Microscopy - iap.uni-jena.de Optical... · Microscopy Lecture 2: Optical System of the Microscopy II 2012-10-22 Herbert Gross Winter term 2012 . 2 Optical System of the Microscopy

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Microscopy

Lecture 2: Optical System of the Microscopy II

2012-10-22

Herbert Gross

Winter term 2012

2 2 Optical System of the Microscopy II

Preliminary time schedule

No Date Main subject Detailed topics Lecturer

1 15.10. Optical system of a microscope I overview, general setup, binoculars, objective lenses, performance and types of lenses, tube optics Gross

2 22.10. Optical system of a microscope II Etendue, pupil, telecentricity, confocal systems, illumination setups, Köhler principle, fluorescence systems and TIRF, adjustment of objective lenses Gross

3 29.10. Physical optics of widefield microscopes

Point spread function, high-NA-effects, apodization, defocussing, index mismatch, coherence, partial coherent imaging Gross

4 05.11. Performance assessment

Wave aberrations and Zernikes, Strehl ratio, point resolution, sine condition, optical transfer function, conoscopic observation, isoplantism, straylight and ghost images, thermal degradation, measuring of system quality

Gross

5 12.11. Fourier optical description basic concepts, 2-point-resolution (Rayleigh, Sparrow), Frequency-based resolution (Abbe), CTF and Born Approximation Heintzmann

6 19.11. Methods, DIC Rytov approximation, a comment on holography, Ptychography, DIC Heintzmann

7 26.11. Imaging of scatter

Multibeam illumination, Cofocal coherent, Incoherent processes (Fluorescence, Raman), OTF for incoherent light, Missing cone problem, imaging of a fluorescent plane, incoherent confocal OTF/PSF

Heintzmann

8 03.12. Incoherent emission to improve resolution Fluorescence, Structured illumination, Image based identification of experimental parameters, image reconstruction Heintzmann

9 10.12. The quantum world in microscopy Photons, Poisson distribution, squeezed light, antibunching, Ghost imaging Wicker

10 17.12. Deconvolution Building a forward model and inverting it based on statistics Wicker

11 07.01. Nonlinear sample response STED, NLSIM, Rabi the information view Wicker

12 14.01. Nonlinear microscopy two-photon cross sections, pulsed excitation, propagation of ultrashort pulses, (image formation in 3D), nonlinear scattering, SHG/THG - symmetry properties Heisterkamp

13 21.01. Raman-CARS microscopy principle, origin of CARS signale, four wave mixing, phase matching conditions, epi/forward CARS, SRS. Heisterkamp

14 28.01 Tissue optics and imaging Tissue optics, scattering&aberrations, optical clearing,Optical tomography, light-sheet/ultramicroscopy Heisterkamp

15 04.02. Optical coherence tomography principle, interferometry, time-domain, frequency domain. Heisterkamp

1. Etendue

2. Pupil

3. Telecentricity

4. Confocal systems

5. Illumination setups

6. Köhler principle

7. Fluorescence systems and TIRF

8. Objective adjustment

3 2 Optical System of the Microscopy II

Contents of 2nd Lecture

2 Optical System of the Microscopy II

Microscope Objective Lens

No rigid relationship between

magnification and aperture

Product of field size and NA fixes the

overall capacity

Variation of image-sided numerical

aperture

NA'

mobj

0.03

1000 20 40 8060

0.02

0.01

NA

1.5

1

0.5

00 100

mobj

80604020

immersion


Etendue of Microscope Objective Lenses

Information capacity,

etendue, space-bandwidth product,

number of PSF‘s resolved in the field

Non-rigid correlation between

magnification and etendue

Largest etendue for medium

magnifications

Immersion systems have larger

etendue

Dfield

in [mm]10-1

100 1

10-2

10-1

100

G [mm2]

air

oil

water

m150 100

10

63 50 40 20 10 5 4 2.5 1.25

2

4NADG field

Relevance of the system pupil :

Brightness of the image

Transfer of energy

Resolution of details,

Information transfer, location of Fourier spectrum

Image quality

Aberrations due to aperture

Image perspective

Perception of depth

Compound systems:

matching of pupils is necessary, location and size


Properties of the Pupil


Entrance and Exit Pupil

exit

pupil

upper

marginal ray

chief

ray

lower coma

raystop

field point

of image

UU'

