DOCSLIB.ORG

Diffraction Effects in Transmitted Optical Beam Difrakční Jevy Ve Vysílaném Optickém Svazku

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Diffraction Effects in Transmitted Optical Beam Difrakční Jevy Ve Vysílaném Optickém Svazku BRNO UNIVERSITY OF TECHNOLOGY VYSOKÉ UČENÍ TECHNICKÉ V BRNĚ FACULTY OF ELECTRICAL ENGINEERING AND COMMUNICATION DEPARTMENT OF RADIO ELECTRONICS FAKULTA ELEKTROTECHNIKY A KOMUNIKAČNÍCH TECHNOLOGIÍ ÚSTAV RADIOELEKTRONIKY DIFFRACTION EFFECTS IN TRANSMITTED OPTICAL BEAM DIFRAKČNÍ JEVY VE VYSÍLANÉM OPTICKÉM SVAZKU DOCTORAL THESIS DIZERTAČNI PRÁCE AUTHOR Ing. JURAJ POLIAK AUTOR PRÁCE SUPERVISOR prof. Ing. OTAKAR WILFERT, CSc. VEDOUCÍ PRÁCE BRNO 2014 ABSTRACT The thesis was set out to investigate on the wave and electromagnetic effects occurring during the restriction of an elliptical Gaussian beam by a circular aperture. First, from the Huygens-Fresnel principle, two models of the Fresnel diffraction were derived. These models provided means for defining contrast of the diffraction pattern that can beused to quantitatively assess the influence of the diffraction effects on the optical link perfor- mance. Second, by means of the electromagnetic optics theory, four expressions (two exact and two approximate) of the geometrical attenuation were derived. The study shows also the misalignment analysis for three cases – lateral displacement and angular misalignment of the transmitter and the receiver, respectively. The expression for the misalignment attenuation of the elliptical Gaussian beam in FSO links was also derived. All the aforementioned models were also experimentally proven in laboratory conditions in order to eliminate other influences. Finally, the thesis discussed and demonstrated the design of the all-optical transceiver. First, the design of the optical transmitter was shown followed by the development of the receiver optomechanical assembly. By means of the geometric and the matrix optics, relevant receiver parameters were calculated and alignment tolerances were estimated. KEYWORDS Free-space optical link, Fresnel diffraction, geometrical loss, pointing error, all-optical transceiver design ABSTRAKT Dizertačná práca pojednáva o vlnových a elektromagnetických javoch, ku ktorým dochádza pri zatienení eliptického Gausovského zväzku kruhovou apretúrou. Najprv boli z Huygensovho-Fresnelovho princípu odvodené dva modely Fresnelovej difrakcie. Tieto modely poskytli nástroj pre zavedenie kontrastu difrakčného obrazca ako veličiny, ktorá kvantifikuje vplyv difrakčných javov na prevádzkové parametre optického spoja. Následne, pomocou nástrojov elektromagnetickej teórie svetla, boli odvodené štyri výrazy (dva presné a dva aproximatívne) popisujúce geometrický útlm optického spoja. Zároveň boli skúmané tri rôzne prípady odsmerovania zväzku - priečne posunutie a uhlové odsmerovanie vysielača, resp. prijímača. Bol odvodený výraz, ktorý tieto prípady kvan- tifikuje ako útlm elipticky symetrického Gausovského zväzku. Všetky vyššie uvedené modely boli overené v laboratórnych podmienkach, aby sa vylúčil vplyv iných javov. Nakoniec práca pojednáva o návrhu plne fotonického optického terminálu. Najprv bol ukázaný návrh optického vysielača nasledovaný vývojom optomechanickej sústavy prijí- mača. Pomocou nástrojov geometrickej a maticovej optiky boli vypočítané parametre spoja a odhad tolerancie pri zamierení spoja. KLÍČOVÁ SLOVA Optický bezdrôtový spoj, Fresnelova difrakcia, geometrický útlm, chyba zamierením, návrh plne optického spoja. POLIAK, Juraj Diffraction effects in transmitted optical beam: doctoral thesis. Brno: Brno University of Technology, Faculty of Electrical Engineering and Communication, Department of Radio Electronics, 2014. 