Detection and Signal Processing

Thewritingofthisbookhasbeeninspiredbytheexperienceofteachinga courseonDetectionandSignalProcessingtograduatestudentsoveraperiod ofmanyyears. Itwasstrikingthatstudentswerenotonlyfascinatedbythe variousdetectionprinciplesandtechnicalperformancesofpracticalsystems, butalsobytheprofessionalismoftheinvolved typical physicalengine- ing. Usuallystudentsarethoroughlytaughtindi?erentcoursesofphysics, whicharemostlystudiedasisolated?elds. Thecourseondetectionands- nalprocessingisbasedontypicalresultsthatwereestablishedindi?erent disciplines like optics, solid state physics, thermodynamics, mathematical statistics,Fouriertransforms,andelectroniccircuitry. Theirsimultaneousand interdependentapplicationbroadenstheinsightofmutualrelationsinthev- ious?elds. Forinstancethe?uctuationsofthermalbackgroundradiationcan bederivedeitherwiththeblackbodytheoryorindependentlywithther- dynamicstoarriveatthesameresult. AlsotheappliedFourierrelationsin thefrequencyandtimedomainsarenolongerabstractmathematicalman- ulationsbutpracticaltoolsandprobablyeasiertounderstandintheapplied technique. Estimatesoftheorderofmagnitudeswithcomparisonofrelevant physicale?ectsnecessarybydesigningadeviceareveryinstructive. Ingeneral theachievementsofvariousdisciplinesarebroughttogethertodesignandto evaluatequantitativelythetechnicalperformancesofdetectiontechniques. Thustheinterestfordetectionandsignalprocessingisbothtolearnthe knowledgefordesigningpracticaldetectionsystemsandtogetacquainted withthethinkingofphysicalengineering. The?rstpartofthebookisdevotedtonoisephenomenaandradiation detectors. Fundamentaldescriptionswithquantitativeanalysesoftheund- lyingphysicalprocessesofbothdetectorsandaccompanyingnoiseleadto understandthepotentialswithrespecttosensitivityandoperatingfrequency domain. Thesecondpartdealswithampli?cationproblemsandtherecovery ofrepetitivesignalsburiedinnoise. Thelastpartisdevotedtosolvingthe problemsconnectedwithreachingtheultimatedetectionlimitorquantum limit. Thisisdoneforheterodynedetectionandphotoncounting. Although VIII Preface heterodynedetectionyieldstheultimatesensitivity,itsspatialmodesel- tivityand,ingeneral,thelowspectralpowerdensityofthesignalrequire sophisticatedprovisions. Thisisdiscussedindetail. Theinherentproblemsare analyzedandappropriatetechnicalsolutionsaredescribedtoreachtheul- matesensitivityfordetectingincoherentradiationandcommunicationsignals thatarerandomlyDopplershifted. Theresultsareillustratedwithexamples ofspacecommunication. Hengelo(O),January2006 W. J. Witteman Contents 1 RandomFluctuations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 2 ThermalNoiseofResistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 3 ShotNoise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1. 3. 1 SpectralDistribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 3. 2 Photons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1. 4 FlickerNoise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1. 5 Generation–RecombinationNoise. . . . . . . . . . . . . . . . . . . . . . . . . . 10 1. 6 ThermalRadiationandItsFluctuations. . . . . . . . . . . . . . . . . . . . 13 1. 7 TemperatureFluctuationsofSmallBodies. . . . . . . . . . . . . . . . . . 18 1. 7. 1 AbsorptionandEmissionFluctuations. . . . . . . . . . . . . . . 20 2 Signal–NoiseRelations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2. 1 SignalLimitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2. 2 BackgroundLimitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2. 2. 1 IdealDetection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2. 3 JohnsonNoise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2. 4 DarkCurrentNoise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2. 5 NoiseandSensitivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2. 6 Ampli?erNoiseandMismatching. . . . . . . . . . . . . . . . . . . . . . . . . . 28 3 ThermalDetectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3. 1 ThermocoupleandThermopile. . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3. 2 Bolometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3. 2. 1 MetallicBolometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3. 2. 2 Thermistor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3. 3 PyroelectricDetector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4 VacuumPhotodetectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4. 1 VacuumPhotodiode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4. 2 Photomultiplier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 X Contents 5 SemiconductorPhotodetectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5. 1 Photoconductors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5. 1. 1 AnalysisoftheDetectionProcess. . . . . . . . . . . . . . . . . . . . 64 5. 1. 2 FrequencyResponse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5. 2 Photodiodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5. 2. 1 P–NJunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5. 2. 2 Current–VoltageCharacteristic. . . . . . . . . . . . . . . . . . . . . . 72 5. 2. 3 PhotonExcitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5. 2. 4 OperationalModes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5. 2. 5 OpenCircuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5. 2. 6 CurrentCircuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5. 2. 7 Reverse-BiasedCircuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5. 3 AvalanchePhotodiodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .