Section5ElectronicDistanceMeasurementEssentiallytheinstrumentsmentionedinthischapterconsistofatransmitter,setupatoneendofthelengthtobemeasured,sendingoutacontinuouswave,tothereceiverattheotherend.Thiswave,termedthecarrierwave,isthenmodulatedandthelengthdeterminedasexplainedChoiceofThisisafundamentalprobleminEDMsystems.Theelectromagneticspectrumiscontinuousfromvisiblelightwithfrequenciesoftheorderof1014HZ,correspondingtowavelengthsoftheorderof10-6m,tolongradiowaveswithfrequenciesof104or105Hz,correspondingtowavelengthsoftheorderof104m.TherelationshipbetweenfrequencyandwavelengthisshowninFig1.Itisconvenienttodividetheinstrumentsincurrentuseintothreedistinctcategoriesdependingonthefrequencyofthecarriersignal:lowfrequencyradiosystemswithcarrierfrequenciesoftheorderof105to106Hz(wavelengthsoftheorderof103or102m),microwaveradiosystemswithcarrierfrequenciesoftheorderof1010Hz(wavelengthsoftheorderof10-2m),visibleandinfra-redlightsystemswithcarrierfrequenciesoftheorderof1014Hz(wavelengthsoftheorderof10-6m).Generallyspeakingitisfoundthatthelowerfrequencysignalsprovidegreaterrangebutrequirelargertransmitters,andbeingaffectedbytheatmospherearethereforelessaccurateforEDMpurposesthanthoseofhigherfrequency.However,formarineandairnavigationandformuchhydrographicworklongrangeisvital,accuracyrequirementsarecomparativelylowandpermanentorsemi-permanenttransmittersareappropriate.Allthesefactorspointtotheuseoflowfrequencysignalsandindeedmostposition-fixingsystemsoperateinthelowormediumfrequencyrange.Intheserangeswavelengthsareoftheorderof102or103mandthephasedifferencescanbemeasureddirectlyintermsofthebasicwave.Forpracticalfieldinstrumentsforengineeringandlandsurveyingthehigherfrequenciesaremostusefulastheinstrumentscanbemadesmallandtransportableandthepropagationthroughtheatmosphereismorestable.However,atthesefrequenciesitismoredifficulttomeasurethephasedifferences,asdiscussedlater,andthewavelengthsaresosmallthatitisimpracticaltousedirectlythewavesthemselvesforthemeasurements.ThesolutionadoptedistomodulatethehighfrequencycarrierwithalowerfrequencywaveandtousethemodulatedwaveformeasurementModulationisaprocesswherebycertaincharacteristicsofthecarrierwavearevariedorselectedinaccordancewithanothersignal.Thecarriersignaldoesnothavetobeatapreciselydeterminedfrequencybutitmustbeproducedefficientlyandinsuchaformthatitcanbemodulatedeasily.Themodulationsignal,beingtheoneusedfortheactualmeasurementhastobeatanaccuraycontrolledfrequency.Itisoftenproducedbyacrystal-controlledoscillatorwhichmaybehousedinathermo-statically-controlledoventoenhancethestabilityofthesignal:awarming-uptimeshouldbeallowedforthemostpreciseresults.Someinstrumentsuseanamplitudemodulation,whilstothersuseafrequencymodulation,thedifferencesbeingindicatedinFig.2,butthedifferenceisunimportantfromthepointofviewoftheoperator.Inamplitudemodulationtheamplitudeofthecarrierwaveisvariedaboveandbelowitsunmodulatedvaluebyanamountproportionaltotheamplitudeofthemodulationsignalandthefrequencyofthatsignal.Theamplitudeofthecarrierremainsconstantinfrequencymodulationbutnowitsfrequencyiscontinuouslyvariedbyanamountproportionaltotheinstantaneousamplitudeofthemodulatingsignalandatthefrequencyofthatsignal.PhasedifferenceandTherearetwooptionsavailableintheuseofmicrowavesfordistancemeasurement,eitherpulsetransittimesorphasechangesbeingmeasured.Intheformercasetheunmodulatedcarrierisusuallyapulsetrainorseriesofpulses,notthecontinuouswavereferredtopreviously.Whenresolutionofdistanceto0.01morbetterisrequiredthelattersystemisusuallyadopted,beingbasedontherelationshipbetweenthetransmittedandreceivedsignal.Consideratransmittersendingoutanoscillatingsignalataconstantfrequency,f,toareceivertouchingit.Werethetwotouching,thenthetransmittedsignalandreceivedsignalwouldbeinphase,butasthereceivermovesawayfromthetransmitterthereceivedsignalwilllagbehindthetransmittedsignalduetothetimeoftravelofthatsignal.Thustherewillbeaphasedifferencebetweenthesignals,andifthedifferenceinphasebetweenthesignalsatthetransmitterandthereceiverismeasuredthedistancebetweenthemcanbededuced.Whenthatdistanceisequaltothewavelengththephasedifferencewillbe2πandthesignalswillbeinphase,asinfacttheywillbeeachtimethedistanceapartisanintegralwavelength.Thereforewithinanunknowndistance,d,allthatonemeasurementofphasedifferencewillgiveistheresidualpartofdoverandaboveanintegralnumberofcompletedwavelengths.Itisnotpossibletocompareinstantaneouslythephaseofthesignalsatatransmitteranddistantreceiver.ThereforeEDMsystemsadoptthetechniqueofeitherretransmittingthesignalbacktothetransmitter(microwaves)orreflectingthesignalbacktothetransmitter(electro-optical)andmakingthephasecomparisonthere.ThusitisalwaysadoublepathwhichisThefundamentalequationwhichrelatesslopedistancetophasedelayorphasedifferencemaybewrittenasdn