DOCSLIB.ORG

Mie Scattering of Electromagnetic Waves

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Mie Scattering of Electromagnetic Waves Sergei Yushanov, Jeffrey S. Crompton*, and Kyle C. Koppenhoefer *Corresponding author AltaSim Technologies, 130 East Wilson Bridge Rd, Suite 140, Columbus, OH, [email protected] Abstract:Scattering of electromagnetic waves spherical particles in terms of infinite series [1- by spherical particles is described by the Mie 3]. solution to Maxwell’s equations. Illumination of an obstacle by an electromagnetic wave excites Scattering may be defined as the redirection of electric charges in the obstacle to oscillate due to radiation from the original propagation direction interaction with the electric field of the incident typically due to interactions with molecules and wave. The oscillating charge radiates particles. Reflection, refraction etc. represent electromagnetic energy in all directions; this specific forms of scattering. Electromagnetic secondary radiation is the radiation scattered by waves scatter when they meet an obstacle due to the obstacle. In addition, the excited elementary the electric charges in the obstacle being charges may absorb radiation and transform part oscillated by the electric field of the incident of the incident energy into other forms, such as wave. Accelerated charges radiate thermal energy. Both scattering and absorption electromagnetic energy in all directions; this remove energy from a beam of light and the secondary radiation is referred to as radiation beam is attenuated. scattered by the obstacle. Thus, charge excitation and re-radiation of the electromagnetic energy In this work, scattering of an incident constitutes scattering. electromagnetic wave by a spherical particle has been analyzed using COMSOL Multiphysics. In addition to re-radiating electromagnetic The nature of the interaction has been considered energy, the excited elementary charges may for materialswith three different properties: transform part of the incident energy into other metallic, magnetic and dielectric. The solutions forms, e.g. thermal energy, via absorption. Both provide details of the absorption, scattering, scattering and absorption remove energy from an extinction, pressure cross-sections, back- electromagnetic wave, thus attenuating the beam. scattering and radiation force exerted on the This attenuation, which is called extinction, particle by an incident plane wave.Results of consists of scattering and absorption: these analyses are compared against the Mie analytical solutions. Extinction = scattering + absorption Keywords: electromagnetic scattering, angle- Scattering and absorption are not mutually resolved low-coherence interferometry, Mie independent processes. This paper considers solution, Maxwell’s equations elastic scattering only: the frequency of the scattered wave is the same as that of incident 1. Introduction wave. Thus, ineleastic scattering phenomena such as Brillouin and Raman scattering are The Mie solution to Maxwell’s equations excluded from this paper. provides the basis for measuring the size of particles through the scattering of 2. Theory electromagnetic radiation. Applications include dust particles in the atmosphere, oil droplet in In scattering problems, the total wave water, and cell nuclei in biological systems (e.g., decomposes onto incident and scattered waves: cancer research). The Mie solution, also called Lorenz-Mie E Einc Esca (1) theory or Lorenz-Mie-Debye theory, provides an analytical solution of Maxwell’s equations for the scattering of electromagnetic radiation by H Hinc H sca (2) Wsca ) by the particle, the absorption ( abs ) and Maxwell’s wave equation is solved with respect scattering ( sca ) cross section can be defined: to scattered electric field: W W (8) 1 2 (3) abs sca E k j E 0 abs , sca sca 0 r sca r 0 Pinc Pinc The scattered magnetic field is calculated from where Faraday’s law: P is incident irradiance, defined as energy flux 1 (4) inc H E 2 sca j sca of the incident wave, W / m Wabs is energy rate absorbed by particle, W The Time-average Poynting vector for time- is scattered energy rate, harmonic fields gives the energy flux: Wsca W The total scattering cross-section, or extinction 1 (5) cross-section, is the amount of energy removed P ReE H , W / m 2 from the incident field due to absorption and 2 scattering. By energy balance, the extinction cross-section is a superposition of the scattering For an incident plane wave, the magnetic field is and absorption cross-sections: related to the electric field by: 2 (9) , m 1 ˆ (6) ext abs sca H inc k Einc The energy loss rate in a particle is: ˆ 1 3 where k is direction of the incident wave Q ReJ E jB H , W / m (10) loss 2 tot propagation, is characteristic / impedance, is permittivity and is Where the total current is a superposition of permeability of ambient medium. Hence, conduction and displacement currents: incident energy flux is calculated as Jtot E jD . Thus, Eq. (10) includes conduction, polarization, and magnetic losses. 