W

lower marginal

ray

upper coma

ray

on axis

point of

image

outer field

point of

object

object

point

on axis

entrance

pupil


Microscope Objective Lens: Pupil

Object space telecentric

Real rear stop is not

defining the pupil

Collimated outgoing

beam

Exit pupil usually

not accessible

object

plane

objective

lens

rear stop

exit pupil

marginal ray

chief ray

telecentric,

entrance pupil infinity

y'p

u

f'f'

chief

ray

exit

pupil

rear

stopobject

plane

pupil



Diameter of pupil only weak correlated with magnification

Pupil distorsion:

Pupil distortion small

(sine condition corrected)

DExP

2

3

4

5

6

7

8

9

10

11

m0 10 20 30 40 50 60 70 80 90 100 110

1sin'

'

uf

yD

p

distExP

a) Lister

0 0.2 0.4 0.6 0.8 10

0.005

0.01

0.015

0.02

0.025

0.03

0.035

yp y

p

b) 100x0.93 oil

c) Laikin

yp

0 0.2 0.4 0.6 0.8 10

0.002

0.004

0.006

0.008

0.01

0.012

d) Schwarzschild

yp0 0.2 0.4 0.6 0.8 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x 10-3

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

x 10-3

Ddist ExP D

dist ExP

Ddist ExP

Ddist ExP



Imaging of the pupil is important

Residual aberrations :

sharp edge of aperture is

desired

Real systems : smooth

illumination profile

I(r)

1

0.5

00 1 2

r

[mm]

ideal

edge

lens

pupil

stop

v



Example of larger residual aberrations

of pupil image :

1. axial shift of pupil with field size

2. no sharp imaging of aperture stop

3. coloured edge of stop boundary

480 nm

0

11.6°

546 nm 644 nm

16.3°

20.0°

23.1°

30

15

0

diffraction limit

-0.5 0.50

Dspot

[m]

z

[mm]

axis

11.6°

16.3°

20°

23.1°



Vignetting of the pupil :

1. truncation of the bundle for finite field sizes

2. chief ray not identical with centroid

3. perturbation of telecentricity

4. in microscopic systems mostly at the

front lens

chief ray

telecentric

chief ray not

telecentric

full aperture

vignetted

aperture

centre of

gravity

shifted


Vignetting

Truncation at front lens

Pupil vignetting:

crescent shape of

light cone

Illumination fall-off towards

field boundary

cover

glass oil

front

lens

truncating

edge

axis

zone

field

1

0.675

pupil shape

I(r)/Io

1

0.5

00 10.5

y/ymax


Vignetting

Truncation of regions with large

aberrations as correction method

Improved performance

Psf elliptical, anisotropiuc resolution

Energy reduced

DS

0.5

1

0.8

00 10.5

y'/ymax

480 nm

546 nm

644 nm

diffraction limit

solid line : vignetted

dashed line : without vignetting

axis field zone field edge

yxyxx

Special stop positions:

1. stop in back focal plane: object sided telecentricity

2. stop in front focal plane: image sided telecentricity

3. stop in intermediate focal plane: both-sided telecentricity

Telecentricity:

1. pupil in infinity

2. chief ray parallel to the optical axis


Telecentricity

telecentric

stop

object image

chief rays

parallel to axis

in image spacef f'

imageobject telecentric

stop

chief rays

parallel to axis

in object space

a) image sided telecentric b) object sided telecentric

Design problems with telecentricity:

Usual telecentricity only fulfilled for one wavelength

Telecentricity is related to the centroid ray.

