Lens Design II. Lecture 12: Mirror systems Herbert Gross. Winter term

Transcription

1 Lens Design II Lecture 1: Mirror systems Herbert Gross Winter term 016

2 Preliminary Schedule Aberrations and optimization Repetition Structural modifications Zero operands, lens splitting, lens addition, lens removal, material selection Aspheres Correction with aspheres, Forbes approach, optimal location of aspheres, several aspheres Freeforms Freeform surfaces Field flattening Astigmatism and field curvature, thick meniscus, plus-minus pairs, field lenses Chromatical correction I Achromatization, axial versus transversal, glass selection rules, burried surfaces Chromatical correction II secondary spectrum, apochromatic correction, spherochromatism Special correction topics I Symmetry, wide field systems,stop position Special correction topics II Anamorphotic lenses, telecentricity Higher order aberrations high NA systems, broken achromates, induced aberrations Further topics Sensitivity, scan systems, eyepieces Mirror systems special aspects, double passes, catadioptric systems Zoom systems mechanical compensation, optical compensation Diffractive elements color correction, ray equivalent model, straylight, third order aberrations, manufacturing Realization aspects Tolerancing, adjustment

3 3 Contents 1. General properties. Image orientation 3. Telescope systems 4. Further Examples

4 4 General Properties of Mirror Systems Geometry: 1. bending needs the separation of ray bundles. helps in folding systems to more compact size 3. switches image orientation in the plane of incidence 4. for centered usage of mirros: central obscuration, spider legs for mounting Correction: 1. astigmatism for oblique incidence. no color aberrations 3. positive contribution to Pethval curvature 4. usually more sensitive for off-axis field: coma Miscellaneous: 1. coating is HR, mostly metallic, no ghost images. surface accuracy approximately 4 times more sensitive 3. only option for very large diameter (astronomy) 4. aspherical or freeform shape easier to fabricate 5. preferred as scanning or adaptive component 6. plane bending mirrors often realized as prisms 7. only option for extreme UV due to transmission problems

5 5 Modelling Problems with Mirrors Mirror inverts the system: left handed into right handed coordinate system Vectorial calculation with tensor calculus possible Possible solutions for correct ray tracing: 1. distances negative behind the mirror only obsvious for normal incidence. refractive index negative behind the mirror seems to be unphysical, only formal solution For complicated prisms with multiple reflections: tunnel diagram with unfolded reflections

6 Tunnel Diagram Tunnel diagram: Unfoldung the ray path with invariant sign of the z-component of the optical axis Optical effect of prisms corresponds to plane parallel plates More rigorous model: Exact geometry of various prisms can cause vignetting 1 3 3

7 Modelling a Mirror Surface Problem in coordinate system based raytracing of mirror systems: right-handed systems becomes left-handed Possible solutions: spherical mirror folded mirror surface 1. Folding the mirror - light propagation direction changed z-component inverted - tunnel diagram for prism. negative refractive index 3. inversion of the x-axis C F z r f' P=P'

8 Transformation of Image Orientation Modification of the image orientation with four options: 1. Invariant image orientation. Reverted image ( side reversal ) 3. Inverted image ( upside down ) 4. Complete image inversion y (inverted-reverted image) Image side reversal in the principal plane of one mirror x mirror 1 Inversion for an odd number of reflections y - z- folding plane Special case roof prims: Corresponds to one reflection in the edge plane, Corresponds to two reflections perpendicular to the edge plane mirror y x z y x z

9 Transformation of Image Orientation image reversion in the folding plane (upside down) image unchanged original image reversion perpendicular to the folding plane folding plane image inversion

10 Telescopic System Types Cassegrain M 1 Schmidt catadioptric M corrector plate field D 1 D y focus r d 1 s' p a s marginal rays f 1 primary mirror Schiefspiegler, Maksutow obscuration-free L1 M1 Kutter Tri-Schiefspiegler Buchroeder Tri-Schiefspiegler M1 M1 M L L3 L4, L5 M M M3 M3 Ref: F. Blechinger

11 Catadioptric Telescopes Maksutov compact L1 M1 M L L3 L4, L5 Klevtsov M1 M L1, L

12 1 Avoiding Mirror Obscuration Avoiding the central obscuration in mirror systems Field bias or aperture offset as opportunities Ref.: K. Fuerschbach

13 Astigmatism of Oblique Mirrors Mirror with finite incidence angle: effective focal lengths mirror f tan Rcos i f sag R cos i s i Mirror introduces astigmatism s' ast s R sin i R cos i R cos i s s cos i C focal line L R s' sag s' ast s' / R Parametric behavior of scales astigmatism s / R = s / R = 1 s / R = s / R = s / R = i

14 Non-Axisymmetric Systems: Pilot Axis Ray 14 For an oblique ray, the effective curvatures of the spherical surface depend on azimuth Astigmatism of oblique used curved surfaces In particular large effects in case of mirrors Propagation of curvature components according to Coddington equations n'cos l' tan i' ncos l tan i n'cosi' ncosi R n' l' sag n l sag n'cos i' ncos i R y x y' C x C y surface C y x' z' C x R x R' x R y R' y

