Correction of systematic delay errors of an optical delay device

Abstract

A method, a system, and an electronic device for determining systematic delay errors for an optical delay device are disclosed. A time-domain signal of a sample is recorded using a THz time-domain setup utilizing the delay device for adjustment of a delay between a THz signal and a light signal overlapping in a THz receiver, the sample having at least one absorption line in the THz range. An optimization algorithm configured to find a candidate delay error curve by iteratively: generating a candidate delay error curve, reconstructing a time-domain signal by applying the candidate delay error curve to the recorded time-domain signal; calculating a frequency spectrum based on the reconstructed time-domain signal; and determining one or more absorption line features in the calculated frequency spectrum. An objective of the optimization algorithm is to find the candidate delay error curve that results in absorption lines in the frequency spectrum that most resemble true absorption lines. The optimization algorithm finds a delay error curve corresponding to an extremum in an objective function comprising the one or more absorption line features. The determined delay error curve can be used to correct or calibrate for linear and nonlinear systematic delay error of the delay device. Fig. 1 is to be published with the abstract.

Description

[0001]oecanveenaon reevacee.sno aa mrecuaor,, sesnevme,n aonn reeavceesoor s cuocrre ac mne ssemacea errors o an ame-omaneraerz ssem. o, ssem, anevce uzn anme-ozm caronsse-craoerz z ssems, suc as usen zme-oman secrosco z-nvesaeeunrreamaeon secrosco z- ,roves a uuousoons a o an accurac naroeres o maerasneeraerzreuenc rane.e rea samerear oaone a ona ennevro rensmuensas cnonuenocens.n aa vrarceuar o,aecorersc ssuec co ansrnsrumenaon, oemeeaeweene arrva oeenerae z raaon aeeeco an manuaon excaon s crucaor accurae anrecse measureme or an eeecor are useo conro smeaean, renceuconrs aena eeecvroc ns. eora o meos anevces near voce co acuaors, ro nesca suc co ansroneear o screcwa- sravmenea. saes, eea sevces are sueco ranommeer as we as ssemacnear an nonnearea errors. resonsseesm,acseereass e arnrors no cnanneoarr exeamaveourennreoauceevcesneaasreza oon oneren nonnear armoncsoronn voce cos. nezoeecrc crsas, or eaers aoner e a. “nereromer-aeeraerzme-oman secrosco,” .xress, ecrosco,”ecamrornascsev, e a “orrecoens ocrecraor aera arnoeacrerosrsorn aeevraaenrzemae- eroromrsann rozvmee v-eromarenc sses meemassuremncenusn o ane onercearomeeaern or aen s osecma ennceoeenr.ese aroacesoeeaevce an uso nonvoveeermnn anea er en o errorsneren aroaces aresavanaeous sncenroucon o a rors oeeaevce.enereromeer or an oca encoerne s onansrumenaon suc as anow comex anow cos. sem ma noeesraenerms o rousness, sze, noswenm aascorneaorneneas o errrors u mazn as aonnee crorerreecnecea aernnrnom a msuoreon reneecsone z snao use, see e.. , , oraa e a “n eaon-ase meoorreuencns c oae zeraerzme-oman secro raon o aroac meers z ,” .omm. , - .ese corresonesnroov aen aeaere cormmnraesosno on o srs seremcacnn oearee reaco errreorsm oe-eomeaan senvace., occoeranev,ceesr.es a neeorevces an meosor correcn ssemac nonnearea errors rec moerno aormee-erommnann s aneaa o e arr soarm cureve usonr a aeazmevec-eomsansc soesue. uzen meeoe coamresesor ausmen o aeaeween a z sna an vce samea a sna overann a z recever,e sa vn aeas one asoronne, or arue ornown asoron secrum measure one ommaen saesu a aenasor one asoronne,e asoronnesn wn aanw oe zme- eneran a cana weena a r earnrore cur,veozrez.e meo comrsese ses o oman sna a n e canaeea erreora curveevcoeeeneran a reconsruceme- cacuan areuenc secrum oe reconsruceme-oma rencoreme-oman sna more asoronneeauresne cacuaereuenc secrum sna an eermnn one or eermnaon o curve-narameers.e meo comrses re, seuac as curve n an mes usn eren canaeea error curvesn conuncon w an on smezason - a mue conureon a canaeea error curve corresonno an exremumn an oeocrmuncon comrsn e one or more asoronneeaures. ve a vea oueencvceauvnec oo,n a m reasemeaesne or seeceoe a measure o, suc asouan or ouu an corresonneaures nceeweene one or moreeermne asoronneeaures reera corresonsoe oeeerm aneeas one asoronne oe same.e exremum asoronneeaures - mos resemes a a csooronneeaurea – amon eeermnen anown asoron secrum oe same.rresonneaure oe aeas one asoronne marove a scaar vaueauanave rene an aernaveormuaon,e oecveunconeaureseermnerome reconsrucere cs a smar eween one or more secraeaures o an asoronne oe same.eue snmc-oman sna an corresonnnown