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SpringerSeriesin optical sciences 149 foundedbyH.K.V.Lotsch Editor-in-Chief: W.T.Rhodes,Atlanta EditorialBoard: A.Adibi,Atlanta T.Asakura,Sapporo T.W.Ha¨nsch,Garching T.Kamiya,Tokyo F.Krausz,Garching B.Monemar,Linko¨ping H.Venghaus,Berlin H.Weber,Berlin H.Weinfurter,Mu¨nchen SpringerSeriesin optical sciences TheSpringerSeriesinOpticalSciences,undertheleadershipofEditor-in-ChiefWilliamT.Rhodes,Georgia InstituteofTechnology,USA,providesanexpandingselectionofresearchmonographsinallmajorareasof optics:lasersandquantumoptics,ultrafastphenomena,opticalspectroscopytechniques,optoelectronics, quantuminformation,informationoptics,appliedlasertechnology,industrialapplications,andother topicsofcontemporaryinterest. Withthisbroadcoverageoftopics,theseriesisofusetoallresearchscientistsandengineerswhoneed up-to-datereferencebooks. Theeditorsencourageprospectiveauthorstocorrespondwiththeminadvanceofsubmittingamanu- script.SubmissionofmanuscriptsshouldbemadetotheEditor-in-ChieforoneoftheEditors.Seealso www.springer.com/series/624 Editor-in-Chief WilliamT.Rhodes GeorgiaInstituteofTechnology SchoolofElectricalandComputerEngineering Atlanta,GA30332-0250,USA E-mail:[email protected] EditorialBoard AliAdibi BoMonemar GeorgiaInstituteofTechnology DepartmentofPhysics SchoolofElectricalandComputerEngineering andMeasurementTechnology Atlanta,GA30332-0250,USA MaterialsScienceDivision E-mail:[email protected] Linko¨pingUniversity ToshimitsuAsakura 58183Linko¨ping,Sweden E-mail:[email protected] Hokkai-GakuenUniversity FacultyofEngineering HerbertVenghaus 1-1,Minami-26,Nishi11,Chuo-ku FraunhoferInstitutfu¨rNachrichtentechnik Sapporo,Hokkaido064-0926,Japan Heinrich-Hertz-Institut E-mail:[email protected] Einsteinufer37 TheodorW.Ha¨nsch 10587Berlin,Germany Max-Planck-Institutfu¨rQuantenoptik E-mail:[email protected] Hans-Kopfermann-Straße1 HorstWeber 85748Garching,Germany E-mail:[email protected] TechnischeUniversita¨tBerlin TakeshiKamiya OptischesInstitut Straßedes17.Juni135 MinistryofEducation,Culture,Sports 10623Berlin,Germany ScienceandTechnology E-mail:[email protected] NationalInstitutionforAcademicDegrees 3-29-1Otsuka,Bunkyo-ku HaraldWeinfurter Tokyo112-0012,Japan Ludwig-Maximilians-Universita¨tMu¨nchen E-mail:[email protected] SektionPhysik FerencKrausz Schellingstraße4/III Ludwig-Maximilians-Universita¨tMu¨nchen 80799Mu¨nchen,Germany Lehrstuhlfu¨rExperimentellePhysik E-mail:[email protected] AmCoulombwall1 85748Garching,Germany and Max-Planck-Institutfu¨rQuantenoptik Hans-Kopfermann-Straße1 85748Garching,Germany E-mail:[email protected] PleaseviewavailabletitlesinSpringerSeriesinOpticalSciences onserieshomepagehttp://www.springer.com/series/624 Vladimir V. Protopopov Laser Heterodyning With234Figures ABC Dr.VladimirV.Protopopov SamsungElectronicsCo.,Ltd. MechatronicsCenter 416Maetan-dong,Yeongton-gu 443-742Suwon-si,Gyeonggi-do,RepublicofKorea E-mail:[email protected] SpringerSeriesinOpticalSciences ISSN0342-4111 e-ISSN1556-1534 ISBN978-3-642-02337-8 e-ISBN978-3-642-02338-5 DOI10.1007/978-3-642-02338-5 Springer HeidelbergDordrechtLondonNewYork LibraryofCongressControlNumber:2009929705 (cid:2)c Springer-VerlagBerlinHeidelberg2009 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerial isconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broad- casting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthis publicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawof September9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. ViolationsareliabletoprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnot imply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotective lawsandregulationsandthereforefreeforgeneraluse. Coverdesign:SPiPublisherServices Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface Laser heterodyning is an electro-optical phenomenon of time-dependent interference between two optical waves with slightly different frequencies at the sensitive area of a photodetector, resulting in a harmonically oscillating photocurrent. The amplitude and phase of such an electrical signal preserve informationabouttheamplitudesandphasesoftheinterferingopticalwaves, which provides the unique possibility of coherent analysis of optical fields in the electronic domain, thereby taking advantage of the high speed and accu- racy of modern signal processing techniques. Laserheterodyningfindsnumerousapplicationsinspectroscopy,polarimetry,radiometry,laserradarsandlidars,microscopyandotherareas.Therefore, it is remarkable that such a widely used optical phenomenon has never be- fore been comprehensively reviewed in a single work, as has been done many times for