1 2 1 2 (7) The total absorbed energy is derived by P E kˆ c E kˆ inc 2 inc 2 inc integration of energy loss over the volume of the particle: where c 1/ is speed of light. W Q dV (11) abs loss V P 1 ሾ ሿ 2.1 Cross-Section Calculations ReE jD E jB H dV , ܹ 2 VP Important physical quantities can be obtained from scattered fields. One of these is the cross The scattered energy is derived by integration the section, which can be defined as the net rate at Poynting vector over an imaginary sphere around which electromagnetic energy W crosses the the particle: surface of an imaginary sphere centered at the W P ndS (12) particle divided by the incident irradiation sca sca Pinc S . To quantify the rate of the electromagnetic 1 Re E H ndS , [W] energy that is absorbed (Wabs ) and scattered ( sca sca 2 S eikr (13) wheren is unit vector normal to the imaginary r eikx f sphere. r where f is the scattering amplitude, is scattering angle, and k / c is the wave vector. The optical theorem states that the relation between the total cross section and the scattering amplitude. It is usually written in the form: Figure 1.Imaginary sphere S around a particle 4 (14) ext Imf 0 / Einc volume V p enclosed by surface S p . Scattering k amplitude is evaluated in the forward direction at point F . where f 0 is the scattering amplitude in the 2.2 Optical Theorem forward direction 0 . Thus, the optical In physics, the optical theorem is a general law theorem relates extinction cross-section to the of wave scattering theory, which relates the imaginary part of the scattering amplitude forward scattering amplitude to the total cross evaluated in the forward direction. Yet, section of the scattering object. The optical extinction is due to the scattering and absorption. theorem has a long history and is common to all Scattering involves all directions whereas kinds of seemingly disparate scattering absorption is often independent of direction, so phenomena involving acoustic waves, why should the optical theorem depend on only electromagnetic waves and elementary particles. the forward direction, and how is absorption The theorem can be derived directly from a involved? Berg, and Sorensen [4] provide a treatment of a scalar wave [1]. Scattering is a physical explanation of these features of the superposition of the incident and scattered optical theorem. waves, as schematically shown in Figure 2. COMSOLincludes a built-in far-field computation node that automatically calculates the far-field variables defined as: (15) E far lim rE sca r The far-field variables, e.g., E far , represent the scattering amplitude rather than the physical Figure 2.Generic scattering geometry. An incoming electric field and are measured in units ikx plane wave e scattered off a particle. A great E far m V / m V . distance away scattered wave is approximated by a Thus, the extinction cross-section can be directly ikr spherical wave e / r . calculated, without evaluation of absorption and scattering cross-sections, as: If a plane wave is incident on an object, then the wave amplitude a great distance away from the 4 2 (16) ext ImE far 0 , m scattering object, neglecting higher order terms, kEinc is given by: 2.3Radiation Pressure Cross-Section symmetric about a scattering angle of 90 . If the particle scatters more light towards the In addition to energy, the electromagnetic wave forward direction ( 0 ), the factor g is carries momentum P / c ; therefore, a beam of light that interacts with a particle will exert a positive. The factor g is negative if the force on the particle, called radiation pressure. scattering is directed more towards the back Debye, in 1909, was probably the first to direction ( 180 ). calculate the radiation force on a small particle. By integrating the Maxwell stress tensor over the 2.4Radiation Force surface of the sphere, he demonstrated that: The radiation pressure cross section can be used 2 (17) to calculate force that a particle experiences in pr ext cos sca , m the incidence direction [5]: 1 (19) where is the pressure cross-section, and F P , N pr c pr inc g cos is so called asymmetry parameter. This expression for pressure cross-section holds Where the pressure cross-section is given by for any small particle illuminated by a beam of Eq.(17). Alternatively, this force can be light [2]. The radiation cross section is directly calculated by integration of Maxwell’s stress related to the radiation force. tensor over the surface of the particle. The time- The asymmetry parameter g can be interpreted averaged Maxwell’s stress tensor is: as the mean direction of the scattered light and is ˆ 1 1 ˆ (20) T ReE D H B E D H BI, Pa defined as an average of the scattering angle 2 2 weighted with respect to scattered power flow: where D E is electric flux density, B H is cos Psca n dS (18) S magnetic flux density, and ˆ is unit tensor of cos I second rank.
Recommended publications
  • An Atmospheric Radiation Model for Cerro Paranal

