DOCSLIB.ORG

Linear Polarizers

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Linear Polarizers Lecture 5: Linear Polarizers Outline 1 Jones and Mueller Matrices for Linear Polarizers 2 Wire Grid Polarizers 3 Polaroid-type Polarizers Polarizers 4 Crystal-based Polarizers polarizer: optical element that produces (at least partially) 5 Thin-Film Polarizers polarized light when the input light beam is unpolarized polarizer can be linear, circular, or in general, elliptical, depending 6 Polarizer Selection Guide on the type of polarization that emerges linear polarizers by far the most common large variety of polarizers that all have their respective advantages and disadvantages Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 1 Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 2 Mueller Matric for Linear Polarizer Jones Matrix for Linear Polarizers 0 2 2 2 2 1 px + py px − py 0 0 linear polarizer described by its transmittance of electrical field in 2 2 2 2 1 B px − py px + py 0 0 C two orthogonal directions Mp = B C 2 @ 0 0 2px py 0 A Jones matrix for linear polarizer: 0 0 0 2px py px 0 Jp = unpolarized incoming beam will always be linearly polarized 0 py emerging Stokes vector only completely polarized if 2 2 2 2 real values 0 ≤ px ≤ 1 and 0 ≤ py ≤ 1 are transmission factors for px + py = px − py x and y-components of electric field partial linear polarizer produces partially polarized beam from unpolarized light E0 = p E ; E0 = p E x x x y y y real polarizers always only partial polarizers px = 1; py = 0: linear polarizer in +Q direction polarized incoming beam ) emerging beam is, in general, elliptically polarized because of non-zero diagonal terms 2px py px = 0; py = 1: linear polarizer in −Q direction totally polarized beam remains totally polarized even when px = py : neutral density filter passing partial linear polarizer ) ideal partial polarizer does not depolarize Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 3 Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 4 Mueller Matrix for Ideal Linear Polarizer at Angle θ Characterizing Linear Polarizers 0 1 cos 2θ sin 2θ 0 1 2 parameters describe linear polarizer performance: 1 B cos 2θ cos2 2θ sin 2θ cos 2θ 0 C k1: (intensity) transmittance of polarizer for fully linearly polarized Mpol (θ) = B C beam at angle that maximize transmitted intensity 2 @ sin 2θ sin 2θ cos 2θ sin2 2θ 0 A k : minimum transmittance for incoming linearly polarized beam 0 0 0 0 2 2 2 k1 = px , k2 = py if px > py Poincare Sphere ratio of k1 to k2 is called extinction ratio contrast k1 and k2 are functions of wavelength can be determined from transmittances for unpolarized light of parallel and crossed identical polarizers 1 2 2 Tparallel = 2 k1 + k2 Tcrossed = k1k2 also used: degree of polarizability or polarizance defined by polarizer is a point on the Poincaré sphere transmitted intensity: cos2(l=2), l is arch length of great circle k − k P = 1 2 between incoming polarization and polarizer on Poincaré sphere k1 + k2 Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 5 Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 6 Wire Grid Polarizers Wire Grid Polarizers for the Infrared parallel conducting wires, spacing d λ act as polarizer . rule of thumb: plane of polarization perpendicular to wires is transmitted d < λ/2 ) strong polarization because electric field component parallel to wires induces d λ ) high transmission of both polarization states (weak electrical currents in wires, which strongly attenuates transmitted polarization) electric field parallel to wires mostly used in infrared because wire spacing becomes very small induced electrical current such that polarization parallel to wires is at visible wavelengths reflected made by depositing thin-film metallic grid on substrate can make polarizing beam-splitter with wire grid polarizer, reflects, free-standing wire grid for longer wavelengths transmits orthogonal linear polarization states Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 7 Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 8 Wire-Grid Polarizers for the Visible MOXTEK Inc. ProFlux Polarcor (Corning) Corning Polarcor excellent performance at high glass polarizer with high light/energy levels performance for 600 to 90% of energy reflected instead 2300 nm of absorbed borosilicate glass containing good in high heat environment aligned silver nano-particles in surface layers trade-off between transmission and contrast elongated, conducting silver particles act as small wires polarization occurs in 25 to 50 µm top layer maximum diameter currently limited to 20 mm contrast ratio > 10000 Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 9 Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 10 Dichroic Materials dichroic materials preferentially absorb O-type and E-type Dichroic