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LDI17 Lens Design I 3 Properties of Optical Systems II.Pdf Lens Design I Lecture 3: Properties of optical systems II 2017-04-20 Herbert Gross Summer term 2017 www.iap.uni-jena.de 2 Preliminary Schedule - Lens Design I 2017 Introduction, Zemax interface, menues, file handling, preferences, Editors, updates, 1 06.04. Basics windows, coordinates, System description, 3D geometry, aperture, field, wavelength Diameters, stop and pupil, vignetting, Layouts, Materials, Glass catalogs, Raytrace, 2 13.04. Properties of optical systems I Ray fans and sampling, Footprints Types of surfaces, cardinal elements, lens properties, Imaging, magnification, Properties of optical systems II 3 20.04. paraxial approximation and modelling, telecentricity, infinity object distance and afocal image, local/global coordinates Properties of optical systems III Component reversal, system insertion, scaling of systems, aspheres, gratings and 4 27.04. diffractive surfaces, gradient media, solves 5 04.05. Advanced handling I Miscellaneous, fold mirror, universal plot, slider, multiconfiguration, lens catalogs Representation of geometrical aberrations, Spot diagram, Transverse aberration 6 11.05. Aberrations I diagrams, Aberration expansions, Primary aberrations 7 18.05. Aberrations II Wave aberrations, Zernike polynomials, measurement of quality 8 01.06. Aberrations III Point spread function, Optical transfer function Principles of nonlinear optimization, Optimization in optical design, general process, 9 08.06. Optimization I optimization in Zemax Initial systems, special issues, sensitivity of variables in optical systems, global 10 15.06. Optimization II optimization methods System merging, ray aiming, moving stop, double pass, IO of data, stock lens 11 22.06. Advanced handling II matching Symmetry principle, lens bending, correcting spherical aberration, coma, 12 29.06. Correction I astigmatism, field curvature, chromatical correction Field lenses, stop position influence, retrofocus and telephoto setup, aspheres and 13 06.07. Correction II higher orders, freeform systems, miscellaneous 3 Contents 3rd Lecture 1. Types of surfaces 2. Cardinal elements 3. Lens properties 4. Imaging 5. Special infinity cases 6. Paraxial approximation 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 spherical and conic sections . Even asphere classical asphere . Paraxial ideal lens . Paraxial XY ideal toric lens . Coordinate break change of coordinate system . Diffraction grating line grating . Gradient 1 gradient medium . Toroidal cylindrical lens . Zernike Fringe sag surface as superposition of Zernike functions . Extended polynomial generalized asphere . Black Box Lens hidden system, from vendors . ABCD paraxial segment Cardinal elements of a lens . Focal points: 1. incoming parallel ray intersects the axis in F‘ y 2. ray through F is leaves the lens P' u' F' parallel to the axis f ' focal plane . Principal plane P: location of apparent ray bending principal plane s BFL nodal planes s P' . Nodal points: u' N N' Ray through N goes through N‘ and preserves the direction u Notations of a lens P principal point S vertex of the surface O n n n F focal point 1 2 s intersection point y of a ray with axis N N' F F' u S' u' f focal length PF S P P' y' r radius of surface O' curvature s s' d thickness SS‘ f f' f f' n refrative index BFL BFL sP s'P' a' a d Main properties of a lens . Main notations and properties of a lens: 1 1 - radii of curvature r , r 1 2 c1 c2 curvatures c r1 r2 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 y ' y . Focal length (paraxial) f F , f ' tanu tanu' n n' . Optical power F f f ' . Back focal length intersection length, measured from the vertex point sF' f 'sH ' Lens shape . Different shapes of singlet lenses: 1. 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 negative lens meniscus lens Lens bending und shift of principal plane . Ray path at a lens of constant focal length and different bending R R . Quantitative parameter of description X: X 1 2 R2 R1 . The ray angle inside the lens changes . 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 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' 11 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 12 Limitation of Principal Surface Definition . A r4eal microscopic lens has a nearly perfect spherical shape of the principal surface 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 pupil field O stop . Image field size: point 2 Chief ray chief ray object . Aperture/size of marginal light cone: ray optical system marginal ray axis O1 O'1 defined by pupil stop image O'2 Formulas for surface and lens imaging n' n n'n 1 . Single surface imaging equation s' s r f ' 1 1 1 . Thin lens in air n 1 focal length f ' r1 r2 . Thin lens in air with one plane r surface, focal length f ' n 1 r . Thin symmetrical bi-lens f ' 2n 1 . Thick lens in air 1 1 1 n 12 d n 1 focal length f ' r r nr r 1 2 1 2 Imaging equation s' . Imaging by a lens in air: 4f' lens makers formula real object virtual image real image 1 1 1 real image s' s f 2f' . Magnification s' 2f' 4f' m s s - 4f' -2f' . Real imaging: s < 0 , s' > 0 real object -2f' . Intersection lengths s, s' virtual image virtual object virtual image measured with respective to the principal planes P, P' - 4f' Magnification . Lateral magnification for finite imaging y' f tanu m . Scaling of image size y f 'tanu' principal planes y focal point focal point F P P' F' image object z f f' z' y' s s' Angle Magnification . Afocal systems with object/image in infinity tan w' nh . Definition with field angle w angular magnification tan w n'h' w' w f . Relation with finite-distance magnification m f ' Object or field at infinity . Image in infinity: image - collimated exit ray bundle image at infinity - realized in binoculars eye lens . Object in infinity field lens stop - input ray bundle collimated - realized in telescopes - aperture defined by diameter lens acts as aperture stop not by angle collimated entrance bundle object at infinity image in focal plane 19 Telecentricity . Special stop positions: 1. 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: 1. pupil in infinity 2. chief ray parallel to the optical axis object object sides chief rays telecentric image parallel to the optical axis stop 20 Telecentricity . Double telecentric system: stop in intermediate focus . Realization in lithographic projection systems object lens f1 telecentric lens f2 image stop f1 f2 f1 f2 21 Telecentricity, Infinity Object and Afocal Image 1.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 22 Infinity cases entrance case object image exit pupil example sample layout pupil . Systematic of all 1 finite finite finite finite relay infinity cases infinity 2 finite finite finite image metrology lens telecentric . Physically impossible: infinity infinity lithographic 3 finite finite object image projection lens 1. object and entrance telecentric telecentric 4f-system pupil in infinity afocal zoom 4 infinity infinity finite finite telescopes 2. image and exit beam expander pupil in infinity 5 finite finite infinity finite metrology lens camera lens 6 infinity finite finite finite focussing lens eyepiece 7 finite infinity finite finite collimator infinity 8 finite infinity object finite microscopic lens telecentric infinity infinity metrology 9 infinity finite finite image lens telecentric 10 infinity finite infinity finite impossible 11 finite infinity finite infinity impossible 12 infinity infinity infinity finite impossible 13 infinity finite infinity infinity impossible 14 infinity infinity finite infinity impossible 15 finite infinity infinity infinity impossible 16 infinity infinity infinity infinity impossible 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 Paraxial approximation Paraxial approximation: .
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