113 p. Supervised by prof. Ing. Otakar Wil- fert, CSc. DECLARATION I declare that I have written my doctoral thesis on the theme of “Diffraction effects in transmitted optical beam” independently, under the guidance of the doctoral thesis supervisor and using the technical literature and other sources of information which are all quoted in the thesis and detailed in the list of literature at the end of the thesis. As the author of the doctoral thesis I furthermore declare that, as regards the creation of this doctoral thesis, I have not infringed any copyright. In particular, I have not unlawfully encroached on anyone’s personal and/or ownership rights and I am fully aware of the consequences in the case of breaking Regulation S 11 and the following of the Copyright Act No 121/2000 Sb., and of the rights related to intellectual property right and changes in some Acts (Intellectual Property Act) and formulated in later regulations, inclusive of the possible consequences resulting from the provisions of Criminal Act No 40/2009 Sb., Section 2, Head VI, Part 4. Brno . ................................... (author’s signature) ACKNOWLEDGEMENT I would like to express the deepest appreciation to my Professor Otakar Wilfert, who was great mentor in my countless queries. Without his guidance and persistent help this dissertation would not have been possible. I would like to thank to Professor Zdeněk Kolka, who provided me not only a unique opportunity and free hand during development and testing of the optical and optome- chanical parts of the photonic FSO link, but also financial support without which this would not have been possible. In addition, many thanks to Professor Jiří Komrska, who introduced me to the beauty of Wave Optics and mainly to the theory of diffraction, and whose enthusiasm and physicist’s point-of-view were a motor in the theoretical part of the research. A big thank you to Professor Erich Leitgeb whose guidance and nice words came always at the perfect time for encouragement, professional and personal advices as well as for the introduction (not only) to the European OWC community. I would also like to thank to the OptaBro team, Department of Radio Electronics and to SIX Research Centre for their financial and personal support granted through my doctoral studies. Last, but not least, I would like to thank to my family and to my life partner Lucia for their continuous support during my studies and for always believing in me. Brno . ................................... (author’s signature) Faculty of Electrical Engineering and Communication Brno University of Technology Technicka 12, CZ-61600 Brno Czech Republic http://www.six.feec.vutbr.cz ACKNOWLEDGEMENT Výzkum popísaný v této doktorské práci bol realizovaný v laboratóriách podporených z projektu SIX; registračné číslo CZ.1.05/2.1.00/03.0072, operační program Výzkum a vývoj pro inovace. Brno . ................................... (author’s signature) CONTENTS Introduction 14 1 State of the art 16 1.1 Optical wireless communications . 16 1.2 Atmospheric effects in FSO systems . 16 1.3 Deterministic effects in FSO systems . 21 1.3.1 Thermal and wind effects . 22 1.3.2 Geometrical loss . 22 1.3.3 Diffraction effects . 23 2 Objectives of the thesis 25 3 Wave effects in OWC 26 3.1 Gaussian beam . 26 3.2 Fresnel diffraction integral . 31 3.3 Fresnel diffraction in form of integration of Bessel functions . 36 3.4 Fresnel diffraction in form of FFT . 38 3.5 Diffraction effect assessment . 39 3.5.1 Experimental verification of models . 39 3.5.2 Model based on the Bessel functions integration . 41 3.5.3 Model based on the FFT . 43 3.6 Summary . 44 4 Geometrical and pointing loss 49 4.1 Derivation of exact expressions . 50 4.2 Derivation of approximative expressions . 54 4.3 Misalignment loss . 58 4.4 Experimental Verification and Discussion . 62 4.5 Summary . 69 5 All-optical FSO transceiver 71 5.1 Dual-wavelength single-aperture transmitter . 71 5.1.1 WDM-based DAS . 72 5.1.2 POF-based DAS . 73 5.1.3 Dual-core fibre-based DAS . 75 5.2 All-optical receiver: optomechanical design . 78 5.2.1 Telescope selection . 78 5.2.2 Fibre-coupling elements . 79 5.2.3 Final RX OMA design . 80 5.2.4 OMA alignment tolerances . 