13 lecture 13 zoom and confocal systems

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www.iap.uni-jena.de Design and Correction of Optical Systems Lecture 13: Zoom and Confocal Systems 2013-07-10 Herbert Gross Summer term 2013

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Page 1: 13 Lecture 13 Zoom and Confocal Systems

www.iap.uni-jena.de

Design and Correction of Optical

Systems

Lecture 13: Zoom and Confocal Systems

2013-07-10

Herbert Gross

Summer term 2013

Page 2: 13 Lecture 13 Zoom and Confocal Systems

2

Preliminary Schedule

1 10.04. Basics Law of refraction, Fresnel formulas, optical system model, raytrace, calculation

approaches

2 17.04. Materials and Components Dispersion, anormal dispersion, glass map, liquids and plastics, lenses, mirrors,

aspheres, diffractive elements

3 24.04. Paraxial Optics Paraxial approximation, basic notations, imaging equation, multi-component

systems, matrix calculation, Lagrange invariant, phase space visualization

4 08.05. Optical Systems Pupil, ray sets and sampling, aperture and vignetting, telecentricity, symmetry,

photometry

5 15.05. Geometrical Aberrations Longitudinal and transverse aberrations, spot diagram, polynomial expansion,

primary aberrations, chromatical aberrations, Seidels surface contributions

6 22.05. Wave Aberrations Fermat principle and Eikonal, wave aberrations, expansion and higher orders,

Zernike polynomials, measurement of system quality

7 29.05. PSF and Transfer function Diffraction, point spread function, PSF with aberrations, optical transfer function,

Fourier imaging model

8 05.06. Further Performance Criteria Rayleigh and Marechal criteria, Strehl definition, 2-point resolution, MTF-based

criteria, further options

9 12.06. Optimization and Correction Principles of optimization, initial setups, constraints, sensitivity, optimization of

optical systems, global approaches

10 19.06. Correction Principles I Symmetry, lens bending, lens splitting, special options for spherical aberration,

astigmatism, coma and distortion, aspheres

11 26.06. Correction Principles II Field flattening and Petzval theorem, chromatical correction, achromate,

apochromate, sensitivity analysis, diffractive elements

12 03.07. Optical System Classification Overview, photographic lenses, microscopic objectives, lithographic systems,

eyepieces, scan systems, telescopes, endoscopes

13 10.07. Special System Examples Zoom systems, confocal systems

Page 3: 13 Lecture 13 Zoom and Confocal Systems

1. Principle of zoom systems

2. Various setups for zoom systems

3. Simple calculation schemes

4. Example systems

5. Miscellaneous topics concerning zoom systems

6. Confocal principle

7. Confocal chromatical sensor

8. Confocal microscope

3

Contents

Page 4: 13 Lecture 13 Zoom and Confocal Systems

Zoom Lenses

Change of focal length

Magnification enlarged / scene reduced

a) focal length f = 30 mm c) focal length f = 250 mmb) focal length f = 100 mm

Ref: W. Osten

Page 5: 13 Lecture 13 Zoom and Confocal Systems

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)

Page 6: 13 Lecture 13 Zoom and Confocal Systems

Change of Focal Length

Distance t increased

First lens fixed

moved

lenschanged

distance

t changed focal

length f

Page 7: 13 Lecture 13 Zoom and Confocal Systems

Change of Focal Length

Distance t increased

Image plane fixed

two lenses moved

t f

image

plane

Page 8: 13 Lecture 13 Zoom and Confocal Systems

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

'

''

Page 9: 13 Lecture 13 Zoom and Confocal Systems

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

Page 10: 13 Lecture 13 Zoom and Confocal Systems

Principle of Smallest Change

Goal :

smallest change of length

Preferred points of operation:

m = 1 , m = -1

Setup :

1. Change of magnification :

variator group

2. Correcting the image

location: compensator group

)1/()/(4)/(2

2/2)/(

2

1

24

2

fsfsfs

fsfs

dL

dmf

-10 -8 -6 -4 -2 0 2-10

-8

-6

-4

-2

0

2

4

6

8

10

L / f

s / f

f dm/dL

m

Page 11: 13 Lecture 13 Zoom and Confocal Systems

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

Page 12: 13 Lecture 13 Zoom and Confocal Systems

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

Page 13: 13 Lecture 13 Zoom and Confocal Systems

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)

Page 14: 13 Lecture 13 Zoom and Confocal Systems

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

Page 15: 13 Lecture 13 Zoom and Confocal Systems

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

Page 16: 13 Lecture 13 Zoom and Confocal Systems

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

Page 17: 13 Lecture 13 Zoom and Confocal Systems

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

Page 18: 13 Lecture 13 Zoom and Confocal Systems

Matrix Solution: Optical Compensated Afocal Zoom

Shifting from middle position:

Matrix

Middle position:

Conditions:

a) symmetrical zoom position : = 1

b) asymmetrical zoom position : < 1

f1

f1f

2

tm

tm

f1

f1

f2

tm

+ztm

-z

21

2

2121 FFtFtFtA mmmm

2

2

1

2

21

2

121 222 FFtFFFtFFC mmm

1

01

10

1

1

01

10

1

1

01

121 F

zt

F

zt

FDC

BA mm

aa

aa

21

2

221

2

2121 FFzFzFFtFFtA mma

2

2

1

2

2

2

1

2

21121 22 FFzFFtFFtFFFC mma

AD

u

u 1'0

'

0

ux

uC 1)( min ma tA

0)0( mC

Page 19: 13 Lecture 13 Zoom and Confocal Systems

Symmetrical Afocal Setup

Calculation:

Example:

2

max

min

max

M

13 1max12

1

11

max

max

1

mt

max

max

1

minmax

11

tt

1

1

max

max

1

1

t

111

max

max

1

2

t

1

122

max

max

1

mtL

0 20 40 60 80 100 1200

0.5

1

1.5

2

2.5

3

3.5

4

max

= 4

min

= 1/4

2. lens

1. lens

= 1

Page 20: 13 Lecture 13 Zoom and Confocal Systems

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

Page 21: 13 Lecture 13 Zoom and Confocal Systems

Optical Compensation

Rayleigh range changes with m:

Optimized zeros

2

2

2

4

in

uDNA

R

image plane

with defocuszoom system

fixed

relay lensobject

+ Ru

- Ru

z

m

Page 22: 13 Lecture 13 Zoom and Confocal Systems

General Three Component Optical Compensated System

Setup

Calculation:

Tube lengths:

Focal length:

Deviation:

z

coupled movement : z

F'1

F2 F'

2

F'3F

3

f1

f2

f3

t1 t

1

e1

e2

lens 1 lens 2 lens 3

image

plane

21101 ffte 32202 ffte

21

2

212

2

21

2

2

2

1

2

2

2

321

2

2

21

2

2

2

3112

23

eefzeezz

eef

effeefz

eef

feeezz

z

2

2121

2

2

321

zzeeeef

ffff

Page 23: 13 Lecture 13 Zoom and Confocal Systems

Three Component Optical Compensated System

Approximated solution:

- auxiliary parameters B,C

- practical starting values for B, C

12

2

2 eefB 12 ttC

BM

MC

M

MCz

22

max1

1

41

1

2

12

max

2

3 112 B

zBCf

22CB

BBf

21CB

CBe

12 eCe

max21321 22 zeefffL

f1 f2 f3 Focal length f

Image location

Parameter B/C

2

+ + + – + 0–1

+ + – + + 0.5–1

+ – + + + 0–0.5

+ – – no solution

– + + + – 0–1

– + – – – 0.5–1

– – + – – 0.5–1

– – – no solution

Page 24: 13 Lecture 13 Zoom and Confocal Systems

Three Component Optical Compensated System

Typical deviation behaviour

-1 -0.5 0 0.5

-0.05

0

0.05

M = 1.3

M = 1.5

M = 2.0

M = 2.5

M = 3.0

1

z/zmax

z [a.u.]

Page 25: 13 Lecture 13 Zoom and Confocal Systems

Performance Variation over z

System layout of a simple but real example

f = 200 mm

f = 100 mm

f = 50 mm

f = 67 mm

f = 133 mm

f1 f

2f3 f

4

t2

Page 26: 13 Lecture 13 Zoom and Confocal Systems

Performance Variation over z

Seidel

surface

contrib.

coma distortion axial chromatical lateral chromatical

lens 1

lens 2

lens 3

sum

spherical aberration

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

-0.1

0

0.1

-0.1

0

0.1

-0.1

0

0.1

-0.1

0

0.1

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

-0.2

-0.1

0

0.1

0.2

-0.2

-0.1

0

0.1

0.2

-0.2

-0.1

0

0.1

0.2

-0.2

-0.1

0

0.1

0.2

1 2 3 4 5

-5

0

5

1 2 3 4 5

-5

0

5

1 2 3 4 5

-5

0

5

1 2 3 4 5

-5

0

5

1 2 3 4 5

-5

0

5

1 2 3 4 5

-5

0

5

1 2 3 4 5

-5

0

5

1 2 3 4 5

-5

0

5

1 2 3 4 5

-0.5

0

0.5

1 2 3 4 5

-0.5

0

0.5

1 2 3 4 5

-0.5

0

0.5

1 2 3 4 5

-

0.5

0

0.5

Page 27: 13 Lecture 13 Zoom and Confocal Systems

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

Page 28: 13 Lecture 13 Zoom and Confocal Systems

Combined Zoom with Focussing

Photography:

Additional floating element for focussing

Problem : Breathing, change of field size during focussing

non-telecentric chief ray at focussing group

s = 2.5 m

f = 134 mmf = 100 mm f = 162 mm

infinity

focussing G1

G2

G3

G4 G

5

Page 29: 13 Lecture 13 Zoom and Confocal Systems

Combined Zoom with Focussing

System without breathing

Special movement of focus group

zoom

group 1

zoom

group 2

focusing group

infinity

common movement

separated movementfront part rear part

object

distance

0

2.5 m

0.25 m

0.4

0.6

vergence

in [dpt]

0100200300z

[mm]

Page 30: 13 Lecture 13 Zoom and Confocal Systems

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)

Page 31: 13 Lecture 13 Zoom and Confocal Systems

Fixed Pupil Position

Usual:

1. two moving groups

2. Pupil locations changes

Three moving groups : Pupil position can be held constant

Scheme and parameters:

object imagef1

f2 f

3EnPExP

s

p

p'

t1

t2

s'

P'P

Page 32: 13 Lecture 13 Zoom and Confocal Systems

Fixed Pupil Position

Calculation straightforward

Large solution space

Example 1 for illustration :

ln|m|

z

[mm]-200 -150 -100 -50 0 50 100

-1.5

-1

-0.5

0

0.5

1

1.5

Page 33: 13 Lecture 13 Zoom and Confocal Systems

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

Page 34: 13 Lecture 13 Zoom and Confocal Systems

Stop Position

Example with the stop at three different locations

Comparison of Seidel contributions

Best correction for the stop at rear group

a) f = 18 mm

stop at

1st

lens

stop at

2nd

lens

stop at

3rd

lens

b) f = 50 mm c) f = 125 mmstop

Page 35: 13 Lecture 13 Zoom and Confocal Systems

Stop Position

Seidel

lens 1

lens 2

lens 3

sum

sph coma ast dist la chr

a) stop at 1st lens b) stop at 2nd lens

sph coma ast dist la chr

c) stop at 3rd lens

sph coma ast dist la chr

Page 36: 13 Lecture 13 Zoom and Confocal Systems

Correction of Zoom Systems

Typical compensator group

Typical variator group

Principle:

- No compensation for all movement positions possible

- Correcting every group

Page 37: 13 Lecture 13 Zoom and Confocal Systems

Color Correction of the Moving Groups

Axial and lateral

color:

Comparison of

singlet/doublet

solution

= 0.3

= 0.57

= 1.0

= 1.7

= 3.0

lateral colour [a.u.]

axial colour [a.u.]

a) Singlet solution b) Doublet solution

0 0.5 1 1.5 2 2.5 3 3.5

10-4

10-3

10-2

10-1

100

0 0.5 1 1.5 2 2.5 3 3.510

-3

10-2

10-1

100

101

102

Singlets

Doublets

Singlets

Doublets

Page 38: 13 Lecture 13 Zoom and Confocal Systems

Example Optical Compensated Zoom

Five components, optical

compensated

Deviation curve

f = 400 mm

f = 234 mm

f = 162 mm

f = 127 mm

f = 100 mm

t1

z [mm]

f [mm]

image

plane

scaled

z/Ru

100 150 200 250 300 350 400-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

z

1

2

-2

-1diffraction

limited range

Page 39: 13 Lecture 13 Zoom and Confocal Systems

Example Optical Compensated Zoom

Five components, optical

compensated

Wrms and single

Zernike coefficients Wrms

[] c40

[]

t1

[mm]

a) b)

60 80 100 120 140 160 180 200 2200

5

10

15

20

60 80 100 120 140 160 180 200 220-40

-30

-20

-10

0

10

t1

[mm]

60 80 100 120 140 160 180 200 220-1

0

1

2

3

4

5

6

60 80 100 120 140 160 180 200 220-1.5

-1

-0.5

0

0.5

1

c31

[] c)

t1

[mm]

t1

[mm]

c22

[] d)

Page 40: 13 Lecture 13 Zoom and Confocal Systems

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

Page 41: 13 Lecture 13 Zoom and Confocal Systems

Solid State Zoom Systems

Solution

areas

Second solution:

Intermediate image

1

[1/mm]

< 0

2

[1/mm]