d=doubledistance,i.e.totaltravelofλ=modulationwavelength=n=numberofcompletewavelengthswithinφ=phasedifferencebetweentheoutgoing inga=anadditiveconstantrelatedtogeometricalandelectricalμ=refractivef=Generallynisunknownanddcanbefoundbyrepeatingthemeasurementsofphasedifferenceatfrequenciesdifferingfroma'fine'measuringfrequency.Incertaininstrumentsthisprocessiscarriedoutautomaticallywhereasinotherstheprocessiscarriedoutbytheoperators.InFig3twomodulationfrequenciesareshownwiththephasedelaysthenarisingduetothedistancedoftravel.Thewavelengthsaresuchthatfivegivenbyonefrequencyoccupythesamelengthasfourgivenbytheother(lower)frequency.Thisparticularlength(200m)isalsocoveredbyonewholewavelengthwhosefrequencyisequaltothedifferenceofthetwomodulationfrequencies.Moreoverthedifferenceinphasebetweenthetwoisalwaysequaltothephaseofthewavegivenbythedifferencefrequency.Thus,measuringthetwophasedelaysconsequenttotravellineradoubledistanceupto200misequivalent,onsubtraction,tomeasuringthephasewhichwouldhavebeengivenhadthedifferencefrequencybeenapplied.Aphasedifferenceofπappliestoadistanceof200m,andsoifaphasedifferenceof1.54πbededucedonsubtraction,adoubledistanceof1.54π×200/2πmisinvolved,i.e.154m.Naturallywhenadistanceinexcessof200misbeingmeasured,thisparticulardifferencefrequencygivesanunknownnumberofwholelengthsof200mplusapartlengthof200m.Thusasetoffrequencieshastobeapplied,whichwhenrelatedtothebasic'fine'frequencyallowsstagesofdoubledistancesuchas2000m,20000mand200000mtobeevaluatedwithoutambiguity.Inthemeasurementillustratedthephasedifferencewiththelowerwavelengthwasandsincethiscorrespondsto1.70π×40/2π,i.e.34.0m,thedistancemeasuredmustthereforehavebeen(n×40+34.0)wherenisaninteger.Themeasurementwiththesecondwavelengthwasmadeprimarilytoenablentobeidentified.Thefiguresintheillustrationhavebeenarrangedtobeexact,andsothedistancecalculatedusingthedifferencefrequencyworksoutexactlyas154m,i.e.(3×40+34).Inpracticetheremaybesmallinaccuraciesinthemeasurementsandtheresultfromthedifferencefrequencymaynottallyexactlywiththemeasurement,e.g.ifthephaseinthesecondmeasurementhadbeen0.15πtheresultwouldhavebeen1.55π×200/2π,i.e.155mbutthedistancewasknowntobe(n×40+34.0)andtheresultiscloseenoughtoenablentobeidentifiedas3givingthedistanceas154.0masbefore.ThisisanimportantpointwhichshouldbewellunderstoodasitisthiswhichisthereasonfortheuniqueaccuracyofEDM.Ifthewavelengthiscorrectandtheintegralnumberofwavelengthsiscorrectlyidentifiedthenthemajorpartofthedistanceisdeterminedwithouterror;theonlypartofthedistancewhichismeasuredistheresidualpartoverandaboveanintegralnumberofEffectiveIthasbeenmentionedabovethatthelengthofthedoublepathisalwaysmeasuredbyEDMTomeasureadistanceDwithasignalofwavelengthλandadoubledistanced=2Dwithsignalofwavelength2λgivesanidenticalresultinrespectofbothnumbersofcompletewavelengthsandresidualphasedifference.Insteadofdeterminingtheactualdoubledistancetravelledbythesignalandthendividingitbytwo,itisconvenienttouseaneffectivewavelengthofhalfthetruewavelengthandthencetocalculatethesingledistancedirectly.ByusingeffectivewavelengthsofλA=20mandλE=25mthesamesingledistanceof77mwouldhavebeenInpracticetoachievehighprecisionλAiskeptcomparativelyshort,10mbeingacommonPrecisionisdeterminedalsobytheaccuracyofmeasurementofφ.Someinstrumentsresolvetoonly1%phaseothersto0.1%orPhasemeasurementsmaybeachievedinvariousways,byaresolverwhichconsistsofastatorandrotor,thelatterbeingplacedintoanangularpositionwithrespecttotheformercorrespondingtothephasedifferencebetweenthetransmittedandreturnedsignals,byavariablelightbyadigitalsysteminwhichthetransmittedwavewhenpassingthroughzerovoltageactivatesacounterwhichcountspulsesofaselectedfrequencyuntilstoppedbythereturnedItis mendedthatreferencebemadetoElectromagneticDistanceMeasurement,secondedition(GranadaTechnicalBooks)byC.D.Burnsideformoredetailedinformationonthis