81 5.3 Non-standard atmospheric effects . 84 5.4 Summary . 87 6 Conclusion 89 Bibliography 91 List of symbols, physical constants and abbreviations 98 List of appendices 105 A Sheet specifications of used components 106 Curriculum Vitae 110 List of Publications 112 LIST OF FIGURES 1.1 Atmospheric transmittance based on absorption analysis using LOW- TRAN. A zenith path from 0 km to 120 km altitude as well as the midlatitude summer atmospheric model are assumed. Atmospheric transmission windows are highlighted in grey color [3]. 18 1.2 Schematic of dual-wavelength FSO system . 21 1.3 Realisation of the dual-wavelength testing FSO transmitter at the Department of Radio Electronics, Brno University of Technology. 21 1.4 Experimental observation of the Fresnel diffraction in the planar op- tical beam transmission. Wavalength 휆 = 632.8 nm, TXA radius 푟TXA = 4.0 mm, beam radius in the TXA plane 푤TXA = 14 mm, distance 퐿 = 6.32 mm, which corresponds to the number 푁f of ob- servable Fresnel zones at the distance 퐿 푁f = 4............. 24 3.1 Evolution of the beam widths 푤푥(푧) and 푤푦(푧) (a) and evolution of the beam radii 푅푥(푧) and 푅푦(푧) (b) along the 푧 axis, where nega- tive and positive values represent a converging and a diverging wave, respectively. 푧 = 0 corresponds to the location of beam waist. Sim- ulation parameters: 푤0푥 = 0.1 mm, 푤0푦 = 0.25 mm, 휆 = 633 nm, distance Δ푧 between both beam waists was 360 mm due to astigmatism. 30 3.2 To the explanation of Huygens-Fresnel principle in Cartesian coordi- nates. 32 3.3 To the derivation of the Fresnel zone diameter 푟푛 [25]. 푀0 is point in the plane ΣTXA and 푃 point in the plane ΣRXA............. 34 3.4 To the explanation of Hyugens-Fresnel principle in cylindrical coor- dinates. 37 3.5 Simulation of Fresnel diffraction effect in FSO systems. Top left- primary elliptical Gaussian beam with beam-widths 푤푥 = 1.72 mm and 푤푦 = 0.48 mm in 푥 and 푦 axis, respectively. Top right - circular aperture (TXA) with radius 푟TXA = 1 mm. Central plot shows the diffracted beam in the plane of observation 푟RXA and bottom left and right - optical intensity of the diffracted beam along 푥 and 푦 axis, re- spectively. In the bottom left section, power 푃out transmitted through the circular aperture is calculated relative to the total radiated power 푃in of the optical source. 40 3.6 Measured data (×) is in very good agreement with the model based on the integration of the Bessel function (3.44) (*) and FFT-based model (3.29) (♢).
Load more

Recommended publications
  • Beam Profiling by Michael Scaggs
    Beam Profiling by Michael Scaggs Haas Laser Technologies, Inc. Introduction Lasers are ubiquitous in industry today. Carbon Dioxide, Nd:YAG, Excimer and Fiber lasers are used in many industries and a myriad of applications. Each laser type has its own unique properties that make them more suitable than others. Nevertheless, at the end of the day, it comes down to what does the focused or imaged laser beam look like at the work piece? This is where beam profiling comes into play and is an important part of quality control to ensure that the laser is doing what it intended to. In a vast majority of cases the laser beam is simply focused to a small spot with a simple focusing lens to cut, scribe, etch, mark, anneal, or drill a material. If there is a problem with the beam delivery optics, the laser or the alignment of the system, this problem will show up quite markedly in the beam profile at the work piece. What is Beam Profiling? Beam profiling is a means to quantify the intensity profile of a laser beam at a particular point in space. In material processing, the "point in space" is at the work piece being treated or machined. Beam profiling is accomplished with a device referred to a beam profiler. A beam profiler can be based upon a CCD or CMOS camera, a scanning slit, pin hole or a knife edge. In all systems, the intensity profile of the beam is analyzed within a fixed or range of spatial Haas Laser Technologies, Inc.