resua errorrom aaramerc, aevaonro ar mae exresse,or exame, as a nee or sarness, or a comnaon oesm anown asoronreuenc, a mercase on ea error curveaes an exremum o se o.ecev oemzaon aormenes a canae a mos accurae reroucesenown secra caracuenrcsocns, o correes saomnne.oe canae oueu meno a ma senaer aormez urasnnsm aer ozmcae-o cmouane seu comrsn a sourceor e zransmer c oe source va ars ocaa, oca coueooenure souorc eem va a a sezc sna wen exce e sna a z recever recevee z snarome zransmoenr a on ccoanaur,e z receverenosoneo eneran an eecrceecon snaas a resu o anneeraocoenece receve z sna sna a same saceosoneore z sna receve eweezn receeverzo snaass an e sronua ane seamze s sancae re acneveeeaeevzce re sceev uer.or ausmen o aeaeweene omaznm seeu-o amnan an s eseecmrosncsceovscee c.omersnz am me-emomoran c srcuserm, a comrocressessor ce zme-nerace, werene eecroncevces conure rcur, an an oman sna recore e z rec o conroeeaevce receve ame- meooreermnn aea error cuervveero arn aeeaermenvece a.ea error curve usn escose cnrc euerc,ro annc anevnceersaces,c woseere.nee e eeeccrroonncceevvccee csomrses a memor crcur, arocessor meooreermnn aea error curveor aeaev ccoen.ureoerormescose on comuer reaae sorae meumsscose.e c ee e oerc mroornecroevracmeso coemrorrmsnenssruccosoens, m weco woreonm e eexu ree mcur r neeaa n a ae en s a eoer eca rroen mceeuvmce s coarunse evce. ror curveor aea cusreve oo ar aeaea erroerv ccuervesorsc aoseea.eevc uesee coemrmrnsees usne meeeoao errroere crumrvneno r aecoea error suc as aus, correc, or carae, ame-oman sna recore usn eeaevce.nsruc, nesa arn s asveamnaace oeae errroersse on asecoasureevcae c aaneae eerreorrm cunreve.a cacesnear as we as non- oses an no a rveanuaree a ooenare csoemnonsecnossuore aazem me-eoomanor seeuer.mnn eea error curve ese arn a as avanosa-ero ocesesnre sseen orscno resauremea.e meo cane useo carae aeaevce oeo aseov se aen oneer aeraurese anoo awvnanaeease oeescrreseonn os ecxoasmuree wsereecoom we re raeere aaren e aacerawns,n wc: nceo .s aow-carusran an exemar meo accornoescosure. sc.ossur ae.aramusran an exemar zme-oman seu an ssem accornos s.- are carsusran smuae an exermena resus reaeoescose meo. warous exemar emomens aneas areescreerenaer, w reerenceoeures emeno remeevnans.. sou e noe aeures are onneneoacaeeescron oe one scoe oee are nonene as an exausveescron oescosure or as amaon or avanaes sownscosure.n a on, anusrae emomen nees noave a e asecs emomens no ne.cesns aasec or an avanaeescren conuncon w aarcuar emomens even no sorusmraee,o ora no em soo exmecn anes ccarnee.raccen an oerx,s u,n z…ers anooora a a m ‘cuarvee’m, aa ‘scanaun’,c anon ae ‘seencerunm o’ mna onee or re morreese vnareaes a se oaaonss asoe caseoreea error curve,eme-oman sna, an ereuenc or saeracmruemerse.rens. ea.se avceow a-cccoarrnusoraen ascno esxuerme.ar meo oreermnn aea error curveor aneenaeeovcraeves. aeev aceuosrm aenussn acna o rceaaevneo a on a oacaaa an oca snaraves ors eres an exac reaoneween ocaaen anraveme,evenn o aen soeer ocaa. e reevan mea an e scaen oe ocaa e o n aen x w an amoun . eeaevce ausse oca ea .n one or more e x,s ausmenas a one-o-one corresonence w aemoraransaon sae, so smomens,eeaevce comrses one or more o are srecer, eecrcea un. aeeane, roan scea sae, voce coeaevce,ezo- enevaronmeveces are sueco ssemacea errors, an ese w var overmeueo wear an secrum onae conuseo,n ws.cs caenmaeac eorro arnmnesenaressoernsce oe c noarrrreoswo ansonrroenueeanucres. cureve oeac cvaen oene mee usoeo cosrro usee recoreme-oman snaoeermne aea error meo comrses recornec o ar commeensaeor ssemac errorsneeaevce.e eren canaeea error curvesa are- usoemaon sna o a same an consrucn carae,e recoreme-oman sna.reu reconsruc , suc as aus, correc, or reconsruceme-oman snas, an w e seanmce s,e.ec.r aa are oane rome comrsn one or more asoronnes, asoronneen asoron secrum oe same,reuenc secrum corresonno eac canaeeaa eurrreosr c areeermne ne aorms useon e canaeea error curveau rervseu.snen,e an ca ocmsaon secrum w asoronnes mos resemnrue asoronnesnerms oeuaeereuenc asoronneeaures.ere,eerm “rue asoronnes”s useo reero aso ermne nown asoron secrum oe same recore usn a carae ssem.e “rruonnesn a nes” mae caracerze caeaures o ca asoronnes suc aser se aaseo orron cnoonwnureaures o secc asoronnes oe same.reera,e omzaon aormsuncone coon a canaeea error curve corresonno an exremumn an oecve eermnem arssornoe asoronneeaures.e exremumreera corresonsoe asoronne oen saneeaurea mos resemes a corresonneaure oe aeas one , , an mmue.eumnnens.ee onmeseaso cna anormnvoveserormn e ses , mae seece or