    An Atmospheric Radiation Model for Cerro Paranal

    Astronomy & Astrophysics manuscript no. nolletal2012a c ESO 2012 May 10, 2012 An atmospheric radiation model for Cerro Paranal I. The optical spectral range⋆ S. Noll1, W. Kausch1, M. Barden1, A. M. Jones1, C. Szyszka1, S. Kimeswenger1, and J. Vinther2 1 Institut f¨ur Astro- und Teilchenphysik, Universit¨at Innsbruck, Technikerstr. 25/8, 6020 Innsbruck, Austria e-mail: [email protected] 2 European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany Received; accepted ABSTRACT Aims. The Earth’s atmosphere affects ground-based astronomical observations. Scattering, absorption, and radiation processes dete- riorate the signal-to-noise ratio of the data received. For scheduling astronomical observations it is, therefore, important to accurately estimate the wavelength-dependent effect of the Earth’s atmosphere on the observed flux. Methods. In order to increase the accuracy of the exposure time calculator of the European Southern Observatory’s (ESO) Very Large Telescope (VLT) at Cerro Paranal, an atmospheric model was developed as part of the Austrian ESO In-Kind contribution. It includes all relevant components, such as scattered moonlight, scattered starlight, zodiacal light, atmospheric thermal radiation and absorption, and non-thermal airglow emission. This paper focuses on atmospheric scattering processes that mostly affect the blue (< 0.55 µm) wavelength regime, and airglow emission lines and continuum that dominate the red (> 0.55 µm) wavelength regime. While the former is mainly investigated by means of radiative transfer models, the intensity and variability of the latter is studied with a sample of 1186 VLT FORS 1 spectra. Results. For a set of parameters such as the object altitude angle, Moon-object angular distance, ecliptic latitude, bimonthly period, and solar radio flux, our model predicts atmospheric radiation and transmission at a requested resolution.
  • Glossary Physics (I-Introduction)

    Glossary Physics (I-Introduction)

    1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay.
  • Arxiv:1710.01658V1 [Physics.Optics] 4 Oct 2017 to Ask the Question “What Is the RI of the Small Parti- Cles Contained in the Inhomogeneous Sample?”

    Arxiv:1710.01658V1 [Physics.Optics] 4 Oct 2017 to Ask the Question “What Is the RI of the Small Parti- Cles Contained in the Inhomogeneous Sample?”