    [Show full text]
  • 5.Laser Vocabulary
    ! Laser Beam Measurement Vocabulary Wavelength: In physics, the wavelength of a sinusoidal wave is the spatial period of the wave— the distance over which the wave's shape repeats,[1] and the inverse of the spatial frequency. It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns.[2][3] Wavelength is commonly designated by the Greek letter lambda (λ). " λ: The Greek symbol lambda is used to express wavelength. Gaussian: The graph of a Gaussian is a characteristic symmetric "bell curve" shape. The parameter a, is the height of the curve's peak, b is the position of the center of the peak and c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell". Gaussian functions are widely used in statistics where they describe the normal distributions, in signal processing where they serve to define Gaussian filters, in image processing where two- dimensional Gaussians are used for Gaussian blurs, and in mathematics where they are used to solve heat equations and diffusion equations and to define the Weierstrass transform. 3050 North 300 West North Logan, UT 84341 Tel: 435-753-3729 www.ophiropt.com/photonics https://en.wikipedia.org/wiki/Gaussian_function " A Gaussian beam is a beam that has a normal distribution in all directions similar to the images below. The intensity is highest in the center of the beam and dissipates as it reaches the perimeter of the beam.
    [Show full text]
  • Fresnel Diffraction.Nb Optics 505 - James C
    Fresnel Diffraction.nb Optics 505 - James C. Wyant 1 13 Fresnel Diffraction In this section we will look at the Fresnel diffraction for both circular apertures and rectangular apertures. To help our physical understanding we will begin our discussion by describing Fresnel zones. 13.1 Fresnel Zones In the study of Fresnel diffraction it is convenient to divide the aperture into regions called Fresnel zones. Figure 1 shows a point source, S, illuminating an aperture a distance z1away. The observation point, P, is a distance to the right of the aperture. Let the line SP be normal to the plane containing the aperture. Then we can write S r1 Q ρ z1 r2 z2 P Fig. 1. Spherical wave illuminating aperture. !!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!! 2 2 2 2 SQP = r1 + r2 = z1 +r + z2 +r 1 2 1 1 = z1 + z2 + þþþþ r J þþþþþþþ + þþþþþþþN + 2 z1 z2 The aperture can be divided into regions bounded by concentric circles r = constant defined such that r1 + r2 differ by l 2 in going from one boundary to the next. These regions are called Fresnel zones or half-period zones. If z1and z2 are sufficiently large compared to the size of the aperture the higher order terms of the expan- sion can be neglected to yield the following result. l 1 2 1 1 n þþþþ = þþþþ rn J þþþþþþþ + þþþþþþþN 2 2 z1 z2 Fresnel Diffraction.nb Optics 505 - James C. Wyant 2 Solving for rn, the radius of the nth Fresnel zone, yields !!!!!!!!!!! !!!!!!!! !!!!!!!!!!! rn = n l Lorr1 = l L, r2 = 2 l L, , where (1) 1 L = þþþþþþþþþþþþþþþþþþþþ þþþþþ1 + þþþþþ1 z1 z2 Figure 2 shows a drawing of Fresnel zones where every other zone is made dark.
    [Show full text]
  • Laser Beam Profile Meaurement System Time
    Measurement of Laser Beam Profile and Propagation Characteristics 1. Laser Beam Measurement Capabilities Laser beam profiling plays an important role in such applications as laser welding, laser focusing, and laser free-space communications. In these applications, laser profiling enables to capture the data needed to evaluate the change in the beam width and determine the details of the instantaneous beam shape, allowing manufacturers to evaluate the position of hot spots in the center of the beam and the changes in the beam’s shape. Digital wavefront cameras (DWC) with software can be used for measuring laser beam propagation parameters and wavefronts in pulsed and continuous modes, for lasers operating at visible to far- infrared wavelengths: - beam propagation ratio M²; - width of the laser beam at waist w0; - laser beam divergence angle θ x, θ y; - waist location z-z0; - Rayleigh range zRx, zRy; - Ellipticity; - PSF; - Wavefront; - Zernike aberration modes. These parameters allow: - controlling power density of your laser; - controlling beam size, shape, uniformity, focus point and divergence; - aligning delivery optics; - aligning laser devices to lenses; - tuning laser amplifiers. Accurate knowledge of these parameters can strongly affect the laser performance for your application, as they highlight problems in laser beams and what corrections need to be taken to get it right. Figure 1. Characteristics of a laser beam as it passes through a focusing lens. http://www.SintecOptronics.com http://www.Sintec.sg 1 2. Beam Propagation Parameters M², or Beam Propagation Ratio, is a value that indicates how close a laser beam is to being a single mode TEM00 beam.