usen correcnme-oman snaaes reecaor eerror curveeeaaseeevnceo.un, sn onnae o or a m soarme exee umsnar a emzommee-nosm,e meo comrses recorn ame-oman e an seu uzn eeaevceor ausmen o aea sucwe aesn arevz sna an a sna overann a z recever.s arecae a anown,eas on ous recore or sanar reerence, asoron secrum oe same sou ave a , ze asozr.oenconre wn on amea-nomwa oe zme-oman seu anor wn a ranes roune erormene ar o zmne- somnaasn usn zme-oman seuss we-nown annrouconoeraerzmeoman secrosco ecznues, see e..eu e a. “uora:n ,o:. . .an eren-ns”ourna o e scs , ex rumenaon coces an seu-varaons ans a,uz a recaevveeren caosmsm coonm.onens comrsn a source, aeaevce, a zransmer, ewmeee-no amanz s snnaa o an a az s snan caan oveer warenn ans, wereesnaesemoraea e snae a z recever an esnaes amue o searae seesce correseonzn recever aea.e measureons one-axs are or sameme-oman snas coae re sraea resouonx oeeaevce.us, a recore amue o an snaeece e z rseecneever a a seea o.ones sa,c sn, wew sesnan mae consan.e. anx are consan soa-vaues are eusan ore seen sameon sacn ma var overe recore ra ameon resecv ne soa anx areuncons anxx,ransorme an.ns werreenuencoman,eme-oman sna s reresene sourer secrum’n .a an asv,u wsraeree vesnaesereuenc.e curves w een ‘rue oman, resecve. an exemar zuseneme-oman an ereuenc cnur ovnees o cro mmorrese esx:emear emomens,e consrucon o eren canaeea error resence o ssemancermanereco a canaeea error curveoreeaevce.ne recore uzn eevce wnvnosven a aeeaaevce, everon,s on ame-oman sna s, w s reresenn e errorneea e orror sorea.eea error curve caneven recore or same uzn eeaevce weuse caonaenvces,o urea. me-oman sna msae wren as = s or euvaen as a se oaaonnsnowsn,,se.an er orore sc an e meosoesermntreue or esmaesea error soreeaevce soaeruevem oe- cuorman snatruecane oanerome recoreme-oman snas. ‘canae’ea error muvees a coenresnru ccaen vearseso.n oeuncon s, an e omsaon aormnvoves consrucn cnom oners oers moerene erxaemnar em a roecomnesnrusc, reeco -n ssurucn e recoreme-oman sna om c as an ause, carae or correce -me- canana seneaareceor,ro surc c as a se o reconsruceme – snaars s, s, a n e emomens, a nurvee coanea reecoreea eme-oman snas.n one or more exemarneroan e reconsruce se oaaonrror curveoe recoreme-oman sna comrses oman sna w eusanea vaues.ss mas c,o sm arnseo coenerae a reconsruceme- e correceme-snaarss, s an consrucn a newunsserucn a onnmeeroaor rom aesreea vaues .,or exame,e recoreme-srecnoaars,-s s wnaerarsreco, wrec ao non-consan sameonrec soacn , maereerre aeneroaor see recore s sameon sacnne reconsruce sna. esoee cna ocnuea orn more ex aemreauren ecm soecmreunms,a osean onne reco corresonnreuenc secra comrses:reuencoman,eme-oman sna cane rerenssernuceemse-ooumraern sna.ne wren asv, were vesnaesereuenc, or euvaen a se oreuenracns –o mrma ans arsmve,nev.n mucanra wnasos.rmaonseweene nueme me anreuencomans are roune an maene on caec our maoerer eexeumencar s eemcroumm ceons,eermnn one or more asoronneeauresn s mrsesuanneaures oe cacuaereuenc reseecmrume,r wuec a cane useoescreow we asoronnesne cacuae secrumne secrumsaor maonnee cs.arrue asoronnesn areuenc secrum are ca sar s sae.eenn one canaaceerezae erroreauures suc aseroson,ernee, an er mae more oressromnen, an eeauresnucaonn, asoronnesne cacuae secrumreuenc secruma conans ors execeo conaen onaese or m onor see acosonrs oonen ceas.cuae e sarness o an asoronnes auanae caracersc, anosse aso seaaueresunacnuees sourc exa amsue oreane w-e a,ae re msaoxnamnucmereuenc,,e seeness oroenn,e orne exemar emomens,eermn .n one or morereuenc secrum comrseseenrmnn, one or more asoronneeauresne cacuae ne-e o an asoronne, anne saneeua cnacueaereuenc secrum, one or more o a an asoronne.oowsae oecveuncon ose om,saon a, reosronamncereuenc o eeermne asoronneeauresa one wanso use as a measureore s aousor comrse resemanceo arue asoronne.n one or more exemar emomens,e oecveounnes seeceo measure, suc asouan, a resemanceeweeneeermne asoronncneon eaeures an corresonneaures oe aeas one asoronnen an asoron secrum o – am saome.ere,e exremumreera corresonsoeeermne asoronneeaurea samen aseoreoenrmnnee. asoronneeaures - mos resemes a corresonneaure oenu oannea orv meore ex exreemsseasr eem aoreemmeenns,eewe oene ocnvee oru mncoroeneseremnnee so oeucrau aea scuareasr, v sauea ne-e, resonancereuenc, oru w uc aseaure aa maxmum , an corresonnnown ase osn o,o arn e axasoronne oe same.e seccormuaon oe oecveuncon mae measuresa camre, asoue or reaveevaons, curve-n resuas, or oer sasca vaue.e omzacerzee coseness oe measure secraeaureosnown reerence secraeauresaeon a aormenes a canaeea