Lens Design I. Lecture 1: Basics Herbert Gross. Summer term

Transcription

1 Lens Design I Lecture 1: Basics Herbert Gross Summer term

2 2 Preliminary Schedule Basics Properties of optical systems I Properties of optical systems II 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 Advanced handling I Miscellaneous, fold mirror, universal plot, slider, multiconfiguration, lens catalogs Aberrations I Representation of geometrical aberrations, Spot diagram, Transverse aberration diagrams, Aberration expansions, Primary aberrations Aberrations II Wave aberrations, Zernike polynomials, measurement of quality Aberrations III Point spread function, Optical transfer function Optimization I Optimization II 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, material index fit, stock lens matching, macro language Correction I 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 3 Contents 1 st Lecture 1. Introduction 2. Zemax interface, menues, file handling, preferences 3. Editors, updates, windows 4. Coordinate systems and notations 5. Aperture, field, wavelength 6. System description 7. 3D geometry

4 4 Modelling of Optical Systems Principal purpose of calculations: Imaging model with levels of refinement System, data of the structure (radii, distances, indices,...) Analysis imaging aberration theorie Synthesis lens design Function, data of properties, quality performance (spot diameter, MTF, Strehl ratio,...) Paraxial model (focal length, magnification, aperture,..) linear approximation Analytical approximation and classification (aberrations,..) Taylor expansion Geometrical optics (transverse aberrations, wave aberration, distortion,...) with diffraction approximation --> 0 Wave optics (point spread function, OTF,...) Ref: W. Richter

5 5 Modelling of Optical Systems Five levels of modelling: 1. Geometrical raytrace with analysis 2. Equivalent geometrical quantities, classification 3. Physical model: complex pupil function 4. Primary physical quantities 5. Secondary physical quantities Blue arrows: conversion of quantities Geometrical raytrace with Snells law Geometrical equivalents classification Physical model Primary physical quantities Secondary physical quantities ray tracing intersection points optical path length reference sphere wave aberration W exponential function of the phase pupil function Kirchhoff integral integration autocorrelation Duffieux integral orthogonal expansion optical transfer function approximation diameter of the spot Zernike coefficients Fourier transform Luneburg integral ( far field ) point spread function (PSF) maximum of the squared amplitude Fourier transform squared amplitude Rayleigh unit equivalence types of aberrations longitudinal aberrations final analysis reference ray in the image space Strehl number approximation threshold value spatial frequency resolution analysis sum of coefficients Marechal approximation sum of squares Marechal approximation rms value integration of spatial frequencies geometrical optical transfer function transverse aberration differen tiation definition single types of aberrations Marechal approximation final analysis reference ray in the image plane full aperture geometrical spot diagramm Fourier transform threshold value spatial frequency approximation spot diameter

6 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 7 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 + j angle positive: counterclockwise reference

8 8 Description of Optical Systems 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

9 9 System Model Single step: - surface and transition - parameters: radius, diameter, thickness, refractive index, aspherical constants, conic parameter, decenter, tilt,... diameter D j surface j medium j t j / n j radius r j Complete system: - sequence of surfaces - object has index 0 - image has index N - tn does not exist Ray path has fixed sequence (N-1)-N thickness index surface index object plane surfaces image plane 2 3 j N-2 N-1 (N) 3... j... N-2 N-1 N

10 System data 10 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....

11 11 Definition of Aperture and Field Imaging on axis: circular / rotational symmetry Only spherical aberration and chromatical aberrations Finite field size, object 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 object plane marginal/rim ray u w entrance pupil chief ray chief ray exit pupil R' AP w' u' image plane O'

12 12 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'

13 13 Important Test Wavelengths 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

14 14 Important Surface Types 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

15 Settings and Environment 15 The settings can be customized in the preferences All the settings can be saved Important: - data file folders - graphics parameters - editor cell size and Text font - preferred fast button functions - colors - language (don t use German!)

16 16 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

17 17 System data tables Menu: Menu: Reports / Prescription data reports / prescription data

18 System data tables 18

19 19 Selection of Wavelengths Setting of wavelengths: - maximum of 24 values - weighting factors allow for spectral modelling - unit is always mm - selection of primary wavelength: paraxial data are based on it

20 20 3D Geometry 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

21 21 3D Geometry Auxiliary menus: 1. Tilt/Decenter element 2. Folding mirror

22 22 3D Geometry 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

23 23 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

24 24 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