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...