error curveor wc e reconsruce enown same carac vearsuec os.e oecveuncon corresonnoe es areemen w avanae ceaocuusaoereeuenc secrumen reresene as a se oaaarsv,v, mae asoronneeaures s.e ous,ana onars a maemacaunconoacaeeeermnaon o more asoronneeauresnee ca ocru maoree exemar emomens,eermnn one or ars secon oe cacuaereuenc secrruemu,enec secrum comrses n a curveo e same, aneermnn one or more asoronnersea suecon comrsn an asoronne oo a se oaaonarss a roune oeraon an numerousre wsromee curve. n a curve a e, anow we ee curve ‘s’eaa can asoeuean-noew.nn a onreoa ocr mes mae emomens,eermnn one or more asoronneeauresromee curve core exemar eermnn a a-auraame-earrnameee or oeceve cuurnv omrses eermneu ec-on a.roun e asoronne an usn e ann one or m moure exeemmeasr us emnomereenns c,ane maeo comrses reean ses , , omza eea error curvesn conuncon w e omzaoonn a aoorrmm coon oumrezeo eeermne asoronneeaures, suc as w e exremumn an oecveuncon comnrsn ae canaeea error curve corresonno an wors,e omzaon aorms useon re ocnoen osrr more asoronneeaures.n oer reconsruceea – snaars s, s,a omuczeesmee a-soomranon snneae oar se o mac exece asoronneeaures. ures, suc aso saoruous eex naomees aaneeausre asre maes ocrr mea neorenearear, w reerenceoeures wen reevan. srucures oruncons are reresene e reerencewno scae an a eemens o smar asoe noe aeures are onneneoaca neumeeraesscrrouono ouee eures. sou nonene as an exausveescron oescosure or as amaon onexa smcoes.e are scosure.n a on, anusrae exame nees noave a e asecs or avanaee os soewn. mn aeseoc oar a enx aamvane aane caenscreeracn ccoenunnc anon o wer a exaamrceusar ev eexames no necessar so exc escre. n no sousrae, or no uneersuarnesn are secesmcaoscu aren, w sme oeeor car, an e mere soweas wc a numeras are useorenca or corresroenansaavres.eene ou.rouou,e same reerencene –oown,u msoraree exenma.r a ermeoscmusesnes. reaeoe overa meo as we ase ses ecorn ame-oman sna o a same nco.roara sesow as avnen ex semsemara scmeuaae errome-oman snaeen ‘ameuse’a e ssemacea error rn comarsono a smuaeme-oman sna wou snaeen ‘re sreceer’en rec ‘orruee uussne’. ae.aae svcoewsa avnn ex seumsaarn raec sorseemamce-eoaman erarvornn v ceorm smaraso snuos aanmae- sosmeamna scnaeae eerrnor. ‘near sae’ recore usn aeaevce an onze omr me-oroem eaxenm seaur emusorameenns, a.me a-nom coamn srsnna: o a sames recore uzn - - a a sourceor ouun a ranszransmer oca coue sonae source va ars ocaa ,e z - a zm reecer cvoenr ourecao e cmo a z sna wen mouae e sna receverenosoneo rueceeoe source va a secon ocaa ,e z eec receve z sna veenee z sna rome zransmer an conureo neraconeweene z sn ran an eecrceecon snaas a resu o an - a sea smame sace osoneorae anz sena s rencaeve e z receveroassrou - reeceveeaee svca eece s a zen re ucevoerr. anusme,n oe aeaeaeveceweesnoesone snna an e z sna u m as weeosoneners ocaa orno. secon ocaa , aneennazsransmer an recever cane,us nomeo,ooconucveeraerz see c.omneos eexem o maarneesre anaerso oom sexmerc wonu ac soerm acnon au mceora scru acnuerennawcc maan or oe anenna.ere,e oca sna excese semconucor we a oweoe anennaoesoreransmer ore currenenera voaeass a e recever. er a cae z recevers a ene anennas measureore are eua a caene seu. neecors exs, an new ones maeeveoe a oseone sneawese sneno seourrs an secon ocaas an , ca aeam s er emomens,eeaevcec mea a cnomreseaevce.n one or more exemarmrovee rane an e resouon o e a comnaon o searaeeaevces servno eeaevce ma comrse a com enuceea.n one or more exemar emomens, an secon ocaas an .naon o searaeeaevcesosonen eac oers aerozme-oman seu reresenseasc seuor recornme-oman snas. eren e..aoceers e u a,znwoeecraenes oe soraurceersz a cnross-cor srenaaosn a sree wceroscnoown,oee sescesrsoenv,e swese , :. . . nne onrea oer m coorme eomneonsmeanses, o onne m oar muroere ceoemcoomne wnaser o-ecenoozm.e-oroemnaen seu are ma ere e comnen aooncnerae crcu aown a smaerra aen c momonens seu.or exame,e source,eeaevce, an e zransmer ano rreec rous maememene as csacaenore-coue moues. evereaeu sraemnee sacze ranos a same wose asoron secrumas aeas one narrow asoron aaseous same e oe zme-oman seu.n one or more emomens,e sames ma sm ee s suacce ase awmeoesneerc azr croamnsmrsenr w aaner r veaceovr,ern w.c casee same sace com rresenrenceeoz.me,-oemanz semue-om anan a sne euecro mnaceear o a zme-oman ssem , arocessor crcur , an annerace, wer vce comrsn a memor crcur conroeeaevce an receve ame-oman sennae re eceocrreoncevecez resc ceovneru.reo aneneer eaecceronc maevcreoveea caon conunreecoon csonor aoeaesseoe reecoaevce an e z recever sna.ore eecroncevce o auonomous recor