www.iap.uni-jena.de

Lens Design II

Lecture 13: Zoom systems

2017-01-18

Herbert Gross

Winter term 2016

2

Preliminary Schedule

1 19.10. Aberrations and optimization Repetition

2 26.10. Structural modifications Zero operands, lens splitting, lens addition, lens removal, material selection

3 02.11. Aspheres Correction with aspheres, Forbes approach, optimal location of aspheres, several aspheres

4 09.11. Freeforms Freeform surfaces

5 16.11. Field flattening Astigmatism and field curvature, thick meniscus, plus-minus pairs, field lenses

6 23.11. Chromatical correction I Achromatization, axial versus transversal, glass selection rules, burried surfaces

7 30.11. Chromatical correction II secondary spectrum, apochromatic correction, spherochromatism

8 07.12. Special correction topics I Symmetry, wide field systems,stop position

9 14.12. Special correction topics II Anamorphotic lenses, telecentricity

10 21.12. Higher order aberrations high NA systems, broken achromates, induced aberrations

11 04.01. Further topics Sensitivity, scan systems, eyepieces

12 11.01. Mirror systems special aspects, double passes, catadioptric systems

13 18.01. Zoom systems mechanical compensation, optical compensation

14 25.01. Diffractive elements color correction, ray equivalent model, straylight, third order aberrations, manufacturing

15 01.02. Realization aspects Tolerancing, adjustment

1. Introduction

2. Calculation

3. Further aspects

4. Examples

3

Contents

Zoom Systems

Motivation for zooming:

Enlargement of image details

Foveated imaging

Adaptation of field of view

Basic Principle

Two thin lenses in a certain distance t:

Focal length

Refractive power

Kinds of zoom systems

tff

fff

21

21

2121 FFtFFF

221 FFF

1

22

h

h

c) Infinite-infinite (I-I)

b) Infinite-finite (I-F)

a) Finite-finite (F-F)

Change of Focal Length

Distance t increased

First lens fixed

moved

lenschanged

distance

t changed focal

length f

Change of Focal Length

Distance t increased

Image plane fixed

two lenses moved

t f

image

plane

Two Solutions

Paraxial matrix formulation:

Two states of the system,

Invariant image position s

Quadratic equation for s:

always two solutions with

m' = 1/m

zA

C D

B

x x'

object

planeimage

plane

u u'

s s'

zoom system

.''

''' const

DsC

BsA

DCs

BAss

DCs

BAs

Du

xC

Bu

xA

DuCx

BuAx

u

xs

'

''

Principle of Smallest Change of Total Track

Zoom factor : ratio of magnification change

Equivalent : ratio of focal lengths

Zoom system :

- change of magnification

- constant length

mmfL

12

min

max

m

mM

min

max

f

fM

min

max

M

-4 -3 -2 -1 0 1 2 3 4-10

-5

0

5

10

m

L/f

Mechanical Compensated Zoom Systems

Simple explanation of variator and compensator

Movement of variator arbitrary

Compensator movement

depends on variator

Perfect invariance of

image plane possible

objective

lens

variator

linear

compensator

nonlinearrelay

lens

P

P

P

image

plane

Optical Compensated Zoom Systems

Combined movement of two rigid coupled lenses

Image plane location only approximately constant

Only one moving part

image with

defocusfixed group coupled

moved lensesrelay lens fixed

P

P

P

Two-Component F-F System

Setup :

Given : L, m, f1, f2 :

Wüllner equations:

f1

f2

L

t1

t2

t3

object image

m

mffffL

LLt

2

2121

2

2

1

42

221

221211

tffm

tffmfft

213 ttLt

221

21

tff

fff

Two-Component F-F System

Solution space :

focal lengths:

1. f1 > L/4

2. f2 > L/4

3. 1/f1 + 1/f2 < 4/L

Calculation with Newton-

imaging equation and

tj > 0

Ranges with 0 - 1- 2 - 3 - 4

solutions for focal lengths

1

[1/L]

2 [1/L]

0 4 15-15 10-10 -5

no solution

1

2

3

4

3

2

2

15

-15

4

10

0

-10

-5

a)

b)

c)

d)

Two-Component F-F System

Examples:

1. Number of solutions

2. Zoom curves

3. m-ranges

d) f1= L/3

f2 = L/3

t1 = 25 , t

2 = 29.3 , m = -1.35

t1 = 16.5 , t

2 = 16.7 , m = -11.8

t1 = 11.3 , t

2 = 80.7 , m = -13.5

t1 = 5.9 , t

2 = 7.6 , m = -4.8

t1 = 16.4 , t

2 = 26.6 , m = +6.0

t1 = 3.1 , t

2 = 4.3 , m = -16

L

m

c) f1

= L/10

f2 = -L/10

t2

t1

t1

t2

t1

t2

t1

t2

b) f1

=-L/10

f2 = L/10

a) f1

= L/12

f2 = L/12

t2

t1

0 20 40 60 80 100

0 20 40 60 80 100L

0 20 40 60 80 100L

L

m

m

m

0 20 40 60 80 100-4

-3

-2

-1

0

-25

-20

-15

-10

-5

0

-8

-6

-4

-2

0

-20

-10

0

10

20

t1

t2

Symmetrical Afocal Setup

Telescope angle magnification :

