Advanced Lens Design

Transcription

1 Advanced Lens Design Lecture : Introduction 3--5 Herbert Gross Winter term 3

2 Overview Time: Tuesday, Location: PaPool, Helmholtweg 4 Web page on IAP homepage under learning/materials provides slides, exercises, solutions, inormations Seminar: Exercises and solutions o given problems Time: Tuesday, Location: PaPool, Helmholtweg 4 Mentors: Minyi Zhong and Morit Eßlinger starting date: 3-- Shit o some dates could be possible Written examination, 9

3 3 Literature. ischer/tadic-galeb Optical System Design, McGraw Hill. Malacara/Malacara Handbook o Lens Design, Dekker Laikin Lens Design, Dekker 7 4. Smith Modern Optical Engineering, Graw Hill 5. Geary Lens Design with practical Examples, Willmann-Bell 6. Bentley ield guide to lens desin, SPIE Press, 7. Kinglslake/Johnson Lens Design undamentals, SPIE Press, 8. Gross et. al. Handbook o Optical Systems, Vol 3, Wiley, 6 9. Cox A system o optical design, ocal Press, 967. Slyusarev Aberration and Optical Design Theory, Hilger 984. Smith Practical Computer-Aided Lens Design, Willman Bell 998. Kidger undamental Optical Design, SPIE 3. Kidger Intermediate Optical Design, SPIE 4

4 4 Preliminary Schedule 5.. Introduction Paraxial optics, ideal lenses, optical systems, raytrace, Zemax handling.. Optimiation I Basic principles, paraxial layout, thin lenses, transition to thick lenses, scaling, Delano diagram, bending Optimiation II merit unction requirements, eectiveness o variables Optimiation III complex ormulations, solves, hard and sot constraints 5.. Structural modiications ero operands, lens splitting, aspheriation, cementing, lens addition, lens removal Aberrations and perormance Geometrical aberrations, wave aberrations, PS, OT, sine condition, aplanatism, isoplanatism Aspheres and reeorms spherical correction with aspheres, orbes approach, distortion correction, reeorm suraces, optimal location o aspheres, several aspheres ield lattening thick meniscus, plus-minus pairs, ield lenses 9.. Chromatical correction Achromatiation, apochromatic correction, dialyt, Schupman principle, axial versus transversal, glass selection rules, burried suraces 7.. Special topics symmetry, sensitivity, anamorphotic lenses 7.. Higher order aberrations high NA systems, broken achromates, Merte suraces, AC meniscus lenses 4.. Advanced optimiation local optimiation, control o iteration, global approaches, strategies growing requirements, AC-approach o Shaer 3.. Mirror systems special aspects, bending o ray paths, catadioptric systems Diractive elements color correction, straylight suppression, third order aberrations Tolerancing and adjustment tolerances, procedure, adjustment, compensators

5 5 Contents. Introduction. Paraxial optics 3. Raytrace 4. Optical systems 5. Zemax

6 Modelling o Optical Systems Principal purpose o calculations: Imaging model with levels o reinement System, data o the structure (radii, distances, indices,...) Analysis imaging aberration theorie Synthesis lens design unction, data o properties, quality perormance (spot diameter, MT, Strehl ratio,...) Paraxial model (ocal length, magniication, aperture,..) linear approximation Analytical approximation and classiication (aberrations,..) Taylor expansion Geometrical optics (transverse aberrations, wave aberration, distortion,...) with diraction approximation --> Wave optics (point spread unction, OT,...) Re: W. Richter

7 Single surace imaging equation Thin lens in air ocal length Thin lens in air with one plane surace, ocal length Thin symmetrical bi-lens Thick lens in air ocal length r n n s n s n r r n n r n r r r n d n r r n ormulas or surace and lens imaging

8 Paraxial Approximation Paraxiality is given or small angles relative to the optical axis or all rays Large numerical aperture angle u violates the paraxiality, spherical aberration occurs Large ield angles w violates the paraxiality, coma, astigmatism, distortion, ield curvature occurs

