Overview – Schedule for Basic Microscopy Training – MBL – December 2008

I. Basics 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

IV. Practical Aspects Glass

Airy Disk, PSF

Aberrations

Selecting an Objective

Overview

Morning

Before D

inner

II

Properties, Terms, Phenomena of LightProperties, Terms, Phenomena of Light

December 2008December 2008

Rudi Rottenfusser – Carl Zeiss MicroImaging

I. Properties of Light and Basic Theories– Corpuscular, Wave Theories (Quantum Theory not considered)

II. Characteristics of Waves; Spectrum– Amplitude– Wavelength / Spectrum– Metric Terms

III. Interaction of Waves with each other– Coherence - Incoherence– Interference (Coherence)

IV. Phenomena of Light - Interaction of Waves with Material– Diffraction – Reflection– Refraction– Critical Angle– Total Reflection – Dispersion, Cover Slips– Transmission; Absorbance; ND Filters– Polarized Light

Basics about Light and Waves

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. 

Corpuscular 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.  

Wave Theory(Excerpt from Encyclopedia Britannica)

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

11

Wavelength

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.

II - Characteristics of Waves

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.

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.

frequencywavelengthperiod

wavelengthvelocity

II - Characteristics of Waves

The frequency remains constant while light travels through different media. It is the wavelength, which changes.

A combination of all wavelengths originating from the source

What is “White Light”?

Pl.note that wavelength relationship exceeds visible range

II - Characteristics of Waves

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

(µm)

En

erg

y

Speed of light = 2,99,792458 300,000 km/sec

Energy

c

hhE 23410626176.6 Wsh

Metric

P

refi

xes

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

Tera 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

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

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

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)

13) Ångstrøm – used primarily in Electron Microscopy

Exam

ple

s:

English/metric conversion (exact): 1” = 25.4 mm | 1/1000” = 1 mil = 25.4 µm

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

State of Polarization

II - Characteristics of Waves

Will be covered in great detail during Bob Hard’s Pol Section later on

Small phase differences between 2 waves cannot be detected by the human eye

Shifts between waves (Phase)

III – Interaction of Waves

• Coherence - What is it?

• Constructive Interference

• Destructive Interference

• Difference between Coherent and Incoherent waves

Interference

III – Interaction of Waves

d) Interference

Constructive Interference

BAC 222 2 BABABAI Intensity

Amplitude

Interference Term

Coh

ere

nt W

aves

Example:

A=5 >I = 25

B=3 >I = 9

C=5+3=8 >I = 64

III – Interaction of Waves

d) Interference

Constructive Interference

Destructive Interference

Amplitudes

Intensity

BAC 222 2 BABABAI

Interference Term

Coh

ere

nt W

aves

Example:

A=5 >I = 25

B=3 >I = 9

C=5-3=2 >I = 4

III – Interaction of Waves

Intensity 2222222222 JIHGFEDCBAI

From “msnucleus.org”

ABCDEFGHIJ

Incoherent Waves

III – Interaction of Waves

Phenomena of Light Phenomena of Light

IV – Interaction of Waves with Material

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

90°

’

(angle of incidence) = ’(angle of reflection)

Normal (perpendicul

ar to interface of

different materials)

Variations

(Types of Reflection)

Specular Diffuse Retro

- the bending of light as it passes from one material to another

n1

1

2

n2

Normal (perpendicular to interface of different materials)

Snell’s Law:

n1 sin 1 = n2 sin 2

Refraction

2

1

1sin

2sin

n

nβ

Medium Refractive Index

Vacuum 1

Air 1.0003

Water 1.33

Glycerin 1.46

Immersion Oil 1.518

Glass 1.56 – 1.46

Diamond 2.42

Quartz 1.544e / 1.553o

medium

sm

medium

vacuum

velocityvelocity

velocityn

81099792.2

Refractive indexRefractive index n

Velocity in medium [km/s]

299792.458

299703

225408

205337

197492

192175 - 205337

123881

194166 / 193041

medium

skm

medium nv

299792

n1

1

2

n2 n1

Light beam through a plane-parallel glass plate

4

3

2

1

?

