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Geometrical optics, Microscopy

Transmission (conventional light) microscopy

Fluorescence microscopy

Electron microscopy (transmission, scanning)

György Vereb

Department of Biophysics and Cell Biology, University of Debrecen

Textbook:

107-109

388-397

398-399

605-607

Interconnection with other lectures:

Lect. 3. Application of fluorescence

Lect. 6. Lasers

Lect. 22. The human eye

Lect. 24. Flow cytometry, confocal laser scanning microscopy

Lect. 27. Modern microscopic techniques

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Major points for discussion

• Geometrical optics, Snell’s law

• Image formation by simple lenses

• Lens aberrations

• Image formation in the compound microscope

• Transmission light microscopy

• Fluorescence microscopy

• Scanning vs. full field imaging

• Resolution

• Electron microscopy (transmission, scanning)

Why bother?

• Foundations for understanding how optical devices used in medicine

work• Usage of the microscope (anatomy, pathology, microbiology, haematology)

• Otoscope, ophthalmoscope, endoscopes

• Biomedical research

• Foundations for ophthalmology

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121

2

sin

sin

cin

r c

Snell – Descartes law

BASIC PRINCIPLES OF GEOMETRICAL OPTICS

incident

light ray

refracted

light ray

reflected

light ray

normal to

surface

Medium 2

Medium 1

!

In this example, medium 2 is

optically denser than medium 1,

and therefore the speed of light

(c2) in it, is lesser. Consequently,

its index of refraction relative to

medium 1 is greater than 1.

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!

Focusing

F

F

focal point

Optical axis

Collimation

Image formation of thin lenses I

21

11)1(

1

RRn

f

The more curved the lens, the closer

it focuses

→ higher refractive power:

fdiopterD

1)(

Unit: 1/m

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Image formation of thin lenses II !

oif

111

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Image formation of real (thick) lenses

21

2

21

)1(11)1(

1

RR

d

n

n

RRn

f

Major planes

object

image

Outlook

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Healthy eye

• Images of both close and distant objects are formed

on the retina

Short-sighted (near-sighted) eye

(myopia)

• The axis of the eye is longer than physiological, or

its minimal refractive power is still too high

• A sharp image of the close object is formed on the

retina, but the image of a distant object is formed in

front of the retina, so it is smeared on the retina

• Correction: with a diverging lens

Far-sighted eye (hypermetropia)

• The axis of the lens is shorter than physiological, or

its maximal refractive power is not high enough

• A sharp image of the distant object is formed on the

retina, but the image of a close object is formed

behind the retina, so it is smeared on the retina

• Correction: with a converging lens

!Image formation by the human eye and its most frequent defects

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LENS ABERRATIONS

Monochromatic Chromatic

Spherical aberration

Coma

Astigmatism

Field curvature

Manifestiations:

-Longitudinal

-Lateral

Astigmatism

Distortion

Also with perfect, symmetric lenses

With imperfect lenses

cause: physical thickness →

smaller refractive power closer to

the centre

cause: refractive index

depends on wavelength

→ red is focussed farther

!

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Distortion

object “pincushion” “barrel”

•Does not affect the sharpness of the image

•Magnification is different in the center than at the edges

5*

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•Light rays are refracted (bent)

•Refractive index depends on wavelength

•Red is refracted to the smallest extet, violet the most

•Hence white or polychromatic light is separated into

components of different wavelenghts

dispersion

Chromatic aberrations!

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• Monochromatic aberrations

Also with perfect lenses, cause: physical thickness → smaller refractive power

closer to the centre

– Spherical aberration: for parallel rays, focal point is closer for rays further

away from the optical axis

– Coma: divergent rays at large angles, point source off the optical axis

– Astigmatism: divergent rays at small angles, point source off the optical axis

– Field curvature: focal sphere instead of focal plane, related to astigmatism

With imperfect lenses

– Distorsion

– Astigmatism: the lens is cylindrical (has different refractive power along at

least two axes, also seen when rays are parallel to the optical axis

• Chromatic aberration

Also with perfect lenses, cause: refractive index decreases with increasing

wavelength. Manifestations:

– Longitudinal chromatic aberration

– Lateral chromatic aberration

LENS ABERRATIONS

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Anton Van Leeuwenhoek’s

Simple Microscope - 1670

Outlook

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Magnification: product of individual magnifications

Mi= I / O = i / o

Image formation in the conventional light microscope

compound microscope

objective and ocular

magnified, inverted, virtual image

F12F1

2F1 F2

!

F2

F1

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F1

2F1

2F1 F2

Film

CCD camera chip

Variations for

increasing contrast:

dark field

phase contrast

polarization

Taking the image in the conventional (full field) light

microscope!

