Optical Design with Zemax

Transcription

1 Optical Design with Zemax Lecture 1: Introduction Herbert Gross Summer term

2 Lecture data 2 Planned dates: Shift of some days can not be avoided Tuesday, Location: Computerpool, Helmholtzweg 4 Web page on IAP homepage under learning provides slides and exercise Zemax files Content(stype of the lecture: Not: pure Zemax handling But: - optical design with Zemax as tool - understanding of simulation opportunities and limits - learning by doing - mix of theory/principles, presented examples and own exercises - questions and dialog welcome The content is adapted and is changed depending on progress

3 Preliminary time schedule 3

4 Literature on optical design 4 1. Kingslake Lens design fundamentals, SPIE Press, 2010 (x) 2. Mouroulis / McDonald Geometrical Optics and Optical Design, Oxford, 1997 (x) 3. Fischer / Tadic-Galeb Optical System Design, McGraw Hill, 2000 (x) 4. Malacara / Malacara Handbook of Lens Design, Dekker, 1994 (x) 5. Laikin Lens Design, Dekker, 2007 (x) 6. W. Smith Modern Optical Engineering, Graw Hill, 2000 (x) 7. W. Smith Modern lens design, McGraw Hill, 2005 (x) 8. Geary Lens Design with practical Examples, Willmann-Bell, 2002 (x) 9. Gross (Ed.) Handbook of optical systems, Vol 1-5, Wiley, Shannon The art and science of optical design, Cambridge Univ. Press, G. Smith Practical computer-aided lens design, Willman Bell, 1998

5 Contents 5 1. Introduction 2. Zemax interface, menues, file handling, preferences 3. Editors, updates, windows 4. Coordinate systems and notations 5. System description 6. Component reversal, system insertion, scaling 7. Solves and pickups, variables 8. 3D geometry 9. Aperture, field, wavelength 10. Diameters, stop and pupil, vignetting 11. Layouts 12. Glass catalogs 13. Raytrace 14. Ray fans and sampling 15. Footprints

6 Zemax interface There are 4 types of windows in Zemax: 1. Editors for data input: lens data, extra data, multiconfiguration, tolerances 2. Output windows for graphical representation of results Here mostly setting-windowss are supported to optimize the layout 3. Text windows for output in ASCII numerical numbers (can be exported) 4. Dialog boxes for data input, error reports and more There are several files associates with Zemax 1. Data files (.ZMX) 2. Session files (.SES) for system settings (can be de-activated) 3. Glass catalogs, lens catalogs, coating catalogs, BRDF catalogs, macros, images, POP data, refractive index files,... There are in general two working modes of Zemax 1. Sequential raytrace (or partial non-sequencial) 2. Non-sequential

7 Zemax interface Helpful shortcuts: 1. F3 undo 2. F2 edit a cell in the editor 3. cntr A multiconfiguration toggle 4. cntr V variable toggle 5. F6 merit function editor 6. cntr U update 7. shift cntr Q quick focus Window options: 1. several export options 2. fixed aspect ratios 3. clone 4. adding comments or graphics

8 Coordinate systems and sign of quantities Coordinate systems 2D sections: y-z shown y / meridional section tangential plane x / sagittal plane Sign of lengths, radii, angles: z / optical axis - s + s - R 2 + R 1 negative: to the left positive: + R to the right C 2 positive: C to the right negative: C to the left C 1 + angle positive: counterclockwise reference

9 Description of optical systems 9 Interface surfaces - mathematical modelled surfaces - planes, spheres, aspheres, conics, free shaped surfaces, Size of components - thickness and distances along the axis - transversal size,circular diameter, complicated contours Geometry of the setup - special case: rotational symmetry - general case: 3D, tilt angles, offsets and decentrations, needs vectorial approach Materials - refractive indices for all used wavelengths - other properties: absorption, birefringence, nonlinear coefficients, index gradients, Special surfaces - gratings, diffractive elements - arrays, scattering surfaces

10 System model Single step: - surface and transition - parameters: radius, diameter, thickness, refractive index, aspherical constants, conic parameter, decenter, tilt,... diameter D surface medium t / n radius r Complete system: - sequence of surfaces - obect has index 0 - image has index N - tn does not exist Ray path has fixed sequence (N-1)-N thickness index surface index obect plane surfaces image plane 2 3 N-2 N-1 (N) N-2 N-1 N

11 System data tables Menu: Menu: Reports / Prescription data reports / prescription data

12 System data tables

13 System data Necessary data for system calculation: 1. system surfaces with parameters (radius) 2. distances with parameters (length, material) 3. stop surface 4. wavelength(s) 5. aperture 6. field point(s) Optional inputs: 1. finite diameters 2. vignetting factors 3. decenter and tilt 4. coordinate reference 5. weighting factors 6. multi configurations 7....