-0.05 0 0.05 0.1 0.15-0.2

-0.1

0

0.1

-0.05 0 0.05 0.1 0.15

-20

-15

-10

-5

0

5

10

15

20

25

1

[1/mm]

> 0

msolution a solution a solution bsolution b

f1

f2

ts

s'

Page 42: 13 Lecture 13 Zoom and Confocal Systems

Zoom System with 2 Stages

2-stage cascaded zoom system

Intermediate image plane

Zoom factor M = 300

970 mm

Zwischen-

bildBild1. Zoom

Gruppe2. Zoom

Gruppe

3. Zoom

Gruppe

4. Zoom

Gruppe

Hauptzoom Relay-Zoom

Ref: Caldwell, USP 7227682 (2007)

Page 43: 13 Lecture 13 Zoom and Confocal Systems

Confocal Distance Sensor

Principle of the confocal distance sensor

objective

lens

beam

splitter pinhole detector

in focus

out of focus

Illumination

pinhole

objective

-6 -4 -2 0 2 4 60

0.2

0.4

0.6

0.8

1

S [a.u.] dS/dz [a.u.]

DPH

= 0.3 Dairy

DPH

= 1.0 Dairy

DPH

= 1.8 Dairy

z

[Ru]

z [Ru]

linearity

-3 -2 -1 0 1 2 3-1

-0.5

0

0.5

1

a) b)

Page 44: 13 Lecture 13 Zoom and Confocal Systems

Chromatical Confocal Sensor

Spectral sensitive sensor

Objective lens with large axial

chromatical aberration

white light

source

pinhole

focussing

objectiveconfocale

pinhole

detector

grating

measuring

range

chromatical

objective

z

[mm]-4.0 -2.0 0 4.02.0

480 nm

546 nm

656 nm

-6 -4 -2 0 2 4 6 8 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

z

[mm]

E

480 nm

546 nm

656 nm

Page 45: 13 Lecture 13 Zoom and Confocal Systems

Confocal Imaging with Hyper Chromate

Wide field 20x0.5

Confocal with chromate at

low aperture 20x0.5

Confocal with chromate at

high aperture 50x0.9

Ref: R. Semmler

Page 46: 13 Lecture 13 Zoom and Confocal Systems

Goal: 1. large chromatical spreading (large CHL) z 2. large numerical aperture 3. corrected spherochromatism

In the case of a large ratio z / f, the numerical aperture shows a considerable change in the measuring interval

Design approach:

1. Achromate with positive flint

and negative crown

2. Achromates cascaded

3. Improved spherochromatism

by asphere

4. monochromatic lens with

buried surface adapter

Principle

z

= 644 nm

= 546 nm

= 480 nm

Page 47: 13 Lecture 13 Zoom and Confocal Systems

47

NA=0.3 z=3 no doublet.ZMXConfiguration 1 of 3

Layout

Hyper chromate07.03.2013Total Axial Length: 60.45674 mm

Surface: IMA

0.0000 (deg)

Config 1

4.00

Config 2 Config 3

NA=0.3 z=3 no doublet.ZMXConfiguration: All 3

Configuration Matrix Spot Diagram

Hyper chromate07.03.2013 Units are µm. Airy Radius: 1.563 µm

Scale bar : 4 Reference : Chief Ray

-5 -4 -3 -2 -1 0 1 2 3 4 5

Pupil Radius: 9.7107 Millimeters

Millimeters

NA=0.3 z=3 no doublet.ZMXConfiguration 1 of 3

Longitudinal Aberration

Hyper chromate07.03.2013Wavelengths: 0.450 0.546 0.675

Spherical Coma Astigmatism Field Curvature Distortion Axial Color Lateral Color

SUM1 2 3 STO

NA=0.3 z=3 no doublet.zmxConfiguration 1 of 3

Seidel Diagram

Hyper chromate2013/3/7Wavelength: 0.4500 µm.Maximum aberration scale is 0.50000 Millimeters.Grid lines are spaced 0.05000 Millimeters.

1st surface: aspherical

Case 1-1

NAimage = 0.3, NAobject = 0.22

Δz = 3 mm, f = 13 mm

zfree = 16.3 mm

Optical Design

Page 48: 13 Lecture 13 Zoom and Confocal Systems

Fourier optical model:

- object/sample to be assumed as a plane mirror

- fiber source incoherent, diameter Dfib, uniformly radiating

- optical system with point spread function hpsf

- confocal detection by fiber (pinhole) size Dfib

Incoherent imaging model to get the

intensity of at the fiber

Calculation of the confocal signal by

integration over the pinhole

Confocal Depth Measuring System

focal plane

for

selected

sample

surface

fiber

recoupling into fiber

confocal selection

D

z

hyperchromatic

system

2

)()(),( zhaIzaI psffibima

ar

imaconf dydxzaIzaS ),(),(

Page 49: 13 Lecture 13 Zoom and Confocal Systems

Confocal Signal for Different Pinhole Sizes

Numerical result for different sizes a of the fiber radius

The width increases with the fiber diameter

The diffraction fine structure disappears with growing a

S()

