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 http://micro.magnet.fsu.edu/primer/java/lenses/converginglenses/index.html

Diffraction of Light 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. Sin=/d /d http://micro.magnet.fsu.edu/primer/java/diffraction/basicdiffraction/index.html Single slit diffraction pattern and location of dark fringes is given by sin=/d. Bragg’s law. Light with short wavelength is diffracted at a smaller angle. Diffraction of light plays a paramount role in limiting the resolving power of any optical instrument (for example: cameras, binoculars, telescopes, microscopes, and the eye). The resolving power is the optical instrument's ability to produce separate images of two adjacent points. This is often determined by the quality of the lenses and mirrors in the instrument as well as the properties of the surrounding medium (usually air). The wave-like nature of light forces an ultimate limit to the resolving power of all optical instruments. All optical instruments have circular apertures that produce diffraction patterns similar to those described above. No matter how perfect the lens may be, the image of a point source of light produced by the lens is accompanied by secondary and higher order maxima. This could be eliminated only if the lens had an infinite diameter. Two objects separated by a distance less than (1) can not be resolved, no matter how high the power of magnification. (1)1.22(/d) is the angular position of the first order diffraction minima (the first dark ring). 1st 2nd 3rd film Light waves interfere constructively and destructively.

Resolution of Microscope – Rayleigh Criteria Rayleigh Criteria: Angular separation  of the two points is such that the central 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 I II Diffraction happens when path difference between the two beams are equal to n. N is an integer. 2dsin=, Bragg Law. 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 http://micro.magnet.fsu.edu/primer/java/imageformation/rayleighdisks/index.html Refractive index n= /n Immersion oil n=1.515

Numerical Aperture (NA) NA=1 - theoretical maximum numerical aperture of a lens operating with air as the imaging medium Angular aperture (72 degrees)  One half of A-A http://micro.magnet.fsu.edu/primer/java/microscopy/immersion/index.html One of the most important factors in determining the resolution of an objective is the angular aperture, which has a practical upper limit of about 72 degrees (with a sine value of 0.95). NA of an objective is a measure of its ability to gather light and resolve fine specimen detail at a fixed object distance. NA = n(sin ) n: refractive index of the imaging medium between the front lens of objective and specimen cover glass

Resolution of a Microscope (lateral) The smallest distance between two specimen points that can still be distinguished as two separate entities dmin = 0.61l/NA NA=nsin() l – illumination wavelength (light) NA – numerical aperture -one half of the objective angular aperture n-imaging medium refractive index http://micro.magnet.fsu.edu/primer/java/imageformation/airyna/index.html -Effect of wavelength and NA on image resolution -Numerical Aperture and Image Resolution dmin ~ 0.3m for a midspectrum l of 0.55m

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)

Optical Aberrations Reduce the resolution of microscope Two primary causes of non-ideal lens action: 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 Astigmatism, field curvature and comatic aberrations are easily corrected with proper lens fabrication.

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. http://micro.magnet.fsu.edu/primer/java/aberrations/spherical/index.html The spherical aberration is caused by the spherical shape of the lens surfaces, hence spherical aberration. The center remains more in focus than the edges of the image and the intensity of the edges falls relative to that of the center. This defect appears in both on-axis and off-axis image points

Defects in 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 http://micro.magnet.fsu.edu/primer/java/aberrations/chromatic/index.html Light is not monochromatic. Light of different wavelengths is brought to focus at different distances from the center of the lens. This occurs because the refractive index of a transparent isotropic material is greater for light of shorter wavelength than for light of longer wavelength.-dispersion. A converging lens can be combined with a weaker diverging lens, so that the chromatic aberrations cancel for certain wavelengths: The combination – achromatic doublet

Axial resolution – Depth of Field Depth of focus (F mm) Depth of Field (F m) (F mm) NA F F 0.1 0.13 15.5 0.4 3.8 5.8 .95 80.0 0.19 Depth of focus is important in photomicrography. The distance above and below geometric image plane within which the image is in focus The axial range through which an object can be focused without any appreciable change in image sharpness M NA F F F is determined by NA.

