Transcript Document

Overview – Schedule for Basic Microscopy Training – MBL – December 2008
Overview
I.
Basics
Morning

Properties of Light

Basic Theories – Corpuscular, Wave (Quantum Theory omitted)

Terms

Interaction of Light with Materials
II.
Geometric Optics

Understanding Beam Paths

Constructing a “Microscope”
III.
The modern Microscope and its Components

Basic Discussion of Components – from the Light Source to the Eyepieces

Proper Setup and Alignment – Koehler Illumination
Before Dinner
IV.
Practical Aspects

Glass

Airy Disk, PSF

Aberrations

Selecting an Objective
I
Properties, Terms, Phenomena of Light
December 2008
Rudi Rottenfusser – Carl Zeiss MicroImaging
Basics about Light and Waves
I.
Properties of Light and Basic Theories
–
II.
Corpuscular, Wave Theories (Quantum Theory not considered)
Characteristics of Waves; Spectrum
–
–
–
III.
Amplitude
Wavelength / Spectrum
Metric Terms
Interaction of Waves with each other
–
–
IV.
Coherence - Incoherence
Interference (Coherence)
Phenomena of Light - Interaction of Waves with Material
–
–
–
–
–
–
–
–
Diffraction
Reflection
Refraction
Critical Angle
Total Reflection
Dispersion, Cover Slips
Transmission; Absorbance; ND Filters
Polarized Light
Corpuscular Theory
(Excerpt from Encyclopedia Britannica)

The apparent linear propagation of light was known since
antiquity. The ancient Greeks believed that light consisted of a
stream of corpuscles.

The first measurement of the velocity of light was carried out
by the Danish astronomer Olaus Roemer in 1676. Today the
velocity of light is known very accurately as 2.992926• 108 m/sec
(  300,000 km/sec  187,500 miles/sec).

Any satisfactory theory of light must explain its origin and
disappearance and its changes in speed and direction while it
passes through various media. Partial answers to these questions
were proposed in the 17th century by Newton, who based them
on the assumptions of a corpuscular theory.
Wave Theory
(Excerpt from Encyclopedia Britannica)

The English scientist Robert Hooke and the Dutch
astronomer, mathematician, and physicist Christiaan
Huygens, propose a “wave” theory in place of the
corpuscular theory.

In the early 19th century, the British physicist and
physician Thomas Young distinguishes between the two
theories by demonstrating interference. The French
physicist Augustin Jean Fresnel decisively favors the wave
theory.

In 1872 Ernst Abbe formulates his theory of microscopic
imaging, defining what’s known as the Abbe sine condition,
which becomes the basis for modern microscope design.
II - Characteristics of Waves
Amplitude
The Amplitude of a wave is half the difference in height
between the crest and the trough.
The Intensity is proportional to the square of the amplitude.
II - Characteristics of Waves
Wavelength 
1
1
II - Characteristics of Waves
Related Terms
 The period of a wave is the time it takes for two
crests or two troughs to travel to the same point in
space.
Example: Measure the time from the peak of a water wave as it passes by
a specific marker to the next peak passing by the same spot.
 The frequency of a wave is the reciprocal of its
period = 1/period [Hz or 1/sec]
Example: If the period of a wave is three seconds, then the frequency of the
wave is 1/3 per second, or 0.33 Hz.
II - Characteristics of Waves
 The velocity (or speed) at which a wave travels can
be calculated from the wavelength and the period.
 It is determined by dividing the distance one wave
travels by the time it takes to do this.
wavelength
velocity 
 wavelength  frequency
period
The frequency remains constant while light travels
through different media. It is the wavelength, which
changes.
II - Characteristics of Waves
What is “White Light”?
A combination of
all wavelengths
originating from
the source
Pl.note that wavelength relationship
exceeds visible range
(µm)
Named Spectral Lines
404.7
h
Violet Hg
435.8
g
Blue Hg
480.0
F‘
Blue Cd
486.1
F
Blue H
546.1
e
Green Hg
587.6
d
Yellow He
589.3
D
Sodium
643.8
C‘
Red Cd
656.3
C
Red H
706.5
r
Red He
759.4
A
Potassium
Energy
E  h   h 
c