Polarizers one polarization state O-type polarizers transmit ordinary ray (k = 0), attenuate absorption depends on wavelength ) o extraordinary ray (k > 0) different colors depending on angles of e illumination and viewing O-type polarizers transmit independent of angle of incidence because index of refraction of the ordinary beam is independent arises from anisotropy of complex index of the angle of incidence of refraction E-type polarizers transmit extraordinary ray and absorb ordinary natural dichroic crystals: tourmaline, ray herapathite E-type polarizers attenuate light in any direction except for waves W.B. Herapath discovered in 1852 salt of propagating perpendicular to c-axis quinine with polarizing properties; made first artificial crystals large enough to O-type dichroic polarizers much preferred over E-type polarizers study under microscope difficult to produce uniform, large dichroic crystals Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 11 Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 12 Polaroid-type Polarizers Field-of-View of Dichroic Sheet Polarizers conducting, needle-like particles aligned on common axis perpendicular to surface normal model them with uniaxially anisotropic medium with complex H-type sheet polarizers: stretched polyvynil alcohol (PVA) sheet, indices of refraction laminated to sheet of cellulose acetate butyrate, treated with transmitted polarization state sees real index of refraction iodine absorbed polarization state sees complex index of refraction with different H-type polarizers have different amounts of iodine in PVA imaginary part large enough to reduce intensity by orders of PVA-iodine complex analogous to short, conducting wire magnitude Polaroid names (e.g. HN-38) identify overall type (H) color dichroic polarizers have limited field of view, largely a geometrical (N=neutral), approximate transmittance for unpolarized light effect inherent to uniaxial medium K-type similar to H-type, but environmentally more stable HR-type based on a PVA-polyvinylene-iodine complex, works well from 0.7 to 2.3 µm Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 13 Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 14 Beam Displacer, Savart and Modified Savart Plates Crystal-Based Polarizers Beam Displacer uniaxial crystals are basis of highest quality polarizers precise arrangement of atom/molecules and anisotropy separate incoming beam into two beams with precisely orthogonal polarization polarizing beam-splitters (both beams usable) and polarizing prisms (only one useful state) most simple crystal polarizer: polarizing beam displacer prisms can be cemented or air spaced single uniaxial crystal block with optic axis at ∼45◦ air-spaced: good for short wavelengths, high power densities ordinary ray passes without deflection cemented: much better optical quality extraordinary ray deflected by dispersion angle α calcite is most often used in crystal-based polarizers because of very large birefringence, low absorption in visible beam separation d as function of block length D: many other suitable materials (n2 − n2) tan θ d = D tan α = D e o 2 2 2 ne + no tan θ Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 15 Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 16 Focus Difference and Astigmatism converging beam focus difference between ordinary and extraordinary rays: Beam Displacer Problems 2 2 sin 2θ ne − no = 2 2 2 2 2 no sin θ + ne cos θ θ is angle of optic axis with normal to interface astigmatism leads to two focus positions longitudinal astigmatism D tan θ tan αno ordinary and extraordinary beams have different path lengths l = q 2 2 2 2 extraordinary ray suffers from crystal astigmatism ne no sin θ + ne cos θ for imaging system, ’smearing’ of image given by transverse l astigmatism t = F where F is the F-number of the beam rule of thumb for calcite: astigmatic focus difference l ∼5% of thickness Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 17 Christoph U. Keller, Utrecht University, [email protected] Lecture 5: Linear Polarizers 18 Beam Separation and Astigmatism Savart Plate beam separation d (solid), longitudinal astigmatism l (dashed) of extraordinary beam for 10-mm calcite beam displacer at 630 nm avoid difference of focal point position problem by splitting calcite into two pieces crossed at 90◦ optic axis orientation of 45◦ close to optimum exchanges ordinary and extraordinary beams half-way ) both beams have same optical path length beam separation increases almost linearly for small optic axis p angles splitting reduced by 2 for same total length of calcite astigmatism increases much more slowly both beams now show crystal astigmatism, oriented in opposite directions; amount of astigmatism half of single-piece beam possible to trade off beam separation versus astigmatism displacer Christoph U.
