Measuring the linear polarization of $gamma$s in 20-170 GeV range

圆极化与线计划的设置英文回答：Circular polarization and linear polarization are two different settings used in various applications,particularly in the field of optics and telecommunications. Let's discuss each of them separately.Circular polarization refers to the polarization stateof an electromagnetic wave in which the electric fieldvector rotates in a circular pattern as the wave propagates. This rotation can be either clockwise or counterclockwise. Circular polarization is achieved by combining two orthogonal linearly polarized waves with a phase difference of 90 degrees. The resulting circularly polarized wave has equal amplitude in both orthogonal directions and aconstant magnitude of electric field vector.Circular polarization has several advantages overlinear polarization. One of the main advantages is itsimmunity to certain types of interference, such as reflections. This makes circularly polarized waves idealfor applications where signal degradation due toreflections is a concern, such as satellite communications. Circular polarization also allows for better penetration through obstacles, making it suitable for applications in wireless communication systems.Linear polarization, on the other hand, refers to the polarization state of an electromagnetic wave in which the electric field vector oscillates in a single plane. This can be either horizontal or vertical, or any other angle in between. Linear polarization is achieved by transmitting a wave with a specific orientation of the electric field vector.Linear polarization is commonly used in many applications, including television broadcasting, radar systems, and optical communication. It allows for efficient transmission and reception of signals, as the receiver antenna can be aligned with the same polarization as the transmitted signal. However, linearly polarized waves aremore susceptible to interference from reflections andcross-polarization effects, which can lead to signal degradation.In terms of setting up circular polarization and linear polarization, different techniques and devices can be used. For circular polarization, a combination of two orthogonal linearly polarized waves with a phase difference of 90 degrees is required. This can be achieved using devices such as quarter-wave plates or circular polarizers.For linear polarization, the orientation of theelectric field vector needs to be controlled. This can be done using devices such as polarizers or waveplates. Polarizers are commonly used to convert unpolarized light into linearly polarized light by selectively transmitting waves with a specific polarization orientation. Waveplates, on the other hand, can be used to rotate the polarization state of a wave by a desired angle.中文回答：圆极化和线极化是在光学和通信领域中使用的两种不同设置。

Relative intensity noise (RIN) measuring procedure相对强度噪声（RIN)测量程序This procedure describes a component test which may not be appropriate for a system level test depending on the implementation.这是一个组件测试流程，根据应用环境来看，它可能不适合于系统级的测试。

A.5.1 Test objective 测试目标When lasers which are subject to reflection induced noise effects are operated in a cable plant with a low optical return loss the lasers will produce an amount of noise which is a function of the magnitude and polarization state of the reflected light.当受到反射引起的噪声影响的激光器在具有低光回损的电缆设备中工作时,激光器将产生一定量的噪声，这个噪声是反射光的大小和偏振态的函数。

The magnitude of the reflected light tends to be relatively constant. However，the polarization state varies significantly as a function of many cable parameters，particularly cable placement. 反射光的大小趋于相对恒定。

然而，偏振态受许多电缆参数的影响而呈现出一定的函数关系，特别是随电缆的放置而显著变化.In a cable plant which is physically fixed in place the variation is slow. If the fibre is subject to motion, such as occurs in a jumper cable, the change may be sudden and extreme. The effect is unpredictable changes in the noise from the laser with the result that the communication link may exhibit sudden and unexplainable bursts of errors.在固定的电缆设备中，变化是缓慢的。

a r X i v :h e p -p h /9711228v 1 4 N o v 1997hep-ph/9711228October 1997O (α)QED Corrections to Polarized Elastic µe and Deep Inelastic lN ScatteringDima Bardin a,b,c ,Johannes Bl¨u mlein a ,Penka Christova a,d ,and Lida Kalinovskaya a,caDESY–Zeuthen,Platanenallee 6,D–15735Zeuthen,GermanybINFN,Sezione di Torino,Torino,ItalycJINR,ul.Joliot-Curie 6,RU–141980Dubna,RussiadBishop Konstantin Preslavsky University of Shoumen,9700Shoumen,BulgariaAbstractTwo computer codes relevant for the description of deep inelastic scattering offpolarized targets are discussed.The code µe la deals with radiative corrections to elastic µe scattering,one method applied for muon beam polarimetry.The code HECTOR allows to calculate both the radiative corrections for unpolarized and polarized deep inelastic scattering,including higher order QED corrections.1IntroductionThe exact knowledge of QED,QCD,and electroweak (EW)radiative corrections (RC)to the deep inelastic scattering (DIS)processes is necessary for a precise determination of the nucleon structure functions.The present and forthcoming high statistics measurements of polarized structure functions in the SLAC experiments,by HERMES,and later by COMPASS require the knowledge of the RC to the DIS polarized cross-sections at the percent level.Several codes based on different approaches for the calculation of the RC to DIS experiments,mainly for non-polarized DIS,were developped and thoroughly compared in the past,cf.[1].Later on the radiative corrections for a vast amount of experimentally relevant sets of kinematic variables were calculated [2],including also semi-inclusive situations as the RC’s in the case of tagged photons [3].Furthermore the radiative corrections to elastic µ-e scattering,a process to monitor (polarized)muon beams,were calculated [4].The corresponding codes are :•HECTOR 1.00,(1994-1995)[5],by the Dubna-Zeuthen Group.It calculates QED,QCD and EW corrections for variety of measuremets for unpolarized DIS.•µe la 1.00,(March 1996)[4],calculates O (α)QED correction for polarized µe elastic scattering.•HECTOR1.11,(1996)extends HECTOR1.00including the radiative corrections for polarized DIS[6],and for DIS with tagged photons[3].The beta-version of the code is available from http://www.ifh.de/.2The Programµe laMuon beams may be monitored using the processes ofµdecay andµe scattering in case of atomic targets.Both processes were used by the SMC experiment.Similar techniques will be used by the COMPASS experiment.For the cross section measurement the radiative corrections to these processes have to be known at high precision.For this purpose a renewed calculation of the radiative corrections toσ(µe→µe)was performed[4].The differential cross-section of polarized elasticµe scattering in the Born approximation reads,cf.[7],dσBORNm e Eµ (Y−y)2(1−P e Pµ) ,(1)where y=yµ=1−E′µ/Eµ=E′e/Eµ=y e,Y=(1+mµ/2/Eµ)−1=y max,mµ,m e–muon and electron masses,Eµ,E′µ,E′e the energies of the incoming and outgoing muon,and outgoing electron respectively,in the laboratory frame.Pµand P e denote the longitudinal polarizations of muon beam and electron target.At Born level yµand y e agree.However,both quantities are different under inclusion of radiative corrections due to bremsstrahlung.The correction factors may be rather different depending on which variables(yµor y e)are used.In the SMC analysis the yµ-distribution was used to measure the electron spin-flip asymmetry A expµe.Since previous calculations,[8,9],referred to y e,and only ref.[9]took polarizations into account,a new calculation was performed,including the complete O(α)QED correction for the yµ-distribution,longitudinal polarizations for both leptons,theµ-mass effects,and neglecting m e wherever possible.Furthermore the present calculation allows for cuts on the electron re-coil energy(35GeV),the energy balance(40GeV),and angular cuts for both outgoing leptons (1mrad).The default values are given in parentheses.Up to order O(α3),14Feynman graphs contribute to the cross-section forµ-e scattering, which may be subdivided into12=2×6pieces,which are separately gauge invariantdσQEDdyµ.(2) One may express(2)also asdσQEDdyµ+P e Pµdσpol kk=1−Born cross-section,k=b;2−RC for the muonic current:vertex+bremsstrahlung,k=µµ;3−amm contribution from muonic current,k=amm;4−RC for the electronic current:vertex+bremsstrahlung,k=ee;5−µe interference:two-photon exchange+muon-electron bremsstrahlung interference,k=µe;6−vacuum polarization correction,runningα,k=vp.The FORTRAN code for the scattering cross section(2)µe la was used in a recent analysis of the SMC collaboration.The RC,δA yµ,to the asymmetry A QEDµeshown infigures1and2is defined asδA yµ=A QEDµedσunpol.(4)The results may be summarized as follows.The O(α)QED RC to polarized elasticµe scattering were calculated for thefirst time using the variable yµ.A rather general FORTRAN codeµe la for this process was created allowing for the inclusion of kinematic cuts.Since under the conditions of the SMC experiment the corrections turn out to be small our calculation justifies their neglection. 3Program HECTOR3.1Different approaches to RC for DISThe radiative corrections to deep inelastic scattering are treated using two basic approaches. One possibility consists in generating events on the basis of matrix elements including the RC’s. This approach is suited for detector simulations,but requests a very hughe number of events to obtain the corrections at a high precision.Alternatively,semi-analytic codes allow a fast and very precise evaluation,even including a series of basic cuts andflexible adjustment to specific phase space requirements,which may be caused by the way kinematic variables are experimentally measured,cf.[2,5].Recently,a third approach,the so-called deterministic approach,was followed,cf.[10].It treats the RC’s completely exclusively combining features of fast computing with the possibility to apply any cuts.Some elements of this approach were used inµe la and in the branch of HECTOR1.11,in which DIS with tagged photons is calculated.Concerning the theoretical treatment three approaches are in use to calculate the radiative corrections:1)the model-independent approach(MI);2)the leading-log approximation(LLA); and3)an approach based on the quark-parton model(QPM)in evaluating the radiative correc-tions to the scattering cross-section.In the model-independent approach the QED corrections are only evaluated for the leptonic tensor.Strictly it applies only for neutral current processes.The hadronic tensor can be dealt with in its most general form on the Lorentz-level.Both lepton-hadron corrections as well as pure hadronic corrections are neglected.This is justified in a series of cases in which these corrections turn out to be very small.The leading logarithmic approximation is one of the semi-analytic treatments in which the different collinear singularities of O((αln(Q2/m2l))n)are evaluated and other corrections are neglected.The QPM-approach deals with the full set of diagrams on the quark level.Within this method,any corrections(lepton-hadron interference, EW)can be included.However,it has limited precision too,now due to use of QPM-model itself. Details on the realization of these approaches within the code HECTOR are given in ref.[5,11].3.2O (α)QED Corrections for Polarized Deep Inelastic ScatteringTo introduce basic notation,we show the Born diagramr rr r j r r r r l ∓( k 1,m )l ∓( k 2,m )X ( p ′,M h )p ( p ,M )γ,Z ¨¨¨¨B ¨¨¨¨£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡z r r r r r r r r r r r r r rr ¨¨¨¨B ¨¨¨¨r r r r j r r r r and the Born cross-section,which is presented as the product of the leptonic and hadronic tensordσBorn =2πα2p.k 1,x =Q 2q 2F 1(x,Q 2)+p µ p ν2p.qF 3(x,Q 2)+ie µνλσq λs σ(p.q )2G 2(x,Q 2)+p µ s ν+ s µ p νp.q1(p.q )2G 4(x,Q 2)+−g µν+q µq νp.qG 5(x,Q 2),(8)wherep µ=p µ−p.qq 2q µ,and s is the four vector of nucleon polarization,which is given by s =λp M (0, n )in the nucleonrest frame.The combined structure functions in eq.(8)F1,2(x,Q2)=Q2e Fγγ1,2(x,Q2)+2|Q e|(v l−p eλl a l)χ(Q2)FγZ1,2(x,Q2)+ v2l+a2l−2p eλl v l a l χ2(Q2)F ZZ1,2(x,Q2),F3(x,Q2)=2|Q e|(p e a l−λl v l)χ(Q2)FγZ3(x,Q2),+ 2p e v l a l−λl v2l+a2l χ2(Q2)F ZZ3(x,Q2),G1,2(x,Q2)=−Q2eλl gγγ1,2(x,Q2)+2|Q e|(p e a l−λl v l)χ(Q2)gγZ1,2(x,Q2),+ 2p e v l a l−λl v2l+a2l χ2(Q2)g ZZ1,2(x,Q2),G3,4,5(x,Q2)=2|Q e|(v l−p eλl a l)χ(Q2)gγZ3,4,5(x,Q2),+ v2l+a2l−2p eλl v l a l χ2(Q2)g ZZ3,4,5(x,Q2),(9) are expressed via the hadronic structure functions,the Z-boson-lepton couplings v l,a l,and the ratio of the propagators for the photon and Z-bosonχ(Q2)=Gµ2M2ZQ2+M2Z.(10)Furthermore we use the parameter p e for which p e=1for a scattered lepton and p e=−1for a scattered antilepton.The hadronic structure functions can be expressed in terms of parton densities accounting for the twist-2contributions only,see[12].Here,a series of relations between the different structure functions are used in leading order QCD.The DIS cross-section on the Born-leveld2σBorndxdy +d2σpol Borndxdy =2πα2S ,S U3(y,Q2)=x 1−(1−y)2 ,(13) and the polarized partdσpol BornQ4λp N f p S5i=1S p gi(x,y)G i(x,Q2).(14)Here,S p gi(x,y)are functions,similar to(13),and may be found in[6].Furthermore we used the abbrevationsf L=1, n L=λp N k 12πSy 1−y−M2xy2π1−yThe O(α)DIS cross-section readsd2σQED,1πδVRd2σBorndx l dy l=d2σunpolQED,1dx l dy l.(16)All partial cross-sections have a form similar to the Born cross-section and are expressed in terms of kinematic functions and combinations of structure functions.In the O(α)approximation the measured cross-section,σrad,is define asd2σraddx l dy l +d2σQED,1dx l dy l+d2σpol radd2σBorn−1.(18)The radiative corrections calculated for leptonic variables grow towards high y and smaller values of x.Thefigures compare the results obtained in LLA,accounting for initial(i)andfinal state (f)radiation,as well as the Compton contribution(c2)with the result of the complete calculation of the leptonic corrections.In most of the phase space the LLA correction provides an excellent description,except of extreme kinematic ranges.A comparison of the radiative corrections for polarized deep inelastic scattering between the codes HECTOR and POLRAD[17]was carried out.It had to be performed under simplified conditions due to the restrictions of POLRAD.Corresponding results may be found in[11,13,14].3.3ConclusionsFor the evaluation of the QED radiative corrections to deep inelastic scattering of polarized targets two codes HECTOR and POLRAD exist.The code HECTOR allows a completely general study of the radiative corrections in the model independent approach in O(α)for neutral current reac-tions including Z-boson exchange.Furthermore,the LLA corrections are available in1st and2nd order,including soft-photon resummation and for charged current reactions.POLRAD contains a branch which may be used for some semi-inclusive DIS processes.The initial state radia-tive corrections(to2nd order in LLA+soft photon exponentiation)to these(and many more processes)can be calculated in detail with the code HECTOR,if the corresponding user-supplied routine USRBRN is used together with this package.This applies both for neutral and charged current processes as well as a large variety of different measurements of kinematic variables. Aside the leptonic corrections,which were studied in detail already,further investigations may concern QED corrections to the hadronic tensor as well as the interference terms. References[1]Proceedings of the Workshop on Physics at HERA,1991Hamburg(DESY,Hamburg,1992),W.Buchm¨u ller and G.Ingelman(eds.).[2]J.Bl¨u mlein,Z.Phys.C65(1995)293.[3]D.Bardin,L.Kalinovskaya and T.Riemann,DESY96–213,Z.Phys.C in print.[4]D.Bardin and L.Kalinovskaya,µe la,version1.00,March1996.The source code is availablefrom http://www.ifh.de/~bardin.[5]A.Arbuzov,D.Bardin,J.Bl¨u mlein,L.Kalinovskaya and T.Riemann,Comput.Phys.Commun.94(1996)128,hep-ph/9510410[6]D.Bardin,J.Bl¨u mlein,P.Christova and L.Kalinovskaya,DESY96–189,hep-ph/9612435,Nucl.Phys.B in print.[7]SMC collaboration,D.Adams et al.,Phys.Lett.B396(1997)338;Phys.Rev.D56(1997)5330,and references therein.[8]A.I.Nikischov,Sov.J.Exp.Theor.Phys.Lett.9(1960)757;P.van Nieuwenhuizen,Nucl.Phys.B28(1971)429;D.Bardin and N.Shumeiko,Nucl.Phys.B127(1977)242.[9]T.V.Kukhto,N.M.Shumeiko and S.I.Timoshin,J.Phys.G13(1987)725.[10]G.Passarino,mun.97(1996)261.[11]D.Bardin,J.Bl¨u mlein,P.Christova,L.Kalinovskaya,and T.Riemann,Acta Phys.PolonicaB28(1997)511.[12]J.Bl¨u mlein and N.Kochelev,Phys.Lett.B381(1996)296;Nucl.Phys.B498(1997)285.[13]D.Bardin,J.Bl¨u mlein,P.Christova and L.Kalinovskaya,Preprint DESY96–198,hep-ph/9609399,in:Proceedings of the Workshop‘Future Physics at HERA’,G.Ingelman,A.De Roeck,R.Klanner(eds.),Vol.1,p.13;hep-ph/9609399.[14]D.Bardin,Contribution to the Proceedings of the International Conference on High EnergyPhysics,Warsaw,August1996.[15]M.Gl¨u ck,E.Reya,M.Stratmann and W.Vogelsang,Phys.Rev.D53(1996)4775.[16]S.Wandzura and F.Wilczek,Phys.Lett.B72(1977)195.[17]I.Akushevich,A.Il’ichev,N.Shumeiko,A.Soroko and A.Tolkachev,hep-ph/9706516.-20-18-16-14-12-10-8-6-4-200.10.20.30.40.50.60.70.80.91elaFigure 1:The QED radiative corrections to asymmetry without experimental cuts.-1-0.8-0.6-0.4-0.200.20.40.60.810.10.20.30.40.50.60.70.80.91elaFigure 2:The QED radiative corrections to asymmetry with experimental cuts.-50-40-30-20-100102030405000.10.20.30.40.50.60.70.80.91HectorFigure 3:A comparison of complete and LLA RC’s in the kinematic regime of HERMES for neutral current longitudinally polarized DIS in leptonic variables.The polarized parton densities [15]are used.The structure function g 2is calculated using the Wandzura–Wilczek relation.c 2stands for the Compton contribution,see [6]for details.-20-100102030405000.10.20.30.40.50.60.70.80.91HectorFigure 4:The same as in fig.3,but for energies in the range of the SMC-experiment.-20-10010203040500.10.20.30.40.50.60.70.80.91HectorFigure 5:The same as in fig.4for x =10−3.-200-150-100-5005010015020000.10.20.30.40.50.60.70.80.91HectorFigure 6:A comparison of complete and LLA RC’s at HERA collider kinematic regime for neutral current deep inelastic scattering offa longitudinally polarized target measuring the kinematic variables at the leptonic vertex.。

