Absorption and Scattering PDF

Absorption and Scattering Third session  Absorption Coefficient. To d a y ’s Content Absorption Cross-Section Molar Absorption Coefficient Absorption Coefficient Absorption Coefficient as a Probability...

Absorption and Scattering Third session  Absorption Coefficient. To d a y ’s Content Absorption Cross-Section Molar Absorption Coefficient Absorption Coefficient Absorption Coefficient as a Probability Spectrophotometry Measuring Absorption Spectra Transmittance and Absorbance Spectroscopic Inversion.  Optical Scattering. To d a y ’s Content The Physical Basis of Scattering Molecular Scattering Refractive Index Scattering Coefficient...  For a photon of frequency the Absorption likelihood of a transition from state a coefficient to state b is often given in terms of Absorption the absorption cross-section, Cross Section The absorption cross-section is the ratio of the power absorbed by the molecule to the incident power per unit area, so has units of area.  Absorption Coefficient Absorption Cross-Section  Absorption Coefficient The description of the absorption of a single molecule is not much use on its own in tissue Absorption Molar optics, and it is necessary to move to a description Coefficient of the absorption of bulk matter consisting of very many molecules. The molar absorption coefficient is obtained by summing the absorption cross-sections of all the molecules in one mole of ansubstance.  is just NA mole One Absorption molecules, where Avogadro’s Coefficient constant NA= 6.022×10-23, so Molar Absorption :NA gives multiplying by Coefficient  As most biological media contain Absorption any types of absorbers, eg. blood, lipids, Coefficient water, melanin, the total absorption coefficient of a material consisting of K chromophores is the sum of the molar absorption coefficients weighted by their concentrations:  the probability that a Absorption Coefficient as photon will be absorbed while a Probability travelling the distance is  a plane wave of continuous Absorption light irradiating a purely Coefficient as a Probability absorbing, non-scattering medium. The intensity of the light will decrease in the direction of propagation as the light is absorbed.  The measurement of optical Spectrophoto- metry absorption spectra is known as spectrophotometry. Measuring the detected intensity can be Absorption written as Spectra Io IL Spectrophoto- metry Measuring Absorption Spectra  Given a sample that contains Spectroscopic Inversion several known chromophores, it is often possible to estimate the concentrations of each constituent by making measurements at multiple wavelengths  a sample containing a mixture Spectroscopic Inversion of three chromophores, a, b and c,with specific extinction coefficients  Three measurements of the Spectroscopic absorbance are made using a Inversion spectrophotometer at wavelengths Spectroscopic Inversion Optical Scattering  In biological tissue the scattering is often a dominant characteristic, and explains why skin, for example, is opaque.  Photon scattering can be O p t i c a l divided into two classes: Scattering Elastic,in which energy is conserved and so the scattered light has the same frequency as the incident light, Inelastic, in which energy is lost or gained and so the scattered light has a different frequency from the incident light.  Elastic scattering is much Optical Scattering more significant in most biological tissues at visible and NIR wavelengths.  When the frequency does not The Physical Basis excite any resonance in the of Scattering molecule then the oscillating Molecular Scattering dipole as it is a moving charge will radiate an EM wave as any accelerating charge would. Photon of equal energy to the incoming photon will be reradiated in a random direction.  Light travels at speed in the The Physical o f Basis vacuum, and c/v at speed in Scattering theglass “why does the wave Refractive seem to travel at a slower Index speed in the glass”?  The many scattered waves add The Physical o f Basis together, and add to the original Scattering incident wave, in such a way as to result in a wave which is Refractive phase shifted from the Index original.  the emergent wave moves The Physical of Basis through the medium with Scattering speed c/n , Refractive Index  Because it appears to move with a different speed, the light The Physical appears to refract, and is bent Basis on entering a medium with a Scattering different refractive index. Refractive Index The Physical o f Basis Scattering Refractive Index  microscopic scattering: The Physical o f Basis Macroscopic scattering Scattering the cause of scattering is Refractive variations in the density of the Index scatterers, The refractive index will be spatially varying and the light will be refracted in various directions:  The key factor in determining S c T h e Physical Basis whether a refractive of Scattering index fluctuation will scatter strongly is Refractive the relationship between Indexattering the size of the scatterer the wavelength of the light Coefficient  Consider a collimated beam Scattering Coefficient of light travelling in the z- direction through a thin, elastically scattering, non- absorbing medium  As the beam passes through Scattering coefficient the medium, some of the light will be scattered out of the beam into different directions and the intensity of the beam will follow an exponential decay, where is called the scattering coefficient.  Probability that a photon will Scattering coefficient be scattered while travelling the short distance between. The reduced scattering coefficient is a lumped property incorporating the scattering coefficient µs and the anisotropy g: µs' = µs(1 - g) [cm-1]. The mean free path is the average distance traveled by a moving particle (such as an atom, a molecule, a photon) between successive impacts The purpose of µs' is to describe the diffusion of photons in a random walk of step size of 1/µs' [cm] where each step involves isotropic scattering cattering properties of tissue include the scattering coefficient (µs), which describes the mean free path between scattering events, Reduced scattering coefficient can be defined as inverse distance between effectively scattering events, where photon loses all memory of its initial direction. This combined coefficient is very often used in measurement tissue optical properties and is fundamental parameter in diffusion theory. Typical value of scattering coefficient is between 0.2 cm−1 and 400 cm−1. For g = 0.9 it gives us reduced scattering coefficient between 0.02 cm−1 and 40 cm−1  The diffusion of light remains almost the same when varying µs and g yet keeping µs unchanged. This explains why µa and µs instead of µa, µs and g, are commonly used in optical imaging. Light absorption and scattering coefficients depend on the optical properties of constituent particles and their concentration. The g-factor measures how much forward peaked is the angular distribution of light when it is scattered once by a particle in the medium, and is independent of the concentration of the scatterers The scattering mean free path is the average distance between scattering events (in biological tissues around 100 µm) The transport mean free path can be thought of as the mean distance after which a photon’s direction becomes random (in biological tissues around 1 mm)