an ora an oanemeomannerace ma asoroveaa conneconoe source.nemeoman sna,e oeer eaeocnroncevce s conureoerorm an oescose meos or meo ses oroc rousn.ee oeraons oe eecroncevce mae emoeneorm o execuae c se..,nes o coe, sowarerorams, ec.a are sore on a non-ransor cormcuurer re.aae meume..,e memor crcur an are execue erocessor eu eercmreornm ecore mee, nvecee oe n sosra w coo anns o re,u suree co e un ce cacrrron on oauc.ev msc aoe, a w m s wea eee e ce c aso rcn rrs eeere ouu vn ac m aoenesc ao ane oaearraeons ma rmware, or some comnaon oarware,rmware anor soware. ware or remeo mvaemeor me crcuumr, a vo maae mee omnoer or co mmoreon oen a, au neorn,- avoaase m meemmoorr c coommoonneen, aarrve, a suaeevces.n a ca arranemen,e memor crcur mancue a nonn, or oer comonenoronermaa sorae an a voae memor comonenau -voae memor memororerocessor crcur .e memor crcur ma excanencons as ssem rocessor crcur over aaaus.onrones an an aressuseweenaae w me c.rcur ,erocessor crcur an enerace maeresenu are no semowonrn . eneran a canaeea error curveoreeaevce ne ovncee o cro mmorrese esxemrovarn em aomens,eneran a canaeea error curveoreea ^^ar aramerzaon o aea error curve s^^ ^^1, ... , ^^^^arameerse reeamoeers ^^, ... , ^^suc as aonoma oeree ^^ −.nese emomens, canane oe sae error cur eneran a new se oarameers aneneran a new enerae se oar verome se oarameers as a reazaon oearamerzaon.euncon ameers, or aeasar oearameers, are use as varaes oe oecvene a.enn exxe.mar emomen oeneran a canaeea error curvesescrenea meonreer raannom a neawra smee oersa arnamoereresneorra eanc o rneee or moonre o saerameers maas comrseeneran o ceurv o ne or asoronneeaureseermneor arevous canaeea error en.e one or more eenrearanne as c oaneaaeeevcaes e mrroar cuarvvee, seuac e arsro arn cunrvaes c oan a ceareane saa eerro orr courm, an rovn aea error curvearamerzaonavn a sae or maem rve, ma comrse w aeaevce eo wc eeaevceeons..c soawsc aan e exressons assocae ea error curveor a er srecereaevce. xemareermne econsrucn me-oman sna. weconnsreu rcanone o o a amsec-reoema sen s onnaow conmmres-ess cnaacuaaano nnesw.aecrson osrumce-osnaaaons ,us nomeo,neroaonecnues suc asonomaneroaon,n maaeeerormeneroaon, sneneroaon, or raonaunconneroaon. r-annon cunrv eexesmeasrcr eemonmeean on reeco anseruncxn. ame-oman sna usn e canaeea error ann reuenc secrarom reconsruceme-oman snas annreuenc secraromme-oman snas comrsesransormn eme-snaaaeocnnsnueos suecre asuenocureromraanns.orms,ranscsroeremaoounre mraranesoerrmorme, o,ruass noouremreranos,orm e s.nae'srreocueessnce cosmaonrsen os.reuenc-secraens aaons, aownore anass o snn eaxemseasrcr emeonmeean on oea annen axr.euenc secrumrom a reconsruceme-oman n a curveo secon oreuenc secrum comnr ase csu crveooos an se ac soenc oro ascroecue mnoce secrum conssn oreuenc-secra amuears measurn e smar eweene meaore asoronneeaure an omzn auncon smar eweene measure an e msuore an e moeereuenc-amuears.e oecveuncon,n an exemar emomeereuenc-amuearssuane usn e suare error, mean asoue error or meane rena avne e errrororr.uncon suc as,u nomeo, mean ens ecxremeanre emaonmeen a oe cnurxv.e-no easeeeermnaon o asoronneeauress eermne asoronneeaures reeue snacm seecarsumwo m oar m coorme arsseorwoo onr mneosren aseorozn rannees, o ane seu,ene cacuae eermneor eac asoronne an en comne.enc asoronneeaures mae emomens, e sameaswo or more asoronnee,n one or more exemar asoronneeaures comrses reean eeermnns on oe z rane,eermnnorwo or more secons oereuenc sec ne or more asoronneeaures comnn eeermne one or m rum, eac secon comrsn an asoronne, an comnee a assoorro ore asoronneeauresrom eac semenno one or more comn onnnneeeeaauurreess,. an werene oecveuncon comrsese one or more sne ecxreummsare esmcroemnene oaenerme annen asxo.ronneeauresrom a cacuaereuenc exxerceumeumn a on omescavoenu ancoron cmomornsn a cane asaoereoan enrerorea cuurrvees. corresonno an vemnzraooenm a.oremosa a ore a an c oassm oza aoonr amosa are useon eesosse souono a maxmzes aven oecveuncon suc asrmson e oma souona mnmzes or an omsaon aorm uses an erroruncon.ne searcor an oma souon, e omzaonn numer , suc as comrses, an oecveunconauaneseoa o arameer or varaenccaerms avn aeenenc, suc aseneenen on, a oecveuncon caneaesven oeoeua ae omsaon aorm seeso omse.eo an exremum,neco ave an aeraca enae vaue, suc as corresonn mos oma souon.non,ervave, sn, ec., seeceoencave oe omse or cnurveresenscosure,e omzaon aorms conureoen a canaeea error we asaoreons, wen a eoe recoreme-oman sna, areuenc-oman secrum nown asor neeauresa mos reseme or mac corresonneaures o aeas one aorms cononunreeno an