0.58 0.585 0.59 0.595 0.6 0.605 0.61 0.615 0.620

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

a = 0

a = 10 mm

a = 5 mm

a = 20 mm

Page 50: 13 Lecture 13 Zoom and Confocal Systems

Confocal Laser Scan Microscope

Complete setup: objective / tube lens / scan lens / pinhole lens

Scanning of illumination / descanning of signal

Scan mirror conjugate to system pupil plane

Digital image processing necessary

object

plane

objective

lens

pupil

plane

tube

lens

intermediate

image

scan

lens

scan

mirror

laser

source

beam

forming

pinhole

lens

pupil imaging

axis point

field point

Page 51: 13 Lecture 13 Zoom and Confocal Systems

Fourier optical model:

- illumination with point spread function hill

- object function plane, tobj, scanned

- detection with point spread function hdet

- detector function by pinhole size Dph

General transform of amplitudes

illhUU 12

Confocal Laser Scan -Microscope

illumination

hill

sourceobject tobj

scan

pinhole

detector

Dph

detection

hdet

U1 U2 U’2 U3 U’3

objtUU 22'

det23 ' hUU

phDUU 33'

Page 52: 13 Lecture 13 Zoom and Confocal Systems

Ref: M.Wald

2

objdetillima thhI

objdetillima thhI 2

phillima DhhI 2

det

2

Image Formation Confocal LSM

Special cases:

Brightfield, perfectly small pinhole

D=d(x)d(y), imaging coherent

Fluorescence, coherence destroyed

perfectly small pinhole

Point like object tobj = d(x) d(y)

Point object and perfectly small

pinhole

Plane mirror object tobj = const.

perfectly small pinhole

22

detillima hhI

dydxzyxhI detima

2)2,,(

det ill

det ill dethhill

Page 53: 13 Lecture 13 Zoom and Confocal Systems

Normalized transverse coordinate v

Usual PSF: Airy

Confocal imaging:

Identical PSF for illumination and observation

assumed

Resolution improvement be factor 1.4 for

FWhM

sin'

2 xv

4

1 )(2)(

v

vJvI

2

1 )(2)(

v

vJvI

Confocal Microscopy: PSF and Lateral Resolution

-8 -6 -4 -2 0 2 4 6 80

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

I(v)

incoherent

coherent

Page 54: 13 Lecture 13 Zoom and Confocal Systems

Normalized axial coordinate

Conventional wide field imaging:

Intensity on axis

Axial resolution

Confocal imaging:

Intensity on axis

Axial resolution improved by factor 1.41

for FWhM

4

2/

)2/sin()(

u

uuI

2

2/

)2/sin()(

u

uuI

Confocal Microscopy: Axial Sectioning

cos1'

45.0)(

nz approx

wide

cos1'

319.0

nzconfo

)2/(sin8 2

zu

u

I(u)

-5 -4 -3 -2 -1 0 1 2 3 4 50,

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,

incoherent

coherent

Page 55: 13 Lecture 13 Zoom and Confocal Systems

Large pinhole: geometrical optic

Small pinhole:

- Diffraction dominates

- Scaling by Airy diameter a = D/DAiry

- diffraction relevant for pinholes

D < Dairy

Confocal signal:

Integral over pinhole size

Size of Pinhole and Cnfocality

a

dvvvuUuS0

22),()(

x / DAiry

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

DPH / DAiry

NA = 0.30

NA = 0.60

NA = 0.75

NA = 0.90

geometrical

-25 -20 -15 -10 -5 0 5 10 15 20 250

2

4

6

8

10

12

S(u)

u

a = 3

a = 2

a = 1

a = 0.5

Page 56: 13 Lecture 13 Zoom and Confocal Systems

Confocal Signal with Spherical Aberration

S(u)

u-30 -20 -10 0 10 20 30

0

1

2

3

4

5

6

7

8

9

10

relative pinhole size:a = 3a = 2a = 1a = 0.5

spherical aberration 2

Spherical aberration:

- PSF broadened

- PSF no longer symmetrical around image plane during defocus

Confocal signal:

- loss in contrast

- decreased resolution

Page 57: 13 Lecture 13 Zoom and Confocal Systems

Depth resolved

images

Confocal Images

Ref.: M. Kempe