27.F.Banhart,J.Mater.Sci.41,4505(2006).28.V.H.Crespi,N.G.Chopra,M.L.Cohen,A.Zettl,S.G.Louie,Phys.Rev.B 54,5927(1996).29.The extent of displacement may vary depending on the tiltangle,because the local thickness of the specimen along the axis of the excitation may change.However,the skin depth of the MWNT ring specimen for the 532-nm light is deduced to be 2m m [absorption coefficient a =1.0×104cm −1(35)],which exceeds the largest local thickness along the ring specimen at a tilt angle of 35°.In addition,the absorption cross section of MWNTs is reported to be weakly dependent on the polarization of the incident beam for thick tubes (36).To further suppress any polarizationdependence,we set the polarization of the optical excitation beam so that it was not along the long axis of the tube.Consequently,the heat gradient and thermal stress are uniform for the tilt angles recorded in this study.30.P.Poncharal,Z.L.Wang,D.Ugarte,W.A.de Heer,Science 283,1513(1999).31.L.Meirovich,Elements of Vibration Analysis (McGraw-Hill,New York,ed.2,1986).32.X.-L.Wei,Y.Liu,Q.Chen,M.-S.Wang,L.-M.Peng,Adv.Funct.Mater.18,1555(2008).33.M.M.J.Treacy,T.W.Ebbesen,J.M.Gibson,Nature 381,678(1996).34.G.V.Hartland,Annu.Rev.Phys.Chem.57,403(2006).35.T.Nakamiya et al .,Thin Solid Films 517,3854(2009).36.C.Ni,P.R.Bandaru,Carbon 47,2898(2009).37.S.Jonic,C.Vénien-Bryan,Curr.Opin.Pharmacol.9,636(2009).38.Supported by NSF (grant DMR-0964886)and Air ForceOffice of Scientific Research (grant FA9550-07-1-0484)in the Physical Biology Center for Ultrafast Science and Technology supported by Gordon and Betty Moore Foundation at Caltech.A patent application has been filed by Caltech based on the methodology presented herein.Supporting Online Material/cgi/content/full/328/5986/1668/DC1Movies S1to S35April 2010;accepted 19May 201010.1126/science.1190470Measurement of the Instantaneous Velocity of a Brownian ParticleTongcang Li,Simon Kheifets,David Medellin,Mark G.Raizen *Brownian motion of particles affects many branches of science.We report on the Brownian motion of micrometer-sized beads of glass held in air by an optical tweezer,over a wide range of pressures,and we measured the instantaneous velocity of a Brownian particle.Our results provide direct verification of the energy equipartition theorem for a Brownian particle.For short times,the ballistic regime of Brownian motion was observed,in contrast to the usual diffusive regime.We discuss the applications of these methods toward cooling the center-of-mass motion of a bead in vacuum to the quantum ground motional state.In 1907,Albert Einstein published a paper in which he considered the instantaneous ve-locity of a Brownian particle (1,2).By mea-suring this quantity,one could prove that “the kinetic energy of the motion of the centre of grav-ity of a particle is independent of the size and nature of the particle and independent of the nature of its environment.”This is one of the basic tenets of statistical mechanics,known as the equipartition theorem.However,because of the very rapid randomization of the motion,Einstein concluded that the instantaneous veloc-ity of a Brownian particle would be impossible to measure in practice.We report here on the measurement of the instantaneous velocity of a Brownian particle in a system consisting of a single,micrometer-sized SiO 2bead held in a dual-beam optical tweezer in air,over a wide range of pressures.The velocity data were used to verify the Maxwell-Boltzmann velocity distribution and the equipartition theorem for a Brownian particle.The ability to measure instantaneous velocity enables new fundamental tests of statistical mechanics of Brownian par-ticles and is also a necessary step toward the cool-ing of a particle to the quantum ground motional state in vacuum.The earliest quantitative studies of Brownian motion were focused on measuring velocities,and they generated enormous controversy (3,4).The measured velocities of Brownian particles (3)were almost 1000-fold smaller than what was predicted by the energy equipartition theorem.Recent experiments with fast detectors that studied Brownian motion in liquid (5–7)and gaseous (8–10)environments observed nondiffusive mo-tion of a Brownian particle.Einstein ’s theory predicts that 〈[D x (t )]2〉¼2Dt ,where 〈[D x (t )]2〉is the mean square displace-ment (MSD)in one dimension of a free Brown-ian particle during time t ,and D is the diffusion constant (11).The diffusion constant can be cal-culated by D ¼k B T =g ,where k B is Boltz-mann ’s constant,T is the temperature,and g is the Stokes friction coefficient.The mean veloc-ity measured over an interval of time t is v ≡ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi〈[D x (t )]2〉p /t ¼ffiffiffiffiffiffi2D p /ffit p .This diverges as t ap-proaches 0and therefore does not represent the real velocity of the particle (1,2).The equation 〈[D x (t )]2〉¼2Dt ,however,is valid only when t >>t p ;that is,in the diffusive regime.Here,t p ¼m =g is the momentum relaxa-tion time of a particle with mass m .At very short time scales (t <<t p ),the dynamics of a particle are dominated by its inertia,and the motion is ballistic.The dynamics of a Brownian particle over all time scales can be described by a Langevin equation (12).The MSD of a Brownian particle at very short time scales is predicted to be 〈[D x (t )]2〉¼(k B T /m )t 2,and its instantaneous velocity can be measured as v ¼D x ðt Þ=t ,when t <<t p (13).For a 1-m m-diameter silica (SiO 2)sphere in water,t p is about 0.1m s and the root mean square (rms)velocity is about 2mm/s in one dimension.To measure the instantaneous velocity with 10%uncertainty,one would require 2-pm spatial res-olution in 10ns,far beyond what is experimen-tally achievable today (7).Because of the lower viscosity of gas,compared with liquid,the t p of a particle in air is much larger.This lowers the technical demand for both temporal and spatial resolution.The main difficulty of performing high-precision measurements of a Brownian particle in air,however,is that the particle will fall under the influence of gravity.We overcome this problem by using optical tweezers to simultaneously trap and monitor a silica bead in air and vacuum,al-lowing long-duration,ultra –high-resolution mea-surements of its motion.Center for Nonlinear Dynamics and Department of Physics,University of Texas at Austin,Austin,TX 78712,USA.*To whom correspondence should be addressed.E-mail:raizen@Fig.1.Simplified schematic showing the counterpropa-gating dual-beam optical tweezers,and a novel detec-tion system that has a 75-MHz bandwidth and ultralow noise.The s -polarized beam is re-flected by a polarizing beam-splitter cube after it passes through a trapped bead inside a vacuum chamber.For detec-tion,it is split by a mirror with a sharp edge.The p -polarized beam passes through the cube.Vacuum Chambers -polarized SCIENCE VOL 32825JUNE 20101673REPORTSo n M a y 21, 2017h t t p ://s c i e n c e .s c i e n c e m a g .o r g /D o w n l o a d e d f r o mFor small displacements,the effect of optical tweezers on the bead ’s motion can be approxi-mated by a harmonic potential.The MSD of a Brownian particle in an underdamped harmon-ic trap in air can be obtained by solving the Langevin equation (14)〈[D x (t )]2〉¼2k B T 01−e −t =2t pcos w 1t þsin w 1t 1t p ð1Þwhere w 0is the resonant frequency of the trapand w 1≡ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiw 20−1/(2t p )2q .The normalized veloc-ity autocorrelation function (V ACF)of the par-ticle is (14)y (t )¼e−t =2t pcos w 1t −sin w 1t2w 1t pð2ÞIn the simplified scheme of our optical trap and vacuum chamber (Fig.1),the trap is formed inside a vacuum chamber by two counterpropa-gating laser beams focused to the same point by two identical aspheric lenses with focal lengths of 3.1mm and numerical apertures of 0.68(15).The two 1064-nm-wavelength laser beams are orthogonally polarized,and their frequencies dif-fer by 160MHz to avoid interference.The scat-tering forces exerted on the bead by the two beams cancel,and the gradient forces near the center of the focus create a three-dimensional harmonic potential for the bead.When the bead deviates from the center of the trap,it deflects both trapping beams.The position of the bead ismonitored by measuring the deflection of one of the beams,which is split by a mirror with a sharp edge.The difference between the two halves is measured by a fast balanced detector (7,16).The lifetime of a bead in our trap in air is much longer than our measurement times over a wide range of pressures and trap strengths.We have tested it by trapping a 4.7-m m bead in air con-tinuously for 46hours,during which the power of both laser beams was repeatedly changed from 5mW to 2.0W.The trap becomes less stable in vacuum.The lowest pressure at which we have trapped a bead without extra stabilization is about 0.1Pa.For studying the Brownian motion of a trapped bead,unless otherwise stated,the powers of the two laser beams were 10.7and 14.1mW (15),the diameter of the bead was 3m m,the temperature of the system was 297K,and the air pressure was 99.8or 2.75kPa.The trapping was stable and the heating due to laser absorption was negligible un-der these conditions.In typical samples of position and velocity traces of a trapped bead (Fig.2),the position traces of the bead at these two pressures appear to be very similar.On the other hand,the velocity traces are clearly different.The instanta-neous velocity of the bead at 99.8kPa changes more frequently than that at 2.75kPa,because the momentum relaxation time is shorter at higher pressure.Figure 3shows the MSDs of a 3-m m silica bead as a function of time.The measured MSDs fit with Eq.1over three decades of time for both pressures.The calibration factor a =position/voltage of the detection system is the only fit-ting parameter of Eq.1for each pressure.t p and w 0are obtained from the measured normalized V ACF.The two values of a obtained for these two pressures differ by 10.8%.This is because the vacuum chamber is distorted slightly when the pressure is decreased from 99.8to 2.75kPa.The measured MSDs are completely different from those predicted by Einstein ’s theory of Brownian motion in a diffusive regime.TheFig.3.