asoron secrum oe same.n oer wors,e omzaonreuenc secrumas anso oreermnee canaeea error curve wose cacuaeeaures oe same asorroonnnneeauresa reseme corresonn asoronne mac comun aarameer or ae mseasuer mos.e oecveuncon servesouan s areemeneweeneeermne asorone,neceaa a scaar vaue,uann eeree o e, orne w , an corresonn reeren ures, suc as resonancereuenc,ne eeermne asoronneeaures as ce vaues.narcuar,e oecveuncon maae reerence vaues,or exame usn nu varaes an evauae aevaonromenown aorm seeso mnmze or maxm a suare-error or oersance merc.e omzaon en aarameerze canaeeaze erreo orecveuncon,eenn onsormuaon,o suc an omzaonroceuresroven cuerv aeeanxese coses mac.n exame o coomrresereseenscosure,oowsae oecveuncon oe omsaon aorm sou eermne aseoermne asoronneeauresa one wanso use as a measureore exame,e oercovneune resemanceoe aeas one asoronne oe same.or ence,e oecveuncon cou useeeermne asoronneeaures asnu varaes. eermne asor nconsreera a measure o a resemanceeweene one or more e same.n ononneeaures an corresonneaures oe aeas one asoronne o omzaon aore omr m soer mee exemar emomens,e omzaon aorms aoca oroa e oecveuncon cornsnone a as coarnoaneneeeaa eurrreosr. curve corresonno an exremumneaarnnn meroenes o.nm oznae oorn m aoroer exemms eaxrs, emncounme ons,mzea oonm azaoronm as ren on macne erarameer omzaon, w erara orms aea meers reaeoeeermne asoronne araures.n one or more emomens,e omzaon mnmzes aossunconeenn on mnmmuemer os ^^1,e ..o.ss , ^^u^^nrcomon asa arsasmocearzee w can a caaneeaae eerraor c eurrrovre c sur^v^e ^^1,r .o.u. , ^^^^.e .. , ^^, an aea error curveoreeaevce caneeermne. arameers ^^1, .nn eex^^ aemnare e ameonmxe.n o an omzaon aorm an ememenaonereosescre cnan onea ore moerea e emrroor cmurevnes c,orrees moenono a rnes euxrsemnumene aner omneacovne ourn sceeocn coonmrsn oee aessoronneeaures.xermensemonsran e meo aseen carre ou an are sreccreerneane aenx.ne exermens, ame-oman snas recore usn are a zmee-aomevcenownoave a susana ssemacea error.e recorns mae w me-oman seaun se suow snonwnn. , wc comrsese comonensescreore zeen ‘re srecer’.e corres.onen recreorueencm se-ecomruamns s cnaacusa seow annn sow.nna w. . as a c-onurao, annoeaerremae- soameann sownnaos raevceo orne a w smae s sasmeme zme-oman seuu usn morerecse an accuraeanere srecer.e recore acea error, an wcsus corresonnreuenc secrum are sownn s.a an ,mee-eonma ‘nn sena an eme-oman snasromere srecer annear saen .a aaera srsaoe o’.n eou e,s aarenrom . ae conseuenc vae a w esnereuenc secra areramac, an soreuceer.oceuorove a meannunerreaon oereuenc secrumromere excerom sasacaoucuaeaon usn sesm wmerenerromec m,eaesuuresmeesn an nosee.r secra sou eenca esnnerane meo can accaoerneao erreor csucrvoessureo,r ane orme szareocn aerora amres eexecue reconsruceme-oman snas a n e canaeea error cnur uvseesooenerae oman sna recore usn ere srecer.orresonnreuenc secra are c eme- ase one reconsruceme-oman snas, an asoroneauresne caaccuuaaereuenc secra areuane.e ses oe o e suc mzaon aorm are reeae muemes, sua asree or moremes, un an exremumne oecveuncons oane accorno a reeeer smonn creron.n one or more emomens, son creron cane wen a arameerse numer oeraonss reace anor wene canene oecveuncon ore son creerowneen successveeraonsaseow areeermne reso. er suae sna. caneormuaeeenn on e..erecsonne recorn oe recore oe.ccve suowse resun “es” canaeea error curve corresonno an exremumn an a,enecnon ‘ ceocmorsn e asoronneeaures aseermne e omzaon aorm. ea error curveromnscrucoe’e, sowseme-oman snas oane a n e canae seen, a muceer correson me-oman sna recore usn ere srecer.s cane oane.e secrum corresoennce w eme-oman sna recore usn enear saes avn amos exac corresonencenooe reconsrucemeoman snas sownn . , cane useoeermneea error curvee secrumromenear sae.ence,e meo eaevce suc as are srecer. corresonno an unnown ssemac errorrom a eecn ees canaeea error curve nun ocneon or a mcroorses e am raonem oen csa,n exeacueneae e orrorm cuzaon aorm comrses evauan e oecve an exremum oe oecveuncon. s exremurvmes co an enn enuarameersae or mos oma maceweeneeermne asorornresneoneaso orsncave oe omseeaures oe same.ne meo accornoescosure, eures an enown reerence eermnerom a cacuae areuenc secrum wc cacuaeacro asoronneeaures oman sna wcs aaneneraerom a canaeea error curmve a reconsruceme-eaureeermnerome exremumne oecveuncon correson.us,e asoronne canaeea error curve amon a eenerae canaeea errors cuorv a mos oma snce eac canaeea error curve cane useoeermne a reco es.n oer wors, an a corresonnreuenc-oman secrum,e canaeea ensruceme-oman sna asoronneeaures mos conssen w e reerence vaue rror