    Extinction spectra of suspensions of microspheres: Determination of spectral refractive index and particle size distribution with nanometer accuracy Jonas Gienger,∗ Markus Bär, and Jörg Neukammer Physikalisch-Technische Bundesanstalt (PTB), Abbestraße 2–12, 10587 Berlin, Germany (Dated: Compiled October 5, 2017) A method is presented to infer simultaneously the wavelength-dependent real refractive index (RI) of the material of microspheres and their size distribution from extinction measurements of particle suspensions. To derive the averaged spectral optical extinction cross section of the microspheres from such ensemble measurements, we determined the particle concentration by flow cytometry to an accuracy of typically 2% and adjusted the particle concentration to ensure that perturbations due to multiple scattering are negligible. For analysis of the extinction spectra we employ Mie theory, a series-expansion representation of the refractive index and nonlinear numerical optimization. In contrast to other approaches, our method offers the advantage to simultaneously determine size, size distribution and spectral refractive index of ensembles of microparticles including uncertainty estimation. I. INTRODUCTION can be inferred from measurements of the scattering and absorption of light by the particles. The refractive index (RI) describes the refraction of a A reference case is that of homogeneous spheres de- beam of light at a (macroscopic) interface between any scribed by a single refractive index, since an analytical two materials. Consequently, a variety of experimental solution for the mathematical problem of light scatter- methods exist for measuring the RI of a material that rely ing exists for this class of particles (Mie theory) [12, 13]. on the refraction or reflection of light at a planar interface This makes the analysis of light scattering data feasible between the sample and some other known material, such and at the same time is a good approximation for many as air, water or an optical glass.
  • Lecture 6: Spectroscopy and Photochemistry II

    Lecture 6: Spectroscopy and Photochemistry II

    Lecture 6: Spectroscopy and Photochemistry II Required Reading: FP Chapter 3 Suggested Reading: SP Chapter 3 Atmospheric Chemistry CHEM-5151 / ATOC-5151 Spring 2005 Prof. Jose-Luis Jimenez Outline of Lecture • The Sun as a radiation source • Attenuation from the atmosphere – Scattering by gases & aerosols – Absorption by gases • Beer-Lamber law • Atmospheric photochemistry – Calculation of photolysis rates – Radiation fluxes – Radiation models 1 Reminder of EM Spectrum Blackbody Radiation Linear Scale Log Scale From R.P. Turco, Earth Under Siege: From Air Pollution to Global Change, Oxford UP, 2002. 2 Solar & Earth Radiation Spectra • Sun is a radiation source with an effective blackbody temperature of about 5800 K • Earth receives circa 1368 W/m2 of energy from solar radiation From Turco From S. Nidkorodov • Question: are relative vertical scales ok in right plot? Solar Radiation Spectrum II From F-P&P •Solar spectrum is strongly modulated by atmospheric scattering and absorption From Turco 3 Solar Radiation Spectrum III UV Photon Energy ↑ C B A From Turco Solar Radiation Spectrum IV • Solar spectrum is strongly O3 modulated by atmospheric absorptions O 2 • Remember that UV photons have most energy –O2 absorbs extreme UV in mesosphere; O3 absorbs most UV in stratosphere – Chemistry of those regions partially driven by those absorptions – Only light with λ>290 nm penetrates into the lower troposphere – Biomolecules have same bonds (e.g. C-H), bonds can break with UV absorption => damage to life • Importance of protection From F-P&P provided by O3 layer 4 Solar Radiation Spectrum vs. altitude From F-P&P • Very high energy photons are depleted high up in the atmosphere • Some photochemistry is possible in stratosphere but not in troposphere • Only λ > 290 nm in trop.
  • 12 Light Scattering AQ1

    12 Light Scattering AQ1

    12 Light Scattering AQ1 Lev T. Perelman CONTENTS 12.1 Introduction ......................................................................................................................... 321 12.2 Basic Principles of Light Scattering ....................................................................................323 12.3 Light Scattering Spectroscopy ............................................................................................325 12.4 Early Cancer Detection with Light Scattering Spectroscopy .............................................326 12.5 Confocal Light Absorption and Scattering Spectroscopic Microscopy ............................. 329 12.6 Light Scattering Spectroscopy of Single Nanoparticles ..................................................... 333 12.7 Conclusions ......................................................................................................................... 335 Acknowledgment ........................................................................................................................... 335 References ...................................................................................................................................... 335 12.1 INTRODUCTION Light scattering in biological tissues originates from the tissue inhomogeneities such as cellular organelles, extracellular matrix, blood vessels, etc. This often translates into unique angular, polari- zation, and spectroscopic features of scattered light emerging from tissue and therefore information about tissue
  • 7. Gamma and X-Ray Interactions in Matter