h  6.626176  10 34Ws 2
Prefix Symbol
Factor
Zeta
Z
1021
1,000,000,000,000,000,000,000
Exa
E
1018
1,000,000,000,000,000,000
Peta
P
1015
1,000,000,000,000,000
1)
T
1012
1,000,000,000,000
Giga 2)
G
109
1,000,000,000
Mega 3)
M
106
1,000,000
kilo 4)
k
103
1,000
hecto 5)
h
102
100
Deka
D
101
10
100
1
Tera
1) TBytes = TeraBytes = 1012 Bytes
(storage capacity of computers)
2) Ghz = Gigahertz = 109 Hertz = 109 1/s
(frequency)
3) M = MegOhm = Million Ohm
(resistance)
4) kW
= kilowatt = 1000 Watt
(power)  ¾ HP
Examples:
Metric Prefixes
deci 6)
d
10-1
0.1
centi 7)
c
10-2
0.01
milli 8)
m
10-3
0.001
micro 9)
µ
10-6
0.000 001
nano 10)
n
10-9
0.000 000 001
Ångstrøm 13)
Å
10-10
0.000 000 000 1
pico 11)
p
10-12
0.000 000 000 001
femto 12)
f
10-15
0.000 000 000 000 001
atto
a
10-18
0.000 000 000 000 000 001
zepto
z
10-21
0.000 000 000 000 000 000 001
English/metric conversion (exact): 1” = 25.4 mm
5) hl = hectoliter = Hundred liters
(volume of barrels)
6) (dm)3
= decimeter3 = cubic decimeter = 1 liter
7) cm = centimeter
(length)  3/8”
8) mV = millivolt
(voltage)
9) µA = microampere
(current)
10) ng = nanogram
(weight)
11) pf = picofarad
(capacitance)
|
12) fl = femtoliter
(volume)
1 Nm = 1 Ws
N = Newton = force
that’s given to a mass of 1
kg and acceleration of 1
m/s2
Ws = Watt sec or Joule
= energy released in one
second by a current of one
Ampere through a
resistance of one Ohm
13) Ångstrøm – used primarily in Electron Microscopy
1/1000” = 1 mil = 25.4 µm
II - Characteristics of Waves
State of Polarization
Will be covered in great detail
during Bob Hard’s Pol Section
later on
III – Interaction of Waves
Shifts between waves (Phase)
d
Small phase differences between 2 waves
cannot be detected by the human eye
III – Interaction of Waves
Interference
• Coherence - What is it?
• Constructive Interference
• Destructive Interference
• Difference between Coherent and
Incoherent waves
III – Interaction of Waves
d) Interference
Constructive Interference
Coherent Waves
Amplitude
Intensity
Example:
A=5
>I = 25
B=3
>I = 9
C=5+3=8 >I = 64
Interference
Term
C  A B
2
I   A  B   A2  2 AB  B 2
III – Interaction of Waves
d) Interference
Constructive
Interference
Destructive Interference
Coherent Waves
Amplitudes
Intensity
Example:
A=5
>I = 25
B=3
>I = 9
C=5-3=2 >I = 4
Interference
Term
C  A B
2
I   A  B   A2  2 AB  B 2
III – Interaction of Waves
Incoherent Waves
A
B
C
D
E
F
G
H
I
J
Intensity
From “msnucleus.org”
I  A2  B 2  C 2  D 2  E 2  F 2  G 2  H 2  I 2  J 2
IV – Interaction of Waves with Material
Phenomena of Light
Reflection
Normal
(perpendicular
to interface
of different
materials)