15 15 Astigmatism at Curved Mirrors Image surfaces for a concave mirror y : image height s bar : stop position Special cases of flat image shells as a function of the stop position a) stop a center: zero astigmatism b) stop at distance 0.4 R: stop P B T T=0 c) stop at distance C 0.9 R: B = 0 (best plane) R/ d) stop at mirror: S = 0 R s' s' T S y' R y' R a) astigmatism A = 0 b) tangential flat S c) best image flat d) sagittal flat P S B T stop C s R R s R 1 1 P S B T P S B stop T 0.4 R stop C C R R 0.9 R

16 Schiefspiegler-Telescopes Telescopes with tilted elements Anastigmatic solution for two mirrors y d obj r 1 r r 1 d object plane d d 3 d 4 4 image mirror M, r image plane ima d 5 d mirror M 1, r 1 y 1

17 17 Correction of 3D Mirror Systems Problem: oblique incidence on curved mirrors creates macroscopic astigmatism Different solution approaches as tradeoffs between performanbce vs cost/complexity M 1 circular symmetric asphere M pupil freeform M 3 freeform image Setup Correction Drawbacks 1 All spherical Select incidence angles to fulfill Coddington equations, compensation over all mirrors Confocal conic section 3 Centered aspheres 4 Spherical Toric surfaces Perfect on axis, if focal points coincide, rotations optimized to avoid collisions Biased sub-aperture or field, centered surfaces Astigmatism at any surface corrected 5 Freeform All but one surface spherical, one freeform surface compensates all coma and astigmatism 1. only limited solution space (Korsch). coma remains 3. induced aberrations, only small aperture possible 1. Correction offaxis hard. all aspheres is costly 1. astigmatism and coma coupled 1. all non-spherical is costly. coma remains 1. large induced aberrations. Simultaneous resolution and field correction needs freeforms

18 18 Finding of Initial Systems Conic section inital system approach for 4-mirror system - F 1 is common to parabola and hyperbola - F is common to hyperbola and ellipsoid 1 - F 3 is commob to ellipsoid 1 and ellipsoid - image point F 4 is also focal point of ellipsoid Perfect imaging on axis F 3 parabola F F 1 hyperbola F 4 ellipsoid 1 image H. Zhu, Proc. SPIE 97 (014) W1 ellipsoid

19 19 TMA Schiefspiegler vs Freeform Solutions First approach of a corrected obscuration-free three mirror system: - coaxial circular symmetric system - one common optical axis - used for off-axis field part only (field biased approach) - typically: astigmatism corrected with incidence angle in complete system - coupling of astigmatism and coma at every surface (one degree of freedom lost) - overall performance reduced Second approach of a corrected onscuration-free three mirror system: - vertex-centered unobscured three freeform mirrors - low-order correction of freeform surfaces, coma and astigmatism independent corrected - overall performance improved in comparison to first approach K. Thompson, Proc. SPIE 9633 (015)

20 Gracing Incidence-Xray Telescope Xray telescopewolter type I Nested shells with gracing incidence Increase of numerical aperture by several shells paraboloids hyperboloids Wolter type I towards paraboloid focus point rays detector nested cylindrical shells

21 Gracing Incidence-Xray Telescope Woltertyp 1. Paraboloid. Hyperboloid

22 Mangin Mirror Principle: Backside mirror, catadioptric lens Advantages: Mirror can be made spherical Refractive surface corrects spherical System can be made nearly aplanatic F S sph, S coma corrected spherical coma /r 1

23 Mangin Mirror Seidel surface contributions of a real lens: Spherical correction perfect Residual axial chromatic unavoidable spherical coma astigmatism 0-5 curvature distortion 0 axial chromatic lateral chromatic sum

24 Offner-System Concentric system of Offner: relation d 1 d r 1 r object M image r 1 r d d 1 Due to symmetry: Perfect correction of field aberrations in third order 0.1 astigmatism curvature distortion M1 1 M M1 sum

25 Dyson-System Catadioptric system with m = -1 according Dyson Advantage : flat field Application: lithography and projection Relation: r n 1 n L r M Residual aberration : astigmatism y T S r L n r M object image mirror z

26 Lithographic Optics I-Design H-Design X-Design

27 EUV - Mirror System System: Only mirrors mask illumination source projection wafer

28 Microscope Objective Lens: Catadioptric Lenses Catadioptric lenses: 1. Schwarzschild design: first large mirror. Newton design: first small mirror Advantageous: 1. Large working distance. Field flattening 3. Colour correction a) Schwarzschild b) Newton Drawback: central obscuration reduces contrast / resolution

29 Retro Reflecting Systems Solution : Double hemisphere Correction with two materials a) BK7 10 r b) SF59 M r 1 Combined shells: c) SF59 / TIF6-1 r 1 n r -1 n 3 n 1 r 3

30 Retro Reflecting Systems 3. Solution: Offner-setup Only small field angles possible r 4. Solution: Gradient-index ball lens Only academic y d = r / F z R f

31 Retro Reflecting Systems 5. Solution: Lens-mirror-combination Relation for plano-convex lens : r r n n 1 r m r m Limitation : Field aberrations

32 Retro Reflecting Systems Special version: ball lens with mirror r sph max r m 6. Solution: axicon Useful only on axis incoming collimated beam

33 Retro Reflecting Systems 7. Solution : Corner-cube mirror triangular area plane front surface ray path 1 Two possible realizations : 1. Only mirror. Corner filled with glass hexagonal area corrugated front surface 3 Material enhances backreflection and maximum field P()/P air n = 1.5 n = Log P()/P sin max n