    [Show full text]
  • Optics of Gaussian Beams 16
    CHAPTER SIXTEEN Optics of Gaussian Beams 16 Optics of Gaussian Beams 16.1 Introduction In this chapter we shall look from a wave standpoint at how narrow beams of light travel through optical systems. We shall see that special solutions to the electromagnetic wave equation exist that take the form of narrow beams – called Gaussian beams. These beams of light have a characteristic radial intensity profile whose width varies along the beam. Because these Gaussian beams behave somewhat like spherical waves, we can match them to the curvature of the mirror of an optical resonator to find exactly what form of beam will result from a particular resonator geometry. 16.2 Beam-Like Solutions of the Wave Equation We expect intuitively that the transverse modes of a laser system will take the form of narrow beams of light which propagate between the mirrors of the laser resonator and maintain a field distribution which remains distributed around and near the axis of the system. We shall therefore need to find solutions of the wave equation which take the form of narrow beams and then see how we can make these solutions compatible with a given laser cavity. Now, the wave equation is, for any field or potential component U0 of Beam-Like Solutions of the Wave Equation 517 an electromagnetic wave ∂2U ∇2U − µ 0 =0 (16.1) 0 r 0 ∂t2 where r is the dielectric constant, which may be a function of position. The non-plane wave solutions that we are looking for are of the form i(ωt−k(r)·r) U0 = U(x, y, z)e (16.2) We allow the wave vector k(r) to be a function of r to include situations where the medium has a non-uniform refractive index.
    [Show full text]
  • Angular Spectrum Description of Light Propagation in Planar Diffractive Optical Elements
    Angular spectrum description of light propagation in planar diffractive optical elements Rosemarie Hild HTWK-Leipzig, Fachbereich Informatik, Mathematik und Naturwissenschaften D-04251 Leipzig, PF 30 11 66 Tel.: 49 341 5804429 Fax:49 341 5808416 e-mail:[email protected] Abstract The description of the light propagation in or between planar diffractive optical elements is done with the angular spec- trum method. That means, the confinement to the paraxial approximation is removed. In addition it is not necessary to make a difference between Fraunhofer and Fresnel diffraction as usually done by the solution of the of the Rayleigh Sommerfeld formula. The diffraction properties of slits of varying width are analysed first. The transitional phenomena between Fresnel and Fraunhofer diffraction will be discussed from the view point of metrology. The transition phenomena is characterised as a problem of reduced resolution or low pass filtering in free space propagation. The light distributions produced by a plane screen , including slits, line and space structures or phase varying structures are investigated in detail. Keywords: Optical Metrology in Production Engineering, Photon Management- diffractive optics, microscopy, nanotechnology 1. Introduction The knowledge of the light intensity distributions that are created by planar diffractive optical elements is very important in modern technologies like microoptics, the optical lithography or in the combination of both techniques 1. The theoretical problem consists in the description of the imaging properties of small optical elements or small diffrac- tion apertures up to the region of the wave length. In general the light intensities created in free space or optical media by such elements, are calculated with the solution of the diffraction integral.