    7. Gamma and X-Ray Interactions in Matter

    Photon interactions in matter Gamma- and X-Ray • Compton effect • Photoelectric effect Interactions in Matter • Pair production • Rayleigh (coherent) scattering Chapter 7 • Photonuclear interactions F.A. Attix, Introduction to Radiological Kinematics Physics and Radiation Dosimetry Interaction cross sections Energy-transfer cross sections Mass attenuation coefficients 1 2 Compton interaction A.H. Compton • Inelastic photon scattering by an electron • Arthur Holly Compton (September 10, 1892 – March 15, 1962) • Main assumption: the electron struck by the • Received Nobel prize in physics 1927 for incoming photon is unbound and stationary his discovery of the Compton effect – The largest contribution from binding is under • Was a key figure in the Manhattan Project, condition of high Z, low energy and creation of first nuclear reactor, which went critical in December 1942 – Under these conditions photoelectric effect is dominant Born and buried in • Consider two aspects: kinematics and cross Wooster, OH http://en.wikipedia.org/wiki/Arthur_Compton sections http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=22551 3 4 Compton interaction: Kinematics Compton interaction: Kinematics • An earlier theory of -ray scattering by Thomson, based on observations only at low energies, predicted that the scattered photon should always have the same energy as the incident one, regardless of h or • The failure of the Thomson theory to describe high-energy photon scattering necessitated the • Inelastic collision • After the collision the electron departs
  • Solutions 7: Interacting Quantum Field Theory: Λφ4

    Solutions 7: Interacting Quantum Field Theory: Λφ4

    QFT PS7 Solutions: Interacting Quantum Field Theory: λφ4 (4/1/19) 1 Solutions 7: Interacting Quantum Field Theory: λφ4 Matrix Elements vs. Green Functions. Physical quantities in QFT are derived from matrix elements M which represent probability amplitudes. Since particles are characterised by having a certain three momentum and a mass, and hence a specified energy, we specify such physical calculations in terms of such \on-shell" values i.e. four-momenta where p2 = m2. For instance the notation in momentum space for a ! scattering in scalar Yukawa theory uses four-momenta labels p1 and p2 flowing into the diagram for initial states, with q1 and q2 flowing out of the diagram for the final states, all of which are on-shell. However most manipulations in QFT, and in particular in this problem sheet, work with Green func- tions not matrix elements. Green functions are defined for arbitrary values of four momenta including unphysical off-shell values where p2 6= m2. So much of the information encoded in a Green function has no obvious physical meaning. Of course to extract the corresponding physical matrix element from the Greens function we would have to apply such physical constraints in order to get the physics of scattering of real physical particles. Alternatively our Green function may be part of an analysis of a much bigger diagram so it represents contributions from virtual particles to some more complicated physical process. ∗1. The full propagator in λφ4 theory Consider a theory of a real scalar field φ 1 1 λ L = (@ φ)(@µφ) − m2φ2 − φ4 (1) 2 µ 2 4! (i) A theory with a gφ3=(3!) interaction term will not have an energy which is bounded below.
  • 12 Scattering in Three Dimensions

