Characterization of NanomaterialsStructural characterization methods:- Optical microscopy, various electron microscopy (EM) includingscanning electron microscopy (SEM) and transmission microscopy(TEM) and scanning probe microscopies (SPM).

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• The electro-magnetic (EM) spectrumThe Light

Wavelength increases

Light as a wave

Wave equation

n refractive index

Electric and magnetic fied propagate in the space with velocity c.

λ is the wavelengthand ν is the frequency

The electromagnetic waves are transverse waves.

The most simple waves are the sinusoidal ones.

Frequenza angolare Numero d’onda

Electromagnetic waves

Time is fixed: t=0

Electric field variation as a function of the position

Electromagnetic waves

Position is fixed: x=0

Electric field variation as a function of the time

Electromagnetic waves

In 3 dimensions:

Wavevector Position vector

Wave propagation

The optical rayspropagate along a linein a homogeneousmedium.When one ray is atthe boundary betweentwo matarials,medium (1) andmedium (2), the beamis partially reflectedand partiallyrefracted.

The behaviour of the light is described by the concept of opticalray.

Reflection and refraction are governed by the Snell-Cartesiolaws.

Geometrical Optics

n1

n2

Snell-Cartesio laws

First law of Snell-Cartesio:

The angle of incidence is equal to thereflection

i = rln1

n2

RefractionThe refraction is the deviation of an optical ray when thebeam passes through the interface between two differentmaterials.In the two materials the speed of the beam light isdifferent.

II law of Snell-Cartesio and refraction index

The incidence angle and therefraction angle are related oneeach other by:

n is the refractive index of amaterial and it is a property ofthe medium related to the speedof propagation of the opticalbeam (wave) in that medium.It is defined as the ratiobetween the speed of light invacuum and the speed of lightin the medium.All the materials have n>1.

n1 sin(i) = n2 sin(r) n1

n2

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Geometrical optics and lenses

A positive lens converges parallelincident rays, forms a real imageand magnifies when held in frontof the eye.

A negative lens causes parallelincident rays to diverge and doesnot form a real image. When held infront of the eye, it reduces ordemagnifies the object.

A lens is a piece of glass (or another transparent material such asplexiglas or other polymers) with smooth curved surfaces (opticallytreated to allow a good transmission of the light).

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Images can be defined as regions where rays, or theextensions of rays, become convergent as the result ofrefraction by a lens. If the rays intersect and physicallyreunite, the image is said to be real. A real image can beseen on a viewing screen or recorded on a piece of film when ascreen or film is placed in the image plane.

If rays diverge, but the imaginary backward extensions ofthe rays become convergent and intersect, the image is saidto be virtual. The plane occupied by a virtual image cannotbe observed on a viewing screen or recorded on film.

To be perceived, a real image must be formed on theretina of the eye. In the case of viewing an image in amicroscope, a real image is formed on the retina but isperceived as a virtual image located some 25 cm in front ofthe eye.

Real and virtual images

Video: 4 Lenses

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Planes and axis for lensThe principal plane and focal plane of alens are defined as those planes, within thelens and in the focused image, respectively,where rays or extensions of rays intersectand physically reunite.

The optic axis is the horizontal line passing through the center of the lens and perpendicular to its principal plane.

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The rules governing ray tracing fora simple lens are:

1. A light ray passing through thecenter of a lens is not deviated.

2. A light ray parallel with theoptic axis will, after refraction,pass through the rear focal point.

3. A ray passing through the frontfocal point will be refracted in adirection parallel to the axis.

The intersection of any two of thethree key rays just describedidentifies the location of the imageplane.

Ray tracing for a lens

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Lens equation describes the relationship between focal length f and object and image distances, a and b:

1/f = 1/a + 1/b or b = af /(a - f )

The magnification factor M of an image is described as:

M = b/a or M = f/(a - f)

Lens equation

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• a < f : No real image. If the eyeis placed behind the lens, avirtual image is perceived on thefar side of the lens.

• a = f : The image distance b isinfinite, so no image exists thatcan be projected on a screen.This is the case for imageformation in a telescope.

• 2f > a > f : A real magnifiedimage is formed. Thisarrangement is used forproducing the first real image ina microscope.

• a = 2f : (b = 2f). A real image isformed, but there is nomagnification and M = 1.

• a > 2f : A real demagnifiedimage is formed and M < 1.

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Human eyeSensitive to radiation in the visible region of theelectromagnetic spectrum (400 – 700 nm).

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Cornea and lens of the eye behave like a single glass lens ofvariable focal length, forming a real image on the curved retina.

Image formation in human eye

Video: 5-Eye vision

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Retina contains rods and cones that are photoreceptive cells thattranslate the incoming light into signals that get transmitted to thebrain, via the optic nerve, to be translated into colors, andsubsequently coelesced into images. Rods translate intensity andcones translate color.

Vision in human eye

1. Composite lens: composed by the crystalline lens andcornea. The composite lens can change its shape modify thefocal length accordingly.