    [Show full text]
  • Optimal Focusing Conditions of Lenses Using Gaussian Beams
    BNL-112564-2016-JA File # 93496 Optimal focusing conditions of lenses using Gaussian beams Juan Manuel Franco, Moises Cywiak, David Cywiak, Mourad Idir Submitted to Optics Communications June 2016 Photon Sciences Department Brookhaven National Laboratory U.S. Department of Energy USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22) Notice: This manuscript has been authored by employees of Brookhaven Science Associates, LLC under Contract No. DE- SC0012704 with the U.S. Department of Energy. The publisher by accepting the manuscript for publication acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. 1 DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or any third party’s use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof or its contractors or subcontractors. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
    [Show full text]
  • Chapter on Diffraction
    Chapter 3 Diffraction While the particle description of Chapter 1 works amazingly well to understand how ra- diation is generated and transported in (and out of) astrophysical objects, it falls short when we investigate how we detect this radiation with our telescopes. In particular the diffraction limit of a telescope is the limit in spatial resolution a telescope of a given size can achieve because of the wave nature of light. Diffraction gives rise to a “Point Spread Function”, meaning that a point source on the sky will appear as a blob of a certain size on your image plane. The size of this blob limits your spatial resolution. The only way to improve this is to go to a larger telescope. Since the theory of diffraction is such a fundamental part of the theory of telescopes, and since it gives a good demonstration of the wave-like nature of light, this chapter is devoted to a relatively detailed ab-initio study of diffraction and the derivation of the point spread function. Literature: Born & Wolf, “Principles of Optics”, 1959, 2002, Press Syndicate of the Univeristy of Cambridge, ISBN 0521642221. A classic. Steward, “Fourier Optics: An Introduction”, 2nd Edition, 2004, Dover Publications, ISBN 0486435040 Goodman, “Introduction to Fourier Optics”, 3rd Edition, 2005, Roberts & Company Publishers, ISBN 0974707724 3.1 Fresnel diffraction Let us construct a simple “Camera Obscura” type of telescope, as shown in Fig. 3.1. We have a point-source at location “a”, and we point our telescope exactly at that source. Our telescope consists simply of a screen with a circular hole called the aperture or alternatively the pupil.
    [Show full text]
  • Huygens Principle; Young Interferometer; Fresnel Diffraction
    Today • Interference – inadequacy of a single intensity measurement to determine the optical field – Michelson interferometer • measuring – distance – index of refraction – Mach-Zehnder interferometer • measuring – wavefront MIT 2.71/2.710 03/30/09 wk8-a- 1 A reminder: phase delay in wave propagation z t t z = 2.875λ phasor due In general, to propagation (path delay) real representation phasor representation MIT 2.71/2.710 03/30/09 wk8-a- 2 Phase delay from a plane wave propagating at angle θ towards a vertical screen path delay increases linearly with x x λ vertical screen (plane of observation) θ z z=fixed (not to scale) Phasor representation: may also be written as: MIT 2.71/2.710 03/30/09 wk8-a- 3 Phase delay from a spherical wave propagating from distance z0 towards a vertical screen x z=z0 path delay increases quadratically with x λ vertical screen (plane of observation) z z=fixed (not to scale) Phasor representation: may also be written as: MIT 2.71/2.710 03/30/09 wk8-a- 4 The significance of phase delays • The intensity of plane and spherical waves, observed on a screen, is very similar so they cannot be reliably discriminated – note that the 1/(x2+y2+z2) intensity variation in the case of the spherical wave is too weak in the paraxial case z>>|x|, |y| so in practice it cannot be measured reliably • In many other cases, the phase of the field carries important information, for example – the “history” of where the field has been through • distance traveled • materials in the path • generally, the “optical path length” is inscribed
    [Show full text]
  • Monte Carlo Ray-Trace Diffraction Based on the Huygens-Fresnel Principle
    Monte Carlo Ray-Trace Diffraction Based On the Huygens-Fresnel Principle J. R. MAHAN,1 N. Q. VINH,2,* V. X. HO,2 N. B. MUNIR1 1Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA 2Department of Physics and Center for Soft Matter and Biological Physics, Virginia Tech, Blacksburg, VA 24061, USA *Corresponding author: [email protected] The goal of this effort is to establish the conditions and limits under which the Huygens-Fresnel principle accurately describes diffraction in the Monte Carlo ray-trace environment. This goal is achieved by systematic intercomparison of dedicated experimental, theoretical, and numerical results. We evaluate the success of the Huygens-Fresnel principle by predicting and carefully measuring the diffraction fringes produced by both single slit and circular apertures. We then compare the results from the analytical and numerical approaches with each other and with dedicated experimental results. We conclude that use of the MCRT method to accurately describe diffraction requires that careful attention be paid to the interplay among the number of aperture points, the number of rays traced per aperture point, and the number of bins on the screen. This conclusion is supported by standard statistical analysis, including the adjusted coefficient of determination, adj, the root-mean-square deviation, RMSD, and the reduced chi-square statistics, . OCIS codes: (050.1940) Diffraction; (260.0260) Physical optics; (050.1755) Computational electromagnetic methods; Monte Carlo Ray-Trace, Huygens-Fresnel principle, obliquity factor 1. INTRODUCTION here. We compare the results from the analytical and numerical approaches with each other and with the dedicated experimental The Monte Carlo ray-trace (MCRT) method has long been utilized to results.