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Application of fluorescence in the microscope

Contrast enhancement

•Against the dark background, every photon represents a 100%

increase of light intensity

•A Fluorescent labels can be bound to virtually any specific

molecule

•A Most fluorescent labels cause no harm to living cells and are

compatible with vital processes

!

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GFP-fusion

proteins

Microinjecting

labeled

molecule or

antibody

Labeled antibody,

Fab, ScFv

(for intracellular

epitopes

permeabilization

needed)

In situ detection of molecules using fluorescence

5*

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Sketch of the (epi)fluorescence microscope

ocular

objective

dichroic

mirror

observer

Condenser

lens

emission

filter

Excitation

filter

sample

lamp

!

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Imaging modalities

I. Full field

Illumination: full field (all the area that is observed)

Detection: full field, by

eye,

SLR camera (film),

electronic camera

II. Scanning

Illumination : point (i.e. laser source)

Detection : from point

without regard to where the photons arrive

onto the surface of the detector

e.g. Photomultiplier tube (PMT),

avalanche photodiode (APD)

Scanning : stage

laser beam (with moving mirrors)

!

!

5*

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x y

PMT

SCANNINGOutlook

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x, the limit of resolution (in the image plane), is independent of

the magnification of the lens

Limit of resolution(condition of perceiving the image of two points as two spots)

x

!

5*

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a

Resolving power in the fluorescence microscope

(lateral)

Limit of resolution (fluorescence microscope):

(the observed point is a light source):

d=0.61 l / NA

Numeric aperture: NA=n sina

~ proportion of photons entering the objectiveobjective

d: resolved distance (limit of resolution)

D: =1/d, resolving power (the smaller the d, the larger the power!)

l: wavelength of the light illuminating or emitted from the object

n: refractive index of the medium between the object and the lens

a: half angle of aperture (the angle between the outermost light ray

still entering the objective and the optical axis)

!

Green light (500 nm) and NA=1.4

yield d = 0,61*500/1.4=220 nm

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a

Resolving power (lateral)

Transmission (conventional)

light microscope

Limit of resolution:

d= l / (NAobjective +NAcondenser) → d ≈ l / 2NA

Numeric aperture: NA=n sina

~ proportion of photons entering the objectiveobjective

condenser

d: resolved distance (limit of resolution)

D: =1/d, resolving power (the smaller the d, the larger the power!)

l: wavelength of the light illuminating or emitted from the object

n: refractive index of the medium between the object and the lens

a: half angle of aperture (the angle between the outermost light ray

still entering the objective and the optical axis)

!

Increasing resolution:

Decrease λ (UV, X-ray, electron)

Increase NA

(n: immersion oil; α: large lens, close up)

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Electron Microscopy

Wave property of the electron is utilized

Transmission Electron Microscopy (TEM)

Scanning Electron Microscopy (SEM)

!

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Outlook

Outlook

Wavelength of the electron beam !

Wavelength (λ) of the electrons is determined by the

accelerating voltage (V)

Thus, very high voltages (up to 100 kV) are used to produce

small values of λ (<0.005 nm)

(de Broglie, 1924)

λ = 0.1(150/V)0.5

λ =𝒉

𝒑=

𝒉

𝒎𝒗

Considering the relativistic increase of mass at high velocity:

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Interaction of the Electron Beam with the Sample

(TEM)

(SEM)!

!

5*

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In a transmission electron microscope, beams of electrons are

focussed using magnetic lenses.

Image formation follows the same principles as in

conventional transmission light microscopy (an interference

image is formed)

The resolving power produced is up to 500,000 times greater

than the human eye.

Because a vacuum is needed, tissue has to be specially

prepared, and living cells cannot be examined

Transmission Electron Microscope (TEM)

!

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Transmission Electron Microscope5*

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Mitochondria

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• An electron beam scans the surface of the specimen

• Secondary electrons are released from the surface, and collected by a special electron detector

• The secondary electron current is converted into an image, which appears on a computer screen and gives an impression of the outer shape of the specimen

• For better contrast, the surface can be covered with a material of high atomic number (eg. Os)

INFO: a few SEM devices detect the backscattered electrons, and not secondary electrons

Scanning Electron Microscope!

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Scanning Electron Microscope5*

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Human Hair

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Minimum equations:

121

2

sin

sin

cin

r c

21

11)1(

1

RRn

f

fdiopterD

1)(

advanced equations:

oif

111

D=1/d

NA=n sina d=0.61 l / NA

d= l / (NAobjective +NAcondenser) → d ≈ l / 2NA

!

Outlook

𝜆 =ℎ

𝑝=

ℎ

𝑚𝑣

minimum / basic information

for explanation / orientation purposes

5* To impress the examiner