Load more

Recommended publications
  • Dual Beam Detection Technique to Study Magneto-Optical Kerr
    DUAL BEAM DETECTION TECHNIQUE TO STUDY MAGNETO-OPTICAL KERR EFFECT By Shankar Chandra Acharya, Msc A thesis submitted to the Graduate Council of Texas State University in partial fulfillment of the requirements for the degree of Master of Science with a Major in Physics May 2019 Committee Members: Wilhelmus J Geerts, Chair Nikoleta Theodoropoulou Alexander Zakhidov COPYRIGHT By Shankar Chandra Acharya 2019 FAIR USE AND AUTHOR’S PERMISSION STATEMENT Fair Use This work is protected by the Copyright Laws of the United States (Public Law 94-553, section 107). Consistent with fair use as defined in the Copyright Laws, brief quotations from this material are allowed with proper acknowledgement. Use of this material for financial gain without the author’s express written permission is not allowed. Duplication Permission As the copyright holder of this work I, Shankar Chandra Acharya, authorize duplication of this work, in whole or in part, for educational or scholarly purposes only. ACKNOWLEDGEMENTS First of all, I would like to than my supervisor Dr. Wilhelmus J Geerts for his constant support and guidance. I feel grateful to have worked under such an inspiring researcher who has given me this opportunity to learn and explore scientific knowledge. I would also like to thank my committee members Dr. Nikoleta Theodoropoulou and Dr. Alexander Zakhidov for their constructive feedback which have contributed to my thesis project. I am grateful for my family and friends for their motivation and encouragement all these years of my studies. My mother and father have supported me during the difficult times and inspired me throughout my research.
    [Show full text]
  • De Sénarmont Bias Retardation in DIC Microscopy Stanley Schwartz1, Douglas B
    de Sénarmont Bias Retardation in DIC Microscopy Stanley Schwartz1, Douglas B. Murphy2, Kenneth R. Spring3, and Michael W. Davidson4 1Bioscience Department, Nikon Instruments, Inc., 1300 Walt Whitman Road, Melville, New York 11747. 2Department of Cell Biology and Anatomy and Microscope Facility, Johns Hopkins University School of Medicine, 725 N. Wolfe Street, 107 WBSB, Baltimore, Maryland 21205. 3National Heart, Lung, and Blood Institute, National Institutes of Health, Building 10, Room 6N260, Bethesda, Maryland 20892 4National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 3231 Keywords: microscopy, de Senarmont, Henri Hureau de Sénarmont, Francis Smith, Georges Nomarski, William Hyde Wollaston, Michel- Levy color chart, contrast-enhancement techniques, depth of field, bias, retardation, compensating, plates, DIC, differential interference, contrast, prisms, compensators, shadow-cast, relief, pseudo, three-dimensional, birefringence, optical staining, sectioning, spherical aberrations, wavefronts, shear, fast, slow, axes, axis, linear, circularly, elliptically, polarized light, polarizers, analyzers, orthogonal, path, differences, OPD, gradients, phase, ordinary, extraordinary, maximum extinction, quarter-wavelength, full-wave plates, first-order red, halo, artifacts, interference plane, VEC, video enhanced, VE-DIC, Newtonian, interference colors, Nikon, Eclipse E600, microscopes, buccal, mucosa, epithelial, cheek cells, ctenoid, fish scales, Obelia, hydroids, polyps, coelenterates, murine, rodents, rats,
    [Show full text]
  • Chapter 8 Polarization
