optical microscopy introduction lens formula, image formation and magnification resolution and lens...
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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
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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.
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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
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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
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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
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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)
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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)
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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
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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
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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.
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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
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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
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Basic components and their functions
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Olympus BX51
Research Microscope
Cutaway Diagram
Beam splitter
camera
Reflected light
Transmitted light
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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
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Light Sources
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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
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Specimen Stage
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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
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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
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(Diaphragm)
Eyepieces (Oculars) work in combination with microscope objectives to further magnify the intermediate image
Eyepiece
M=(L/fo)(25/fe)
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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
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Olympus BX51
Research Microscope
Cutaway Diagram
Beam splitter
camera
Reflected light
Transmitted light
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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
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Polarized Light Microscope Configuration
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Typical examples of applications
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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
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Grain Size Examination
Objective Lens
x100
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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
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Liquid Phase Sintering – Reflective OM
Microstructure of MgO-2% kaolin body resultingfrom reactive-liquid phase sintering.
Amorphousphase
40m
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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).
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Polarized Optical Microscopy (POM)
(a) Surface features of a microprocessor integrated circuit(b)Apollo 14 Moon rock
Reflected POM Transmitted POM
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Phase Identification by Reflected Polarized Optical Microscopy
YBa2Cu307-x superconductor material: (a) tetragonal phase and (b) orthorhombic phase with multiple twinning (arrowed) (100 x).
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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
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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.
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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
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Transmitted Dark Field Illumination
specimen
I I
distance distance
Oblique rays
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Contrast Enhancement
OM images of the green alga Micrasterias
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Crystals Growth-Interference contrast microscopy
Growth spiral on cadmium iodide crystals growingFrom water solution (1025x).
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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
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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)
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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
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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
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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.
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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
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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/