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 2.99792 108 ms velocity vacuum n velocity medium velocity medium 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