Design and Correction of optical Sstems Part 5: Properties of Optical Sstems Summer term 2012 Herbert Gross
Overview 2 1. Basics 2012-04-18 2. Materials 2012-04-25 3. Components 2012-05-02 4. Paraxial optics 2012-05-09 5. Properties of optical sstems 2012-05-16 6. Photometr 2012-05-23 7. Geometrical aberrations 2012-05-30 8. Wave optical aberrations 2012-06-06 9. Fourier optical image formation 2012-06-13 10. Performance criteria 1 2012-06-20 11. Performance criteria 2 2012-06-27 12. Measurement of sstem qualit 2012-07-04 13. Correction of aberrations 1 2012-07-11 14. Optical sstem classification 2012-07-18 2012-04-18
Contents Part 5 3 5.1 Pupil - basic notations - special ras - ra sets - pupil - vignetting 5.2 Canonical coordinates - normalized properties - pupil sphere - aplanatic imaging sstems 5.3 Special imaging setups - telecentricit - anamorphotic imaging - Scheimpflug condition - measurement basic sstem parameters 5.4 Delano diagram - basic idea -examples
Definition Field of View and Aperture 4 Imaging on axis: circular / rotational smmetr onl spherical aberration and chromatical aberrations Finite field size, object point off-axis: - chief ra as reference - skew ra bundles: coma and distortion - Vignetting, cone of ra bundle not circular smmetric - to distinguish: tangential and sagittal plane
Special Ras 5 Marginal ra : connects the center of the object field and the rim of the pupil Chief ra : connects the outer point of the field of view and the center of the pupil Coma ras: connects the rim of the object field and the rim of the pupil
Size of Aperture 6 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 ra Approximation for small apertures: D EX W' U' 1 F # 2 NA marginal ra f'
Special Ras in 3D 7 Meridional ras: in main cross section plane Sagittal ras: perpendicular to main cross section plane sagittal coma ra upper meridional coma ra p axis Coma ras: Going through field point and edge of pupil Oblique ras: without smmetr meridional marginal ra field point axis point chief ra axis sagittal ra pupil plane lower meridional coma ra skew ra x p x object plane
Tangential- and Sagittal Plane 8 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 ' x object plane x' image plane sagittal plane z lens meridional plane
Ra-Fan Selection for Transverse Aberration Plots 9 Transverse aberrations: Ra deviation form ideal image point in meridional and sagittal plane respectivel The sampling of the pupil is onl filled in two perpendicular directions along the axes No information on the performance of ras in the quadrants of the pupil x tangential ra fan object point sagittal ra fan pupil
Ra Fan and Ra Cone 10 Ra fan: 2-dimensional plane set of ras Ra cone: 3-dimensional filled ra cone object point pupil grid
Pupil Sampling 11 Pupil sampling in 3D for spot diagram: all ras from one object point through all pupil points in 2D Light cone completl filled with ras
Pupil Sampling 12 Pupil sampling for calculation of tranverse aberrations: all ras from one object point to all pupil points on x- and -axis Two planes with 1-dimensional ra fans No complete information: no skew ras
Pupil Sampling 13
Pupil Sampling Spot Artefacts 14 Artefacts due to regular gridding of the pupil of the spot in the image plane In realit a smooth densit of the spot is true The line structures are discretization effects of the sampling
Diaphragm in Optical Sstems 15 Pupil stop defines: 1. chief ra angle w 2. aperture cone angle u The chief ra gives the center line of the oblique ra cone of an off-axis object point The coma ras limit the off-axis ra cone The marginal ras limit the axial ra cone stop pupil object coma ra u aperture angle w field angle marginal ra image ' chief ra
Diaphragm in Optical Sstems 16 The phsical stop defines the aperture cone angle u The real sstem ma be complex The entrance pupil fixes the acceptance cone in the object space The exit pupil fixes the acceptance cone in the image space Ref: Julie Bentle
Properties of the Pupil 17 Relevance of the sstem pupil : Brightness of the image Transfer of energ Resolution of details Information transfer Image qualit Aberrations due to aperture Image perspective Perception of depth Compound sstems: matching of pupils is necessar, location and size
Entrance and Exit Pupil 18 object point on axis lower marginal ra upper marginal ra U chief ra W U' field point of image on axis point of image upper coma ra outer field point of object exit pupil lower coma ra stop entrance pupil