14 1. Introduction System changes 14 Useful commands for system changes: 1. Scaling (e.g. patents) 2. Insert system with other system file File - Insert Lens 2. Reverse system

15 Surface properties and settings Setting of surface properties surface type additional drawing switches diameter local tilt and decenter operator and sampling for POP coating scattering options

16 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

17 Solves Examples for solves: 1. last radius forces given image aperture 2. 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

18 Solves Open different menus with a right-mouse-click in the corresponding editor cell Solves can be chosen individually Individual data for every surface in this menu

19 3D geometry 19 General input of tilt and decenter: Coordinate break surface Change of coordinate system with lateral translation and 3 rotations angles Direct listing in lens editor Not shown in layout drawing

20 3D geometry 20 Auxiliary menus: 1. Tilt/Decenter element 2. Folding mirror

21 3D geometry 21 Local tilt and decenter of a surface 1. no direct visibility in lens editor only + near surface index 2. input in surface properties 3. with effect on following system surfaces

22 Definition of aperture and field Imaging on axis: circular / rotational symmetry Only spherical aberration and chromatical aberrations Finite field size, obect point off-axis: - chief ray as reference y y p y' p y' - skew ray bundels: coma and distortion - Vignetting, cone of ray bundle not circular symmetric - to distinguish: tangential and sagittal plane O obect plane marginal/rim ray u w entrance pupil chief ray chief ray exit pupil R' AP w' u' image plane O'

23 Aperture definition Quantitative measures of relative opening / size of accepted light cone Numerical aperture NA n F-number sin u' exit pupil image plane F# f ' D EX chief ray Approximation for small apertures: D EX W' U' 1 F# 2 NA marginal ray f'

24 Optical system stop Pupil stop defines: 1. chief ray angle w 2. aperture cone angle u The chief ray gives the center line of the oblique ray cone of an off-axis obect point The coma rays limit the off-axis ray cone The marginal rays limit the axial ray cone stop pupil y obect coma ray u aperture angle w field angle marginal ray image y' chief ray

25 Optical system stop The physical stop defines the aperture cone angle u black box details complicated The real system may be complex?? image obect real system The entrance pupil fixes the acceptance cone in the obect space The exit pupil fixes the acceptance cone in the image space obect u image stop ExP EnP Ref: Julie Bentley

26 Properties of the pupil Relevance of the system pupil : Brightness of the image Transfer of energy Resolution of details Information transfer Image quality Aberrations due to aperture Image perspective Perception of depth Compound systems: matching of pupils is necessary, location and size

27 Entrance and exit pupil obect point on axis lower marginal ray upper marginal ray U chief ray W U' field point of image on axis point of image upper coma ray outer field point of obect exit pupil lower coma ray stop entrance pupil

28 Pupil sphere Generalization of paraxial picture: Principal surface works as effective location of ray bending Paraxial approximation: plane Real systems with corrected sine-condition (aplanatic): principal sphere P effektive surface of ray bending P' y U' f'

29 Pupil sphere Pupil sphere: equidistant sinesampling obect y o entrance pupil exit pupil image y' U sin(u) sin(u') U' z obect y o pupil sphere equidistant sin(u) angle U nonequidistant

30 Aperture data in Zemax Different possible options for specification of the aperture in Zemax: 1. Entrance pupil diameter 2. Image space F# 3. Obect space NA 4. Paraxial working F# 5. Obect cone angle 6. Floating by stop size Stop location: 1. Fixes the chief ray intersection point 2. input not necessary for telecentric obect space 3. is used for aperture determination in case of aiming Special cases: 1. Obect in infinity (NA, cone angle input impossible) 2. Image in infinity (afocal) 3. Obect space telecentric

