DOCSLIB.ORG

4. Development of Angle Resolved Low Coherence Interferometry (A/LCI) Using the T- Matrix Method

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
4. Development of Angle Resolved Low Coherence Interferometry (A/LCI) Using the T- Matrix Method Diagnostic Imaging and Assessment Using Angle Resolved Low Coherence Interferometry by Michael G. Giacomelli Department of Biomedical Engineering Duke University Date:_______________________ Approved: ___________________________ Adam Wax, Supervisor ___________________________ Joseph Izatt ___________________________ David Brady ___________________________ Tuan Vo- Dinh ___________________________ Sina Farsiu Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Biomedical Engineering in the Graduate School of Duke University 2012 i v ABSTRACT Diagnostic Imaging and Detection using Angle Resolved Low Coherence Interferometry by Michael Giacomelli Department of Biomedical Engineering Duke University Date:_______________________ Approved: ___________________________ Adam Wax, Supervisor ___________________________ Joseph Izatt ___________________________ David Brady ___________________________ Tuan Vo- Dinh ___________________________ Sina Farsiu An abstract of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Biomedical Engineering in the Graduate School of Duke University 2012 Copyright by Michael G. Giacomelli 2012 Abstract The redistribution of incident light into scattered fields ultimately limits the ability to image into biological media. However, these scattered fields also contain information about the structure and distribution of protein complexes, organelles, cells and whole tissues that can be used to assess the health of tissue or to enhance imaging contrast by excluding confounding signals. The interpretation of scattered fields depends on a detailed understanding of the scattering process as well as sophisticated measurement systems. In this work, the development of new instruments based on low coherence interferometry (LCI) is presented in order to perform precise, depth-resolved measurements of scattered fields. Combined with LCI, the application of new light scattering models based on both analytic and numerical methods is presented in order to interpret scattered field measurements in terms of scatterer geometry and tissue health. The first portion of this work discusses the application of a new light scattering model to the measurement recorded with an existing technique, Angle Resolved Low Coherence Interferometry (a/LCI). In the a/LCI technique, biological samples are interrogated with collimated light and the energy per scattering angle at each depth in the volume is recorded interferometrically. A light scattering model is then used to invert the scattering measurements and measure the geometry of cell nuclei. A new light scattering model is presented that can recover information about the size, refractive iv index, and for the first time, shape of cell nuclei. This model is validated and then applied to the study of cell biology in a series of experiments measuring cell swelling, cell deformation, and finally detecting the onset of apoptosis. The second portion of this work introduces an improved version of a/LCI based on two dimension angle-resolved measurement and Fourier domain low coherence interferometry. A new system based on fiber scanning is presented for high speed and polarization-resolved measurements of scattered fields. The combined system is validated with phantoms and is shown to be able to uniquely determine the size and shape of scattering particles using a single measurement. Finally, determination of the orientation of scatterers relative to electric field is considered. The third portion of this work develops the use of angle-resolved interferometry for imaging through highly scattering media by exploiting the tendency of scatterers to forward scatter light. A new interferometers is developed that can image through very large numbers of scattering events with acceptable resolution. A computational model capable of reproducing experimental measurements is developed and used to understand the performance of the technique. Finally, theoretical arguments are presented suggesting the feasibility of adapting the technique to Fourier domain acquisition. The final portion of the work develops a method for processing 2D angle resolved measurements using optical autocorrelation. In this method, measurements v over a range of angles are fused into a single depth scan that incorporates the component of scattered light only from certain spatial scales. The utility of the technique is demonstrated using a gene knockout model of retinal degeneration in mice. Optical autocorrelation is shown to be a potentially useful biomarker of tissue disease. vi Contents Abstract ......................................................................................................................................... iv List of Tables ................................................................................................................................ xii List of Figures ............................................................................................................................ xiii Acknowledgements ................................................................................................................ xxiv 1. Introduction ............................................................................................................................... 1 1.1 Light and Matter ............................................................................................................... 1 1.2 Motivation ......................................................................................................................... 4 1.3 Organization ...................................................................................................................... 7 2. Background ................................................................................................................................ 8 2.1 Low Coherence Interferometry ...................................................................................... 8 2.1.1 Optical Coherence Tomography ............................................................................. 13 2.2 Modeling of Light and Matter Interactions ................................................................ 14 2.2.1 Mie Theory ................................................................................................................. 14 2.2.2 T-matrix ...................................................................................................................... 17 2.3 Light Scattering Techniques .......................................................................................... 18 2.3.1 Light Scattering Spectroscopy ................................................................................. 18 2.3.2 Fourier-Domain Low Coherence Interferometry .................................................. 19 2.3.3 Confocal Light Absorption and Scattering Spectroscopy (CLASS).................... 21 2.3.4 Two Dimension Angular Optical Spectroscopy ................................................... 22 2.3.5 4D Elastic Light Scattering Spectroscopy ............................................................... 22 vii 2.3.6 Angle-Resolved Low Coherence Interferometry .................................................. 23 2.3.7 Fourier Holographic Light Scattering Angular Spectroscopy ............................ 24 2.4 Angle-Resolved Low Coherence Interferometry Processing ................................... 25 2.4.1 Depth Extraction ........................................................................................................ 25 2.4.2 Correlation Filtering .................................................................................................. 25 2.4.3 χ2 Error Calculation ................................................................................................... 27 2.4.4 χ2 Database Preparation ........................................................................................... 28 2.5 Summary .......................................................................................................................... 28 3. Development of Advanced Light Scattering Models ......................................................... 30 3.1 Background ..................................................................................................................... 30 3.2 Scattering Coordinate System ....................................................................................... 34 3.3 Distributed Computing Software for Computation of T-matrix Databases .......... 36 3.3.1 MySQL Server ............................................................................................................ 38 3.3.2 DC Worker Software ................................................................................................. 40 3.3.3 T-matrix Software ...................................................................................................... 40 3.3.4 Client Software .......................................................................................................... 41 3.4 Validation of the T-matrix Using Non-spherical Phantoms ..................................... 42 3.4.1 Development of Spheroidal Phantoms .................................................................. 42 3.4.2 Determining Spheroid Size ...................................................................................... 44 3.5 Summary .........................................................................................................................
Load more

Recommended publications
  • Coherent X-Rays: Overview by Malcolm Howells
    Coherent x-rays: overview by Malcolm Howells Lecture 1 of the series COHERENT X-RAYS AND THEIR APPLICATIONS A series of tutorial–level lectures edited by Malcolm Howells* *ESRF Experiments Division ESRF Lecture Series on Coherent X-rays and their Applications, Lecture 1, Malcolm Howells CONTENTS Introduction to the series Books History The idea of coherence - temporal, spatial Young's slit experiment Coherent experiment design Coherent optics The diffraction integral Linear systems - convolution Wave propagation and passage through a transparency Optical propagators - examples Future lectures: 1. Today 2. Quantitative coherence and application to x-ray beam lines (MRH) 3. Optical components for coherent x-ray beams (A. Snigirev) 4. Coherence and x-ray microscopes (MRH) 5. Phase contrast and imaging in 2D and 3D (P. Cloetens) 6. Scanning transmission x-ray microscopy: principles and applications (J. Susini) 7. Coherent x-ray diffraction imaging: history, principles, techniques and limitations (MRH) 8. X-ray photon correlation spectroscopy (A. Madsen) 9. Coherent x-ray diffraction imaging and other coherence techniques: current achievements, future projections (MRH) ESRF Lecture Series on Coherent X-rays and their Applications, Lecture 1, Malcolm Howells COHERENT X-RAYS AND THEIR APPLICATIONS A series of tutorial–level lectures edited by Malcolm Howells* Mondays 5.00 pm in the Auditorium except where otherwise stated 1. Coherent x-rays: overview (Malcolm Howells) (April 7) (5.30 pm) 2. Coherence theory: application to x-ray beam lines (Malcolm Howells) (April 21) 3. Optical components for coherent x-ray beams (Anatoli Snigirev) (April 28) 4. Coherence and x-ray microscopes (Malcolm Howells) (May 26) (CTRL room ) 5.