other subjects such as interferometry. I think there are several possible reasons for this. Perhaps, it is due to the multidisciplinary nature of laser heterodyning, which spans such very different areas of optics as interference, coherence and diffraction of laser fields, beam propagation, imaging and phase-contrast imaging, photodetectors and instrumentation, scattering, and the statistics of random optical fields. Perhaps, it is due to the fusion of optics with electrical engineering, which requires essential knowledge in both areas, in signal processing techniques particularly And of course, it is due to the extreme diversity of applications, ranging from stellar interferometry to microscopy.Whateverthereason,anattempthasnowbeenmadetopresenta consistentandcomprehensivereviewofthefullrangeofphysicalandtechnical applications of laser heterodyning, and this book is the result of it. Unlike an ordinary survey book that presents only general phenomenol- ogy and extensive citations, this book offers deep physical and mathematical insights into different phenomena, explaining carefully every detail. This requires from a reader a familiarity with advanced mathematics, theory of lin- earopticalsystems,electrodynamicsandstatisticalradiophysicsaswellasthe willingnesstofollowcomputations.However,thosewhoarenotinterestedinit mayskipthemathematicalderivationswithoutlossofunderstandingbecause VI Preface all the mathematically derived conclusions are finally explained on the basis of general physical laws. The basic concepts of various practically important applications of laser heterodyning, which sometimes cannot be readily found in the literature, are also carefully explained in every detail. This is particularly helpful for students, postgraduates, and application engineers. In order tomakethisbookasinterestingaspossibleforreaders,Itookeveryopportu- nitytosubstitutedullwordingwithvisualinterpretationofthesubject,using figures. Therefore, the book is well illustrated above the common level of a scientific publication. As the final comment, it is a pleasure to express my deep gratitude to Dr. Claus Ascheron for his trust and encouragement and appreciation of the efforts of Adelheid Duhm, Elke Sauer, and Elumalai Balamurugan of the Springer publication team, which made this book possible. Suwon, Vladimir Protopopov June 2009 Contents 1 Principles of Optical Heterodyning ........................ 1 1.1 Heterodyne Detection of Regular Signals ................... 1 1.1.1 Interference of Optical Fields at the Detector Sensitive Area .................................... 1 1.1.2 Spectrum of the Output Signal Under Regular Modulation of Optical Fields........................ 4 1.1.3 Optimal Conditions for Wavefronts .................. 7 1.1.4 Siegman Antenna Theorem ......................... 11 1.1.5 Practical Schemes of Wavefront Matching ............ 15 1.1.6 Tolerances on Aberrations of Optical Systems......... 23 1.2 Heterodyne Detection of Random Signals................... 30 1.2.1 Spectrum of the Photocurrent....................... 30 1.2.2 Heterodyning with Partial Spatial Coherence of Optical Waves .................................. 36 1.3 Sensitivity of an Ideal Heterodyne Receiver ................. 40 1.3.1 Sensitivity of an Ideal Heterodyne Receiver to Narrow-Band Laser Signals....................... 40 1.3.2 Sensitivity of an Ideal Heterodyne Receiver to Wide-Band Optical Signals....................... 45 References .................................................. 48 2 Laser Heterodyne Spectroscopy............................ 51 2.1 Laser Heterodyne Spectroscopy of Scattered Radiation ....... 51 2.1.1 Historical Introduction............................. 51 2.1.2 The Principles of Heterodyne and Homodyne Spectroscopy ..................................... 52 2.1.3 Basics of Single Scattering.......................... 58 2.1.4 Finite Width of Laser Spectrum..................... 65 2.1.5 Signal-to-Noise Ratio in Spectroscopic Measurements .................................... 71 2.1.6 Some Experimental Results......................... 77 VIII Contents 2.2 High-Frequency Heterodyne Spectroscopy .................. 81 2.2.1 Historical Introduction............................. 81 2.2.2 Secondary Frequency Standards with CO -Lasers...... 82 2 2.2.3 High-Frequency Mixing Devices ..................... 85 2.2.4 Measuring Frequencies of Molecular Transitions ....... 90 2.2.5 Optical Frequency Synthesis Spectroscopy ............ 90 2.3 Frequency-Modulation Spectroscopy ....................... 