(A )The MSDs of a 3-m m silica bead trapped in air at 99.8kPa (red square)and 2.75kPa (black circle).They are calculated from 40mil-lion position measure-ments for each pressure.The “noise ”signal (blue triangle)is recorded when there is no particle in the optical trap.The solid lines are theoretical predictions of Eq.1.The prediction of Einstein ’s theory of free Brownian motion in the diffusive regime is shown in dashed lines for com-parison.(B )MSDs at shorttime scales are shown in detail.The dash-dotted line indicates ballistic Brownian motion of a freeparticle.AFig.2.One-dimensional trajectories of a 3-m m-diameter silica bead trapped in air at 99.8kPa (A )and 2.75kPa (B ).The instantaneous velocities of the bead corresponding to these trajectories are shown in (C )and (D ).25JUNE 2010VOL 328SCIENCE 1674REPORTSo n M a y 21, 2017h t t p ://s c i e n c e .s c i e n c e m a g .o r g /D o w n l o a d e d f r o mslopes of measured MSD curves at short time scales are double those of the MSD curves of diffusive Brownian motion in the log-log plot (Fig.3A).This is because the MSD is propor-tional to t 2for ballistic Brownian motion,whereas it is proportional to t for diffusive Brownian mo-tion.In addition,the MSD curves are indepen-dent of air pressure at short time scales,which is predicted by 〈½D x ðt Þ 2〉¼ðk B T =m Þt 2for bal-listic Brownian motion,whereas the MSD in the diffusive regime does depend on the air pressure.At long time scales,the MSD saturates at a con-stant value because of the optical trap.Figure 3B displays more detail of the Brownian motion at short time scales.It clearly demonstrates that we have observed ballistic Brownian motion.The distributions of the measured instanta-neous velocities (Fig.4A)agree very well with the Maxwell-Boltzmann distribution.The mea-sured rms velocities are v rms =0.422mm/s at 99.8kPa and v rms =0.425mm/s at 2.75kPa.These values are very close to the prediction of the energy equipartition theorem,v rms ¼ffiffiffiffiffiffiffiffiffiffiffiffiffik B T /m p ,which is 0.429mm/s.As expected,the velocity distribution is independent of pressure.The rms value of the noise signal is 0.021mm/s,which means we have 1.0Åspatial resolution in 5m s.This measurement noise is about 4.8%of the rms velocity.Figure 4A represents direct verification of the Maxwell-Boltzmann distribution of veloc-ities and the equipartition theorem of energy for Brownian motion.For a Brownian particle in liquid,the inertial effects of the liquid become im-portant.The measured rms velocity of the particle will be v rms ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffik B T /m *p in the ballistic regime,where the effective mass m *is the sum of the mass of the particle and half of the mass of the displaced fluid (17).This is different from the equipar-tition theorem.To measure the true instantaneous velocity in liquid as predicted by the equiparti-tion theorem,the temporal resolution must be much shorter than the time scale of acoustic damping,which is about 1ns for a 1-m m particle in liquid (17).Figure 4B shows the normalized V ACF of the bead at two different pressures.At 2.75kPa,one can see the oscillations due to the optical trap.Equation 2is independent of the calibration factor a of the detection system.The only in-dependent variable is time t ,which we can mea-sure with high precision.Thus the normalized V ACF provides an accurate method to measure t p and w 0.By fitting the normalized V ACF with Eq.2,we obtained t p =48.5T 0.1m s,w 0=2p ·(3064T 4)Hz at 99.8kPa and t p =147.3T 0.1m s,w 0=2p ·(3168T 0.5)Hz at 2.75kPa.The trapping frequency changed by 3%because of the distortion of the vacuum chamber at dif-ferent pressures.For a particle at a certain pres-sure and temperature,t p should be independent of the trapping frequency.We verified this by changing the total power of the two laser beams from 25to 220mW.The measured t p changed less than 1.3%for both pressures,thus proving that the fitting method is accurate,and the heat-ing due to the laser beams (which would change the viscosity and affect t p )is negligible.We can also calculate the diameter of the silica bead from the t p value at 99.8kPa (18).The obtained diameter is 2.79m m.This is within the uncer-tainty range given by the supplier of the 3.0-m m silica beads.We used this value in the calcu-lation of MSD and normalized V ACF.The ability to measure the instantaneous ve-locity of a Brownian particle will be invaluable in studying nonequilibrium statistical mechanics (19,20)and can be used to cool Brownian mo-tion by applying a feedback force with a direction opposite to the velocity (21,22).In a vacuum,our optically trapped particle should be an ideal system for investigating quantum effects in a mechanical system (16,23–25)because of its near-perfect isolation from the thermal bining feedback cooling and cavity cooling,we expect to cool the Brownian motion of a bead starting from room temperature to the quantum regime,as predicted by recent theoret-ical calculations (24,25).We have directly ver-ified the energy equipartition theorem of Brownian motion.However,we also expect to observe de-viation from this theorem when the bead is cooled to the quantum regime.The kinetic energy of thebead will not approach zero even at 0K because of its zero-point energy.The rotational energy of the bead should also become quantized.References and Notes1.A.Einstein,Zeit.f.Elektrochemie 13,41(1907).2.A.Einstein,Investigations on the Theory of the Brownian Movement ,R.Fürth,Ed.,A.D.Cowper,Transl.(Methuen,London,1926),pp.63–67.3.F.M.Exner,Ann.Phys.2,843(1900).4.M.Kerker,c.51,764(1974).5.B.Luki ćet al .,Phys.Rev.Lett.95,160601(2005).6.Y.Han et al .,Science 314,626(2006).7.I.Chavez,R.Huang,K.Henderson,E.-L.Florin,M.G.Raizen,Rev.Sci.Instrum.79,105104(2008).8.P.D.Fedele,Y.W.Kim,Phys.Rev.Lett.44,691(1980).9.J.Blum et al .,Phys.Rev.Lett.97,230601(2006).10.D.R.Burnham,P.J.Reece,D.McGloin,Brownian dynamicsof optically trapped liquid aerosols.In press;preprint available at /abs/0907.4582.11.A.Einstein,Ann.Phys.17,549(1905).ngevin,C.R.Acad.Sci.(Paris)146,530(1908).13.G.E.Uhlenbeck,L.S.Ornstein,Phys.Rev.36,823(1930).14.M.C.Wang,G.E.Uhlenbeck,Rev.Mod.Phys.17,323(1945).15.Materials and methods are available as supportingmaterial on Science online.16.K.G.Libbrecht,E.D.Black,Phys.Lett.A 321,99(2004).17.R.Zwanzig,M.Bixon,J.Fluid Mech.69,21(1975).18.A.Moshfegh,M.Shams,G.Ahmadi,R.Ebrahimi,Colloids Surf.A Physicochem.Eng.Asp.345,112(2009).19.R.Kubo,Science 233,330(1986).20.G.M.Wang,E.M.Sevick,E.Mittag,D.J.Searles,D.J.Evans,Phys.Rev.Lett.89,050601(2002).21.A.Hopkins,K.Jacobs,S.Habib,K.Schwab,Phys.Rev.B68,235328(2003).22.D.Kleckner,D.Bouwmeester,Nature 444,75(2006).23.A.Ashkin,J.M.Dziedzic,Appl.Phys.Lett.28,333(1976).24.D.E.Chang et al .,Proc.Natl.Acad.Sci.U.S.A.107,1005(2010).25.O.Romero-Isart,M.L.Juan,R.Quidant,J.Ignacio Cirac,N.J.Phys.12,033015(2010).26.M.G.R.acknowledges support from the Sid W.RichardsonFoundation and the R.A.Welch Foundation grant number F-1258.D.M.acknowledges support fromEl Consejo Nacional de Ciencia y Tecnología (CONACYT)for his graduate fellowship (206429).The authors would also like to thank E.-L.Florin and Z.Yin for helpfuldiscussions and I.Popov for his help with the experiment.Supporting Online Material/cgi/content/full/science.1189403/DC1Materials and Methods10March 2010;accepted 10May 2010Published online 20May 2010;10.1126/science.1189403Include this information when citing this paper.Fig.4.(A )The distribu-tion of the measured in-stantaneous velocities of a 3-m m silica bead.The statistics at each pressure is calculated from 4mil-lion instantaneous veloc-ities.The solid lines are Maxwell-Boltzmann dis-tributions.We obtained v rms =0.422mm/s at 99.8kPa (red square)and v rms =0.425mm/s at 2.75kPa (black circle)from the measurements.The rms value of the noise (blue triangle)is 0.021mm/s.(B )The normalizedvelocity autocorrelation functions of the 3-m m bead at two different pressures.The solid lines are fittings with Eq.2.A B SCIENCEVOL 32825JUNE 20101675REPORTSo n M a y 21, 2017h t t p ://s c i e n c e .s c i e n c e m a g .o r g /D o w n l o a d e d f r o moriginally published online May 20, 2010(5986), 1673-1675. [doi: 10.1126/science.1189403]328Science (May 20, 2010)Tongcang Li, Simon Kheifets, David Medellin and Mark G. Raizen ParticleMeasurement of the Instantaneous Velocity of a BrownianEditor's Summarythe technique also has practical implications for cooling particles to ultralow temperatures.short-time-scale behavior predicted a century ago. As well as testing fundamental principles of physics, Brownian motion, measuring the predicted instantaneous velocity of the particle and verifying the1673, published online 20 May) use a single, optically trapped silica bead to probe the dynamics of (p.et al.Li Einstein described this Brownian motion in terms of statistical thermodynamics. Now, displayed a random motion, jittering under the microscope as if the particles were alive. In 1905, Albert Nearly 200 years ago, the botanist Robert Brown noted that pollen particles floating on a liquid Dancing in the LightThis copy is for your personal, non-commercial use only.Article Tools/content/328/5986/1673article tools:Visit the online version of this article to access the personalization and Permissions/about/permissions.dtlObtain information about reproducing this article: is a registered trademark of AAAS.Science Advancement of Science; all rights reserved. The title Avenue NW, Washington, DC 20005. Copyright 2016 by the American Association for thein December, by the American Association for the Advancement of Science, 1200 New York (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week Science o n M a y 21, 2017h t t p ://s c i e n c e .s c i e n c e m a g .o r g /D o w n l o a d e d f r o m。