    [Show full text]
  • Coherence Length Measurement System Design Description Document
    Coherence Length Measurement System Design Description Document Coherence Length Measurement System Design Description Document ASML / Tao Chen Faculty Advisor: Professor Thomas Brown Pellegrino Conte (Scribe & Document Handler) Lei Ding (Customer Liaison) Maxwell Wolfson (Project Coordinator) Document Number 00007 Revisions Level Date G 5-06-2018 This is a computer-generated document. The electronic Authentication Block master is the official revision. Paper copies are for reference only. Paper copies may be authenticated for specifically stated purposes in the authentication block. 00007 Rev G page 1 Coherence Length Measurement System Design Description Document Rev Description Date Authorization A Initial DDD 1-22-2018 All B Edited System Overview 2-05-2018 All Added Lab Results C Edited System Overview 2-19-2018 All Added New Results D Added New Lab Results 2-26-2018 All Updated FRED Progress E Edited System overview 4-02-2018 All Finalized cost analysis Added new results F Edited Cost Analysis 4-20-2018 All Added new results Added to code analysis G Added Final Results 5-06-2018 All Added Customer Instructions Added to Code 00007 Rev G page 2 Coherence Length Measurement System Design Description Document Table of Contents Revision History 2 Table of Contents 3 Vision Statement 4 Project Scope 4 Theoretical Background 5-7 System Overview 8-10 Cost Analysis 11-13 Spring Semester Timeline 14-15 Lab Results 16-22 FRED Analysis 23-26 Visibility Analysis 27 Design Day Description 28 Conclusions and Future Work 29 Appendix A: Table of All Lab Results 30-40 Appendix B: Visibility Processing Code 41-43 Appendix C: Customer Instructions 44-49 References 50 00007 Rev G page 3 Coherence Length Measurement System Design Description Document Vision Statement: This projects’ goal is to design and assemble an interferometer capable of measuring and reporting information regarding the coherence length of a laser.
    [Show full text]
  • Optics, IDC202 G R O U P
    Optics, IDC202 G R O U P Lecture 3. Rejish Nath Contents 1. Coherence and interference 2. Youngs double slit experiment 3. Alternative setups 4. Theory of coherence 5. Coherence time and length 6. A finite wave train 7. Spatial coherence Literature: 1. Optics, (Eugene Hecht and A. R. Ganesan) 2. Optical Physics, (A. Lipson, S. G. Lipson and H. Lipson) 3. The Optics of Life, (Sönke Johnsen) 4. Modern Optics, (Grant R. Fowles) Course Contents 1. Nature of light (waves and particles) 2. Maxwells equations and wave equation 3. Poynting vector 4. Polarization of light 5. Law of reflection and snell's law 6. Total Internal Reflection and Evanescent waves 7. Concept of coherence and interference 8. Young's double slit experiment 9. Single slit, N-slit Diffraction 10. Grating, Birefringence, Retardation plates 11. Fermat's Principle 12. Optical instruments 13. Human Eye 14. Spontaneous and stimulated emission 15. Concept of Laser 3 Coherence and interference Optical interference is based on the superposition principle. (This is because the Maxwell’s equations are linear differential equations.) The electric field at a point in vacuum: E = E1 + E2 + E3 + E4 + ... is the vector sum of that from the different sources. The same is true for magnetic fields. Remark: This may not be generally true, deviations from linear superposition is the study of nonlinear optical phenomena or simply non-linear optics. Coherence and interference Consider two harmonic, monochromatic, linearly polarised waves = E exp [i(k r !t + φ )] E1 1 1 · − 1 = E exp [i(k r !t + φ )] E2 2 2 · − 2 If the phase difference φ 1 φ 2 is constant, the two sources are said to be mutually coherent.
    [Show full text]
  • New Plasma Diagnosis by Coherence Length Spectroscopy
    New Plasma Diagnosis by Coherence Length Spectroscopy Nopporn Poolyarata and Young W. Kimb aThe Development and Promotion of Science and Technology (DPST), Thailand bDepartment of Physics, Lehigh University 16 Memorial Dr. East, Bethlehem, PA 18015 , USA Abstract A new methodology and instrumentation have been developed for diagnosis of dense high temperature plasmas. In a plasma medium, collision processes shorten the optical coherence length at a given emission wavelength. By measuring the coherence length, the rate of collisions a radiating particle experiences can be determined. A map of the collision rates throughout the plasma can speak volumes about the atomic and thermal state of the plasma. Both the time-integrated and time-resolved interference fringes are obtained 252o using emissions due to the transition between 33sp( P32) 4 p and 252o 33sp() P32 7 d. We have observed that the coherence length indeed decreases with increasing collision rate, and in addition, as a function of time as a result of cumulative collisions. The coherence length was found to be 4200 ± 800 nm at 50 torr where the collision frequency is 2.14× 1011 s -1 , and 2400± 130 nm at 140 torr where the collision frequency is8.13× 1011 s -1 . We have also discovered that the coherence length varies with the direction of the viewing line of sight into the discharge plasma. The anisotropy results from the non-uniform structure in the discharge current, and this is further investigated by intentionally deforming the tip of the cathode. A photographic examination of both the cathode and the anode disc confirms the non-axis-symmetric structure of the plasma, which leads to the asymmetry in the plasma, in agreement with the angular dependence of the coherence length.
    [Show full text]
  • Measurement of Angular Distributions by Use of Low-Coherence Interferometry for Light-Scattering Spectroscopy
    322 OPTICS LETTERS / Vol. 26, No. 6 / March 15, 2001 Measurement of angular distributions by use of low-coherence interferometry for light-scattering spectroscopy Adam Wax, Changhuei Yang, Ramachandra R. Dasari, and Michael S. Feld G. R. Harrison Spectroscopy Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 Received September 11, 2000 We present a novel interferometer for measuring angular distributions of backscattered light. The new sys- tem exploits a low-coherence source in a modified Michelson interferometer to provide depth resolution, as in optical coherence tomography, but includes an imaging system that permits the angle of the reference field to be varied in the detector plane by simple translation of an optical element. We employ this system to examine the angular distribution of light scattered by polystyrene microspheres. The measured data indicate that size information can be recovered from angular-scattering distributions and that the coherence length of the source influences the applicability of Mie theory. © 2001 Optical Society of America OCIS codes: 120.3180, 120.5820, 030.1640, 290.4020. Light-scattering spectroscopy is an established tech- scanning of an optical element and thus can be easily nique that uses the spectrum of backscattered light applied as an adjunct to optical coherence tomogra- to infer structural characteristics, such as size and phy, suggesting that the new method will have great refractive index, of spherical scattering objects.1 It potential for biological imaging. We demonstrate was demonstrated by Yang et al.2 that structural that structural information can be inferred by com- information can be recovered from a subsurface layer parison of the measured angular distributions with of a scattering medium by use of interferometric the predictions of Mie theory.
    [Show full text]
  • Experiment 3
    Experiment 3 Coherence Length Any light source is made up of a large number of individual emitters, each of which can emit for only a brief period of time. The result is the creation of wavetrains of finite length. The average length of the wavetrains is referred to as the coherence length hdi. The object of this experiment is to estimate the coherence length for several different sources using a Michelson Interferometer. In addition, the difference in wavelength between the two Na-D lines will be determined. 3.1 Outline of Theory 3.1.1 Coherence Length A Michelson Interferometer, as previously analyzed, splits the incident beam into two beams which can travel over different distances before being reflected back to the beam splitter where the interference pattern is observed. The following fact, however, must be considered when creating interference fringes. 1. fringes are created only by the interference of two coherent sources, and 2. wavetrains from different emitters are not coherent. 7 8 EXPERIMENT 3. COHERENCE LENGTH This indicates that interference will only be observed if the two sections of a specific wavetrain split by the beam splitter return to the splitter at nearly the same moment to order to interfere with each other. The coherence length can be estimated experimentally by measuring the optical path difference (∆ = 2(d2 − d1)) at the point where the fringes become invisible. The coherence length is hdi≈ 2∆ The value obtained will depend on the sensitivity of the observer’s eye, so it can only be defined as an estimate. As part of the experiment, you will be expected to compare your results with the theoretical estimate for coherence length.
    [Show full text]
  • Delft University of Technology Aliasing, Coherence, and Resolution in A
    Delft University of Technology Aliasing, coherence, and resolution in a lensless holographic microscope Agbana, Tope; Gong, Hai; Amoah, A.S.; Bezzubik, V; Verhaegen, Michel; Vdovin, Gleb DOI 10.1364/OL.42.002271 Publication date 2017 Document Version Accepted author manuscript Published in Optics Letters Citation (APA) Agbana, T., Gong, H., Amoah, A. S., Bezzubik, V., Verhaegen, M., & Vdovin, G. (2017). Aliasing, coherence, and resolution in a lensless holographic microscope. Optics Letters, 42(12), 2271-2274. https://doi.org/10.1364/OL.42.002271 Important note To cite this publication, please use the final published version (if applicable). Please check the document version above. Copyright Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policy Please contact us and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim. This work is downloaded from Delft University of Technology. For technical reasons the number of authors shown on this cover page is limited to a maximum of 10. Letter Optics Letters 1 Aliasing, coherence, and resolution in a lensless holographic microscope TEMITOPE E. AGBANA1,*,H AI GONG1,A BENA S.AMOAH4,V ITALY BEZZUBIK3,M ICHEL VERHAEGEN1, AND GLEB VDOVIN1,2,3 1 Delft University of Technology, DCSC, Mekelweg 2, 2628 CD Delft, The Netherlands 2Flexible Optical B.V., Polakweg 10-11, 2288 GG Rijswijk, The Netherlands 3ITMO University, Kronverksky 49, 197101 St Petersburg, Russia 4Leids Universitair Medisch Centrum,Albinusdreef 2, 2333 ZA Leiden, The Netherlands *Corresponding author: [email protected] Compiled May 18, 2017 We have shown that the maximum achievable resolu- • Spatial aliasing, occurring when the intensity fringes are tion of in-line lensless holographic microscope is lim- undersampled by the sensor.
