Optical Microscopy

• Introduction• Lens formula, Image formation and

Magnification • Resolution and lens defects• Basic components and their functions• Common modes of analysis • Specialized Microscopy Techniques• Typical examples of applications

Diffraction of Light

Sin=/d/d

film

1st 2nd 3rd

Diffraction of light occurs when a light wave passes by a corner (or a barrier) or through an opening (or a slit) that is physically the approximate size of, or even smaller than that light's wavelength.

Light waves interfere constructively and destructively.

Resolution of Microscope – Rayleigh Criteria

Rayleigh Criteria: Angular separation of the two points is such that thecentral maximum of one image falls on the first diffraction minimum of the other

=m 1.22/d

Resolution of Microscope – in terms of Linear separation

To express the resolution in terms of a linear separation r, have to consider the Abbe’s theory

Path difference between the two beams passing the two slits is

Assuming that the two beams are just collected by the objective, then i = and

dmin = /2sin

sinsin did

I II

I II

Resolution of Microscope – Numerical Aperture

If the space between the specimen and the objective is filled with a medium of refractive index n, then wavelength in medium n = /n

The dmin = /2n sin = /2(N.A.) For circular aperture

dmin= 1.22/2(N.A.)=0.61/(N.A.)

where N.A. = n sin is called numerical aperture

Immersion oil n=1.515

NA of an objective is a measure of its ability togather light and resolve fine specimen detail at a fixed object distance. NA = n(sin )n: refractive index of the imaging medium betweenthe front lens of objective and specimen cover glass

Numerical Aperture (NA)

Angular aperture

One half of A-A

NA=1 - theoretical maximum numerical aperture of a lens operating with air as the imaging medium

(72 degrees)

The smallest distance between two specimen points that can still be distinguished as two separate entities

dmin = 0.61/NA NA=nsin

– illumination wavelength (light)NA – numerical aperture -one half of the objective angular aperture n-imaging medium refractive index

dmin ~ 0.3m for a midspectrum of 0.55m

Resolution of a Microscope (lateral)

Factors Affecting Resolution Resolution = dmin = 0.61/(N.A.)

Resolution improves (smaller dmin) if or n or Assuming that sin = 0.95 ( = 71.8°)

(The eye is more sensitive to blue than violet)

Wavelength

Red

Yellow

Green

Blue

Violet

A ir (n= 1) O il (n = 1.515)

0.42 m

0.39 m

0.35 m

0.31 m

0.27 m

0.28 m

0.17 m

0.20 m

0.23 m

0.25 m

650 nm

600 nm

550 nm

475 nm

400 nm

Optical Aberrations

• Spherical (geometrical) aberration – related to the spherical nature of the lens

• Chromatic aberration – arise from variations in the refractive indices of the wide range of frequencies in visible light

Two primary causes of non-ideal lens action:

Astigmatism, field curvature and comatic aberrationsare easily corrected with proper lens fabrication.

Reduce the resolution of microscope

Defects in Lens Spherical Aberration –

Peripheral rays and axial rays have different focal points (caused by spherical shape of the lens surfaces.

causes the image to appear hazy or blurred and slightly out of focus.

very important in terms of the resolution of the lens because it affects the coincident imaging of points along the optical axis and degrade the performance of the lens.

Chromatic Aberration Axial - Blue light is refracted to

the greatest extent followed by green and red light, a phenomenon commonly referred to as dispersion

Lateral - chromatic difference of magnification: the blue image of a detail was slightly larger than the green image or the red image in white light, thus causing color ringing of specimen details at the outer regions of the field of view

Defects in Lens

A converging lens can be combined with a weaker diverging lens, so that the chromatic aberrations cancel for certain wavelengths: The combination – achromatic doublet

Depth of focus (F mm)

The distance above and belowgeometric image plane withinwhich the image is in focus

The axial range through whichan object can be focused withoutany appreciable change in imagesharpness

(F m)

M NA F FM NA F F

Axial resolution – Depth of FieldDepth of Field (F m)

F is determined by NA.

NA F F0.1 0.13 15.50.4 3.8 5.8.95 80.0 0.19

Basic components and their functions

Olympus BX51

Research Microscope

Cutaway Diagram

Beam splitter

camera

Reflected light

Transmitted light

Functions of the Major Parts of a Optical Microscope

Lamp and Condenser: project a parallel beam of light onto the sample for illumination

Sample stage with X-Y movement: sample is placed on the stage and different part of the sample can be viewed due to the X-Y movement capability

Focusing knobs: since the distance between objective and eyepiece is fixed, focusing is achieved by moving the sample relative to the objective lens

Light Sources

Condenser

Light from the microscope light source

Condenser gathers light and concentrates it into a cone of light that illuminates the specimen with uniform intensity over the entire viewfield

Specimen Stage

Objective: does the main part of magnification and resolves the fine details on the samples (mo ~ 10 – 100)

Eyepiece: forms a further magnified virtual image which can be observed directly with eyes (me ~ 10)

Beam splitter and camera: allow a permanent record of the real image from the objective be made on film

Functions of the Major Parts of a Optical Microscope

Objective specifications

Objectives are the most important components of alight microscope: image formation, magnification, thequality of images and the resolution of the microscope

Microscope Objectives

Anatomy of an objective

ricalture

dmin = 0.61/NA

(Diaphragm)

Eyepieces (Oculars) work in combination with microscope objectives to further magnify the intermediate image

Eyepiece

M=(L/fo)(25/fe)

Common Modes of Analysis

• Transmitted OM - transparent specimens thin section of rocks, minerals and single crystals• Reflected OM - opaque specimens most metals, ceramics, semiconductors

Specialized Microscopy Techniques• Polarized OM - specimens with anisotropic optical characterCharacteristics of materials can be determined

morphology (shape and size), phase distribution (amorphous or crystalline), transparency or opacity, color, refractive indices, dispersion of refractive indices, crystal system, birefringence, degree of crystallinity, polymorphism and etc.

Depending on the nature of samples, different illumination methods must be used

Olympus BX51

Research Microscope

Cutaway Diagram

Beam splitter

camera

Reflected light

Transmitted light

When the electric field vectors of light are restricted to a single plane by filtration, then the the light is said to be polarized with respect to the direction of propagation and all waves vibrate in the same plane.

Polarization of Light

Polarized Light Microscope Configuration

Typical examples of applications

Grain Size Examination

A grain boundary intersecting a polished surface is not in equilibrium (a). At elevated temperatures (b), surface diffusion forms a grain-boundary groove in order to balance the surface tension forces.

a

b

Thermal Etching

20m

1200C/30min

1200C/2h

Grain Size Examination

Objective Lens

x100

Grain Growth - Reflected OM

Polycrystalline CaF2 illustrating normal graingrowth. Better grain size distribution.

Large grains in polycrystallinespinel (MgAl2O4) growing bysecondary recrystallization from a fine-grained matrix

30m5m

Liquid Phase Sintering – Reflective OM

Microstructure of MgO-2% kaolin body resultingfrom reactive-liquid phase sintering.

Amorphousphase

40m

Image of Magnetic Domains

Magnetic domains and walls on a (110)-oriented garnet crystal (Transmitted LM with oblique illumination). The domains structure is illustrated in (b).

Polarized Optical Microscopy (POM)

(a) Surface features of a microprocessor integrated circuit(b)Apollo 14 Moon rock

Reflected POM Transmitted POM

Phase Identification by Reflected Polarized Optical Microscopy

                                                                                                                                                                           

                          

YBa2Cu307-x superconductor material: (a) tetragonal phase and (b) orthorhombic phase with multiple twinning (arrowed) (100 x).

Specialized LM Techniques• Enhancement of Contrast

Darkfield Microscopy Phase contrast microscopyDifferential interference contrast microscopy Fluorescence microscopy-mainly organic materials

• Confocal scanning optical microscopy (new) Three-Dimensional Optical Microscopy inspect and measure submicrometer features in semiconductors and other materials

• Hot- and cold-stage microscopymelting, freezing points and eutectics, polymorphs, twin and domain dynamics, phase transformations

• In situ microscopyE-field, stress, etc.

• Special environmental stages-vacuum or gases

ContrastContrast is defined as the difference in light intensity between the specimen and the adjacent background relative to the overall background intensity.

Image contrast, C is defined by

Sspecimen-Sbackgroud SC = = Sspecimen SA

Sspecimen and Sbackgroud are intensities measured from specimen and backgroud, e.g., A and B, in the scanned area.

Angle of Illumination Bright filed illumination – The normal method of illumination,

light comes from above (for reflected OM) Oblique illumination – light is not projected along the optical

axis of the objective lens; better contrast for detail features Dark field illumination – The light is projected onto specimen

surface through a special mirror block and attachment in the objective – the most effective way to improve contrast.

Light stop

ImaxImin

C=Imax-Imin

Imax

C-contrast

Transmitted Dark Field Illumination

specimen

I I

distance distance

Oblique rays

Contrast Enhancement

OM images of the green alga Micrasterias

Crystals Growth-Interference contrast microscopy

Growth spiral on cadmium iodide crystals growingFrom water solution (1025x).

Confocal Scanning Optical Microscopy

Critical dimension measurementsin semiconductor metrologyCross-sectional image with line scan at PR/Si interface of a sample containing 0.6m-wide lines and 1.0m-thick photoresist on silicon.

The bottom width, w, determining the area of the circuit that is protected from further processing, can be measured accurately by using CSOP.

Measurement of the patterned photoresist is important because it allows the process engineer to simultaneously monitor for defects, misalignment, or other artifacts that may affect the manufacturing line.

w

Three-Dimensional Optical Microscopy

Hot-stage POM of Phase Transformations in Pb(Mg1/3Nb2/3)O3-PbTiO3 Crystals

(a) and (b) at 20oC, strongly birefringent domains with extinction directions along <100>cubic, indicating a tetragonal symmetry; (c) at 240oC, phase transition from the tetragonal into cubic phase with increasing isotropic areas at the expense of vanishing strip domains.

n

T(oC)

E-field Induced Phase Transition in Pb(Zn1/3Nb2/3)O3-PbTiO3 Crystals

Schematic diagram forin situ domain observa-tions.

Domain structures of PZN-PTcrystals as a function of E-field; (a) E=20kV/cm, (b) e=23.5kV/cm(c) E=27kV/cmRhombohedral at E=0 andTetragonal was induced at E>20kV/cm

a b cSingle domain

Review - Optical Microscopy• Use visible light as illumination source• Has a resolution of ~o.2m• Range of samples characterized - almost unlimited for solids and liquid crystals• Usually nondestructive; sample preparation may involve material removal•Main use – direct visual observation; preliminary observation for final charac-terization with applications in geology, medicine, materials research and engineering, industries, and etc. • Cost - $15,000-$390,000 or more

Characteristics of Materials Can be determined By OM:

morphology (shape and size), phase distribution (amorphous or crystalline), transparency or opacity, color, refractive indices, dispersion of refractive indices, crystal system, birefringence, degree of crystallinity, polymorphism and etc.

Limits of Optical Microscopy

• Small depth of field <15.5mRough surface

• Low resolution ~0.2m• Shape of specimen

Thin section or polished surface

Glass slide

specimenCover glass

resin

20m

• Lack of compositional and crystallographic information

Optical Microscopy vs Scanning Electron Microscopy

m

OM SEM

Small depth of field Low resolution

Large depth of field High resolution

radiolarian

http://www.mse.iastate.edu/microscopy/