Therefore the telecentricity is disturbed by

vignetting effects


Telecentricity

wtele

[°]

y'/y'max

0 0.2 0.4 0.6 0.8 1-0.2

-0.15

-0.1

-0.05

0

0.05

480 nm

587 nm

656 nm

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

1.2

wtele

[°]

y'/y'max

centre ray with

vignetting

chief

ray

centre ray

with coma

Laser scan microscope

Depth resolution (sectioning) with

confocal pinhole

Transverse scan on field of view

Digital image

Only light comming out of the

conjugate plane is detected

Perfect system: scan mirrors

conjugate to pupil location

System needs a good correction

of the objective lens,

symmetric 3D distribution of

intensity


Confocal Microscope

'

objective

lens

pinhole

lens pinhole CCD

in focus

out of focus

laser

illumination

Depth resolved

images


Confocal Images

Ref.: M. Kempe


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



Scan lens

Diffraction limited

Change in pupil location of

objective lenses is critical

perturbation of telecentricity

scan

mirror

intermediate

image

0.2

480 nm

546 nm

644 nm

0.1

0

Wrms

diffraction limit

0 5 10 in °

w [°]

0 0.2 0.4 0.6 0.8 1-3

-2

-1

0

1

2

3

4

5

y/ymax

paraxial

exact

+ 3 mm

- 3 mm

pupil

location:



Pinhole lens

Only axial colour is essential

Usage on axis only due to

descanning

Variable pinhole size not too small:

small aperture, retrofocus lens

pinhole

-0.5 0 0.5

z in

[mm]

yp

1

0.5

480 nm

546 nm

644 nm

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

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

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


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



Depth signal as a function of wavelength

Disturbance by axial colour aberration

z/Ru

Dph

= Dairy

3

2

1

0

-1

-2

0.4 0.45 0.5 0.55 0.6 0.65 0.7

zestim

image

plane


Illumination Optics: Overview

Four possibilities for practical needs

Epi vs. trans-illumination

Bright vs. dark field illumination

Comparison of light cones for

imaging and illumination parts

axis

observation

epi-dark

field

trans-bright

field

trans-dark

field

epi-bright

field

object

plane



Instrumental realizations

a) incident illumination

bright fieldb) incident illumination

dark fieldc) transmitted illumination

bright field

d) transmitted illumination

dark field

ring

mirrorobservation

illumination

object

plane

ring

mirror

objective

lens

object

plane

observation

illumination

observation

ring

condenser

object

plane

illumination

condenser

object

plane

observation

illumination



Typical images for different illuminations

bright

dark

epi trans

source

collector condenser objective

lens

object

plane

image

plane

field stop aperture stopback focal plane -

pupil


Köhler Illumination Principle

Principle of Köhler

illumination:

Alternating beam paths

of field and pupil

No source structure in

image

Light source conjugated

to system pupil

Differences between

ideal and real ray paths

condenser

object

plane

aperture

stopfield

stop filter

collector

source



Types of settings :

1. Köhler :

source into pupil,

mostly used

2. Critical :

source into field of view,

source structure disturbs image

3. Projection :

source into condenser

4. Arbitrary

condenser object

plane

collectorsource

a) Köhler = 1 fcon f

con

b) = 0.5

c) Projection = 0

d) = -0.5

e) Critical = -1

auxiliary

lens


Illumination Optics: Collector

Requirements and aspects:

1. Large collecting solid angle

2. Correction not critical

3. Thermal loading

large

4. Mostly shell-structure

for high NA

W(yp)

200

a) axis b) field

200

W(yp)

yp

480 nm

546 nm

644 nm

yp

W(yp)

200

a) axis b) field

200

W(yp)

yp

yp

480 nm

546 nm

644 nm


Illumination Optics: Condenser

2. Abbe type, achromatic, NA = 0.9 , aplanatic, residual spherical

3. Aplanatic achromatic, NA = 0.85

y'100m

a) axis b) field

yp

480 nm

546 nm

644 nm

y'100m

yp

x'100m

xp

tangential sagittal

y'100m

a) axis b) field

yp

480 nm

546 nm

644 nm

y'100m

yp

x'100m

xp

tangential sagittal



Dark-field illumination systems

1. Trans-illumination

Cardioid-mirror

Realizations: approximation

of Cardioid curve

C

R

R/2 P

R/2

circle

cardioide2R

object

plane

cardiode

cover slideillumination

cone

object carrier

condenser

immersion



2. Epi-illumination

Complicated ring-shaped components

around objective lens

object

ring lens

illuminationobservation

object

ring lens

illuminationobservationcircle 1

circle 2


Illumination Optics: TIRF-Illumination

cover glass

substrate

illumination

signal

Epi- and trans illumination for TIRF

cover glass

total

internal

reflexion

probe

carrier

illumination

observation

prism

objective lens


Fluorescence Microscopy

Fluorescence microscopy is the most frequently employed mode of light microscopy

used in biomedical reserach today

Setup:

Necessary components:

Dicroitic beam splitter, excitation filter with

sharp edge

UV

source

objectobjective

lens

image

plane

illumination

at 365 nm

fluorescence

red or

infrared

dicroitic

beam splitter

excitation

filter

UV bloc

filter

400350 450 500 550 600 650 700

[nm]0

0.5

1

emission

absorption

Fluorescein

Iso Thio

Cyanate


TIRF Microscopy

Total internal reflection microscopy:

Excitation with evanescent field

Advantages:

1. better axial resolution

2. better SNR, no fluorescence background

Problem in optical design:

Extremly small illumination ring-shaped

channel around the observation light cone

cover

glass

illumination

ring channel

observation

total

internal

reflexion

probe

Objective lens

TIRF 100x1.45

Epi-Fluorescence TIRF


Adjustment of Objective Lenses

Adjustment of air gaps to

optimize spherical aberration

Reduced optimization setup

Compensates residual aberrations due to tolerances (radii, thicknesses,

refractive indices)

8,6,4,2,4,1

jt

cccc

k k

j

jjoj

t2 t

4t6

t8

d2 d4 d6 d8 c20 c40 c60 c80 Wrms

nominal 0.77300 0.17000 3.2200 2.0500 0.00527 -0.0718 0.00232 0.01290 0.0324

d2 varied 0.77320 0.17000 3.2200 2.0500 0.04144 -0.07586 0.00277 0.12854

d4 varied 0.77300 0.17050 3.2200 2.0500 0.03003 -0.07461 0.00264 0.01286

d6 varied 0.77300 0.17000 3.2250 2.0500 0.00728 -0.07367 0.00275 0.01284

d8 varied 0.77300 0.17000 3.2200 2.0550 0.005551 -0.0717 0.00235 0.01290

optimized 0.77297 0.16942 3.12670 3.2110 0.000414 0.00046 0.00030 0.01390 0.00468


Adjustment of Objective Lenses

Significant improvement for one wavelength on axis

Possible decreased performance in the field

Wrms

in

0.3

0

0.15

y/ymax

480 nm

546 nm

644 nm

improve-

ment

0.5 10

solid lines : nominal

dashed lines : adjusted

Example microscopic lens

Adjusting:

1. Axial shifting lens : focus

2. Clocking: astigmatism

3. Lateral shifting lens: coma

Ideal : Strehl DS = 99.62 %

With tolerances : DS = 0.1 %

After adjusting : DS = 99.3 %


Adjustment and Compensation

System with tolerancesStrehl: 0,2%

PSF (intensity normalized)

PSF(energy normalized)

Spherical aberrationcompensator

On axis comacompensator

StopOb

ject pl

ane

Defoc

uscom

pensat

orOn

axis a

stigma

tismcom

pensat

or Nr.

1

On axis astigmatismcompensator Nr. 2

Ref.: M. Peschka

Sucessive steps of improvements


Adjustment and Compensation

PSF(intensitynormalized)

With Tolerances

Step 1 (Z, Z)4 9

Step 2 (Z, Z)7 8

Step 3 (Z, Z)5 6

Step 4 ~ Step 2 (Z, Z)7 8

PSF(energynormalized) Not

adjusted

0.2%

21.77%25.48%

97.2%99.32%

Stre

hl ra

tio [%

]

0

20

40

60

80

100

Step 1Z, Z4 9

Step 2Z, Z7 8

Step 3Z, Z5 6

Step 4~ Step 2Z, Z

7 8

Ref.: M. Peschka

Documents

Microscopy - iap.uni-jena.de Optical... · Microscopy Lecture 2: Optical System of the Microscopy II 2012-10-22 Herbert Gross Winter term 2012 . 2 Optical System of the Microscopy