www.iap.uni-jena.de

Advanced Lens Design

Lecture 13: Mirror systems

2013-01-21

Herbert Gross

Winter term 2013

2

Preliminary Schedule

1 15.10. Introduction Paraxial optics, ideal lenses, optical systems, raytrace, Zemax handling

2 22.10. Optimization I Basic principles, paraxial layout, thin lenses, transition to 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

5 12.11. Structural modifications zero operands, lens splitting, aspherization, cementing, lens addition, lens removal

6 19.11. Aberrations and performance Geometrical aberrations, wave aberrations, PSF, OTF, sine condition, aplanatism, isoplanatism

7 26.11. Aspheres and freeforms

spherical correction with aspheres, Forbes approach, distortion correction, freeform surfaces, optimal location of aspheres, several aspheres

8 03.12. Field flattening thick meniscus, plus-minus pairs, field lenses

9 10.12. Chromatical correction

Achromatization, apochromatic correction, dialyt, Schupman principle, axial versus transversal, glass selection rules, burried surfaces

10 17.12. Special topics symmetry, sensitivity, anamorphotic lenses

11 07.01. Higher order aberrations high NA systems, broken achromates, Merte surfaces, AC meniscus lenses

12 14.01. Advanced optimization strategies

local optimization, control of iteration, global approaches, growing requirements, AC-approach of Shafer

13 21.01. Mirror systems special aspects, bending of ray paths, catadioptric systems

14 28.01. Diffractive elements color correction, straylight suppression, third order aberrations

15 04.02. Tolerancing and adjustment tolerances, procedure, adjustment, compensators

1. General properties

2. Image orientation

3. Telescope systems

4. Further Examples

3

Contents

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

4

General Properties of Mirror Systems

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

5

Modelling Problems with Mirrors

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

3

1 2

2

3

Modelling a Mirror Surface

Problem in coordinate system based raytracing of mirror systems:

right-handed systems becomes left-handed

Possible solutions:

1. Folding the mirror

- light propagation direction changed

z-component inverted

- tunnel diagram for prism

2. negative refractive index

3. inversion of the x-axis

r

spherical

mirror

F

f'

zC

P=P'

folded mirror

surface

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)

Image side reversal in the

principal plane of one mirror

Inversion for an odd number

of reflections

Special case roof prims:

Corresponds to one reflection

in the edge plane,

Corresponds to two reflections

perpendicular to the edge plane

y

x

y

x

y

x

mirror 1

mirror 2

y - z- folding

plane

z

z

Transformation of Image Orientation

image reversion in the

folding plane

(upside down)

image

unchanged

image

inversion

original

folding planeimage reversion

perpendicular to the

folding plane

Astigmatism of Oblique Mirrors

Mirror with finite incidence angle:

effective focal lengths

Mirror introduces astigmatism

Parametric behavior of scales astigmatism

2

costan

iRf

i

Rfsag

cos2

i

Rs

iRsi

iRss ast

cos22

coscos2

sin'

22

i0 10 20 30 40 50 60

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

s / R = 0.2

s / R = 0.4

s / R = 0.6

s / R = 1

s / R = 2

s' / R

s'ast

R

focal

line L

i

C

s

s'sag

mirror

primary mirror

focus

corrector plate

y

r

a

marginal rays

field

Telescopic System Types

Cassegrain

Schiefspiegler,

obscuration-free

Ref: F. Blechinger

d1

s'2

M1

M2

p

f1

D1

D2

s2

M1

M2

M3

M1

M2

M3

Kutter Tri-Schiefspiegler Buchroeder Tri-Schiefspiegler

Schmidt

catadioptric

Maksutow

M1

M2

L1

L2L3 L4, L5

Catadioptric Telescopes

Maksutov compact

Klevtsov

M1

M2

L1

L2L3 L4, L5

M1

L1, L2

M2

Telescopes with tilted elements

Anastigmatic solution

for two mirrors

Schiefspiegler-Telescopes

y

y

obj

1

2

3

4

ima

d1

d2 d

3

d4

d5

object

plane

image

plane

mirror

M1, r

1

mirror

M2, r

2

d

image

22

21

dr

rr

21

21

2

2

Xray telescopeWolter type I

Nested shells with gracing incidence

Increase of numerical aperture by several shells

Gracing Incidence-Xray Telescope

detector

hyperboloids Wolter type I

rays

paraboloids

nested cylindrical

shells

towards paraboloid

focus point

Woltertyp

1. Paraboloid

2. Hyperboloid

Gracing Incidence-Xray Telescope

Mangin Mirror

F

Principle:

Backside mirror, catadioptric lens

Advantages:

Mirror can be made spherical

Refractive surface corrects spherical

System can be made nearly aplanatic

-0.005 -0.0105 -0.0161/r

1

Ssph,

Scoma

40

20

0

-20

-40

corrected

coma

spherical

Mangin Mirror

spherical

coma

astigmatism

curvature

distortion

axial

chromatic

lateral

chromatic

-0.02

0

0.02

-0.01

0

0.01

-5

0

5

-5

0

5

-5

0

5

-0.02

0

0.02

1 2 3 sum-4

-2

0

2

4

Seidel surface contributions of a real

lens:

Spherical correction perfect

Residual axial chromatic unavoidable

Offner-System

object

image

M

r2

r1

d1

d2

-0.1

0

0.1

-0.1

0

0.1

-0.2

0

0.2

curvature

astigmatism

distortion

M11

M2 M12

sum

Concentric system of Offner:

relation

Due to symmetry:

Perfect correction of field aberrations in third order

21

212

rr

dd

Dyson-System

T S

y

-0.10 0-0.20zmirror

object

image

rL

nr

M

Catadioptric system with m = -1 according Dyson

Advantage : flat field

Application: lithography and projection

Relation:

Residual aberration : astigmatism

ML rn

nr

1

Lithographic Optics

H-Design

I-Design

X-Design

EUV - Mirror System

projection

illumination

wafer

mask

source

System:

Only mirrors

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

Drawback:

central obscuration reduces

contrast / resolution

a) Schwarzschild b) Newton

Retro Reflecting Systems

r2

r1

M

a) BK7

c) SF59 / TIF6

10

-1

b) SF59

-1

n3

n2

n1

r3

r2

r1

Solution 2 :

Double hemisphere

Correction with two materials

Combined shells:

Retro Reflecting Systems

r

d = r / 2

3. Solution:

Offner-setup

Only small field angles possible

4. Solution:

Gradient-index ball lens

Only academic

f

Fz

y

R

Retro Reflecting Systems

rm

r2

5°

0°

10°

15°

20°

5. Solution:

Lens-mirror-combination

Relation for plano-convex lens :

Limitation :

Field aberrations

rn

nrm2

1

Retro Reflecting Systems

rsph

rm

max

1.

3.2.

incoming

collimated

beam

Special version: ball lens with mirror

6. Solution: axicon

Useful only on axis

Retro Reflecting Systems

triangular area

plane front surface

hexagonal area

corrugated front

surface

2

1

3

ray path

0 10 20 30 40 50 60 70 80 90

0.2

0.4

0.6

0.8

1

air

n = 1.5

n = 2

0 10 20 30 40 50 60 70 80 90

10-4

10-3

10-2

10-1

100

Log P()/P0P()/P0

0

7. Solution :

Corner-cube mirror

Two possible

realizations :

1. Only mirror

2. Corner filled with

glass

Material enhances

backreflection and

maximum field

3sin max

n