Advanced Lens Design
Lecture 13: Mirror systems 2013-01-21 Herbert Gross
Winter term 2013 www.iap.uni-jena.de
2 Preliminary Schedule
Paraxial optics, ideal lenses, optical systems, raytrace, 1 15.10. Introduction Zemax handling Basic principles, paraxial layout, thin lenses, transition to 2 22.10. Optimization I thick lenses, scaling, Delano diagram, bending 3 29.10. Optimization II merit function requirements, effectiveness of variables 4 05.11. Optimization III complex formulations, solves, hard and soft constraints zero operands, lens splitting, aspherization, cementing, lens 5 12.11. Structural modifications addition, lens removal Geometrical aberrations, wave aberrations, PSF, OTF, sine 6 19.11. Aberrations and performance condition, aplanatism, isoplanatism spherical correction with aspheres, Forbes approach, 7 26.11. Aspheres and freeforms distortion correction, freeform surfaces, optimal location of aspheres, several aspheres 8 03.12. Field flattening thick meniscus, plus-minus pairs, field lenses Achromatization, apochromatic correction, dialyt, Schupman 9 10.12. Chromatical correction principle, axial versus transversal, glass selection rules, burried surfaces 10 17.12. Special topics symmetry, sensitivity, anamorphotic lenses high NA systems, broken achromates, Merte surfaces, AC 11 07.01. Higher order aberrations meniscus lenses Advanced optimization local optimization, control of iteration, global approaches, 12 14.01. strategies growing requirements, AC-approach of Shafer 13 21.01. Mirror systems special aspects, bending of ray paths, catadioptric systems color correction, straylight suppression, third order 14 28.01. Diffractive elements aberrations 15 04.02. Tolerancing and adjustment tolerances, procedure, adjustment, compensators 3 Contents
1. General properties 2. Image orientation 3. Telescope systems 4. Further Examples 4 General Properties of Mirror Systems
. Geometry: 1. bending needs the separation of ray bundles 2. 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 2. 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 2. 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 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 2. refractive index negative behind the mirror seems to be unphysical, only formal solution
. For complicated prisms with multiple reflections: tunnel diagram with unfolded reflections
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
2
1 2 3
3
Modelling a Mirror Surface
. Problem in coordinate system based raytracing of mirror systems: right-handed systems becomes left-handed spherical folded mirror . Possible solutions: mirror surface
1. Folding the mirror - light propagation direction changed z-component inverted - tunnel diagram for prism
2. negative refractive index C z
3. inversion of the x-axis F
r f'
P=P'
Transformation of Image Orientation
. Modification of the image orientation with four options: 1. Invariant image orientation 2. Reverted image ( side reversal ) 3. Inverted image ( upside down ) 4. Complete image inversion (inverted-reverted image) y
. Image side reversal in the mirror 1 principal plane of one mirror x
. Inversion for an odd number y - z- folding of reflections plane
. Special case roof prims: y Corresponds to one reflection in the edge plane, z Corresponds to two reflections x perpendicular to the edge plane mirror 2 y
z x
Transformation of Image Orientation
image reversion in the folding plane image (upside down) unchanged
original
image reversion image perpendicular to the folding plane inversion folding plane
Astigmatism of Oblique Mirrors
mirror . Mirror with finite incidence angle: effective focal lengths Rcosi R s f f i tan 2 sag 2cosi