Basic components and their functions

Olympus BX51 Research Microscope Cutaway Diagram camera Beam splitter Olympus BX51 Research Microscope Cutaway Diagram Reflected light http://micro.magnet.fsu.edu/primer/java/microassembly/index.html -Microscope Assembly 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 http://micro.magnet.fsu.edu/primer/java/kohler/condensercones/index.html http://micro.magnet.fsu.edu/primer/java/kohler/contrast/index.html -Condenser Alignment and Field Diaphragm Opening Size -Condenser Light Cones -Condenser Aperture Diaphragm - Control Of Specimen Contrast 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 http://micro.magnet.fsu.edu/primer/flash/stage/index.html

Functions of the Major Parts of a Optical Microscope 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

Microscope Objectives dmin = 0.61l/NA Anatomy of an objective Objective specifications rical ture http://micro.magnet.fsu.edu/primer/anatomy/specifications.html -Specifications and Identification http://micro.magnet.fsu.edu/primer/java/nuaperture/index.html -Numerical Aperture Light Cones Objectives are the most important components of a light microscope: image formation, magnification, the quality of images and the resolution of the microscope

Eyepiece M=(L/fo)(25/fe) (Diaphragm) http://micro.magnet.fsu.edu/primer/anatomy/oculars.html M=(L/fo)(25/fe) Eyepieces (Oculars) work in combination with microscope objectives to further magnify the intermediate image

Common Modes of Analysis Depending on the nature of samples, different illumination methods must be used 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 character Characteristics 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.

Olympus BX51 Research Microscope Cutaway Diagram camera Beam splitter Olympus BX51 Research Microscope Cutaway Diagram Reflected light http://micro.magnet.fsu.edu/primer/java/microscopy/transmitted/index.html http://micro.magnet.fsu.edu/primer/java/microscopy/diaphragm/index.html http://micro.magnet.fsu.edu/primer/java/microscopy/reflected/index.html Transmitted light

Polarization of Light http://micro.magnet.fsu.edu/primer/java/polarizedlight/filters/index.html 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.

Polarized Light Microscope Configuration http://micro.magnet.fsu.edu/primer/java/polarizedlight/icelandspar/index.html http://micro.magnet.fsu.edu/primer/java/polarizedlight/crystal/index.html Polarized light microscopy is a useful method to generate contrast in birefringent specimens and to determine qualitative and quantitative aspects of crystallographic axes present in various materials.

Typical examples of applications

Grain Size Examination 1200C/30min Thermal Etching a 1200C/2h 20m b 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.

Grain Size Examination Objective Lens x100

Grain Growth - Reflected OM 5mm 30mm Polycrystalline CaF2 illustrating normal grain growth. Better grain size distribution. Large grains in polycrystalline spinel (MgAl2O4) growing by secondary recrystallization from a fine-grained matrix

Liquid Phase Sintering – Reflective OM Amorphous phase 40mm Microstructure of MgO-2% kaolin body resulting from reactive-liquid phase sintering.

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) Reflected POM Transmitted POM http://micro.magnet.fsu.edu/primer/virtual/polarizing/index.html Surface features of a microprocessor integrated circuit Apollo 14 Moon rock

Phase Identification by Reflected Polarized Optical Microscopy                                                                                                                                                                                                       YBa2Cu307-x superconductor material: (a) tetragonal phase and (b) orthorhombic phase with multiple twinning (arrowed) (100 x). Under plane-polarized light, i.e., only analyzer was used and incident beam is unpolarized. The color is due to anisotropic absorption.