    12 Scattering in Three Dimensions

    12 Scattering in three dimensions 12.1 Cross sections and geometry Most experiments in physics consist of sending one particle to collide with another, and looking at what comes out. The quantity we can usually measure is the scattering cross section: by analogy with classical scattering of hard spheres, we assuming that scattering occurs if the particles ‘hit’ each other. The cross section is the apparent ‘target area’. The total scattering cross section can be determined by the reduction in intensity of a beam of particles passing through a region on ‘targets’, while the differential scattering cross section requires detecting the scattered particles at different angles. We will use spherical polar coordinates, with the scattering potential located at the origin and the plane wave incident flux parallel to the z direction. In this coordinate system, scattering processes dσ are symmetric about φ, so dΩ will be independent of φ. We will also use a purely classical concept, the impact parameter b which is defined as the distance of the incident particle from the z-axis prior to scattering. S(k) δΩ I(k) θ z φ Figure 11: Standard spherical coordinate geometry for scattering 12.2 The Born Approximation We can use time-dependent perturbation theory to do an approximate calculation of the cross- section. Provided that the interaction between particle and scattering centre is localised to the region around r = 0, we can regard the incident and scattered particles as free when they are far from the scattering centre. We just need the result that we obtained for a constant perturbation, Fermi’s Golden Rule, to compute the rate of transitions between the initial state (free particle of momentum p) to the final state (free particle of momentum p0).
  • Photon Cross Sections, Attenuation Coefficients, and Energy Absorption Coefficients from 10 Kev to 100 Gev*

    Photon Cross Sections, Attenuation Coefficients, and Energy Absorption Coefficients from 10 Kev to 100 Gev*

    1 of Stanaaros National Bureau Mmin. Bids- r'' Library. Ml gEP 2 5 1969 NSRDS-NBS 29 . A111D1 ^67174 tioton Cross Sections, i NBS Attenuation Coefficients, and & TECH RTC. 1 NATL INST OF STANDARDS _nergy Absorption Coefficients From 10 keV to 100 GeV U.S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS T X J ". j NATIONAL BUREAU OF STANDARDS 1 The National Bureau of Standards was established by an act of Congress March 3, 1901. Today, in addition to serving as the Nation’s central measurement laboratory, the Bureau is a principal focal point in the Federal Government for assuring maximum application of the physical and engineering sciences to the advancement of technology in industry and commerce. To this end the Bureau conducts research and provides central national services in four broad program areas. These are: (1) basic measurements and standards, (2) materials measurements and standards, (3) technological measurements and standards, and (4) transfer of technology. The Bureau comprises the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Center for Radiation Research, the Center for Computer Sciences and Technology, and the Office for Information Programs. THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consistent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation’s scientific community, industry, and com- merce. The Institute consists of an Office of Measurement Services and the following technical divisions: Applied Mathematics—Electricity—Metrology—Mechanics—Heat—Atomic and Molec- ular Physics—Radio Physics -—Radio Engineering -—Time and Frequency -—Astro- physics -—Cryogenics.
  • Calculation of Photon Attenuation Coefficients of Elements And

    Calculation of Photon Attenuation Coefficients of Elements And

    732 ISSN 0214-087X Calculation of photon attenuation coeffrcients of elements and compound Roteta, M.1 Baró, 2 Fernández-Varea, J.M.3 Salvat, F.3 1 CIEMAT. Avenida Complutense 22. 28040 Madrid, Spain. 2 Servéis Científico-Técnics, Universitat de Barcelona. Martí i Franqués s/n. 08028 Barcelona, Spain. 3 Facultat de Física (ECM), Universitat de Barcelona. Diagonal 647. 08028 Barcelona, Spain. CENTRO DE INVESTIGACIONES ENERGÉTICAS, MEDIOAMBIENTALES Y TECNOLÓGICAS MADRID, 1994 CLASIFICACIÓN DOE Y DESCRIPTORES: 990200 662300 COMPUTER LODES COMPUTER CALCULATIONS FORTRAN PROGRAMMING LANGUAGES CROSS SECTIONS PHOTONS Toda correspondencia en relación con este trabajo debe dirigirse al Servicio de Información y Documentación, Centro de Investigaciones Energéticas, Medioam- bientales y Tecnológicas, Ciudad Universitaria, 28040-MADRID, ESPAÑA. Las solicitudes de ejemplares deben dirigirse a este mismo Servicio. Los descriptores se han seleccionado del Thesauro del DOE para describir las materias que contiene este informe con vistas a su recuperación. La catalogación se ha hecho utilizando el documento DOE/TIC-4602 (Rev. 1) Descriptive Cataloguing On- Line, y la clasificación de acuerdo con el documento DOE/TIC.4584-R7 Subject Cate- gories and Scope publicados por el Office of Scientific and Technical Information del Departamento de Energía de los Estados Unidos. Se autoriza la reproducción de los resúmenes analíticos que aparecen en esta publicación. Este trabajo se ha recibido para su impresión en Abril de 1993 Depósito Legal n° M-14874-1994 ISBN 84-7834-235-4 ISSN 0214-087-X ÑIPO 238-94-013-4 IMPRIME CIEMAT Calculation of photon attenuation coefíicients of elements and compounds from approximate semi-analytical formulae M.
  • The Basic Interactions Between Photons and Charged Particles With