    [Show full text]
  • Properties of Helium–Neon Lasers
    PROPERTIES OF HELIUM–NEON LASERS The acronym LASER stands for "Light Amplification through Stimulated Emission of Radiation". It has also become standard to refer to the device itself as a laser. The light emitted by a laser has very special properties which distinguish it from the light given off by an ordinary source of electromagnetic radiation, such as a light-bulb. These special properties make it possible to use laser's for very unusual purposes for which ordinary, even nearly-monochromatic light is not suitable. I. PROPERTIES OF LASER LIGHT A. The light is extremely monochromatic with wavelength l= 632.8 nm B. Consequently, the light has high "temporal coherence", meaning as you travel along the direction of propagation, the components of the electric field continue to oscillate like a sine-wave with a single wavelength, amplitude, and phase. Of course, no light source generates perfect plane-waves. Real wave- trains have finite length. The distance over which the waveform remains similar to a sine-wave is called the coherence-length of the beam, Lc, and it is typically about 10-30 cm for commercial He-Ne lasers. C. The light is unidirectional and aligned so as to be parallel to the body of the laser. D. The light is "spatially coherent". The phase of radiation is nearly constant throughout the cross-sectional width of the beam. This property is a consequence of property C, and is entirely independent of temporal coherence (property B). E. A Brewster-window is often inserted in the laser by the manufacturer to produce light with a definite state of linear polarization.
    [Show full text]
  • 4 Classical Coherence Theory
    4 Classical Coherence Theory This chapter is based largely on Wolf, Introduction to the theory of coherence and po- larization of light [? ]. Until now, we have not been concerned with the nature of the light field itself. Instead, we studied the behavior of light waves in different optical systems. In many cases the wave fields have been monochromatic; sometimes they have consisted of plane waves, sometimes we have considered point sources. In all cases, we have implicitly assumed that the fields possessed the property of complete temporal and spatial coherence: the phase of a wave field at point r0 at time t0 has determined the phase for all other times t > t 0 at all other points r. However, not even a single free atom radiates strictly monochromatic light: −8 ⇒ Life time of excited states τc ∼ 10 sec corresponds to length lc = cτ c ∼ 3m 1 ⇒ Frequency uncertainty △ω ∼ due to this finite life time (or more precisely finite τc transition time between atomic energy levels). ⇒ For atoms interacting with their environments the so called coherence time τc can be much shorter and so will be the so-called coherence length lc In addition, a common light source consists of a very large number of emitters which radiate more or less independently. ⇒ For fixed time t0 and close to the light source this leads to reduced correlations between the phases for the wave field at different locations because different atoms radiate at more or less random times (this is minimized in a Laser). Nevertheless, interference effects (for which coherence is obviously necessary) have been observed well before the invention of the Laser.