’
90°

(angle of incidence)
= ’(angle of reflection)
When a beam of light strikes a surface at an angle
measured from a line perpendicular to that surface, it is
reflected in the opposite direction at an angle equal in size
Variations
(Types of Reflection)
Specular
Diffuse
Retro
Refraction
- the bending of light
as it passes from one material to another
Snell’s Law:
n1 sin b1 = n2 sin b2
Normal
(perpendicular to
interface of
different materials)
n1
b1
b2
n2
n
sin β  sin b 1
2
1 n2
Refractive index n
velocity vacuum
n
velocity medium
Medium
2.99792  108 ms

velocity medium
vmedium 
299792 kms
nmedium
Refractive Index Velocity in medium [km/s]
Vacuum
1
299792.458
Air
1.0003
299703
Water
1.33
225408
Glycerin
1.46
205337
Immersion Oil
1.518
197492
Glass
1.56 – 1.46
192175 - 205337
Diamond
2.42
123881
Quartz
1.544e / 1.553o
194166 / 193041
Light beam through a plane-parallel glass plate
b1
1
b2
n1
n2
2
3
n1
4
?
Light beam through a plane-parallel glass plate
90o
90o
b1
b2
b1
n1
n2
n1
Refraction (Marching Band Analogy)
Refraction (Marching Band Analogy)
Refraction (Marching Band Analogy)
Refraction (Marching Band Analogy)
Refraction (Marching Band Analogy)
Refraction (Marching Band Analogy)
Refraction (Marching Band Analogy)
Refraction (Marching Band Analogy)
Refraction (Marching Band Analogy)
Refraction (Marching Band Analogy)
Refraction (Marching Band Analogy)
Refraction in a Prism
Going from dense to less dense medium
n1
n2
b
“Critical Angle”
Snell’s Law: n1 sin b1 = n2 sin b2
sin b1 = 1
n1
n2
b
n1
sin b critical 
n2
crit.
 n1 
b crit.  sin  n 
 2
1
 n1 
b crit.  sin  n 
 2
1
Example 1
Example 2
Example 3
n1 = air = 1.00
n1 = water (tissue) = 1.35
n1 = air = 1.00
n2 = crown glass = 1.52
n2 = crown glass = 1.52
n2 = diamond = 2.42
sin = 0.658
sin = 0.888
sin = 0.413
Critical angle = 41o
Critical angle = 62.6o
Critical angle = 24.4o
Total Reflection
n1
n2
b
b'
Dispersion
The separation of white light into
spectral colors as a result of different amounts of
refraction by different wavelengths of light.
n  nF '  nC '
nF‘ = refractive index at the blue Cadmium line (480nm)
nC‘ = refractive index at the red Cadmium line (644nm)
Dispersion
in a plane-parallel glass plate
(e.g. slide, cover slip, window of a vessel)
“White” Light
Which expression is commonly used for “unwanted” dispersion?
Chromatic Aberration…
Dispersion of different materials:
Material
nblue (486nm)
nyellow (589nm) nred (656nm)
Crown Glass
1.524
1.517
1.515
0.009
Flint Glass
1.639
1.627
1.622
0.017
Water
1.337
1.333
1.331
0.006
Cargille Oil
1.530
1.520
1.516
0.014
Dispersion (~)
Choose the right
cover glass!
Types and Thickness Ranges
No.0 ......... 0.08 - 0.12 mm
No.1 ......... 0.13 - 0.17 mm
No.1.5....... 0.16 - 0.19 mm
No.2 ......... 0.19 - 0.23 mm
No.3 ......... 0.28 - 0.32 mm
No.4 ......... 0.38 - 0.42 mm
No.5 ......... 0.50 - 0.60 mm
Use 0.170 mm thick cover slips !
Transmission T
I0
I1
I1
λ 
T 
I0
d
Absorbance (Extinction) A
A    C  d  
(Lambert-Beer Law)
 = Absorption Coefficient
C = Concentration
d = Path Length
1
A  log
T
1
T
10
A
Neutral Density (ND) Filters
*standard Zeiss filters
Optical Density
Transmission (%)
f-stop
Optical Density
Transmission (%)
0 (no filter)
100.000
0
1.7
2.000
0.1
80.000
1/3
1.8
1.600
0.2
63.000
2/3
1.9
1.250
0.3
*50.000
1
2
1.000
0.4
40.000
1+ 1/3
2.1
0.800
0.5
32.000
1+ 2/3
2.2
0.630
0.6
*25.000
2
2.3
0.500
0.7
20.000
2.4
0.400
0.8
16.000
2.5
0.320
0.9