9 Paraxial approximation Paraxial approximation: Small angles o rays at every surace Small incidence angles allows or a lineariation o the law o reraction All optical imaging conditions become linear (Gaussian optics), calculation with ABCD matrix calculus is possible No aberrations occur in optical systems There are no truncation eects due to transverse inite sied components Serves as a reerence or ideal system conditions Is the undament or many system properties (ocal length, principal plane, magniication,...) The sag o optical suraces (dierence in between vertex plane and real surace intersection point) can be neglected All waves are plane o spherical (parabolic) The phase actor o spherical waves is quadratic E( x) E ni n i e i x R

10 Linear Collineation General transorm object - image space General rational transormation with linear expression Describes linear collinear transorm x,y, ---> x,y, Inversion Analog in the image space Inserted in only dimensions ocal lengths rom conditions o = and o = Principal planes 3,, y x,,,,3 j d c y b x a j j j j j 3,, y x,,,3, j d c y b x a j j j j j 3 3, d c y b y d c d c o o 3 3, a c c d d c c b 3 3 3, a c c d d c a c c d a P P ),, (, ),, (, ),, ( y x y x y y x x

11 Linear Collineation inite angles: tan(u) must be taken: Magniication: tan u m tan u ocal length: tan u tan u h y O h Invariant: u N N u ny tan un y tan u P P y O a a

12 Two lenses with distance d ocal length distance o inner ocal points e Sequence o thin lenses close together Sequence o suraces with relative ray heights h j, paraxial Magniication n d e d k k k k k k k r n n h h k k k n n s s s s s s m Multi-Surace Systems

13 ocal length e: tube length Image location Two-Lens System lens lens d e s s e d ) ( ) ( d d d s

14 4 What is Ideal? The notation ideal imaging is not unique Ideal is in any case the location o the image point The geometrical ray paths can be dierent or. paraxial. ideal / linear collineation 3. aplanatic The photometric properties are dierent due to non-equidistant sampling I a perect lens is idealied in a sotware as one surace, there are principal discrepances in the location o the intersection points image point aperture angles ideal system paraxial system object point ideal vertex plane optical axis ellipsoidal mirror

15 Ideal lens Ideal lens - one principal plane P = P Aplanatic lens - principal suraces are spheres - the marginal ray heights in the vortex plane are dierent or larger angles - inconsistencies in the layout drawings P P

16 Matrix ormulation o Paraxial Optics Linear relation o ray transport x x Simple case: ree space propagation ray u Advantages o matrix calculus:. simple calculation o component combinations. Automatic correct signs o properties 3. Easy to implement x x u B x x General case: paraxial segment with matrix ABCD-matrix : x A u C B x x M D u u u ray x A B C D x u

17 Matrix ormulation o Paraxial Optics Linear transer o spation coordinate x and angle u x AxBu u CxDu Matrix representation x A u C B x M D u x u Lateral magniication or u= A x / x m Angle magniication o conjugated planes Reractive power or u= D u / u C u / x Composition o systems M M k M... M M k Determinant, only 3 variables detm ADBC n n

18 8 Scheme o Raytrace Ray: straight line between two intersection points System: sequence o spherical suraces Data: - radii, curvature c=/r - vertex distances - reractive indices - transverse diameter Suraces o nd order: Calculation o intersection points ray u j- d s j- oblique thickness i j i j d s j u j analytically possible: ast d j- y j d j computation vertex distance opti ax medium n j- medium n j surace r j- surace r j

19 Raytrace errors Vignetting/truncation o ray at inite sied diameter: can or can not considered (optional) No physical intersection point o ray with surace Total internal relection Negative edge thickness o lenses Negative thickness without mirror-relection Diraction at boundaries index j+ index j regular negative un-physical irregular axis total internal relection intersection: - mathematical possible - physical not realied no intersection point axis axis axis