    Phys 322 Chapter 8 Lecture 22 Polarization Reminder: Exam 2, October 22nd (see webpage) Dichroism = selective absorption of light of certain polarization Linear dichroism - selective absorption of one of the two P-state (linear) orthogonal polarizations Circular dichroism - selective absorption of L-state or R-state circular polarizations Using dichroic materials one can build a polarizer Dichroic crystals Anisotropic crystal structure: one polarization is absorbed more than the other Example: tourmaline Elastic constants for electrons may be different along two axes Polaroid 1928: dichroic sheet polarizer, J-sheet long tiny crystals of herapathite aligned in the plastic sheet Edwin Land 1938: H-sheet 1909-1991 Attach Iodine molecules to polymer molecules - molecular size iodine wires Presently produced: HN-38, HN-32, HN-22 Birefringence Elastic constants for electrons may be different along axes Resonance frequencies will be different for light polarized Refraction index depends on along different axes polarization: birefringence Dichroic crystal - absorbs one of the orthogonal P-states, transmits the other Optic axis of a crystal: the direction of linear polarization along which the resonance is different from the other two axes (assuming them equal) Calcite (CaCO3) Ca C O Image doubles Ordinary rays (o-rays) - unbent Extraordinary rays (e-rays) - bend Calcite (CaCO3) emerging rays are orthogonaly polarized Principal plane - any plane that contains optical axis Principal section - principal plane that is normal to one of the cleavage
    [Show full text]
  • Optimized Morphologic Evaluation of Biostructures by Examination in Polarized Light and Differential Interference Contrast Microscopy
    Rom J Leg Med [22] 275-282 [2014] DOI: 10.4323/rjlm.2014.275 © 2014 Romanian Society of Legal Medicine Optimized morphologic evaluation of biostructures by examination in polarized light and differential interference contrast microscopy Elena Patrascu1, Petru Razvan Melinte1, Gheorghe S. Dragoi2,* _________________________________________________________________________________________ Abstract: Differential interference contrast microscopy (DIC) was possible after the invention of Wollaston prisms that were modified by Nomarski and could duplicate linear polarized light before passing through a specimen (Condenser DIC prism) and to recompose it afterwards (Objective DIC prism), thus creating the phenomenon of interference that depends on the thickness and birefringence of the studied structures. The authors proposed themselves to discuss the performances of this microscope and to widen the area of its usage in the optimized microanatomic analysis of cells and tissues on the native or stained sections. The authors consider it necessary to use DIC microscopy both in forensic medicine (identification of diatoms) as well as in reproduction biology (spermogram) and in early discovery of uterine cervix cancer. Key Words: DIC microscopy, Wollaston prism, Nomarski prism, polarized light, interference. he progresses achieved in the area of wave (Maxwell, 1864) [2] and has a photogenic improvement and diversification of structure (Einstein, 1921) [3]. It consists of an electric T optic systems determined the increase of photonic and a magnetic field, orthogonal, which vibrate in microscopes performances regarding the phase contrast, phase, in the direction of propagation. Within an polarized light and not least, differential interference electromagnetic wave, the electric and the magnetic contrast (DIC) examinations.They assure nowadays fields oscillate simultaneously, but in different planes.