Major positions

Symmetrical layout

f1

f1

f2

asymmetric 1

> 1

tmax

asymmetric 2

tmin

<

symmetric

tm

tm

= 1

last

first

h

h

w

w

'

Magnification First distance

Second distance

|| = |max| > 1 tmax 0

|| = 1 tm tm

|| = 1/|max| < 1 0 tmin

Three-Component Zoom System

Setup:

1. lens

fixed

Given :

M, L

Arbitrary but recommended :

Calculation : central position

third lensfirst lens fixed second lens image

planef1 f

2f3

t1

t2

s'

s'2

f1

s3

LM

MF

11

LM

MF

12

13

)1(13

M

MMFFF

)1(

1

1

1

MF

Mt

)1(

1

1

2

MMF

Mt

)1(

13'

MMF

Ms

Three-Component Zoom System

Arbitrary zoom positions:

given is t1

Example:

121

1122'

tff

tffs

c

bbt

42

2

2

Lstb 21 '

23231 ')'()( sfsftLc

3312121323211321 FFFttFFFtFFFtFFFF

F

[1/mm]

-20 0 20 40 60 80 100 120 140 1600

20

40

60

80

100

120

140

160

180

[mm]

t1

t2

fmin

=16.3 mm

fmax

=163 mm

middle:

fm

=100 mm

Fixed Pupil Position

Example for illustration :

60 80 100 120 140 160 180 200-1.5

-1

-0.5

0

0.5

1

1.5

ln|m|

z

[mm]

m = -0.25

f3 = 40f

2 = -19f

1 = 40

m = -0.38

m = -0.5

m = -0.75

m = -1

m = -1.5

m = -2

m = -3

m = -4

object imageentrance

pupilexit

pupil

Correction of Zoom Systems

Typical compensator group

Typical variator group

Principle:

- No compensation for all movement positions possible

- Correcting every group

Solid State Zoom Systems

Lenses with variable

focal length

Calculation:

Critical value:

First lens focuses onto the second lens

f1

f2

ts

s'

sst

s

s

)1(

1

'

1

1

12

)1(

1

'

1

1

1

tsts

t

11

'

sts

sm

stc

111

Examples

Three component afocal

Spot diagram

Spherical aberration

= 0.41

= 0.60

= 0.91

= 1.41

= 1.91

= 2.41

t2

= 0.41 = 0.60 = 0.91 = 1.41 = 1.91 = 2.41

axis

field

1°

Wrms

[] c40

[]

t2

[mm]

a) b)

0 10 20 30 40 50 600

0.005

0.01

0.015

0.02

0.025

0.03

0 10 20 30 40 50 60-0.025

-0.02

-0.015

-0.01

-0.005

0

t2

[mm]

Real photographic zoom lens

Three moving groups:

1. variator: focal length

2. compensator: focussing

3. object distance

Zoom Lens

e)

f' = 203 mm

w = 5.64°

F# = 16.6

d)

f' = 160 mm

w = 7.13°

F# = 13.7

c)

f' = 120 mm

w = 9.46°

F# = 10.9

b)

f' = 85 mm

w = 13.24°

F# = 8.5

a)

f' = 72 mm

w = 15.52°

F# = 7.7

group 1 group 2 group 3

Examples

Four component afocal zoom

Wave aberration over field = 1.96

= 1.29

= 0.78

= 0.53

= 1.96

= 1.29

= 0.78

= 0.53

0.2

Wrms

[

3.5°

field

angle1.75°0°0

0.1

0.15

0.05

diffraction limit

Example

Professional factor 5 zoom lens with 5

moving groups

Very smooth and excellent correction

f = 29 mm

f = 35 mm

f = 50 mm

f = 70 mm

f = 105 mm

f = 146 mm

spherical coma astigma distortion ax chrom la chrom

1st

group

2nd

group

3rd

group

4th

group

sum

5th

group

curvature

Ref: Tokumaru, USP 4846562 (1988)

Zoom System with 2 Stages

2-stage cascaded zoom system

Intermediate image plane

Zoom factor M = 300

970 mm

intermediate

imageimage1. zoom

group2. zoom

group

3. zoom

group

4. zoom

group

main zoom relay zoom

Ref: Caldwell, USP 7227682 (2007)

Zoom Systems for Stereo Microscopes: SV 4

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.45

10

15

20

25

30

35

40

45

d4

d7

Stereopankrat SV 4 :max

/ min

= 4

= 0.44

= 0.9

= 1.35

= 1.82

= 2.27

Mechanical

compensation

Variable distances:

d3 and d4