31 Diameters and stop sizes Determination of one surface as system stop: - Fixes the chief ray intersection point with axis - can be set in surface properties menu - indicated by STO in lens data editor - determines the aperture for the option 'float by stop size' 2. Diameters in lens data editor - indicated U for user defined - only circular shape - effects drawing - effects ray vignetting - can be used to draw 'nice lenses' with overflow of diameter 3. Diameters as surface properties: - effects on rays in drawing (vignetting) - no effect on lens shapes in drawing - also complicated shapes and decenter possible - indicated in lens data editor by a star

32 Diameters and stop sizes Individual aperture sizes for every field point can be set by the vignetting factors of the Field menu - real diameters at surfaces must be set - reduces light cones are drawn in the layout

33 1. Introduction Layout options 33 Graphical control of system and ray path Principal options in Zemax: 1. 2D section for circular symmetry 2. 3D general drawing Several options in settings Zooming with mouse

34 1. Introduction Layout options 34 Different options for 3D case Multiconfiguration plot possible Rayfan can be chosen

35 1. Introduction Layout options 35 Professional graphic Many layout options Rotation with mouse or arrow buttons

36 Optical materials Important types of optical materials: 1. Glasses 2. Crystals 3. Liquids 4. Plastics, cement 5. Gases 6. Metals Optical parameters for characterization of materials 1. Refractive index, spectral resolved n(l) 2. Spectral transmission T(l) 3. Reflectivity R 4. Absorption 5. Anisotropy, index gradient, eigenfluorescence, Important non-optical parameters 1. Thermal expansion coefficient 2. Hardness 3. Chemical properties (resistence, )

37 Test wavelengths l in [nm] Name Color Element UV Hg UV Hg UV Hg UV Hg UV Hg i UV Hg h violett Hg g blau Hg F' blau Cd F blau H e grün Hg d gelb He D gelb Na HeNe-Laser C' rot Cd C rot H r rot He s IR Cä t IR Hg Nd:YAG-Laser

38 Dispersion and Abbe number Description of dispersion: Abbe number nl l Visual range of wavelengths: n n F ' 1 n C' refractive index n 1.8 n e n n e F ' 1 n C' Typical range of glasses n e = SF1 Flint Two fundamental types of glass: Crone glasses: n small, n large Flint glasses n large, n small BK7 Kron l

39 Dispersion Material with different dispersion values: - Different curvature of the dispersion curve - Stronger change of index over wavelength for large dispersion - Inversion of index sequence at the boundaries of the spectrum possible refractive index n F SK18A l

40 Dispersion formulas Schott formula empirical Sellmeier Based on oscillator model Bausch-Lomb empirical Herzberger Based on oscillator model n a + a l + a l + a l + a l + a l o 1 l l n( l) A+ B + C l l l l D E l n( l) A + Bl + Cl l 2 2 Fl ( l l o) l lo a a n ( l) ao+ a1l l l l l 2 mit l m o o 3 o Hartmann Based on oscillator model n( l) a o + a 3 a1 + l a4 a l 5

41 Relative partial dispersion Relative partial dispersion : Change of dispersion slope with l Definition of local slope for selected wavelengths relative to secondary colors P l l 1 2 n l nl n 1 2 F ' n C' Special selections for characteristic ranges of the visible spectrum l = 656 / 1014 nm far IR l = 656 / 852 nm near IR l = 486 / 546 nm blue edge of VIS l = 435 / 486 nm near UV l = 365 / 435 nm far UV n i - g i : 365 nm UV edge g - F g : 435 nm UV edge F - e e : 546 nm d : 588 nm main color F' : 480 nm C' : 644 nm F : 486 nm C : 656 nm 1. secondary color F - C 2. secondary color C - s s : 852 nm IR edge C - t n(l) t : 1014 nm IR edge l

42 Glass diagram Usual representation of glasses: diagram of refractive index vs dispersion n(n) Left to right: Increasing dispersion decreasing Abbe number