    [Show full text]
  • Optic Axis of a Crystal: the Direction of Linear Polarization Along Which the Resonance Is Different from the Other Two Axes (Assuming Them Equal) Calcite (Caco3)
    Phys 322 Chapter 8 Lecture 22 Polarization Dichroism = selective absorption of light of certain polarization Linear dichroism - selective absorption of one of the two P-state (linear) orthogonal polarizations Circular dichroism - selective absorption of L-state or R-state circular polarizations Using dichroic materials one can build a polarizer Dichroic crystals Anisotropic crystal structure: one polarization is absorbed more than the other Example: tourmaline Elastic constants for electrons may be different along two axes Polaroid 1928: dichroic sheet polarizer, J-sheet long tiny crystals of herapathite aligned in the plastic sheet Edwin Land 1938: H-sheet 1909-1991 Attach Iodine molecules to polymer molecules - molecular size iodine wires Presently produced: HN-38, HN-32, HN-22 Birefringence Elastic constants for electrons may be different along axes Resonance frequencies will be different for light polarized Refraction index depends on along different axes polarization: birefringence Dichroic crystal - absorbs one of the orthogonal P-states, transmits the other Optic axis of a crystal: the direction of linear polarization along which the resonance is different from the other two axes (assuming them equal) Calcite (CaCO3) Ca C O Image doubles Ordinary rays (o-rays) - unbent Extraordinary rays (e-rays) - bend Calcite (CaCO3) emerging rays are orthogonaly polarized Principal plane - any plane that contains optical axis Principal section - principal plane that is normal to one of the cleavage surfaces Birefringence and Huygens’ principle
    [Show full text]
  • Fig: 5, 9 I Inventor Patented May 22, 1934 1959,549
    May 22, 1934. H. SAUER 1,959,549 POLARIZATION PHOTOMETER Filed March 23, 1933 0LLSLL0SLLLSLSLSLLSL0LLL0LLLSLLSLLLTLLLLSLLLLLLLL LLLLLLLLSLLLLS0SSSLSLL0LSLSSSLSLS0SSLLLLLSLSLLL 7 12?% fig: 5, 9 I Inventor Patented May 22, 1934 1959,549 UNITED STATES PATENT OFFICE 1959,549 POLARIZATION PHOTOMETER Hans Sauer, Jena, Germany, assignor to firm Carl Zeiss, Jena, Germany Application March 23, 1933, Serial No. 662,277 in Germany March 24, 1932 4. Claims. (C. 88-23) The invention concerns a polarization pho tions in which the one or the other photometric tometer having a polarization prism, an analyzer Comparison field is just absolutely dark. prism, and a bi-prism. To avoid measuring disturbing light effects, the In the known photometers of this kind, the po light-entrance apertures, the optical members, larization prism, the bi-prism, and the two light and, eventually, diaphragms, may be so posi 60 entrance apertures have such positions relatively tioned that only those two of the ray pencils to each other that the two prisms deviate the ray emanating from the polarization prism enter the pencils emanating from the two light entrance Succeeding optical members which are used for apertures into a plane containing the centres of the comparison measurement. If the analyzer the light entrance apertures or of images of these prism is behind the polarization prism, these two 65 10 apertures. This constructional form is not very prisms are conveniently given such a distance advantageous in So far as using light of different apart and their apertures are so dimensioned that wave-lengths entails the necessity of specially ad only those images due to the polarization prism justing the instrument, which causes those im enter the analyzer prism which are used for meas ages of the light-entrance apertures to touch uring 70 15 each other which are due only to the polarization The accompanying drawing represents a con prism.
    [Show full text]
  • PME557 Engineering Optics
