Gaussian beam by a paraxial ABCD system starting plane receiving plane w' incoming Gaussian beam R w A C B D R' outgoing Gaussian beam paraxial segment w' w B A B w R R' A B B R w A B R C D B D R w

10 Gaussian Beam Propagation Paraxial transform of a beam Intensity I(x,) P I( r, ) w ( ) r w( ) e intensity I [a.u.] x

11 ) 0, ( c L r r e r r c o L w c o L w M Gauß-Schell Beam: Definition Partial coherent beams:. intensity profile gaussian. Coherence function gaussian Extension of gaussian beams with similar description Additional parameter: lateral coherence length L c Normalied degree of coherence Beam quality depends on coherence Approximate model do characterie multimode beams

12 Gauß-Schell Beams Due to the additional parameter: Waist radius and divergence angle are independent. Fixed divergence: waist radius decreases with growing coherence w / wo / o w / wo Fixed waist radius: divergence angle decreases with growing coherence / o

13 Gauß-Schell Beam Transform Similiar to gaussian beam propagation ' T T o T f T Smooth transition between:. coherent gaussian beam =. incoherent geometrical optic = 0 f s'/f' = 0 geometrical optic 0 < < Gauss- Schell beams = Gaussian beams s / f

14 Hermite Gaussian Modes m = 5 m = 4 m = 3 m = m = m = 0 n = 0 n = n = n = 3 n = 4 n = 5

15 Truncated Gaussian Beams Untruncated gaussian beam: theoretical infinite extension Real world: diameter D = a = 3w with % energy loss acceptable Truncation: diffraction ripple occur, depending on ratio x = a / w o Log A a/w o = a/w o = 0-6 a/w o = a/w o = x

16 Gaussian Beam with Spherical Aberration Focussed Gaussian beam with spherical aberration Asymmetry intra - extra focal depending on sign of spherical aberration Gaussian profile perturbed c 9 = 0 c 9 = 0.5 c 9 = -0.5

17 Solution Methods of the Maxwell Equations Maxwellequations exact/ numerical diffraction integrals st approximation nd approximation spectral methods direct solutions of the PDE finite element method Kirchhoffintegral asymptotic approximation mode expansion finite elements boundary element method Rayleigh- Sommerfeld st kind Fresnel approximation plane wave spectrum finite differences hybrid method BEM + FEM Rayleigh- Sommerfeld nd kind Fraunhofer approximation vector potentials Debye approximation boundary edge wave

18 Wave Optical Coherent Beam Propagation Method Calculation Properties / Applications Kirchhoff diffraction integral Fourier method of i k r r i e E( r ) E( r' ) r r' F AP ' ˆ i v ˆ plane waves EI I ( x') F e FE( x) Split step beam propagation df Wave equation: derivatives approximated E E n ( x, y) ik Ek E no Raytracing Ray line law of refraction Coherent mode expansion Incoherent mode expansion rj rj j s sin i ' j n n' sin i Field expansion into modes n E ) * ( x) c n n( x cn E( x) n( x) dx Intensity expansion into coherent modes n I( x) c n ( x) n Small Fresnel numbers, Numerical computation slow Large Fresnel numbers Fast algorithm Near field Complex boundary geometries Nonlinear effects System components with a aberrations Materials with index profile Smooth intensity profiles Fibers and waveguides Partial coherent sources

19 Sampling of the Diffraction Integral Oscillating exponent : Fourier transform reduces on period Most critical sampling usually at boundary defines number of sampling points Steep phase gradients define the sampling High order aberrations are a problem phase quadratic phase 0 wrapped phase x smallest sampling intervall

20 Sampling of the Diffraction Integral Wave with spherical aberration Real part of the electric field for different values of defocussing Optimal defocussing means minimal slope of the difference between wavefront and reference sphere In optimal defocussing the sampling requirements are strongly reduced The important measure is not the absolut aberration value, but the slope a b Re[ U ] c 9 = = c 9 (6x 4 ) = c 9 (6x 4-6x ) r c = c 9 (6x 4-9x ) r r

21 Propagation by Plane / Spherical Waves Expansion field in simple-to-propagate waves. Spherical waves. Plane waves Huygens principle ik r r ' e E( r') E( r) d r r' x x r x' spectral representation E( r') Fˆ xy e ik Fˆ xy E( r) x' e ikr r e ik E(x) E(x)

22 Fresnel Propagation with Equivalence Transform Kirchhoff diffraction integral in Fresnel approximation Fourier transform: plan wave expansion Equivalent form Curvature removed OO Calculation in spherical coordinates E e ( x') ik M M e e Fˆ E( x) e i ( M ) ( ) ' i M x i v x M x M Fˆ E( x') C a a E( x) e i x' x dx x R<0 x' observation plane R'<0 focus starting plane observation plane R '>0 x''

