Lens Design I. Lecture 3: Properties of optical systems II Herbert Gross. Summer term

Transcription

1 Lens Design I Lecture 3: Properties of optical systems II Herbert Gross Summer term 205

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 3rd Lecture. Types of surfaces 2. Cardinal elements 3. Lens properties 4. Imaging 5. Magnification 6. Paraxial approximation and modelling

4 4 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 Standard Even asphere Paraxial Paraxial XY Coordinate break Diffraction grating Gradient 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

5 Surface properties and settings Setting of surface properties

6 Cardinal elements of a lens Focal points:. incoming parallel ray intersects the axis in F 2. ray through F is leaves the lens parallel to the axis Principal plane P: location of apparent ray bending y principal plane P' f ' u' s BFL F' focal plane nodal planes s P' u N N' u' Nodal points: Ray through N goes through N and preserves the direction

7 Notations of a lens P principal point S vertex of the surface F focal point O n n n 2 s f intersection point of a ray with axis focal length PF y u F S P P' N N' S' u' F' r radius of surface curvature y' O' d thickness SS s f f' s' n refrative index f BFL s P s' P' f' BFL a d a'

8 Main properties of a lens Main notations and properties of a lens: - radii of curvature r, r 2 curvatures c sign: r > 0 : center of curvature is located on the right side - thickness d along the axis - diameter D - index of refraction of lens material n Focal length (paraxial) Optical power Back focal length intersection length, measured from the vertex point c r c 2 r yf ' f, f ' tan u F s n f f s n' f ' F ' ' H ' 2 y tan u'

9 Lens shape Different shapes of singlet lenses:. bi-, symmetric 2. plane convex / concave, one surface plane 3. Meniscus, both surface radii with the same sign Convex: bending outside Concave: hollow surface Principal planes P, P : outside for mesicus shaped lenses P P' P P' P P' P P' P P' P P' bi-convex lens plane-convex lens positive meniscus lens bi-concave lens plane-concave lens negative meniscus lens

10 Lens bending und shift of principal plane Ray path at a lens of constant focal length and different bending Quantitative parameter of description X: The ray angle inside the lens changes X R R 2 R 2 R The ray incidence angles at the surfaces changes strongly The principal planes move For invariant location of P, P the position of the lens moves P P' F' X = -4 X = -2 X = 0 X = +2 X = +4

11 Cardinal Elements in Zemax Found in: Analyze / Rays and spots Cardinal elements of a selected index range (lens or group)

12 Cardinal Points of a Lens Real lenses: The surface with the principal points as apparent ray bending points is a curved shell The ideal principal plane exists only in the paraxial approximation P' s' P'

13 3 Limitation of Principal Surface Definition The principal planes in paraxial optics are defined as the locations of the apparent ray bending of a lens of system In the case of a system with corrected sine conditions, these surfaces are spheres Sine condition and pupil spheres are also limited for off-axis points near to the optical axis For object points far from the axis, the apparent locations are complicated surfaces, which may consist of two branches

14 Optical imaging Optical Image formation: All ray emerging from one object point meet in the perfect image point Region near axis: gaussian imaging ideal, paraxial Image field size: Chief ray field point O 2 chief ray pupil stop Aperture/size of light cone: marginal ray defined by pupil stop object axis marginal ray optical system O O' image O' 2

15 Single surface imaging equation Thin lens in air focal length Thin lens in air with one plane surface, focal length Thin symmetrical bi-lens Thick lens in air focal length ' ' ' ' f r n n s n s n 2 ' r r n f ' n r f 2 ' n r f ' r r n d n r r n f Formulas for surface and lens imaging

16 Imaging equation s' Imaging by a lens in air: lens makers formula s' s f real object real image 4f' 2f' virtual image real image Magnification s m ' s - 4f' -2f' 2f' 4f' s Real imaging: s < 0, s' > 0 Intersection lengths s, s' measured with respective to the principal planes P, P' real object virtual image -2f' virtual object virtual image - 4f'

17 Magnification Lateral magnification for finite imaging Scaling of image size m y' y f tan u f ' tan u' principal planes object y focal point focal point F P P' F' z f f' z' image y' s s'

18 Angle Magnification Afocal systems with object/image in infinity Definition with field angle w angular magnification tan w' tan w nh n' h' w' w Relation with finite-distance magnification m f f '

19 Object or field at infinity Image in infinity: - collimated exit ray bundle - realized in binoculars image image at infinity Object in infinity - input ray bundle collimated - realized in telescopes - aperture defined by diameter not by angle lens acts as aperture stop field lens stop eye lens object at infinity collimated entrance bundle image in focal plane

20 20 Telecentricity Special stop positions:. stop in back focal plane: object sided telecentricity 2. stop in front focal plane: image sided telecentricity 3. stop in intermediate focal plane: both-sided telecentricity Telecentricity:. pupil in infinity 2. chief ray parallel to the optical axis object object sides chief rays parallel to the optical axis telecentric stop image

21 2 Telecentricity Double telecentric system: stop in intermediate focus Realization in lithographic projection systems object lens f telecentric lens f 2 stop image f f f 2 f 2

22 22 Telecentricity, Infinity Object and Afocal Image.Telecentric object space Set in menue General / Aperture Means entrance pupil in infinity Chief ray is forced to by parallel to axis Fixation of stop position is obsolete Object distance must be finite Field cannot be given as angle 2.Infinity distant object Aperture cannot be NA Object size cannot be height Cannot be combined with telecentricity 3.Afocal image location Set in menue General / Aperture Aberrations are considered in the angle domain Allows for a plane wave reference Spot automatically scaled in mrad

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

24 Paraxial approximation Paraxial approximation: ni n' i' Small angles of rays at every surface Small incidence angles allows for a linearization of the law of refraction 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 effects due to transverse finite sized components Serves as a reference for ideal system conditions Is the fundament for many system properties (focal length, principal plane, magnification,...) The sag of optical surfaces (difference in z between vertex plane and real surface intersection point) can be neglected i x 2 All waves are plane of spherical (parabolic) R E( x) E0 e The phase factor of spherical waves is quadratic

25 Paraxial approximation Law of refraction nsin I n' sin I' Taylor expansion 3 5 x x sin x x... 3! 5! Linear formulation of the law of refraction ni n' i' Error of the paraxial approximation i'- I') / I' n' =.9 n' =.7 n' =.5 ni i' I' n' I' nsin i arcsin n' i

26 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 classificationl (aberrations,..) Taylor expansion Geometrical optics (transverse aberrations, wave aberration, distortion,...) with diffraction approximation --> 0 Wave optics (point spread function, OTF,...) Ref: W. Richter

27 Modelling of Optical Systems Five levels of modelling:. 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