Specialized LM Techniques Enhancement of Contrast Darkfield Microscopy Phase contrast microscopy Differential 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 microscopy melting, freezing points and eutectics, polymorphs, twin and domain dynamics, phase transformations In situ microscopy E-field, stress, etc. Special environmental stages-vacuum or gases http://micro.magnet.fsu.edu/primer/java/darkfield/cardioid/index.html

Contrast Contrast 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 S C = = Sspecimen SA Sspecimen and Sbackgroud are intensities measured from specimen and backgroud, e.g., A and B, in the scanned area. http://micro.magnet.fsu.edu/primer/virtual/virtualzoo/index.html Contrast produced in the specimen by the absorption of light (directly related to the chemical composition of the absorber and the predominant source of contrast in the ordinary optical microscope, brightness, reflectance, birefringence, light scattering, diffraction, fluorescence, or color variations has been the classical means of imaging specimens in brightfield microscopy.

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 http://micro.magnet.fsu.edu/primer/java/darkfield/abbe/index.html Contrast produced in the specimen by the absorption of light (directly related to the chemical composition of the absorber and the predominant source of contrast in the ordinary transmitted optical microscope. Different phases or variations in thickness absorb light to differing extends which causes them to differ in brightness in specimens of uniform thickness in the former and in specimens with different thickness in the latter. Furthermore, in some cases selective absorption of a particular wavelength or wavelengths of light occurs causing the phases to appear coloured.), brightness, reflectance (light from the surfaces that are perpendicular to the incident beam is reflected back into the objective, while light from tilted areas of the surfaces or grain boundaries is reflected away from the objective, so that they appear dark. Conversely with DF illumination, light reflected from grain surfaces which are almost perpendicular to the optical axis of the microscope is reflected away from the objective, while light from grain boundaries and tilted surfaces is reflected into it. Mainly for opaque specimens.), birefringence, light scattering, diffraction, fluorescence, or color variations has been the classical means of imaging specimens in brightfield microscopy. Imax-Imin Imax C= Imin Imax C-contrast

Transmitted Dark Field Illumination Oblique rays specimen http://micro.magnet.fsu.edu/primer/java/darkfield/cardioid/index.html http://micro.magnet.fsu.edu/primer/virtual/virtualzoo/index.html No zeroth order light reaches the specimen, only light that has been diffracted, refracted and reflected from the surface of the specimen is able to enter the front lens of the objective to form an image. In the absence of a specimen, the viewfield appears totally back, because no light is reflected or diffracted into the objective. I I distance distance

Contrast Enhancement OM images of the green alga Micrasterias

Crystals Growth-Interference contrast microscopy Growth spiral on cadmium iodide crystals growing From water solution (1025x).

Confocal Scanning Optical Microscopy Three-Dimensional Optical Microscopy Critical dimension measurements in semiconductor metrology w Cross-sectional image with line scan at PR/Si interface of a sample containing 0.6m-wide lines and 1.0m-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. http://micro.magnet.fsu.edu/primer/techniques/confocal/index.html http://micro.magnet.fsu.edu/primer/virtual/confocal/index.html Confocal microscopy offers several advantages over conventional optical microscopy, including controllable depth of field, the elimination of image degrading out-of-focus information, and the ability to collect serial optical sections from thick specimens. The key to the confocal approach is the use of spatial filtering to eliminate out-of-focus light or flare in specimens that are thicker than the plane of focus.

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 Single domain Schematic diagram for in situ domain observa- tions. Domain structures of PZN-PT crystals as a function of E-field; E=20kV/cm, (b) e=23.5kV/cm (c) E=27kV/cm Rhombohedral at E=0 and Tetragonal was induced at E>20kV/cm

Review - Optical Microscopy Use visible light as illumination source Has a resolution of ~o.2m 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 <15.5mm Rough surface Low resolution ~0.2mm Shape of specimen Thin section or polished surface Cover glass specimen Glass slide resin 20mm Lack of compositional and crystallographic information

Optical Microscopy vs Scanning Electron Microscopy 25mm radiolarian OM SEM Small depth of field Low resolution Large depth of field High resolution http://www.mse.iastate.edu/microscopy/