Nested Ra Path 19 Optical Image formation: Sequence of pupil and image planes Matching of location and size of image planes necessar (trivial) Matching of location and size of pupils necessar for invariance of energ densit In microscop known as Köhler illumination
20 Pupil Mismatch Telescopic observation with different f-numbers Bad match of pupil location: ke hole effect
Vignetting 21 field Artificial vignetting: Truncation of the free area of the aperture light cone stop truncation D 0.8 D axis truncation Natural Vignetting: Decrease of brightness according to cos w 4 due to oblique projection of areas and changed photometric distances imaging with vignetting A Exp imaging without vignetting imaging with vignetting field angle w complete field of view
Vignetting 22 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 ra lower truncation sagittal trauncation coma ras
Vignetting 23 Truncation of the light cone with asmmetric ra path for off-axis field points Intensit decrease towards the edge of the image Definition of the chief ra: ra through energetic centroid free area of the aperture chief ra projection of the rim of the 1st lens meridional coma ras sagittal coma ras 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
Centroid Ra 24 Ideal chief ra concept: - breaks down in case of complicated beam truncation - there is no longer a clear and simple unique pupil plane Possible criteria: 1. midpoint of ras in meridional section 2. location of largest sagittal section 3. centroid of area of the free pupil Phsical relevant is the energ centroid This is a general definition and still works in 3D limiting apertures meridional plane center of gravit tangential aperture sagittal aperture
25 Vignetting Photographic lens 100mm f/2 1. with strong vignetting ras aimed to boundaries 2. Without vignetting no reall transmitted ras shown Ref: V. Paruchuru
Vignetting 26 Illumination fall off in the image due to vignetting at the field boundar
Pupil Sphere 27 Generalization of paraxial picture: Principal surface works as effective location of ra bending Paraxial approximation: plane Real sstems with corrected sine-condition (aplanatic): principal sphere
Pupil Sphere 28 Pupil sphere: equidistant sinesampling
Canonical Coordinates 29 Aplanatic sstem: Sine condition fulfilled Pupil has spherical shape Normalized canonical coordinates for pupil and field x p x h p EP n sin u x x x' p x' x' h' p EP n' sin u' x'
30 Canonical Coordinates Definition of canonical coordinates of an oblique ra bundle p upper tangential coma ra upper tangential coma ra ' p ' O' h TCU Q chief ra h' TCU Q' R EX U' CR U' TCL R EN h TCL chief ra h' TCL O U TCU U CR U TCL EN lower tangential coma ra lower tangential coma ra EX
Canonical Coordinates 31 Normalized pupil coordinates x p x h p EP x' p x' h' p EP Aplanatic imaging x' p x p Normalized field coordinates x n sin x x' n' sin' x' Paraxial imaging Reference on chied ra Reduced image side coordinates x' x NA nsin u n x nsin sag x sin sin TKO n sin HS sin tan HS
Telecentricit 32 Special stop positions: 1. stop in back focal plane: object sided telecentricit 2. stop in front focal plane: image sided telecentricit 3. stop in intermediate focal plane: both-sided telecentricit Telecentricit: 1. pupil in infinit 2. chief ra parallel to the optical axis object object sides chief ras parallel to the optical axis telecentric stop image
Telecentricit 33 Double telecentric sstem: stop in intermediate focus Realization in lithographic projection sstems
Anamorphotic Imaging Setup 34 Anamorphotic imaging: different magnifications in x- and -cross section, tangential and sagittal magnification Identical image location in both sections Anamorphotic factor clindrical lens 1 clindrical lens 2 n1 u t nk u n1 u s n u k F anamoph t,1 t, k s,1 s, k s t u t u s
Anamorphotic Imaging Setup 35 Realization of an anamorphotic imaging with clindrical lenses x f f x ' x'
Curved Object Surface 36 Object surface is spherical bended with radius R: image is bended b R Paraxial approximation: 2 depth transfer magnification gives 2R Notice: R and R are bended with the same orientation, This behavior is opposite to the curved image in the Petzval picture z z' m z 2 R' R m z image surface R' R ' object surface z'
37 Scheimpflug Imaging Imaging with tilted object plane If principal plane, object and image plane meet in a common point: Scheimpflug condition, sharp imaging possible Scheimpflug equation s s' tantan tan' tan