n1

1

2

n2 n1

Light beam through a plane-parallel glass plate

1

90o 90o

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

n2

n1

“Critical Angle”

.crit

n2

n1

2

11

.sin

n

ncrit

Snell’s Law: n1 sin 1 = n2 sin 2

2

1sinn

ncritical

sin 1 = 1

2

11

.sin

n

ncrit

n1 = water (tissue) = 1.35

n2 = crown glass = 1.52

n1 = air = 1.00

n2 = crown glass = 1.52

Example 1

n1 = air = 1.00

n2 = diamond = 2.42

Example 2 Example 3

sin = 0.658

Critical angle = 41o

sin = 0.888

Critical angle = 62.6o

sin = 0.413

Critical angle = 24.4o

Total Reflection

n2

n1

'

The separation of white light into spectral colors as a result of different amounts of refraction by different wavelengths of light.

Dispersion

nF‘ = refractive index at the blue Cadmium line (480nm)

nC‘ = refractive index at the red Cadmium line (644nm)

'' CF nnn

Dispersion in a plane-parallel glass plate

(e.g. slide, cover slip, window of a vessel)

Which expression is commonly used for “unwanted” dispersion?Chromatic Aberration…

“White” Light

Dispersion of different materials:

Material nblue (486nm) nyellow (589nm) nred (656nm) Dispersion

(~)

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

Use 0.170 mm thick cover slips !

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

Choose the right cover glass!

No.1.5....... 0.16 - 0.19 mm

Absorbance (Extinction) A

λI

IT

0

1

dCA TA

1log

= Absorption Coefficient

C = Concentration

d = Path Length

I0 I1

Transmission T

d

AT

101

(Lambert-Beer Law)

Neutral Density (ND) Filters

Optical Density Transmission (%) f-stop Optical Density Transmission (%) f-stop

0 (no filter) 100.000 0 1.7 2.000  

0.1 80.000 1/3  1.8 1.600 6

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 7

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 8

0.8 16.000   2.5 0.320  

0.9 *12.500 3 2.6 0.250  

1 10.000   2.7 0.200 9

1.1 8.000   2.8 0.160  

1.2 *6.300 4 2.9 0.125  

1.3 5.000   3 0.100 10

1.4 4.000   3.1 0.080  

1.5 *3.200 5 3.2 0.063  

1.6 2.500   3.3 0.050 11

*standard Zeiss filters

Refracted visible light / Dispersion

Primary reflected light

Illumination

Secondary reflected

light

Secondary Refracted + Stray light

Scatter and decrease in intensity with increasing pathlength

Multiple Phenomena in Optical Systems

Filter

Polarized Light

Birefringent Material

Polarizer

Analyzer

Polarized Light

Birefringent Material

Polarizer

Analyzer

Polarizer

Analyzer

Polarized Light

Birefringent Material

Polarizer

AnalyzerPolarizer

Analyzer

Polarized Light

Birefringent Material

Polarizer

Analyzer

Polarized Light

Birefringent Material

Polarizer

Analyzer

• 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.

Birefringence

dn Path Optical

dnndndn boBackgroundObject Difference Path Optical

The Michel Lévy Color Chart

3rd

OrderRed

1st OrderRed

1st OrderRed

2nd OrderRed

2nd

OrderRed

3rd

OrderRed

•An excellent introduction to this chart is provided at McCrone’s website http://www.modernmicroscopy.com/main.asp?article=15

LOW

< 0.010Moderate

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)

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.

Light as an electromagnetic wave

E

y

xz

Ey

Ex

E E

Polarized Light

Polarized Light and Birefringence

Polarized Light and Birefringence

Interface with birefringent Material

n = higher refractive index > slower waven = lower refractive index > faster wave

Linearpolarizer

¼ wave plate

Unpolarizedlight linearlypolarized

Circularlypolarized

How to create circularly polarized light

xz

Ex

E

Circularly Polarized Light

1

1

2

2

3

3

4

4

5

5

E

y

xz

Ey E

x

E E

Sénarmont Compensator*

¼ wave plate, located before analyzer, is oriented with its birefringence parallel to the polarizer 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