“散射光偏振态检测水质颗粒含量的理论与实践研究”课题结题报告光极课题组执笔：梁美怡课题负责人：梁美怡指导老师：冯杰<华南师范大学，物电学院，副教授）彭力<华南师范大学，物电学院，助教）课题组成员：丁友根张俊莲尹凤婷刘斌1、课题研究的意义①用椭偏仪测量水中颗粒的大小，在现代光学研究上具有重要的实际意义。

随着工农业的发展，测量水中颗粒的大小是工农业生产中的控制因素。

因此，椭偏法和水中颗粒大小测量的研究是有现实意义的。

b5E2RGbCAP②使光学从课堂和实验室走进现实生活，提高我们发现问题，分析问题，解决问题的能力，开拓我们的思维。

2、课题研究的理论依据利用在测量散射光的偏振性时，自然光的矢量在oyz平面内沿着一切可能的方向振动，可平均地分解成y和z两个相等的分量[6] 。

入射偏振方向为y方向的线偏振光时，在oxy平面出射的是y方向的线偏振光；入射偏振方向为x方向的线偏振光时，在oxy平面出射的是x方向的线偏振光。

因此，在实验时可把水平和垂直两方向上的y和z两相等的分量替代常在光学实验中使用的自然光，以此为依据设计新的实验方法来测量散射光的偏振度。

p1EanqFDPw用散射光的偏振特性来测量溶液的颗粒线度。

利用微粒散射自然光时，正侧方向的散射光都是线偏振光，且振动面垂直于入射光束的传播方向的性质，通过对正侧方向散射光的光强和偏振度的测量，探究其与散射颗粒线度之间的关系，从而根据有关Mie散射理论，寻求颗粒物线度的测量方法。

DXDiTa9E3d3、课题研究的目标①通过课题研究,获取事实,发现规律,发展理论,探索偏振叠加发在现代光学中的运用,并在实际中实施,在此基础上,收集相关资料数据,不断总结反思,积累一批有价值的实验资料与实验数据.②通过课题研究推进偏振度测量的改进,提高偏振度测量的准确度.RTCrpUDGiT③通过课题研究培养创新精神和实践能力。

促进合作能力,建立严谨的科学态度和科学道德,提高信息素养和学习能力.5PCzVD7HxA④坚持做到理论学习与实践研究相结合,课内与课外相结合,以点带面,辐射到所有学科。

ZEISS Axio ObserverYour Inverted Microscope System for MetallographyProduct InformationVersion 1.050 µmSpherulitic graphite in nodular cast iron seen in C-DIC contrast.Your Inverted Microscope System for MetallographyFast, flexible, economic: Take advantage of Axio Observer’s inverted construction to investigate a large number of samples in no time at all – or to explore heavy ones, just as efficiently. There’s no need to refocus, even when changing magnifi-cation or switching samples. Axio Observer combines the proven quality of ZEISS optics with automated components to give you reliable, reproducible results. Using dedicated software modules you can analyze, for example, non-metallic inclusions, grain sizes and phases – it’s fully automatic. Axio Observer is your open imaging platform: invest in only the features you need today.As requirements change, a simple upgrade keeps your system ready for all materials applications.› In Brief › The Advantages › The Applications › The System› Technology and Details ›ServiceAnimationSimpler. More intelligent. More integrated.Save Time in Metallographic Investigations As an inverted microscope platform, Axio Observer makes work so much more enjoyable. Whether investigating a large number or even heavy samples, you’ll save time in both sample preparation and investigation. Meanwhile, its inverted design facilitates parallel alignment to the objective lens. Observe more samples in less time: simply put your specimen on the stage, focus once and keep the focus for all further magnifications and samples.Upgrade Your SystemKeep an eye on your budget as well as your samples.With Axio Observer, you invest only in the featuresyou need now. You can always upgrade your system,simply and economically, any time you need to.Choose between encoded or motorized compo-nents and a range of accessories – you can dependon having any relevant contrasting techniques yourapplication requires.Count on Reliable Results and Brilliant ImagesYou will appreciate the stable imaging conditionsof Axio Observer, especially when working withhigh magnifications. Homogeneous illuminationacross the entire field of view produces brilliantimages. And you will get reliable, reproducibleresults every time, thanks to the proven opticalquality of ZEISS combined with automated com-ponents. Profit from short time-to-image for yourmetallographic structure analysis with dedicatedsoftware modules, e.g. NMI, Grains, Multiphase.› In Brief› The Advantages› The Applications› The System› Technology and Details › ServiceExpand Your PossibilitiesChoose Between Three Different Stands• Control all motorized components of yourAxio Observer 7 materials with its touchscreendisplay. Automatic Component Recognition(ACR) means it will always recognize the settingsfor objectives and filtersets you have chosen.• Axio Observer 5 materials – nearly all compo-nents can be read out or even motorized• Axio Observer 3 materials with an encodednosepiece, light manager, CAN and USB inter-face that enables a read-out of the magnificationGet Crisp Images with Polarization ContrastInvestigate your samples with polarization contrastusing fixed analyzers, a measuring analyzer rotatingthrough 360° and a rotating analyzer with rotatingfull-wave plate.Now, you can also use a rotatable polarizer tochange the direction of incidence of the polarizedlight. This also makes bireflection and pleochroismvisible on anisotropic samples. In addition, someore phases display anisotropy in the polarized re-flected light, whereby a color change is generateddepending on the placement of the polarizer a fewdegrees +/- from the marked position.Take Advantage of a Variety of Stage InsertsSelect from a variety of stage inserts to tailor thesystem to your needs. The high-grade spring steelwill not yield under loads, even when examiningmany samples. Thus you can be sure that the opticalreference plane is maintained. Stage inserts comewith different inside apertures to match standardspecimen diameters, plus a 10 mm aperture forvery small specimens.› In Brief› The Advantages› The Applications› The System› Technology and Details› ServiceTailored Precisely to Your Applications› The Advantages› The Applications› The System› Technology and Details› Service50 µm50 µm50 µm50 µmBrightfieldDarkfieldPolarization ContrastPolarization with Additional Lambda PlateZEISS Axio Observer at WorkSpherulitic graphite in nodular grey cast iron, spheruliths with ferrite envelope and perlitic ground mass, same position acquired in reflected light with different contrasting techniques, objective: EC Epiplan-NEOFLUAR 50×/0.80 HD DIC› In Brief › The Advantages › The Applications › The System› Technology and Details › Service50 µm50 µm50 µm50 µm50 µmCast aluminum-silicon, reflected light, brightfield, objective: EC Epiplan-NEOFLUAR 20×/0.50 HD DICZEISS Axio Observer at WorkCast aluminum-silicon, reflected light, darkfield, objective: EC Epiplan-NEOFLUAR 20×/0.50 HD DICNiccolite, reflected light, polarization contrast with lambda plate, objective: EC Epiplan-NEOFLUAR 20×/0.50 HD DICZinc, reflected light, polarization contrast with lambda plate, objective: EC Epiplan-NEOFLUAR 20×/0.50 HD DICNiccolite, reflected light, polarization contrast with slightly twisted polarizers, objective: EC Epiplan-NEOFLUAR 20×/0.50 HD DIC› In Brief › The Advantages › The Applications › The System› Technology and Details › Service500 µm500 µm500 µm500 µmBarker-etched aluminum, reflected light, polarization contrast, objective: EC Epiplan-NEOFLUAR 5×/0.13 HD DICZEISS Axio Observer at WorkBarker-etched aluminum, reflected light, polarization contrast with lambda plate, objective: EC Epiplan-NEOFLUAR 5×/0.13 HD DICBarker-etched aluminum, reflected light, circular polarization contrast, objective: EC Epiplan-NEOFLUAR 5×/0.13 HD DICBarker-etched aluminum, reflected light, differential interference contrast with circular polarized light (C-DIC), objective: EC Epiplan-NEOFLUAR 5×/0.13 HD DIC› In Brief › The Advantages › The Applications › The System› Technology and Details › Service1234561 Microscope• Axio Observer 3 materials (encoded)• Axio Observer 5 materials (encoded, partly motorized)• Axio Observer 7 materials (motorized)2 Objectives • EC Epiplan• EC Epiplan-NEOFLUAR • EC Epiplan-APOCHROMATYour Flexible Choice of Components3 Illumination Reflected light:• microLED • HAL 100• HBOTransmitted light:• HAL 100• microLED4 Cameras • Axiocam HRc • Axiocam MRc 5• Axiocam MRc • Axiocam 506 color • Axiocam 503 color • Axiocam ICc 5• Axiocam ICc 1• Axiocam 105 color5 Software • AxioVision • AxioVision LE • ZEN 2 core • ZEN 2 starter6 Accessories• Correlative Microscopy • Fixed, measuring,rotating analyzer and polarizers • Gliding stage, scanning stages› In Brief › The Advantages › The Applications › The System› Technology and Details › ServiceSystem Overview› The Advantages› The Applications› The System› Technology and Details› ServiceSystem Overview› The Advantages› The Applications› The System› Technology and Details› ServiceTechnical Specifications› The Advantages› The Applications› The System› Technology and Details› ServiceTechnical Specifications› The Advantages› The Applications› The System› Technology and Details› ServiceTechnical Specifications› The Advantages› The Applications› The System› Technology and Details› ServiceTechnical Specifications› The Advantages› The Applications› The System› Technology and Details› ServiceTechnical Specifications› The Advantages› The Applications› The System› Technology and Details› ServiceTechnical Specifications› The Advantages› The Applications› The System› Technology and Details› ServiceTechnical Specifications› The Advantages› The Applications› The System› Technology and Details› ServiceBecause the ZEISS microscope system is one of your most important tools, we make sure it is always ready to perform. What’s more, we’ll see to it that you are employing all the options that get the best from your microscope. You can choose from a range of service products, each delivered by highly qualified ZEISS specialists who will support you long beyond the purchase of your system. Our aim is to enable you to experience those special moments that inspire your work.Repair. Maintain. Optimize.Attain maximum uptime with your microscope. A ZEISS Protect Service Agreement lets you budget for operating costs, all the while reducing costly downtime and achieving the best results through the improved performance of your system. Choose from service agreements designed to give you a range of options and control levels. We’ll work with you to select the service program that addresses your system needs and usage requirements, in line with your organization’s standard practices.Our service on-demand also brings you distinct advantages. 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圆极化与线计划的设置英文回答：Circular polarization and linear polarization are two different ways of describing the orientation of electromagnetic waves. In circular polarization, the electric field vector of the wave rotates in a circular pattern as the wave propagates. This rotation can be clockwise or counterclockwise. In linear polarization, the electric field vector of the wave oscillates in a straight line.Circular polarization can be achieved by combining two perpendicular linearly polarized waves with a phase difference of 90 degrees. This can be done using a device called a quarter-wave plate or a combination of a half-wave plate and a linear polarizer. The resulting wave will have a rotating electric field vector.Linear polarization can be achieved by using a linearpolarizer, which is a device that only allows waves with a specific orientation of the electric field vector to pass through. The polarizer absorbs or blocks waves with orientations perpendicular to the desired polarization.The choice between circular polarization and linear polarization depends on the specific application. Circular polarization is often used in satellite communication to minimize signal loss due to the rotation of the satellite and to improve signal reception in areas with high levelsof interference. It is also used in some optical systems to eliminate the effects of birefringence. Linear polarization, on the other hand, is commonly used in antennas, optical filters, and polarization-sensitive detectors.中文回答：圆极化和线极化是描述电磁波方向的两种不同方式。