Scheimpflug Imaging 38 Derivation of Scheimpflug imaging condition with depth magnification z' m z 2 2 ' o 2 ' d P P' z o F' ' o ' s s' z'
Scheimpflug Imaging 39 General propert: - Magnification depends on location in the object plane - anamorphotic magnification - corresponds to macroscopic kestone distortion V sin cos ' f ' ' s x ' s s ' 1 ' sin sin ' s ' 1 ' sin 2 sin Imaging Relation h h' tan' tan ' s' s d ' s s' Objekt Bild
40 Scheimpflug Imaging Example for oblique imaging with Scheimpflug condition Sharp image Strong distortion
Scheimpflug Imaging 41 Kestone distortion real ideal
Measurement of Focal Length with Collimator 42 Collimated incident light Calibrated collimator with focal length f c and test chart with size Selection of sharp image plane Analsis of image size f ' f ' c ' f' c f' ' test chart collimator test optic image
43 Measurement of Focal Length According to Gauss Setup with distance object-image L > 4f Known location of the principal plane P of the sstem distance d P between principal planes Selection of two sstem locations with sharp image Relative axial shift D between the two setups f L d 4 H 4 2 D L d H d P P P' F F' position 1 s' s f f' D F F' position 2 L P P'
Measurement of Focal Length with Focometer 44 Telecentric movable measurement microscope with offset : Abbe focometer Focusing of two different test charts with sizes 1 and 2 Determination of the focal length b tan f e 2 1 u
Measurement of Focal Length b Confocal Setup 45 Setup with fiber and plane mirror for autocollimation Change of distance between test lens and fiber Analsis of the recoupled power into the fiber (confocal) gives the focal point
Delano Diagram 46 Special representation of ra bundles in optical sstems: marginal ra height MR vs. chief ra height CR Delano digram gives useful insight into sstem laout Ever z-position in the sstem corresponds to a point on the line of the diagram Interpretation needs experience lens at pupil position field lens in the focal plane collimator lens marginal ra lens field lens collimator chief ra
Delano Diagram 47 Pupil locations: intersection points with -axis exit pupil Field planes/object/image: intersectioin points with -bar axis Pupillenlagen stop and entrance pupil lens object plane image plane Construction of focal points b parallel lines to initial and final line through origin front focal point F image space object space rear focal point F'
Delano Diagram 48 Influence of lenses: diagram line bended weak negative refractive power weak positive refractive power strong positive refractive power Location of principal planes principal plane P object space image space P
Delano Diagram 49 Conjugated point are located on a straight line through the origin conjugate line conjugate line with m = 1 Distance of a sstem point from origin gives the sstems half diameter conjugate points principal point object space image space curve of the sstem lens 1 lens 2 maximum height of the coma ra at lens 2 lens 3 D/2
Delano Diagram Examples 50 Afocal Kepler-tpe telecope lens 1 objective intermediate focal point lens 2 eepiece Effect of a field lens lens 1 objective intermediate focal point field lens lens 2 eepiece
Delano Diagram Example 51 Microscopic sstem microscope objective aperture stop tube lens telecentric object intermediate image image at infinit exit pupil eepiece
Summar of Important Topics 52 Chief ra and marginal ra define the field size and the aperture size of a sstem Special ra sets are defined to exhaust the light cone The aperture gives the light cone angle The pupil gives the light flux through a sstem In a real sstem the phsical stop, the object space and the image space pupil must be distinguished Vignetting is a partial blocking of outer ras for off-axis field points and obliques cones Apalantic corrected sstems have a spherical shaped pupil Canonical coordinate help to describe sstems in a normalized wa Telecentric sstem have a stop in a focal plane and a axis-parallel chief ra The Scheimpflug-condition allows a sharp imaging for tilted object planes Scheimpflug setups suffer from large distortion The measurement of basic sstem parameters is mainl based on the imaging equation The Delano diagram is defined b a chief-ra vs marginal ra height The Delano diagram helps in understanding complicated combined sstems
Outlook 53 Next lecture: Part 6 Photometr Date: Wednesda, 2012-05-23 Contents: 6.1 Basic notations 6.2 Lambertian radiator 6.3 Flux calculation 6.4 Light transport in optical sstems 6.5 Further modeling