43 Glass data sheet Glass: LAFN7 Part 1 LAFN7 Main data Refractive indices l [nm] n Internal transmission data l [nm] i [10 mm] i [25 mm] relative partial dispersion Anomalous partial dispersion n2325,4 2325,4 1, ,0 0,380 0,090 Ps,t 0,2360 Pc,t 0,0174 n d 1,74950 n1970,1 1970,1 1, ,4 0,700 0,410 PC,s 0,4921 Pc,s 0,0078 ne 1,75458 n1529,6 1529,6 1, ,1 0,940 0,850 Pd,C 0,2941 PF,e - 0,0011 n d 34,95 n1060,0 1060,0 1, ,6 0,984 0,960 Pe,d 0,2369 Pg,F - 0,0025 n e 34,72 nt 1014,0 1, ,0 0,998 0,996 Pg,F 0,5825 Pi,g - 0,0093 n F-n C 0,02145 ns 852,1 1, ,0 0,998 0,996 Pi,h 0,9160 n F'-n C' 0, nr 706,5 1, ,0 0,998 0,995 nc 656,3 1, ,0 0,998 0,995 P's,t 0,2329 nc' 643,8 1, ,0 0,998 0,995 P'C',s 0,5311 n632,8 632,8 1, ,1 0,998 0,994 P'd,C' 0,2446 nd 589,3 1, ,0 0,998 0,994 P'e,d 0,2338 nd 587,6 1, ,0 0,993 0,982 P'g,F' 0,5158 ne 546,1 1, ,8 0,986 0,9 65 P'i,h 0,9037 nf 486,1 1, ,0 0,976 0,940 nf' 480,0 1, ,7 0,950 0,880 ng 435,8 1, ,0 0,940 0,850 nh 404,7 1, ,0 0,910 0,780 ni 365,0 1, ,0 0,840 0,650 n3 34,1 334,1 0, ,0 0,690 0,400 n312,6 312,6 0, ,0 0,550 0,220 n296,7 296,7 0, ,0 0,130 0,010 n280,4 280,4 0, ,1 0,000 0,000 n248,3 248,3 0, ,0 0,000 0, ,0 0,000 0,000

44 Glass data sheet Glass: LAFN7 Part 2 Sellmeier dispersion constants Constants of dn/dt Other properties Temperature coefficients dn rel / dt [10-6/K] dn abs / dt [10-6/K] B 1 1, E+00 D 0 7,27E /+70 C [10-6/K] 5,3 [ C] 1060,0 e g 1060,0 e g B 2 2, E -01 D 1 1,31E /+300 C [10-6/K] 6,4-40/ -20 6,00 7,80 9,70 3,70 5,40 7,20 B 3 1, E+00 D 2-3,32E -11 Tg[ C] /+40 6,30 8,30 10,40 4,80 6,70 8,90 C 1 1, E -02 E0 8,88E -07 T10 13,0[ C] /+80 6,50 8,60 10,90 5,30 7,40 9,70 C 2 4, E -02 E1 9,32E -10 T10 7,6[ C] 573 l TK [ C 3 8, E+01 m] 2,48E -01 cp [J/(g K)] 0,000 l [W/(m K)] 0,770 [g/cm 3] 4,38 E[10 3 N/mm 2] 80 0,280 K[10-6 mm 2/N] 1,77 HK0,1/ HG 3 B 0 CR 3 FR 1 SR 53 AR 2,2 PR 4,3

45 Ranges of glass map Crown glasses n n für n e n für n e Flint glasses e e crown glass LaSF n für n e n für n e e e LaK LaF BaSF SF TiSF PSK PK FK BK SK BaLF BaK K TiK SSK KF BaF LLF LF F TiF flint glass n

46 Ranges of glass map - availability Nearly equal area in the glass diagramm with available materials for all vendors No options with Index / dispersion 1. high / high 2. low / low n Schott Ohara n

47 Scheme of raytrace 47 Ray: straight line between two intersection points System: sequence of spherical surfaces Data: - radii, curvature c=1/r - vertex distances - refractive indices - transverse diameter Surfaces of 2nd order: Calculation of intersection points ray u' -1 d s -1 oblique thickness i i' d s u' analytically possible: fast d -1 y d computation vertex distance opti axi medium n -1 medium n surface r -1 surface r

