Lens Design I. Lecture 2: Properties of optical systems I Herbert Gross. Summer term

Transcription

1 Lens Design I Lecture 2: Properties of optical systems I Herbert Gross Summer term

2 2 Preliminary Schedule Basics Properties of optical systems I Properties of optical systems II Properties of optical systems III Aberrations I 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 Component reversal, system insertion, scaling of systems, aspheres, gratings and diffractive surfaces, gradient media, solves Representation of geometrical aberrations, Spot diagram, Transverse aberration diagrams, Aberration expansions, Primary aberrations, Aberrations II Wave aberrations, Zernike polynomials 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 Optimization II Systematic methods and optimization process, Starting points, Optimization in Zemax Advanced handling I Telecentricity, infinity object distance and afocal image, Local/global coordinates, Add fold mirror, Scale system, Make double pass, Vignetting, Diameter types, Ray aiming, Material index fit Advanced handling II Report graphics, Universal plot, Slider, Visual optimization, IO of data, Multiconfiguration, Fiber coupling, Macro language, Lens catalogs Imaging Fundamentals of Fourier optics, Physical optical image formation, Imaging in Zemax 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 2nd Lecture 1. Diameters 2. Stops and Pupil definition 3. Vignetting 4. Layout 5. Materials and glass catalogs 6. Raytrace 7. Ray fans and sampling 8. Footprints

4 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 object point The coma rays limit the off-axis ray cone The marginal rays limit the axial ray cone stop pupil y object coma ray u aperture angle w field angle marginal ray image y' chief ray

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

6 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

7 Entrance and exit pupil object 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 object exit pupil lower coma ray stop entrance pupil

8 Principal Surface 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'

9 Vignetting 3D-effects due to vignetting Truncation of the at different surfaces for the upper and the lower part of the cone object lens 1 aperture lens 2 image stop upper truncation chief ray lower truncation sagittal trauncation coma rays

10 Vignetting Truncation of the light cone with asymmetric ray path for off-axis field points Intensity decrease towards the edge of the image Definition of the chief ray: ray through energetic centroid free area of the aperture chief ray projection of the rim of the 1st lens meridional coma rays sagittal coma rays Vignetting can be used to avoid uncorrectable coma aberrations in the outer field Projektion der Aperturblende Effective free area with extrem aspect ratio: anamorphic resolution projection of the rim of the 2nd lens

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

12 12 Diameters in Zemax There are several different types of diameters in Zemax: 1. Surface stop - defines the axis intersection of the chief ray - usually no influence on aperture size - only one stop in the system - is indicated in the Lens Data Editor by STO - if the initial aperture is defined, the size of the stop semi-diameter is determined by marginal raytrace

13 13 Diameters in Zemax 2. Userdefined diameter at a surface in the Lens Data Editor (U) - serves also as drawing size in the layout (for nice layouts) - if the diameter in the stop plane is fixed, the initial aperture can be computed automatically by General / Aperture Type / Float by Stop Size This corresponds to a ray aiming 3. Individual diameter of perhaps complicated shape at every surface ( apertures ) - no impact on the drawing - is indicated in the Lens Data Editor by a star - the drawing of vignetted rays can by switched on/off

14 Layout options 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 14

15 Layout options Different options for 3D case Multiconfiguration plot possible Rayfan can be chosen 15

16 Layout options Professional graphic Many layout options Rotation with mouse or arrow buttons 16

17 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, )

18 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

19 Dispersion and Abbe number Description of dispersion: Abbe number n l 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

20 20 Dispersion Material with different dispersion values: - Different slope and 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 F6 flint n small slope large 1.65 crown n large slope small SK18A 1.6 VIS l

21 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 2 2 l 2 2 Fl ( l l o) 2 2 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

22 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 n l 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

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

24 24 Glasses in Zemax Selection of glass catalogs in GENERAL / GLASS CATALOGS Viewing of dispersion curves ANALYSIS / GLASS AND GRADIENT Viewing of glass map

25 25 Glasses in Zemax Viewing of transmission curves also for several glasses in comparison ANALYSIS / GLASS AND GRADIENT Definition of a glass as a variable point in the map (model glass)

26 Glasses in Zemax For optimization Definition of a glass as a variable point in the glass map model glass Establish own glass catalogs with additional glasses preferred choices as an individual library Ref.: B. Böhme 26

27 27 Scheme of raytrace 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' j-1 d s j-1 oblique thickness i j i' j d s j u' j analytically possible: fast d j-1 y j d j computation vertex distance opti axi medium n j-1 medium n j surface r j-1 surface r j

28 28 Vectorial raytrace y j normal vector x j y j+1 intersection point P j e j s j ray intersection point x j+1 General 3D geometry Tilt and decenter of surfaces General shaped free form surfaces surface No j d j distance P j+1 e j+1 surface No j+1 normal vector sj+1 z Full description with 3 components Global and local coordinate systems

29 29 Surfaces in 3D 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 j z F V H j+1 z x j-1

30 30 Raytrace in Zemax Selection of 2 points on the ray on object and entrance pupil plane Real and paraxial rays are tabulated Coordinate reference can be selected to be local or global

31 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 j+1 index j regular negative un-physical irregular axis total internal reflection intersection: - mathematical possible - physical not realized no intersection point axis axis axis

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

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

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

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

36 36 Pupil Sampling Criteria: 1. iso energetic rays 2. good boundary description 3. good spatial resolution polar grid cartesian isoenergetic circular Fibonacci spirals hexagonal statistical pseudo-statistical (Halton)

37 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

38 Footprints Looking for the ray bundle cross ections 38