    [Show full text]
  • 12 Orders of Coherence Control Tailoring the Coherence Length of Diode Lasers
    Appl-1010 August 03, 2010 Diode Lasers 12 Orders of Coherence Control Tailoring the coherence length of diode lasers Anselm Deninger, Ph.D., and Thomas Renner, Ph.D. TOPTICA Photonics AG The control of the coherence properties of laser light is a major success factor in many photonic applications – in areas as diverse as spectroscopy and optical pumping of atoms, nonlinear frequency conversion, interferometry, or laser-based imaging. Established diode laser technology has however only covered individual points of the “coherence length spectrum”. Recently developed electronic techniques for laser coherence control help to fill the remaining gaps, enabling a controlled manipulation of the linewidth and thus, coherence length of diode lasers – from the micron range to Interferometry and holography hundreds of thousands of kilometres. demand long coherence lengths (wavefront image of a lens). Linewidth and coherence The term “coherence” is derived from the Latin verb cohaerere – to join together. A light wave is considered to be coherent if two joint parts of the wave exhibit interference. In laser physics, one distinguishes between two different aspects of coherence, namely temporal and spatial coherence. Spatial coherence denotes the distance between two points of the wave, over which they still interfere with one another. Spatial coherence governs focusability of the laser beam. Temporal coherence, on the other hand, describes the ability of a wave to interfere with a time-shifted copy Some laser imaging methods like of itself. The time during which the phase of the wave changes by a confocal microscopy require a low significant amount (reducing the interference) is referred to as spatial coherence, in order to avoid speckle patterns.
    [Show full text]
  • Lasers for Holographic Applications: Important Performance Parameters
    Lasers for holographic applications: important performance parameters and relevant laser technologies Korbinian Hens*a, Jaroslaw Sperlinga, Ben Sherlikerb, Niklas Waasemc, Allen Ricksc, Jonathan Lewisb, Gunnar Elgcronad aHÜBNER GmbH & Co. KG, Heinrich-Hertz-Str. 2,34123 Kassel, Germany; bTruLife Optics, The Fitting Shop Building, 79 Trinity Buoy Wharf, E14 0FR, London, UK; cCobolt Inc, 2635 North First Street, Suite 228, San Jose, California, 95134, USA; dCobolt AB, Vretenvägen 13, SE-171 54, Solna, Sweden; ABSTRACT There is recently an increasing interest in holographic techniques and holographic optical elements (HOEs) related to virtual reality and augmented reality applications demanding for new laser technologies capable of delivering new wavelengths, higher output powers and in some cases improved control of these parameters. The choice of light sources for optical recording of holograms or production of HOEs for image displays is typically made between fixed RGB wavelengths from individual lasers (457 nm, 473 nm, 491 nm, 515 nm, 532 nm, 561 nm, 640 nm, 660 nm) or tunable laser systems covering broad wavelength ranges with a single source (450 nm – 650 nm, 510 nm – 750 nm) or a combination. Lasers for holographic applications need to have long coherence length (>10 m), excellent wavelength stability and accuracy as well as very good power stability. As new applications for holographic techniques and HOEs often require high volume manufacturing in industrial environments there is additionally a growing demand for laser sources with excellent long-term stability, reliability and long operational lifetimes. We discuss what performance specifications should be considered when looking at using high average power, single frequency (SF) or single longitudinal mode (SLM) lasers to produce holograms and HOEs, as well as describe some of the laser technologies that are capable of delivering these performance specifications.
    [Show full text]
  • Holography & Coherence • for Holography Need Coherent Beams • Two Waves Coherent of Fixed Phase Relationship Between Them for Some Period of Time
    Holography & Coherence • For Holography need coherent beams • Two waves coherent of fixed phase relationship between them for some period of time Coherence • Coherence appear in two ways Spatial Coherence • Waves in phase in time, but at different points in space • Required for interference and diffraction • Before lasers need to place slits far from source or pass light through slit so only part of source seen Temporal Coherence • Correlation of phase at the same point but at different times • Regular sources rapidly change phase relationships • Single atom on 10-8 sec coherent lifetime of atom in an excited state • Much shorter for groups of atoms • For lasers in single mode much longer time Coherence Length and Time • Time of coherence given by τcoh • Coherence time about time taken for photon to pass a given point in space • Coherence length is Lcoh = cτ coh • Best seen in Michelson-Morley experiment • Before lasers paths needed to be nearly equal • With lasers only require 2(L1 − L2 ) < Lcoh • Coherence last 50 - 100 m with lasers Coherence Length and Lasers • It can be shown Coherence time related to laser frequency width ∆ν (linewidth) 1 τ = coh ∆ν • Since the cohrence length is Lcoh = cτ coh • For holography setup distances must be < coherence length • Long coherence lasers have small linewidth, thus high stability Example of Coherence Length Sodium vapour lamp yellow "D" line • λ = 589 nm and linewidth 5.1x1011 Hz • Thus coherence time and length is 1 1 τ = = = 1.96 x10−12 sec coh ∆ν 5.1x1011 8 −12 −4 Lcoh = cτ coh = 2.98x10
    [Show full text]