curvearoucese us,e exremum oe oecveunconeermnese canssa seece ase oma souon. comensaesore nonnearea errornrouce eeaevecee.a error curveaes eavan erreermne ees canaeea error curveor aveneaevce,eeermne veneoar cuerve mae seece or usen correcnme-oman snas recore usn e curveor vceore ssemacea errors oeeaevce.ence,e use o aea error emome anse raeaeevceereeoermo rneec e meo asescren reaono . an an scose.n one or more emomoensruc ame-oman sna recore usn eeaevces reconsrucon erormeurnns, suc reconsruconserormene same wa ase enerae ame-oman sna , suce a esx aec sueo on oe omzaon aorm, suc aso a n e canaeea errroecrocurveoe recor reeconsruceme – snaars s, s, exemar emomens, a n e canaeea errmore c-uorvman snas.n one or more comrsesneroan e reconsruce se oaaonsse, so ae recoreme-oman sna me-oman sna w e same eusanea vaues. s ma conmoenerae a reconsruceneroaor rome correceme-snaarss, s an consrucrsne c ao nnsrucn an even saceme-snaars ewusereco o enaons reco, s . mem reco usee anovee meescro.ones moecusoe m onaee m uezo an e zme-oman seu anor ssemoown. e ormemenen eren was asscosene .z,mee-ozmamne- sosmeamn ss coenmure comoresreosrmee mzemoe-omasn sescuose. reerenceo evce conureo conroeeaevce, receve ame-oman sna a rencoe eecronc recever, aneermne aea error curve usn e meo escren rearoeno .e.nz o seneu or m, sourec em asoo cmonenros,ee eec sroounrcceev,coe auonso cmonousureeeorm connero aeea ezrromr ceu-rvoem uan e meo an an emomens reae ereo. sn eavan erroere crumrvneeo a cna sreaeeceuureemeea- error curve,e eecroncevce ma usee seece one or more emomens,e eec oman snas recore usn eeaevce.ence,n same aneneran a recon roncevces conureo recor ame-oman sna o a curveoe recoreme-omsarnuc senam.e-oman sna a n eeermneea error n a esecersocnrceevnce reao conmorsn. as mesmcoorse c,rc wuerren, ae eroeccersosnorc crecvucers c,o annu arnenoerace ae croomrmueer r meaeaoe sor aasee msceruem sno rrenao onneo or m.ore anro arnam esmsosmceonses r,eaee onee orre moo.reso, ereorams comrsnnsrucons, wc wen execue an eecroncevce causee emcoronmcenesv rceeaeoeerreoor.me meo asescren reaono . an an em sooumee noe a an reerence snso nom e scoe oe cams,ae exemar severa "mneasn ms"a, "unesm" ore "meevncees" a meaasen rearresen meeans oe soamearewma ore aanrw soarew.are, an a enee vraarous exemar meos,evces, noes, an ssemsescreeren areescrene comue cronroexr o meo ses orrocesses, wc maememenen one asec a execuaensraumrouc, emoen a comuer-reaae meum,ncun comuer- com cons, suc asroram coe, execue comuersn newore envronmens. u nouemr-reeaao,ee maeunm maemnocrue rem,ovaaneo amn ncocens-rsemovae soraeevcesncun, a versaescs , emor , comacscs s, oecs, comone ec.enera,roram crcures mancue rounes,rorams, aa es.omns,aa srucures, ec.aerorm seceass ormemen secc asrac re uer-execuaensrucons, assocaeaa srucures, anroram crcures arresen exames ororam coeor execun ses oe meosscoseeren.e examcuaers s oe cuoerrnecse oon sunc a ecxescuorameenmseruncnonse oru anscsoocnaseescarae srunc suurecs r seeress oernsrocesses. amoue caeamueressacvoesureee,n a snow wn ane meascer oev,ou wsoeo usnee srsoeonae are aare v naoronuse cnaeneos snec mocaocnaons mae mae wouearnrome scoe oe came scosure.e sense. anrawns are, accorn,oe rearen anusrave raeran resrcve enx moereoeowane secsecnrconascrormou an,a anneea secenesccraer reanoescosure. roves a aarom smuaon an ex on o an exemar emomen, as we as ma noee ermens.s arecae aeanuae anerms a eeren connecons ann rceaaoonse aaren cueaareo anee srmes aerseon.ne aoveescron, an ae semacea error eneeraoera o mze raoaso ann aeevceese acroer u asneoe coenerocoremeeas12eweene arrva oe saes,n1e–3a,r e vaocce m ceoo acuaeorrsn, ro wan res reececoorse aan a r ec anecva er,o rnon ecsancu ou coonnn ,roneea or sccreaw s-armvenea rousness an cosn a onoe es oea unn see, accurac, cnoerrsecnee aznrenue ancsor ranone4n oersn uesnz sen e narro erors. ereenc ceaer a aac s ees rnrsem eca n wacenre vaar eorurro ar csaonreon reecons oe zuse wn a -recson oca cav suc a erae mue waer5, correcn nonnear errorss morenrcae. s a ressv scon rvenocures ounenncves oaeneaow m-reecuaenncsm s.sowem-raecu eernrcors s ocsceumrranc a err aonr, ceorese coorreseunamena ea errors wosearesreuenc comonensneow z rane, canenrouocenno ..nearsaon oneren nonnear re aeao snaoesears neon onnearezeoeaevcorucr, cs sruson cas ase s,s w,cneren suerromseressn .armoncsoronn vocea cores,u wencc osee orre srecers, or mues oeunamen neuner sanoan. oreuenc comonens aneer ess no exausve, an eacmemenaon o aea un reuresnvua anass. eoreca conseraons oenveeosreacae meo eeecre ose snesemn6a.cnowe-rreesuencea error, we w coseoow an exan on reaeoerue sna ence o ssemac error,e same sna!s were ^"^^^ ^^*^^ ^^^^-ven σ cane an connuousea^^^^∞ ^^ ^ senaon^^^#^^^^^^^ wosereuencoman rere^!