. Mirror introduces astigmatism R C s'sag s2 R sin 2 i s' ast Rcosi R 2cosi s s 2 2cosi focal line L
s'ast s' / R 1 . Parametric behavior of scales astigmatism 0.9 s / R = 2 s / R = 0.6 s / R = 1 0.8
0.7
0.6 s / R = 0.4 0.5
0.4
0.3
0.2
0.1 s / R = 0.2
0 i 0 10 20 30 40 50 60
Telescopic System Types
. Cassegrain . Schmidt M 1 catadioptric
M2 field corrector plate D 2 D1 y
focus r d p a 1 s2 s'2 marginal rays f1 primary mirror . Schiefspiegler, . Maksutow obscuration-free L1 M1 Kutter Tri-Schiefspiegler Buchroeder Tri-Schiefspiegler M1 M1 L2 L3 L4, L5 M2
M2 M2
M3 M3 Ref: F. Blechinger Catadioptric Telescopes
L1 M1 . Maksutov compact
L2 L3 L4, L5 M2
. Klevtsov M1
M2
L1, L2
Schiefspiegler-Telescopes
. Telescopes with tilted elements
. Anastigmatic solution y for two mirrors d 1 1 3 obj d4 d d r r 2 3 2 1 2 object 2 plane 2 r1 2d
4
image
mirror ima d image 5 M2, r2 plane 2 2 mirror y d M1, r1
21
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
Gracing Incidence-Xray Telescope
Woltertyp
1. Paraboloid 2. Hyperboloid
Mangin Mirror
. Principle: Backside mirror, catadioptric lens . Advantages: Mirror can be made spherical F Refractive surface corrects spherical System can be made nearly aplanatic
S S sph, coma corrected
40 spherical 20 coma 0
-20
-40
1/r -0.005 -0.0105 -0.016 1
Mangin Mirror
0.02 . Seidel surface contributions of a real spherical 0 lens: -0.02 Spherical correction perfect 0.01 coma Residual axial chromatic unavoidable 0 -0.01 5
astigmatism 0
-5
5 curvature 0 -5
5
distortion 0
-5 0.02 axial 0 chromatic -0.02 4 lateral 2 0 chromatic -2 -4 1 2 3 sum
Offner-System
object . Concentric system of Offner: r relation 2 M
r1 r1 d1 d2 r2 image 2 d 2 d 1 . Due to symmetry: Perfect correction of field aberrations in third order
0.1 astigmatism 0 -0.1
0.1 curvature 0 -0.1 0.2 distortion 0 -0.2
M11 M2 M12 sum
Dyson-System
. Catadioptric system with m = -1 according Dyson Advantage : flat field Application: lithography and projection . Relation: n 1 r r L n M . Residual aberration : astigmatism y
T S
rL r n M
object
image
mirror z -0.20 -0.10 0
Lithographic Optics
. I-Design
. H-Design
. X-Design
EUV - Mirror System
. System: Only mirrors mask
illumination
source
projection
wafer
Microscope Objective Lens: Catadioptric Lenses
. Catadioptric lenses: 1. Schwarzschild design: first large mirror 2. Newton design: first small mirror
. Advantageous: 1. Large working distance 2. Field flattening
3. Colour correction a) Schwarzschild b) Newton
. Drawback: central obscuration reduces contrast / resolution
Retro Reflecting Systems
a) BK7 . Solution 2 : 10 Double hemisphere Correction with two materials
r2 b) SF59 M
r1
. Combined shells: -1 c) SF59 / TIF6
r1 n 2 r2
-1
n3 r3
n1
Retro Reflecting Systems
. 3. Solution: Offner-setup Only small field angles possible
r
d = r / 2
. 4. Solution: y Gradient-index ball lens Only academic
F z
R
f
Retro Reflecting Systems
. 5. Solution: Lens-mirror-combination r Relation for plano-convex lens : 2
n 1 r r 2 n m rm
Limitation : Field aberrations
20°
15°
10°
5°
0°
Retro Reflecting Systems
r . Special version: ball lens with mirror sph
max r m
. 6. Solution: axicon Useful only on axis 1.
2. 3. incoming collimated beam
Retro Reflecting Systems
ray path . 7. Solution : 1 Corner-cube mirror triangular area 2 plane front surface Two possible hexagonal area realizations : corrugated front 3 surface 1. Only mirror 2. Corner filled with glass
P()/P0 Log P()/P0 0 Material enhances 1 10
backreflection and air -1 0.8 10 n = 1.5 maximum field n = 2 -2 0.6 10
-3 0.4 10 n sin 0.2 10-4 max 3 0 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90