*12.500
2.6
0.250
1
10.000
2.7
0.200
1.1
8.000
2.8
0.160
1.2
*6.300
2.9
0.125
1.3
5.000
3
0.100
1.4
4.000
3.1
0.080
1.5
*3.200
3.2
0.063
1.6
2.500
3.3
0.050
3
4
5
f-stop
6
7
8
9
10
11
Multiple Phenomena in Optical Systems
Primary
reflected light
Filter
Refracted visible light /
Dispersion
Scatter and
decrease in
intensity with
increasing
pathlength
Secondary
reflected
light
Illumination
Secondary Refracted
+ Stray light
Polarized Light
Analyzer
Birefringent
Material
Polarizer
Polarized Light
Analyzer
Polarizer
Analyzer
Birefringent
Material
Polarizer
Polarized Light
Analyzer
Analyzer
Polarizer
Birefringent
Material
Polarizer
Polarized Light
Analyzer
Birefringent
Material
Polarizer
Polarized Light
Analyzer
Birefringent
Material
Polarizer
Birefringence
• The numerical difference between the maximum and minimum
refractive indices of anisotropic substances. nγ - nα.
• Birefringence may be qualitatively expressed as
• low (0 - 0.010),
• moderate (0.010 – 0.050)
• high (>0.050)
• extreme (>0.2)
• Birefringence may be determined by use of compensators, or
estimated through use of a Michel-Lévy Interference Color Chart.
Optical Path  n  d
Optical Path Difference  nObject  d  nBackground  d  no  nb   d
The Michel Lévy Color Chart
3rd
Order
Red
2nd
Order
Red
1st
Order
Red
1st
Order
Red
2nd
Order
Red
3rd
Order
Red
•An excellent introduction to this chart is provided at McCrone’s website
http://www.modernmicroscopy.com/main.asp?article=15
LOW
< 0.010
Moderate
0.010 – 0.050
High
> 0.050
Some Types of Birefringence
• Intrinsic or crystalline
(Quartz, Calcite, Myosin Filaments, Chromosomes, Keratin, Cellulose Fibers)
• Form or Textural (Plasma membranes, Actin filaments, microtubules)
• Edge (resulting from diffraction at edges of objects embedded in a
medium of different refractive Index)
• Strain (resulting from mechanical stress e.g. glass, plastic sheets)
• Circular –also known as- Optical Rotation
(sugars, amino acids, proteins)
Light as an electromagnetic wave
The wave exhibits electric (E) and magnetic (B) fields whose amplitudes oscillate as a
sine function over dimensions of space or time.
The amplitudes of the electric and magnetic components at a particular instant or
location are described as vectors that vibrate in two planes perpendicular to each
other and perpendicular to the direction of propagation.
At any given time or distance the E and B vectors are equal in phase.
For convenience it is common to show only the electric field vector (E vector)
of a wave in graphs and diagrams.
Polarized Light
y
E
z
x
E
E
Ey
Ex


Polarized Light and Birefringence
Polarized Light and Birefringence
Interface with
birefringent Material
ng = higher refractive index > slower wave
n = lower refractive index > faster wave
How to create circularly polarized light
Linear
polarizer
¼ wave plate
Circularly Polarized Light
5
x
E
z
4
3
2
1
5
4
3
2
1

E
y
Sénarmont Compensator*
E
x
z
E
y
E
x
¼ wave plate, located before
analyzer, is oriented with its
birefringence parallel to the
polarizer
E or analyzer. Therefore,
there will be no effect on the
polarized beam.
Birefringence produced by
specimen (occurring at 45˚), will
be converted by ¼ wave plate into
circular polarized light which can
pass through the analyzer.
By rotating the analyzer, it is
possible to introduce “bias”
birefringence because it will not be
parallel to ¼ wave plate any more.
* 1st described by de Sénarmont in 1840