    PME557 Engineering Optics Wei-Chih Wang National Tsinghua University Department of Power Mechanical Engineering 1 W.Wang Class Information • Time: Lecture M 1:20-3:10 (Eng Bldg 1 211) Lab Th 1:10-2:10 PM (TBA) • Instructor: Wei-Chih Wang office: Delta 319 course website: http://depts.washington.edu/mictech/optics/me557.index.html • Suggested Textbooks: - Optical Methods of Engineering Analysis, Gary Cloud, Cambridge University Press. - Handbook on Experimental Mechanics, Albert S. Kobayashi, society of experimental mechanics. - Applied Electromagnetism, Liang Chi Shen, Weber&Schmidt Dubury - Fundamentals of Photonics, B. Saleh, John Wiley& Sons. - Optoelectronics and Photonics: Principles and Practices, S. O. Kasap, Prentice Hall. - Fiber optic Sensors, E. Udd, John Wiley& Sons - Selected papers in photonics, optical sensors, optical MEMS devices and integrated optical devices. 2 W.Wang Class information • Grading Homework and Lab assignments 80% (3 assignments and 3 lab reports) Final Project 20% • Final Project: - Choose topics related to simpleo free space optics design, fiberopic sensors, waveguide sensors or geometric Moiré, Moiré interferometer, photoelasticity for mechanical sensing or simple optical design. - Details of the project will be announced in mid quarter - Four people can work as a team on a project, but each person needs to turn in his/her own final report. - Oral presentation will be held in the end of the quarter on your final project along with a final report. 3 W.Wang Objectives The main goal of this course is to
    [Show full text]
  • An Application of Differential Interference Contrast In
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Directory of Open Access Journals Vol. 2 No. 1, Feb. 2005 CHINA FOUNDRY An application of differential interference contrast in metallographic examination *Xiang CHEN , Yanxiang LI (Department of Mechanical Engineering, Tsinghua University, Beijing 100084, P. R. China) Abstract: As one of the most exciting inspection and powerful analysis methods in modern materials metallographic examinations, the difference interference contrast (DIC) method has many advantages, including relatively low requirement for specimen preparation, obvious relief senses observed under microscope. Details such as fine structures or defects that are not or barely visible in incident-light bright field, could be easily revealed and thus make materials analysis more reliable. Differential interference contrast produces an image that can be readily manipulated using digital and video imaging techniques to further enhance contrast. But, studies of material metallography based on DIC method have rarely carried out. Based on the fundamental principle of the DIC method combing with the computer image analysis, applications of DIC method in materials metallographic examination were investigated in this study. Keywords: difference interference contrast method;metallographic examination; and image analysis CLC number: TG14, TG115.2 Document: A Article ID: 1672-6421(2005) 01-0014-07 1. Introduction Like polarized light, DIC was also primarily developed The difference interference contrast (DIC) method is as an analytical method to determine various optical one of the most exciting inspection and powerful analysis properties of crystals. Thus, it is a method of measure- methods in modern materials metallographic exami- ment, requiring specific knowledge and specially- nations [1], which has many advantages.
    [Show full text]
  • February 8, 2003
    Contents Introduction………………………………………………………….………………. II Non-linear Optical Crystals Beta-BBO Crystal and Devices…………………………………………….….………. 1 KDP, DKDP and ADP Crystals and Devices……………………………...….……... 5 KTP Crystal and Devices…………………………………………………...………….. 8 LBO Crystal and Devices…………………………………………….………………. 12 LiIO3 Crystal and Devices…………………………………………….………………. 16 AgGaS2, AgGaSe2 Crystal and Devices…………………………....………………. 18 Laser Crystals Nd:YVO4 Crystal and Devices…………………………………….………………….. 20 Nd:YAG Crystal and Devices……………………………………………….……….. 23 Electro-Optic Devices Pockels Cells…………………………………………………………………………… 25 Birefringent Crystals YVO4 Crystal and Devices……………………………………….…………………… 29 Prisms/Splitters Glan-Taylor Prism………..……………………………………….…………………… 31 Glan-Thompson Prism………..………………………………….…………………… 32 Rochon Prism…………….……………………………………….…………………… 32 Wollaston Prism………….……………………………………….…………………… 33 Double Wollaston Prism………………………………………….…………………… 33 45° Glan-Thompson Splitting Prism…………………………………….…………… 34 Wave Plates Mica and Quartz wave plates…………………………………….………..………… 35 Appendix Purchasing Information…………………………………………..………….……..… 36 - I - Introduction United Crystals is the leading manufacturer of nonlinear optical (NLO), laser, electro-optical (E-O) and optical crystals and devices with headquarter in Qingdao, China. We’ve provided multi-million pieces of LBO, KTP, BBO, DKDP, KDP, LiIO3, ADP, LiNbO3, LiTaO3, AgGaS2, AgGaSe2, Nd:YVO4, YVO4, Nd:YAG, YAG devices with high quality all over the world in the past decade, especially to North America and Europe.
