Lecture 23 MNS 102: Techniques for Materials and Nano Sciences

• Light Microscopy - Overview

• Basic concepts: Numerical Aperture (NA), working distance (WD), resolution (R), magnification (M), depth of field or depth of focus (DOF)

• Types: Bright Field (BF), Dark Field (DF), Polarized Light, Differential Interference Contrast (DIC), Phase Contrast (PC).

• Fluorescence Microscopy

Human eye can resolve

~ 0.1 mm or 100 microns

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Reference: #1 C. R. Brundle, C. A. Evans, S. Wilson, "Encyclopedia of Materials Characterization", Butterworth-Heinemann, Toronto (1992), Ch. 2.0, 2.1 Reference: Taewoo Lee et al. “Optical Microscopy of Soft Matter Systems” arXiv:1108.3287 - http://arxiv.org/ftp/arxiv/papers/1108/1108.3287.pdf Reference: D.B. Murphy, “Fundamentals of Light Microscopy and Electronic Imaging", Wiley, New York (2001). http://www.biology.uoc.gr/courses/BIOL493/documents/book.pdf

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• c = , where c = 3 x 1010 cm/s

• E = h , where h = 6.62 x 10-27 erg s

• E = h c ()-1 , where ()-1 is the wavenumber

Wavelength sets Information Limit

M R

1 100,000 nm

100 1,000 nm

1,000 100 nm

10,000 10 nm

100,000 1 nm

1,000,000 0.1 nm

Thin Lens Optics

In thin lens optics… Magnification (M) is defined by the ratio of the image distance to object distance, i.e., di / dO

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d0 di

• Human eye ~ 0.1 mm

• Apparent resolvable distance by the eye for a magnified object is: R = 0.1 mm / M

Lens Imperfection • Spherical aberration: Lens curvature

deviates from the ideal shape, which causes different focal distances.

• Chromatic aberration: Lens focusses each wavelength at a different spot, but can be corrected by achromat, fluorite, or apochromat materials.

• Field of view flatness

• Immersion media

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Optical Microscopes: History

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Saw single-cell organism in pond water Saw pores in cork – “cells”

Basic Components

> Illumination source: transmitted light vs reflected light > Condenser Lens > Specimen > Objective Lens > Viewer (eyepiece or CCD)

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A Simple Light Microscope

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Objective

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Numerical Aperture & Working Distance

• Performance of an objective lens is defined by NA and WD.

• Numerical Aperture (NA) of an objective determines the range of angles over which the objective lens could accept light.

• NA = n sin θ, where n = refractive index of the medium between the objective lens and the sample (1 for air, 1.33 for water, 1.56 for oils) and = half-angle of the cone of light collected by the objective lens.

• NA < 1 for air objectives ; NA ≈ 1.5 for oil immersion objectives.

• Working Distance (WD) is the distance between the front lens of the objective to the specimen surface when the inspected area is in focus. This defines the max. specimen height.

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Spatial Resolution set by Rayleigh Criterion

• Resolution = shortest distance between two points that can still be separated = k / NA

where k = 0.61 (Rayleigh) or 0.5 (Abbe)

• NA = Numerical Aperture = n sin where n = refractive index of the medium, and = semi-angle (half-angle) of an objective lens; NA typically < 1

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Effect of NA on the image of a point.

Resolution achieved by separation of Airy disks, when max of 1st disk overlaps first min of 2nd disk (Rayleigh).

θ

θ θ

Resolution and PSF

• NA defines Point Spread Function (PSF), which is light intensity distribution in the image acquired by the microscope from a point source. PSF(r) = [ 2 J1(r a) / (r a) ]2 where a = 2 (NA) / and J1

is the Bessel function of the first kind.

• Airy diffraction pattern gives the first minimum at r = W/2. ∴ For two Airy discs to be resolved, they must be separated by R ≥ W/2. R is the lateral resolution and R = 0.61 / NA is the diffraction limit.

• Higher NA, better resolution – but note R is also limited by the wavelength.

• Smaller WD > larger > larger NA > smaller R (i.e. better resolution). Conversely, large WD > poorer resolution.

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Magnification

Magnification is the enlargement of the incoming angular acceptance. M = tan / tan 0 / 0

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For a typical stereo microscope with: (a) a 0.5X objective and a 1.0X objective, (b) a zoom range of 0.7 to 11.5X and (c) a 0.5X camera adapter, and the image is collected on a 2.2 megapixel camera (with a 1/1.8" or 0.55556“ CCD chip) and projected onto a 24” monitor. Total Magnification = (Objective Mag) x (Zoom Mag) x (Camera Adapter Mag) x (Monitor Size/CCD Chip Size) Low end: Total Mag = 0.5 x 0.7 x 0.50 x (24/0.55556) = 7.6 High end: Total Mag = 1.0 x 11.5 x 0.5 x (24/0.5556) = 248.4 If we just have an eyepiece with a 10X mag, then we have 3.5 (low end) and 115 (high end).

Olympus SZX16 Stereo microscope

d0 di

Depth of Focus or Depth of Field (DOF)

• Depth of Focus refers to the image, while Depth of Field refers to the specimen.

• Depth of Field (or vertical resolution) measures the ability to produce a sharp image from a non-flat surface.

• DOF /NA for a set magnification, & can be increased by inserting an objective aperture.

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Light Microscope Electron Microscope

Wavelength = 500 nm (150/V0) = 0.0055 nm at 50 kV

Refraction Index = n 1.5 (glass) 1.0 (vacuum)

Half-angle = 70 deg 1 deg

Resolution = 0.61 / NA where NA = n sin

200 nm 0.16 nm

Depth of Field (DOF) = distance parallel to the optical axis that a feature on the specimen can be displaced without loss of resolution.

DOF = λ𝑛2−𝑁𝐴2

𝑁𝐴2 +250

𝑀2 M = 10, DOF = 60 m M = 100, DOF = 8 m M = 1,000, DOF = 200 nm

DOF = 0.1 𝑚𝑚

𝑀 𝜃

M = 10, DOF = 1,000 m M = 100, DOF = 100 m M = 1,000, DOF = 10 m M = 10,000, DOF = 1 m

R vs NA

• Higher NA > better (smaller) R

• For the same NA: Smaller > better R

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DOF vs NA

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• Higher NA > poorer (smaller) DOF

• For the same NA: Smaller > poorer DOF

• Ideally, we want small R (i.e. high resolution) and large DOF – and this is mutually exclusive.

Homework 5A: Work through the following site: http://micro.magnet.fsu.edu/primer/anatomy/numaperture.html.

• When NA is increased, what happens to (a) the working distance, and (b) the brightness of the image in focus.

• To resolve two points separated by 1,000 nm (i.e. 1 micron) using light of 500 nm wavelength, what is the smallest NA required? Can one resolve these two points with light of 700 nm wavelength? (Use the Java app at the above site.)

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Types of Light Microscopy

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Based on contrast modes and/or illumination methods:

• Bright Field a conventional light microscope

• Dark Field

• Polarized Light

• Phase contrast Fritz Zemike, Nobel Prize in Physics, 1953

• Differential Interference Contrast (DIC) Georges Nomarski, 1955

• Fluorescence

Except for Fluorescence Microscopy, all five techniques involve transmission, absorption, refraction or scattering of light.

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• Bright Field: Image comes from direct interaction of the specimen with unpolarized white light. Processes include absorption, refraction, scattering, and reflection. Pro: Easy to perform; good contrast of dark colours. Con: Bad contrast of light colours (biological samples); over-illumination.

• Dark Field: Image is formed by collecting only light scattered by the specimen. Oblique illumination. Direct, unscattered light is blocked. Typically used for specimen with sparse scattering objects dispersed in a non-scattering medium. Pro: Effective on highly transmitting specimens (biological samples), less artifacts (no halos). Con: Intense illumination needed and this could cause specimen damage, blind for low scattering samples.

Bright Field vs Dark Field Microscopy

Köhler Illumination

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Kohler illumination is a technique used to provide extremely even specimen illumination and eliminate the image of the illumination source. This is achieved by making the image of light source perfectly defocussed in the sample and image planes.

Homework 5B: In less than one page, discuss the difference between Kohler illumination and critical illumination. Explain how this can be achieved in an optical microscope.

Optics Setup

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Polarization of Light and Wollaston Prisms

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Polarized Light Microscopy

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• A “polarizer” is used to create linearly polarized light for illuminating the specimen, and a second polarizer called the “analyser” to infer the polarization properties of the materials.

• When the polarizer and analyser is crossed, the transmitted light intensity is Iperpendicular = I0 sin2(2) sin2() where is the angle between the polarization vector and the optical axis of the birefringent material, and is the phase (= 2 n d/) introduced by the thickness of the material d and n is the birefringence.

• When the polarizer and analyser is parallel, the transmitted light intensity is Iparallel = I0 [1 sin2(2) sin2()]

• Linearly polarized light is split by the birefringent specimen into two components (extraordinary and ordinary), propagating at different speeds and resulting in elliptical polarization.

• Use pattern to deduce spatial variations of optical axis orientation and the value of n.

Birefringent materials are optically anisotropic materials that have a refractive index that depends on the polarization and propagation direction of light. E.g. SiC, many plastics, CaCO3, ice, rutile TiO2.

Differential Interference Contrast (DIC) & Phase Contrast (PC)

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• Contrast is caused by difference in reflection, absorption, refraction, polarization, and other optical processes.

• DIC and PC are important for enhancing contrast in transparent specimen (e.g. cell).

• PC originates from the small phase shifts of light passing through a transparent specimen.

• DIC corresponds to interferometry due to slopes and valleys of the specimen, producing differences in the optical paths. In effect, the gradient of the refractive index within the specimen produces the DIC.

BF (upper) vs DIC (lower)

Phase Contrast

Change the phase by delaying or advancing a quarter wavelength.

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PC Microscopy

• Small spatial variations in phase are transformed into corresponding changes in the intensity of transmitted light.

• Light passes through an annular ring before the condenser lens and is focussed onto the specimen.

• The light can either pass through the specimen undeviated (yellow) or diffracted with a changed phase (violet) depending on the composition of the specimen.

• Both undeviated and diffracted beams are collected by the objective and transmitted through a phase ring to the eyepiece. The phase ring introduces an additional phase shift to the undeviated light used as the reference.

• Pro: Phase contrast imaging is not sensitive to polarization and birefringence effects. Good for living cells and soft materials.

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Differential Interference Contrast

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• White light is sent to the first polarizer.

• The polarized light is separated into two orthogonally polarized and spatially displaced (sheared) components by the first beam splitter (Nomarski-modified Wollaston prism).

• Each component propagates a different path, leading to different optical path difference after existing the sample.

• After the objective, the two components are recombined by a second beam splitter.

• The polarization of the resulting light is then analysed by the second polarizer (the analyser).

• The result is that the optical path length gradient along the shear direction will enhance contrast due to edges and interfaces of the specimen with different refractive indices.

• More gradient > more contrast.

DIC Microscopy

Transmitted Light vs Reflected Light Illumination

• Thus far, we talk about transmitted light illumination, i.e. light from the illumination source passes through the specimen and is detected on the other side (the objective side). Here, light absorption is an important process, along with diffraction.

• We can also use reflected light illumination , i.e. light from the illumination source comes from the top of the specimen (not below the specimen). Here, light reflection (along with diffraction) is an important process b/c the objective is on the same side of the light illumination.

• Reflected light illumination is more popular in commercial microscopes.

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BF vs DF – Reflected Light Illumination Setup

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PL & DIC – Reflected Light Illumination Setup

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Contrast Modes vs Image Quality

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BF

PL DF

DIC

Fluorescence

• Use of fluorescence in microscopy is very important to quantitative biology.

• Images show locations of the fluorescent markers. All non-stained tissue remains transparent.

• Amount of fluorescence can be measured accurately.

• This has led to recent advances in super-resolution microscopy, with resolution going below 60 nm.

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Fluorescent Materials

• Small organic dye molecules

• Fluorescent proteins – Green FP - M. Chalfie, O. Shimomura, R.Y. Tsien, Nobel Prize in Chemistry 2008

• Quantum dots

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Glow-stick & Chemiluminescence

Oxidation of an diphenyl oxalate (top), decomposition of 1,2-dioxetanedione (middle), relaxation of dye (lower).

Dye could be carcinogenic.

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Fluorescence Microscopy

• Based on fluorescence phenomenon: (a) absorption of light by fluorescent dye molecules or fluorophores at a specific wavelength, thereby promoting to an excited state, followed by (b) emission of light at a longer wavelength. The lifetime of the excited state is usually in nanoseconds.

• The shift between the absorption peak and emission peak is called the Stokes shift and it is caused by non- radiative processes. This allows the use of optical filters to separate the excitation and emission signals.

• A filter cube contains an excitation filter, a dichroic mirror and an emission filter. Dichroic mirror is a very accurate mirror that reflects light of a small range of colours (wavelengths) while passing the other colours.

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Epifluorescence Microscope

Thick section of human skin: green = anti-basal lamina proten; red = neuronal processes; blue = collagen and elastin auto fluoresce Source: www.zeiss.com

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Homework 5C: Discuss in one page or less, the difference between epifluorescence and transfluorescence. Identify the advantage of the former.

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