    [Show full text]
  • Modeling Holographic Grating Imaging Systems Using the Angular Spectrum Propagation Method
    Rochester Institute of Technology RIT Scholar Works Theses 8-15-2006 Modeling holographic grating imaging systems using the angular spectrum propagation method Thomas Blasiak Follow this and additional works at: https://scholarworks.rit.edu/theses Recommended Citation Blasiak, Thomas, "Modeling holographic grating imaging systems using the angular spectrum propagation method" (2006). Thesis. Rochester Institute of Technology. Accessed from This Thesis is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. CHESTER F. CARLSON CENTER FOR IMAGING SCIENCE ROCHESTER INSTITUTE OF TECHNOLOGY ROCHESTER, NEW YORK CERTIFICATE OF APPROVAL ______________________________________________________________ M.S. DEGREE THESIS ______________________________________________________________ The M.S. Degree Thesis of Thomas C. Blasiak has been examined and approved by the thesis committee as satisfactory for the thesis requirement of the Master of Science degree __________________________________Dr. Roger Easton __________________________________Dr. Zoran Ninkov __________________________________Dr. Michael Kotlarchyk Date ii Modeling Holographic Grating Imaging Systems Using The Angular Spectrum Propagation Method by Thomas Blasiak Submitted to the Chester F. Carlson Center for Imaging Science in partial fulfillment of the requirements for the Master of Science Degree at the Rochester Institute of Technology Abstract The goal of this research was to describe the angular spectrum propagation method for the numerical calculation of scalar optical propagation phenomena. The angular spectrum propagation method has some advantages over the Fresnel propagation method for modeling low F# optical systems and non-paraxial systems. An example of one such system was modeled, namely the diffraction and propagation from a holographic diffraction grating.
    [Show full text]
  • Laser Beam Profile & Beam Shaping
    Copyright by Priti Duggal 2006 An Experimental Study of Rim Formation in Single-Shot Femtosecond Laser Ablation of Borosilicate Glass by Priti Duggal, B.Tech. Thesis Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of Master of Science in Engineering The University of Texas at Austin August 2006 An Experimental Study of Rim Formation in Single-Shot Femtosecond Laser Ablation of Borosilicate Glass Approved by Supervising Committee: Adela Ben-Yakar John R. Howell Acknowledgments My sincere thanks to my advisor Dr. Adela Ben-Yakar for showing trust in me and for introducing me to the exciting world of optics and lasers. Through numerous valuable discussions and arguments, she has helped me develop a scientific approach towards my work. I am ready to apply this attitude to my future projects and in other aspects of my life. I would like to express gratitude towards my reader, Dr. Howell, who gave me very helpful feedback at such short notice. My lab-mates have all positively contributed to my thesis in ways more than one. I especially thank Dan and Frederic for spending time to review the initial drafts of my writing. Thanks to Navdeep for giving me a direction in life. I am excited about the future! And, most importantly, I want to thank my parents. I am the person I am, because of you. Thank you. 11 August 2006 iv Abstract An Experimental Study of Rim Formation in Single-Shot Femtosecond Laser Ablation of Borosilicate Glass Priti Duggal, MSE The University of Texas at Austin, 2006 Supervisor: Adela Ben-Yakar Craters made on a dielectric surface by single femtosecond pulses often exhibit an elevated rim surrounding the crater.
    [Show full text]