    The Basic Interactions Between Photons and Charged Particles With

    Outline Chapter 6 The Basic Interactions between • Photon interactions Photons and Charged Particles – Photoelectric effect – Compton scattering with Matter – Pair productions Radiation Dosimetry I – Coherent scattering • Charged particle interactions – Stopping power and range Text: H.E Johns and J.R. Cunningham, The – Bremsstrahlung interaction th physics of radiology, 4 ed. – Bragg peak http://www.utoledo.edu/med/depts/radther Photon interactions Photoelectric effect • Collision between a photon and an • With energy deposition atom results in ejection of a bound – Photoelectric effect electron – Compton scattering • The photon disappears and is replaced by an electron ejected from the atom • No energy deposition in classical Thomson treatment with kinetic energy KE = hν − Eb – Pair production (above the threshold of 1.02 MeV) • Highest probability if the photon – Photo-nuclear interactions for higher energies energy is just above the binding energy (above 10 MeV) of the electron (absorption edge) • Additional energy may be deposited • Without energy deposition locally by Auger electrons and/or – Coherent scattering Photoelectric mass attenuation coefficients fluorescence photons of lead and soft tissue as a function of photon energy. K and L-absorption edges are shown for lead Thomson scattering Photoelectric effect (classical treatment) • Electron tends to be ejected • Elastic scattering of photon (EM wave) on free electron o at 90 for low energy • Electron is accelerated by EM wave and radiates a wave photons, and approaching • No
  • Optical Light Manipulation and Imaging Through Scattering Media

    Optical Light Manipulation and Imaging Through Scattering Media

    Optical light manipulation and imaging through scattering media Thesis by Jian Xu In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2020 Defended September 2, 2020 ii © 2020 Jian Xu ORCID: 0000-0002-4743-2471 All rights reserved except where otherwise noted iii ACKNOWLEDGEMENTS Foremost, I would like to express my sincere thanks to my advisor Prof. Changhuei Yang, for his constant support and guidance during my PhD journey. He created a research environment with a high degree of freedom and encouraged me to explore fields with a lot of unknowns. From his ethics of research, I learned how to be a great scientist and how to do independent research. I also benefited greatly from his high standards and rigorous attitude towards work, with which I will keep in my future path. My committee members, Professor Andrei Faraon, Professor Yanbei Chen, and Professor Palghat P. Vaidyanathan, were extremely supportive. I am grateful for the collaboration and research support from Professor Andrei Faraon and his group, the helpful discussions in optics and statistics with Professor Yanbei Chen, and the great courses and solid knowledge of signal processing from Professor Palghat P. Vaidyanathan. I would also like to thank the members from our lab. Dr. Haojiang Zhou introduced me to the wavefront shaping field and taught me a lot of background knowledge when I was totally unfamiliar with the field. Dr. Haowen Ruan shared many innovative ideas and designs with me, from which I could understand the research field from a unique perspective.