polarized light姓名： 班级 学号： 实验名称：偏振光的实验The purpose of the experiment: to master the spectrometer works, familiar with theprinciples and properties of polarized light. Verify Malus law, and the refractive index of the medium is determined according to Brewster's law.Experimental principle:The various analyzes and measurements in order to study the polarization properties of the polarization state of light and the use of light, various polarizing element: generating a polarized light component, and to change the polarization state of the light elements, etc., the following classification introduced.1..Produce polarized light componentsLight generated from the laser before the invention, the natural light in general are non-polarized light, and therefore produce the components of the polarized light must produce polarized. Based on the role of these elements in the experiment were divided into a polarizer and an analyzer. The polarizer is an element which converts natural light into linearly polarized light, the analyzer is a polarization state of the element used to identify light. In the laser resonator can take advantage of the Brewster angle of the output laser beam is a linearly polarized light.A lot of natural light becomes polarized, a method using light polarization phenomena in the interface reflection and transmission time. Our ancestors in the very early reflection of the horizontal plane light some research, but quantitative study was first performed in 1815 by Brewster. The reflected light perpendicular to the incident surface of the light vibration (called the s component) than parallel to the incident surface of the light vibration (called p component); while the transmitted light is opposite. Changing the incident angle at the time, there is a special phenomenon, i.e., when the incident angle of a specific value, the reflected light becomes completely linearly polarized light (s-component). Refracted light is partially polarized light, and at this time of the reflected light and refracted light vertical, a phenomenon known as Brewster's law. The method is one of the methods of the linearly polarized light can be obtained. As shown inFigure 1. Because this case, {EMBED Equation.3|20πγ=+i ,,if n1 = 1 (for the refractive index of air), then (1)The Called the Brewster angle, so the refractive index of the medium can be measured by the size of the measurement of Brewster angle.Introduced above, we can know that the use of reflection can produce polarized light, the same can also take advantage of transmission (several transmission) to produce polarized light (glass heap). The second is an optical prism, a Nicol prism, a Glan prism, etc., it is birefringence using a crystal made of the principle. When there is a particular direction (optical axis direction) in the crystal, when the spread of the beam in this direction, the light beam does not split, the beamto deviate from the direction of propagation, the light beam will be split into two beams, wherein the light beam comply with the law of refraction called unusual light (o light), another beam of light is generally non-compliance with the law of refraction is called the extraordinary light (e light). O are linearly polarized light and e light (also called completely polarized light), both of the vibration direction of the light vector (in the normal use state) mutually perpendicular. Changing the direction of the incident light ray toward the crystals can be found in the optical axis direction, in this direction, the O ray and e-ray is equal to the velocity of propagation, the same refractive index. The crystals can have an optical axis, called uniaxial crystal, such as calcite, quartz, can have two optical axes, called biaxial crystal, such as mica, sulfur, etc.. Including the optical axis and the plane of each light line called corresponds to the main plane of the light, o photoelectric vector oscillation direction perpendicular to the main plane of o light, e photoelectric vector parallel to the vibration direction of the main plane of the e-ray.Glan prism constituted by two calcite rectangular prism, the air gap, parallel to the optical axis of the calcite prism ridge between the two prisms. Natural light vertically the interface injection prism into o light and e light, o light in the air gap on total reflection, only e light through the prism.The third is the polarizing plate, it is the use of polyvinyl alcohol made of a plastic film, it has a long chain of the comb-shaped structure of molecules, these molecules are arranged in parallel in the same direction, the film allows only perpendicular to the arrangement direction of the light vibrations is passed, resulting in linearly polarized light. Its polarization performance as a Glan prism, but the advantage is cheap, and a large area can be obtained. Polarizer as the polarizer and the analyzer used in this experiment.2.Wave chip:Also known phase retardation plate is to change the polarization state of light elements. It is a plane-parallel plate cut from a uniaxial crystal, due to the wave chip speed vo, ve different (so the refractive index is different), so the resulting o light and e is the light passes through the optical path of the wave wafer. The o light phase when the two beams through wave chip e light relative to the amount of delay,(2)If satisfied, that we call sheet, if met, i.e., we call the sheet, if satisfied, i.e. we call a full-wave plate (M is an integer).Wave chip can be used to test and change the light polarization state, as shown in Figure 4, after the polarizer plus a wave plate, rotating the polarizer or wave plate can be obtained park or elliptical polarized light [details and methods see Document 2,3]. Wave plate is an the ellipsometer important element the ellipsometer can accurately measure the thickness and refractive index of the film, and precision instruments used in materials science.The polarized light from Malus law, Malus law is the most basic and most important laws polarization. Marius discovered in 1809, completely linearly polarized light through the analyzer strong can be expressed as(3)Wherein E is the angle of the direction of polarization of the analyzer and the polarization direction of the polarizer.Experimental apparatus:1, a semiconductor laser (wavelength 650nm), a polarizer 3, the analyzer 4, the spectrometer, and digital galvanometer.Experimental procedures and data processing and analysis:1, the instrument adjustment:(1) First, the two-plane mirror adjust discharge of the semiconductor laser light tube (hereinafter referred to as the tube 1) it is perpendicular to the rotary spindle of the instrument (ie parallel to the plane) and dial, while the spectrometer table and dial plane parallel.(2) check whether the output signal with digital galvanometer connected to the switch of the galvanometer measurement process to select a file on a file, adjust the zero knob, so that the data show "- .000" (minus sign flashing).2, measuring the degree of polarization of the semiconductor laserPolarizer P1 put in tube 1 hit 4th gear range selector 4 stages switch (from the vertical direction of the polarizer will be transferred to 0 ), rotating polarizer find the intensity, the strongest position to record angle and light intensity value Imax. Then, the polarizer is rotated 90 , record the angle and light intensity value Imin. Calculated according to the formula degree of polarization of the laser beam P:(4)Imin = 1.2 Imax = 145.9By (4) can be calculated was:P = 0.9833, verify Malus lawThe galvanometer is still in 4 files do not shift during the measurement. The polarizer on the light intensity and the strongest position analyzer P2 put on the other end the tube 2 and the vertical direction is 0 . Then rotating analyzer P2 the galvanometer light intensity minimum (still in 4th gear can be adjusted to 0). The angle between P1 and P2 are the direction of polarization can be considered at this time for of 90 recording P2 polarization direction at this time the absolute angle value , the value of the relative angle and light intensity value I, after every 10 records once, until P1 and P2 the angle between the direction of polarization of -90 , I0 is the angle between the polarization direction of the P1 and P2 for the light intensity values at 0 made I/I0 cos2 curve (0 90 0 - 90 each one, find the slope and intercept of the least squares method, according to the Malus law slope should be 1, the intercept should be 0, the analysis of the experimental error).1)-90~0Theta Ip Cos^2-90 0 1.06939E-26-85 2 0.0076-80 6.4 0.03015-75 13.2 0.06699-70 22 0.11698-65 32.2 0.17861-60 44.6 0.25-55 57.6 0.32899-50 71.1 0.41318-45 85.3 0.5-40 100 0.58682-35 113 0.67101-30 126 0.75-25 137.6 0.82139-20 146.8 0.88302-15 154.6 0.93301-10 160.2 0.96985-5 163.3 0.99240 164 1Origin linear the contemplated merger analysis error:2)0~90Theta Ip Cos^20 164 15 161.8 0.992410 157.1 0.9698515 150.1 0.9330120 141.3 0.8830225 130.2 0.8213930 118.1 0.7535 104.4 0.6710140 90 0.5868245 75.6 0.550 61.4 0.4131855 48.2 0.3289960 35.7 0.2565 23.7 0.1786170 15 0.1169875 8.3 0.0669980 3 0.0301585 0.3 0.007690 0.1 1.06939E-26 Origin linear the contemplated merger analysis error:4, t he measurement of the Brewster angle:θθ’Δθ84º34’140º25’55º51’124º55’181º45’56º50’40º96º40’56º40’Δθ=56º21’≈57ºAnd theoretically in line with。