20 Deinition o ield o View and Aperture Imaging on axis: circular / rotational symmetry Only spherical aberration and chromatical aberrations inite ield sie, object point o-axis: - chie ray as reerence y y p y p y - skew ray bundels: coma and distortion - Vignetting, cone o ray bundle not circular symmetric - to distinguish: tangential and sagittal plane O object plane marginal/rim ray u w entrance pupil chie ray chie ray exit pupil R AP w u image plane O

21 Sag o a Surace Sag at height y or a spherical surace: y parabola r r Paraxial approximation: quadratic term y p r y height y p = y /(r) sag sphere axis

22 Pupil Sampling Pupil sampling in 3D or spot diagram: all rays rom one object point through all pupil points in D Light cone completly illed with rays object plane entrance pupil exit pupil image plane y o y p y p y x o x p x p x

23 3 Pupil Sampling Pupil sampling or calculation o tranverse aberrations: all rays rom one object point to all pupil points on x- and y-axis Two planes with -dimensional ray ans No complete inormation: 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 sagittal

24 Pupil Sampling Ray plots Spot sagittal ray an tangential aberration Dy sagittal aberration Dx diagrams x p x p tangential ray an Dy y p whole pupil area

25 5 Entrance and Exit Pupil object point on axis lower marginal ray upper marginal ray U chie ray W U ield point o image on axis point o image upper coma ray outer ield point o object exit pupil lower coma ray stop entrance pupil

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

27 Coordinate systems and sign o quantities Coordinate systems D sections: y- shown y / meridional section tangential plane x / sagittal plane Sign o lengths, radii, angles: / optical axis - s + s - R + R negative: to the let positive: + R to the right C positive: C to the right negative: C to the let C j angle positive: counterclockwise reerence

28 System model Single step: - surace and transition - parameters: radius, diameter, thickness, reractive index, aspherical constants, conic parameter, decenter, tilt,... diameter D j surace j medium j t j / n j radius r j Complete system: - sequence o suraces - object has index - image has index N - tn does not exist Ray path has ixed sequence (N-)-N thickness index surace index object plane suraces image plane 3 j N- N- (N) 3... j... N- N- N

29 Layout options Graphical control o system and ray path Principal options in Zemax:. D section or circular symmetry. 3D general drawing Several options in settings Zooming with mouse 9

30 3 Multi Coniguration Multi coniguration editor Establishment o dierent system paths or conigurations Toggle between conigurations with CNTR A Examples:. Zoom systems, lenses moved. Scan systems, mirror rotated 3. Switchable optics, components considered / not taken into account 4. Intererometer, test and reerence arm 5. Camera with dierent object distances 6. Microscope tube system or several objective lenses In the multi coniguration editor, the parameters / dierences must be deined Many output options and the optimiation can take all conigurations into account Special option: showallconiguration in the 3D layout drawing simultaneously. shited, or comparison. with same reerence, overlayed

31 3 Multi Coniguration Demonstrational example: Twyman-Green intererometer

32 3 Wave Aberations in Zemax OPD along x- and y-direction or all ields and colors Wave surace or one wavelength and ield point Change o Wrms value with. wavelength. ield 3. deocus 4. ield position

33 PS in Zemax Only ar ield model (raunhoer) Two dierent algorithms available:. T-based - ast - equidistant exit pupil sampling assumed - high resolution PS needs many points. elementary integration (Huygens) - slow (N 4 ) - independence o pupil and image sampling - valid also or calculation o pupil distortion - gives correct Strehl number Dierent options or representation possible 33

34 PS in Zemax Logarithmic representation 34

35 OT in Zemax Various options:. T based calculation. representation as a unction o - ield sie - deocus 3. Huygens PS integral based 4. geometrical approximation via spot calculation or not diraction limited systems Dierent representation settings: - maximun spatial requency - volume relie - MT / PT - changes over the ield sie 35

36 OT in Zemax Various MT representations 36