Similarly to an optical instrument the eye is composed by:

2. Diaphragm: composed by the iris that can change itsaperture modifying the amount of light entering into theeye.

3. Detector: composed by the receptors (rods and cones)present in the retina.

Vision in human eye

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Schematizationof the eye

The closestobject distancefor a correctfocused imageon the retina isu ~ 25 cm(normal eye).

This influencesthe eye spatialresolution.

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The spatial resolution of the retinal image is determined by threefactors:

- Diffraction of light at the entrance pupil of the eye.

- Imperfections in the focusing (known as aberrations)

- Size of the receptor cells

Spatial resolutionof the retina

Light (of a certainwavelength λ) passingthrough an apertureilluminates the screen inthe form of a circularpattern with diffuse edges(a disk of confusion)whose diameter ∆xexceeds that of theaperture. In fact, for anaperture of smalldiameter, diffractioneffects cause ∆x actuallyto increase as the aperturesize is reduced, inaccordance with theRayleigh criterion:

∆x ~ 0.6 λ / sinα24

Diffraction

Diffraction:for λ ~ 500 nm and taking d ~ 4 mm and f ~ 2 cm, tanα ~ (d/2)/f =0.1 and considering small angle approximation ∆x ~ 3 µm.

Aberration:Imperfect focusing (aberration) of the eye contributes a roughlyequal amount of image blurring, which we therefore take as 3 µm.

Receptor cells:the receptor cells of the retina have diameters in the range 2 µm to6 µm (mean value ~ 4 µm).

The overall image blurring ∆ is ~ 6 µm (obtained summing thesquares of the different contributions).This value corresponds to an angular blurring for distant objectsof about (1/60) degree = 1 minute of arc. Distant objects (ordetails within objects) can be separately distinguished if theysubtend angles larger than this.

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Image blurring

Since the closest object distance for a focused image on theretina is u ~ 25 cm, at this distance the lateral dimensionresolution is ∆R ~ 75 µm. This value can be taken as thediameter of the smallest object that can be resolved(distinguished from neighboring objects) by the unaided eye,known as its spatial resolution.

To resolve a small object of diameter D, we need amagnification M* (>1) such that the magnified diameter (M* D)at the eye's object plane is greater or equal to the objectresolution ∆R (~ 75 µm ) of the eye:

M* = (∆R )/D

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Spatial resolution of the eye

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M* = (∆R )/D

Magnification

The magnification depends on the angle from which the object isobserved or in other words, depends on the ratio between theheight (h) and the distance (d)

α°h

d

Magnification

10°

40°

We can define a linear magnificationas the ratio between the dimensionof the image (yi) and the dimensionof the object (y0).

y0Yi

Magnification

http://zeiss-campus.magnet.fsu.edu/tutorials/basics/simplemagnification/indexflash.html

Microscopia Anna Sgarlata

Magnification

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Zacharias Jansen (Holland 1580–1638) around 1595 invented a compoundlight microscope, with two lenses, with the second lens further magnifyingthe image produced by the first. His microscope produced magnificationsup to nine times (9x).

Galileo Galilei (Italy 1564-1642) in 1624 invented a little telescope similarto a compound microscope based on a tube with two lenses (occhialino(small glasses)).

Antony van Leeuwenhoek (1632–1723) invented a simple (one-lens)microscope around 1670 that magnified up to 200x and achieved twicethe resolution of the best compound microscopes of his day. He became thefirst to see individual cells, bacteria, protozoans and muscle cells.

Robert Hooke (England 1635–1703) further refined the compoundmicroscope, adding a stage to hold the specimen, an illuminator, andcoarse and fine focus controls. Until 1800, microscopes were limited tomagnifications of 30x - 50x, and their images exhibited blurry edges(spherical aberration) and rainbowlike distortions (chromaticaberration). The most significant improvement in microscope optics wasachieved in the nineteenth century, when Carl Zeiss (1816–1888) andErnst Abbe (1840–1905) added the substage condenser and developedsuperior lenses that greatly reduced chromatic and spherical aberration,while permitting vastly improved resolution and higher magnification.

History of Light-Optical Microscopy

Light-Optical Microscopy

He observed bloodcells, bacteria, andstructure within thecells of animaltissue.

One-lens device thathad to be positionedvery accurately,making observationvery difficult.

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Optical microscope scheme

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For practical applications is more convenient to have a compoundmicroscope, containing at least two lenses: an objective (placedclose to the object to be magnified) and an eyepiece (placed fairlyclose to the eye).

An image of the object (specimen) is formed by the objective lens(magnification range 10x-100x), such an image is then viewedthrough the eyepiece (ocular), whose magnification is usually 10x.Total magnification of a microscope is obtained by multiplyingthe objective and eyepiece magnifications. Typically totalmagnifications are in the range 100X to 1000X.

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Optical microscope magnification

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Optical microscope magnificationMagnification is defined as the angle subtended by a(small) object as seen through the microscope, divided bythe angle when the same object is viewed by the nakedeye at a distance of 250 mm.We can express the magnifications of the objective, M0, andeyepiece, Me, as:

M0 = H/h = b/a Me = 250(mm)/fe(mm)

Infinite tube length

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