48 Vectorial raytrace 48 y normal vector x y +1 intersection point P e s ray intersection point x +1 General 3D geometry Tilt and decenter of surfaces General shaped free form surfaces surface No d distance P +1 e +1 surface No +1 normal vector s+1 z Full description with 3 components Global and local coordinate systems

49 Surfaces in 3D 49 Single surface: - tilt and decenter before refraction - decenter and tilt after refraction General setup for position and orientation in 3D r' D R F R D r H H V V tilt before y tilt after K H K V y F shift after global coordinates shift before z V V x F surface No z F V H +1 z x -1

50 Restrictions: - surfaces of second order, fast analytical calculation of intersection point possible - homogeneous media Direction unit vector of the straight ray Vector of intersection point on a surface Ray equation with skew thickness d s index of the surface and the space behind Equation of the surface 2.order The coefficients H, F, G contains the surface shape parameters s r x y z 1 1, 1 + s s d r r 0 2 1, 2 1, + s s G F d d H 50 1 Introduction Vectorial raytrace formulas

51 Special case spherical surface with curvature c = 1/R Coefficients H, G, F Unit vector normal to the surface Insertion of the ray equation into surface equation: skew thickness Angle of incidence Refraction or reflection c H z z y x c G z y x c F + + z c y c x c e 1 s G H F F G d , cosi s e cos ' cos i n n i cos ' cos i i 51 1 Introduction Vectorial raytrace formulas

52 Vectorial raytrace formulas 52 Auxiliary parameter New ray direction vector n +1 cos i' n cosi n s+ 1 s + e n n

53 Raytrace errors Vignetting/truncation of ray at finite sized diameter: can or can not considered (optional) No physical intersection point of ray with surface Total internal reflection Negative edge thickness of lenses Negative thickness without mirror-reflection Diffraction at boundaries index +1 index regular negative un-physical irregular axis total internal reflection intersection: - mathematical possible - physical not realized no intersection point axis axis axis

54 Special rays in 3D Meridional rays: in main cross section plane Sagittal rays: perpendicular to main cross section plane sagittal coma ray upper meridional coma ray yp axis Coma rays: Going through field point and edge of pupil Oblique rays: without symmetry meridional marginal ray y field point axis point chief ray axis sagittal ray pupil plane lower meridional coma ray skew ray x p x obect plane

55 Tangential and sagittal plane Off-axis obect point: 1. Meridional plane / tangential plane / main cross section plane contains obect point and optical axis 2. Sagittal plane: perpendicular to meridional plane through obect point y y' x obect plane x' image plane sagittal plane z lens meridional plane

56 Ray fans and ray cones Ray fan: 2-dimensional plane set of rays Ray cone: 3-dimensional filled ray cone obect point pupil grid

57 Ray fan selection for transverse aberrations plots Transverse aberrations: Ray deviation form ideal image point in meridional and sagittal plane respectively The sampling of the pupil is only filled in two perpendicular directions along the axes No information on the performance of rays in the quadrants of the pupil y x tangential ray fan obect point sagittal ray fan pupil

58 Pupil sampling Pupil sampling for calculation of transverse aberrations: all rays from one obect point to all pupil points on x- and y-axis Two planes with 1-dimensional ray fans No complete information: no skew rays obect plane entrance pupil exit pupil image plane y o y p y' p y' tangential x o x p x' p x' z sagittal

59 Sampling of pupil area Pupil sampling in 3D for spot diagram: all rays from one obect point through all pupil points in 2D Light cone completly filled with rays obect plane entrance pupil exit pupil image plane y o y p y' p y' x o x p x' p x' z

60 Pupil sampling Different types of sampling with pro and con s: 1. Polar grid: not isoenergetic 2. Cartesian: good for FFT, boundary discretization bad 3. Isoenergetic circular: good 4. Hexagonal: good 5. Statistical: good non-regularity, holes? polar grid cartesian isoenergetic circular hexagonal statistical

61 Artefacts of pupil sampling Artefacts due to regular gridding of the pupil of the spot in the image plane In reality a smooth density of the spot is true The line structures are discretization effects of the sampling cartesian hexagonal statistical

62 1. Introduction Footprints 62 Looking for the ray bundle cross sections