94 References ..................................................101 3 Laser Heterodyne Radars and Lidars ......................105 3.1 Introduction ............................................105 3.2 Heterodyne Photoreceivers................................106 3.2.1 Basic Types of Heterodyne Photodetectors ...........106 3.2.2 Sensitivity of Photoresistors and Photodiodes in the Heterodyne Mode............................108 3.3 Laser Heterodynes.......................................122 3.4 Atmospheric Turbulence..................................124 3.5 Probability of Detection and False Alarm...................132 3.5.1 Signal Statistics and Input Circuits of Heterodyne Receivers.........................................132 3.5.2 Detection of Regular Continuous Gaussian Signals without Accumulation .............................136 3.5.3 Detection of Regular Continuous Gaussian Signals with Accumulation ................................138 3.5.4 Non-Gaussian Signals ..............................144 3.5.5 Experimental Results ..............................148 3.6 Retrieving Information from Heterodyne Signals.............150 3.6.1 Measuring Target Velocity..........................150 3.6.2 Synthetic Aperture Method.........................155 3.6.3 Synthetic Aperture: Experimental Results ............170 3.6.4 Linear Frequency Modulation Method ...............175 3.6.5 Linear Frequency Modulation: Experimental Results ...179 3.7 Lidars..................................................180 3.7.1 Range Selectivity in Heterodyne Lidars ..............181 3.7.2 Wind Speed Vector Measurement....................186 References ..................................................188 4 Laser Heterodyne Radiometers ............................191 4.1 Principles of Laser Heterodyne Radiometers ................191 4.1.1 Basic Scheme of a Laser Heterodyne Radiometer ......191 4.1.2 Equivalent Noise Temperature of a Radiometer........193 4.1.3 Sensitivity and Resolution of a Radiometer ...........200 4.1.4 Basic Types of Laser Heterodyne Radiometers ........209 4.2 Characteristics of Laser Heterodyne Radiometers ............213 4.2.1 Sensitivity and Signal-to-Noise Ratio.................213 Contents IX 4.2.2 Resolution........................................217 4.2.3 Applications of Laser Heterodyne Radiometers ........218 4.3 Laser Heterodyne Interferometers..........................220 4.3.1 Introduction ......................................220 4.3.2 InterferenceMethodofMeasuringAngularDimensions of Astrophysical Objects ...........................221 4.3.3 Principle of Operation and Sensitivity of Laser Heterodyne Interferometer..........................226 4.3.4 Phase-Modulation Interferometer....................231 4.3.5 Laser Heterodyne Correlation Interferometer..........235 4.3.6 Some Experimental Results.........................238 References ..................................................240 5 Laser Heterodyne Interferometry and Polarimetry.........243 5.1 Laser Heterodyne Interferometry ..........................245 5.1.1 Precise Position Measurements......................245 5.1.2 Surface Profilometry...............................248 5.1.3 Glass Thickness Measurements......................251 5.2 Heterodyne Polarimetry of Glass Birefringence ..............255 5.2.1 Introduction ......................................255 5.2.2 Principles of the Cross-Polarized Technique...........256 5.2.3 Experimental Results ..............................262 5.3 Kerr Polarimetry ........................................265 5.3.1 Introduction ......................................265 5.3.2 Theoretical Basics of the Magneto-Optical Kerr Effect .......................................268 5.3.3 Experimental Results ..............................273 5.3.4 Laser Heterodyne Kerr Microscopy ..................275 5.4 Surface Polarimetry......................................279 5.4.1 Introduction ......................................279 5.4.2 Principle of Surface Polarimetry.....................280 5.4.3 Principle of Measuring Critical Dimensions ...........282 5.4.4 Experimental Results ..............................287 5.4.5 Measuring Critical Dimensions of Sub-Wavelength Structures........................................290 References ..................................................303 6 Heterodyne Imaging and Beam Steering...................307 6.1 Heterodyne Scanning ....................................307 6.1.1 Introduction ......................................307 6.1.2 Theory of Heterodyne Scanning .....................308 6.1.3 Laser Heterodyne Scanning Microscopy ..............316 6.1.4 Laser Heterodyne Differential Microscopy.............320 6.1.5 Laser Heterodyne Phase-Contrast Microscopy and Super-Resolution ..............................326