    [Show full text]
  • Polarization and Crystal Optics
    Chapter 6: Polarization and Crystal Optics * P6-1. Cascaded Wave Retarders. Show that two cascaded quarter-wave retarders with parallel fast axes are equivalent to a half-wave retarder. What is the result if the fast axes are orthogonal. P6-2. Jones Matrix of a Polarizer. Show that the Jones matrix of a linear polarizer with a transmission axis making an angle θ with the x axis is cos2 sin cos T 2 (FoP 6.1-25) sin cos sin Hint! Derive (FoP 6.1-25) using (FoP 6.1-18), (FoP 6.1-22) and (FoP 6.1-24) * P6-3. Three polarizers are placed after each other. The first is illuminated by unpolarized light with the intensity I0. The transmission direction for the second and the third polarizer is rotated 45˚ and 90˚ in relation to the first respectively. See figure 6-1. Figure 6-1. Unpolarized light with the intensity I0 is passing through three polarizers with different transmission directions. a) Give the intensity between polarizer 1 and 2 in relation to I0. b) Give the intensity between polarizer 2 and 3 in relation to I0. c) Give the intensity after polarizer 3 in relation to I0. * P6-4. Two polarizers can be used as a continuously variable grey filter. What is the angle between the transmission axes, so that 5.0 % of incoming light is transmitted? We assume that we can neglect reflections. P6-5. Give the propagation direction and polarization state for the following waves: a) E Re2iyˆ 3zˆ eitkx b) E Rexˆ izˆ eitky c) E Rexˆ yˆ 3ei / 6 eitkz Page 26 * P6-6.
    [Show full text]
  • Simple, Adjustable Beam Splitting Element for Differential Interferometers Based on Photoelastic Birefringence of a Prismatic Bar ͒ S
    REVIEW OF SCIENTIFIC INSTRUMENTS 76, 113703 ͑2005͒ Simple, adjustable beam splitting element for differential interferometers based on photoelastic birefringence of a prismatic bar ͒ S. R. Sandersona Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, California 91125 ͑Received 6 June 2005; accepted 9 October 2005; published online 23 November 2005͒ We examine the prototypical Toepler optical arrangement for the visualization of phase objects and consider the effect of different contrast elements placed at the focus of the source. In particular, Wollaston prism beam splitting elements based on the crystallographic birefringence of calcite or quartz find application in differential interferometry systems based on the Toepler arrangement. The focus of the current article is a simple low cost alternative to the Wollaston prism that is realized by inserting a prismatic bar constructed of a photoelastic material into the optical path. It is shown that, under the action of an applied bending moment, the prismatic bar functions as a first-order approximation to a Wollaston prism. Results are derived for the divergence angle of the beam splitter for orthogonally polarized rays. The implementation of a practical device is discussed and representative experimental results are presented, taken from the field of shock wave visualization in supersonic flow. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.2132271͔ I. INTRODUCTION image plane of the test section ͑i.e., focused on the midplane of the test section͒, the deflected and phase-shifted rays are Figure 1 illustrates the conventional Toepler arrange- brought back to focus from their deflected state at the detec- ment that represents the prototypical symmetric optical lay- tor plane yielding a uniformly illuminated detector.
    [Show full text]
  • Use of Wollaston Prism for Dual-Reference Digital Holographic Interferometry Jean-Michel Desse, François Olchewsky
    Use of Wollaston prism for dual-reference digital holographic interferometry Jean-Michel Desse, François Olchewsky To cite this version: Jean-Michel Desse, François Olchewsky. Use of Wollaston prism for dual-reference digital holo- graphic interferometry. Digital Holography and 3D Imaging, May 2019, BORDEAUX, France. 10.1364/DH.2019.Tu4B.4. hal-02301557 HAL Id: hal-02301557 https://hal.archives-ouvertes.fr/hal-02301557 Submitted on 30 Sep 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Use of Wollaston prism for dual-reference digital holographic interferometry Jean-Michel Desse 1,2 *, François Olchewsky 1,2 1ONERA, DAAA, 5, rue des Fortifications, CS 90013, F-59045 LILLE, France 2Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, F-59000 LILLE France *[email protected] Abstract: A Wollaston prism is used in digital holographic interferometer developed for analyzing high density gradients encountered in transonic and supersonic flows. Inserted in the reference arm of the interferometer, the Wollaston prism allows generating two orthogonally crossed waves and analyzing shocks waves whatever their orientation. OCIS codes: 090.0090, 090.2880, 090.1995. 1. Introduction As part of the work carried out on the development of digital holographic interferometry by ONERA, the authors propose a new double-reference digital holographic interferometer for the analysis of the strong variations of refractive index encountered, for example, in transonic and supersonic flows.
    [Show full text]