23 Optimal Conditioning of the Fresnel-Propagator Four different cases of propagation in a caustic Starting plane / final plane inside/outside the focal region Flattening transform only necessary outside focal range R < 0 y outside waist region: strong curvature waist plane inside waist region: weak curvature R > 0 case 4 : O - O case : O - I case : I - I case 4 : O - O case 3 : I - O

24 Sampling and Phase Space Wave front with spherical curvature: large angle interval to be sampled Quasi collimated beam: very small angle interval Phase space consideration: smaller number of sampling points necessary u with curvature plane x x p Du max << f Du max large x s radius of curvaturer

25 Beam Propagation in Zemax Setting of initial beam and sampling parameters

26 Beam Propagation in Zemax Individual control of parameters at every surface Model of calculation:. propagator from surface to surface. estimation of sampling by pilot gaussian beam 3. mostly Fresnel propagator with near-far-selection 4. re-sampling possible 5. polariation, finite transmission,... possible

27 Beam Propagation in Zemax Example: Focussing of a tophat beam with one-sided truncation

28 Polariation in Zemax Model:. definition of a starting polariation. every ray carries a Jones vector of polariation, therefore a spatial variation of polariation is obtained. 3. at any interface, the field is decomposed into s- and p-component in the local system 4. changes of the polariation component due to Fresnel formulas or coatings: - amplitude, diattenuation - phase, retardance Spatial variations of the polariation phase accross the pupil are aberrations, the interference is influenced and Psf, MTF, Strehl,... are changed

29 Starting polariation Polariation influences:. surfaces, by Fresnel formulas or coatings. direct input of Jones matrix surfaces with Polariation in Zemax E J E ' y x im re im re im re im re y x y x E E D i D C i C B i B A i A E E D C B A E E ' '

30 Polariation in Zemax Analysis of system polariation:. pupil map shows the spatial variant polariation ellipse. The transmission fan shows the variation of the transmission with the pupil height 3. the transmission table showes the mean values of every surface

31 Polariation in Zemax Single ray polariation raytrace: detailed numbers of - angles - field components - transmission - reflection at all surfaces

32 Polariation in Zemax Detailed polariation analyses are possible at the individual surfaces by using the coating menue options

33 33 Scattering in Zemax Definition of scattering at every surface in the surface properties of sequential mode Possible options:. Lambertian scattering indicatrix. Gaussian scattering function 3. ABg scattering function 4. BSDF scattering function (table) 5. User defined More complex problems only make sense in the non-sequential mode of Zemax, here also non-optical surfaces (mechanics) can be included Surface and volume scattering possible Optional ray-splitting possible Relative fraction of scattering light can be specified

34 34 Scattering in Zemax Definition of scattering at every surface in the surface properties of non-sequential mode Options:. Scatter model. Surface list for important sampling 3. Bulk scattering parameters

35 35 Scattering in Zemax Definition of scattering at a surface in the non-sequential mode. selection of scatter model. for some models: to be fixed: - fraction of scattering - parameter s - number of scattered rays for ray splitting

36 Scattering Functions in Zemax Surface scattering: Projection of the scattered ray on the surface, difference to the specular ray: x Lambertian scattering: isotropic Gaussian scattering F ( ) BSDF x A F BSDF x s ( x) Ae ABg model scatter BSDF by table F BSDF ( x) A B x g Volume scattering: Angle scattering description by probability P Henyey-Greenstein volume scattering (biological tissue model) Rayleigh scattering P( ) 4 g 3 P( ) cos 4 8 g g cos 3/

37 37 Scattering Tables in Zemax Data file with scattering functions: ABg-data.dat File can be edited

38 38 Scattering Input and Viewing in Zemax Tools / Scatter / ABg Scatter Data Catalogs Specification and definition of scattering parameters for a new ABg-modell function: wavelength, angle, A, B, g Analysis / Scatter viewers / Scatter Function Viewer Graphical representation of the scattering function

39 39 Scattering with Importance Sampling Acceleration of computational speed:. scatter to - option, simple. Importance sampling with energy normaliation Importance sampling: - fixation of a sequence of objects of interest - only desired directins of rays are considered - re-scaling of the considered solid angle - per scattering object a maximum of 6 target spheres can be defined

40 40 Bulk Scattering Definition of bulk scattering at the surface menue Wavelength shift for fluorescence is possible Typically angle scattering is assumed Some DLL-model functions are supported:. Mie. Rayleigh 3. Henyey-Greenstein

41 4 Scattering Example I Simple example: single focussing lens Gaussian scattering characteristic at one surface Geometrical imaging of a bar pattern Image with / without Scattering Scattering must be activated in settings Blurring increases with growing s-value

42 4 Scattering Example II Example from samples with non-sequential mode Important sampling accelerates the calculation

43 43 Scattering Bulk Example Volume scattering example Stokes shift is possible for fluorescence