金属腐蚀速率测定实验报告实验报告AbstractThe corrosion rate of metals is a crucial parameter in various industries, as it directly affects the longevity and performance of metallic structures. In this experiment, the corrosion rate of a metal sample was determined using two different methods: the weight loss method and the polarization resistance method. The results showed a correlation between the corrosion rate and the exposure time, as well as the effectiveness of the two methods in measuring corrosion rates. These findings provide valuable insights for industries dealing with metal corrosion prevention and control.1. IntroductionCorrosion is the process of deterioration of materials, especially metals, due to chemical reactions with the environment. It poses significant challenges in various sectors, such as infrastructure, manufacturing, and transportation. Understanding the corrosion rate of metals is essential for designing corrosion-resistant materials and structures. This experiment aims to determine the corrosion rate of a metal sample and compare the effectiveness of different measurement techniques.2. Experimental Procedure2.1 Sample PreparationA metal sample of known composition, in this case, mild steel, was selected for the experiment. The sample was carefully cleaned and dried toremove any surface contaminants that could interfere with the corrosion measurement.2.2 Weight Loss MethodThe weight loss method is a widely used technique for measuring the corrosion rate of metals. In this method, the metal sample is exposed to a corrosive environment for a specific period. After exposure, the sample is cleaned to remove any corrosion products and re-weighed. The difference in weight before and after exposure is used to calculate the corrosion rate.2.3 Polarization Resistance MethodThe polarization resistance method is an electrochemical technique for measuring the corrosion rate. It is based on the measurement of the polarization resistance, which is related to the rate of metal corrosion. In this method, a potentiostat is used to apply a small potential difference to the metal sample while measuring the resulting current. From this data, the polarization resistance and corrosion rate can be calculated.3. Results and DiscussionThe corrosion rate of the metal sample was measured using both the weight loss method and the polarization resistance method. The experiments were conducted over a period of 30 days, and measurements were taken at regular intervals.3.1 Weight Loss Method ResultsThe weight loss method involved immersion of the metal sample in a corrosive solution. After a specified period, the sample was removed,cleaned, and re-weighed. The corrosion rate was calculated by dividing the weight loss by the exposure time and the sample area. The results showed an increase in corrosion rate with increasing exposure time, indicating progressive corrosion of the metal sample.3.2 Polarization Resistance Method ResultsThe polarization resistance method involved applying a small potential difference to the metal sample and measuring the resulting current. Using this data, the polarization resistance and corrosion rate were calculated. The results demonstrated a similar trend to the weight loss method, with a higher corrosion rate observed as the exposure time increased.4. Comparison of Measurement TechniquesBoth the weight loss method and the polarization resistance method provided valuable insights into the corrosion rate of the metal sample. The weight loss method is relatively simple and cost-effective, making it a popular choice in various industries. However, it is limited by factors such as the need for sample removal and potential errors associated with cleaning and weighing. The polarization resistance method, although more complex and expensive, offers higher accuracy and provides real-time data without the need for sample removal. It is particularly suitable for continuous monitoring of corrosion rates in complex environments.5. ConclusionIn this experiment, the corrosion rate of a metal sample was successfully determined using the weight loss method and the polarization resistance method. The results showed a clear correlation between the corrosion rateand the exposure time. Both methods proved effective in measuring the corrosion rate, with the polarization resistance method offering higher accuracy and real-time monitoring capabilities. These findings contribute to the understanding and prevention of metal corrosion in various industries. Future research can explore the application of these methods to different metals and corrosive environments, as well as the development of advanced corrosion prevention techniques.。