νsven sourerransorm ^^^^waere νsereuenc. n ^^^^^^^^^^^^^^ ^^^^ ^^^^wswnseere omwas ecneerrom ,ra aσna nor enun reonreeeassoaeoureenreseroens ree creosseenanoenrvaven,, were ^^semeoman^^^^ ^^ ^^were ν = n se eourerransorm σ^^'ν oreueencourer exansons2ven ^ ^^^ ^^ ^^^^weereeaνunscoenracea . ., aroxmaonor a snmaru enrrcoarsn,veesaor seres ae seconerm, wcs a reasonae rom wc we seeaor scsaoer coe s oecruemr,u we scna ca sn secnrumca ane aaresc. aor s smecaro vsacouesc o an ^a^ nsons-,z aesro wo nuorwer ceoe socwenn.s reoumcuamon asr o sameeeo wreca a meoae s aaree n eoxw assness ses oenm aa scmouwa-ereuzuseroaan moee aseervave o aaussan enc error.euses − - `w σ =.s.eusesenroaaerou a cm moe oum arcon ^meaunmncenersss anree ^^ ss n a o owere, ν an orome re:eson:ances:raaereaaeeaseo7,8.e wnaae,r vae soaumr aesoruosnesnes a z, z an z =s w a ssemac errorveneermne . w ame wnowwromereae=zo.ssearnesνs 9 wnc. exσa,s=e a r c⋅esasurnacneπrνrs%uec,ruesseemanc wasca re are sown.e ssemacea error ans c ane sameuse c an , resecve. omexourer coecens are sownn. conru na,euse secra aon wewo mos sncan error error manonesssassee as a asn ca acuaareen comr.esso anre o soewn sanme.u.nemeoman,eea wnow wen comareoerueuse as can senersa oeme oeuses ex a noae e seennense o.a.e secraroes ranes, aou e same seecrereum o v ssmarasn ser resecerven samaces ra,naen awoves annza amc s owernamc raneeow z. ona,s evenae asorone n sncan cane as sownnense o. e cosen ssem aures an a reucon oe oe waer vaour ac errorrouces a s revousorenza asoronnesn aono aearureromerore va o sne scraosecso.cn aensas ascecso.uneor, suc areacs canave susanamcaons rrororreconroceure nesceroeo.wns s soecons, an exemarroceureo resovee aoremenone caenesseao amnswnn, are ssesnecema oc na errrroowr ansoereoaneasuorrese secrum oeuse, wc can ssemac errorsresen,eroceureereore seesos.nnormea se, o un coerrreceemoe-esssnaaa a a maxmseeeece asoronnees.rs, an oecveun rs aeoreca anass o az secru cons consrucease onsormuae as an omsaonroemm ann cosee vncvonve o s aen as asroereosncrnee..econ,eroceure ecveuncononsrucon sro auue an aosnor.n m,eeumre cuaennceoman reresenaon o ause avnroaae > moee as were se unroaaeuseν =%ν ⋅ ex ^πcnν_,enn%.or a wea asornaseous me=>u?m suc asum ar,oave a≈oreannzacnosreooea,nmaeasnonronnee asoron coecen α =A cane aroxmae werese asor maxmum .nsoenrn. no., wen ^ ence, ssumne re e.orm canesnoenaarnsceeoruses w aanwnez rane,eano an exresson ow eveersnena =eu-resse, … ,onan,cw=ee arcoeesu=ncnno>nνneno-e aare varae aneν, ee moerecon,^^*:^^s ^ nowene as were se mean suar ^- - −∗ = armne *,ν,- ^ suec^o were a an are suaeC c^onsr^  a: ≤: ≤: or  =,… ,,: :anarameers. nne corvnacu os aon s, ceocmrumu,ner:e com mrnsmesswno sees:r.s, aen m,a:se emvaaucaae mo ase asneaer coom a nnaarroown o aera mmnemera re auaanaesee com anromese exerawceeen meaxm osne aesonreoenne a,n wereneeunaeaa wee. mzaones ve, sn a, …sa,meuse^ reresene as a coecon o even saceme-snaars ne9s9rom amD, seDneaxr,eaceoo conan ^^ narrow asoroneaures suc as waer9vaour asoronomsee arean oeac ovemunscaoonn aorm suc aserenavouons aeow res aeco aaramersaon o … ,2nreaamceeerrsaeon ox9, …e, xo2,a:ommcsaoeneonos,oneoeoomsaonarameers x9, … , x2.. enerae aea error esmae σ x, … , x^aw ran mes ee rss e area ^^en aru an mec eo rn sv xer ,…en ,ce: as aonoma oeree n −.^n9s wor2, weara 9 x2 sucezer curve w ^^ conroonmeerse σ^ as a sua ounee error.nce eac conroons,csonncsesseozearncuxr,ves-caooowor a versae reresenaon o conroons reure^^arameers, aarameers arerunncaonesraarn,ea.enzerscwurovre,w ^^an ^^,ers conroons consraneox =, = an e ^^'or consraneoave x =, wc reucese numer conroons. onsruc anneroaor ro o reurearameersom−.σ , s.ns wor, me correceme-snaars9 σ^9, … ,D.^onDsruDc a newuse a cuc o sneneroaors use.. necessar, zeeven saceme-snaars -, … ,D D-oe execer aosaoronneeore cacuansourer ae aere s cane sucen resove.ns wor, we zeroa suc execeuenc sacnνs aeas mes smaerane smaes oe .or eac a assoorroonnnnee,s a. smmercnerva ^^ ^ ^^ ^aroune cenrereoueencserocurumsn szes.%. s evauae:or eac asoronne, ,ven . s ev e acnca9a,re esmae anxeoncreasee:orecomsaon see an rouasunaeses., were %= νHH − − ν%%were =nn^νn ansensoena sou,o;nss.xenao, aeocnaow mnn amssoerr souncn aes ceenreereer-ueenaco enorcesca n∗ven . suca. cane evauae10. aorms useo ernrocre, c wonevreeraeer, aen oa remcaonsarruacmoene crsan aree u csoemoueee arsmnn seee aesov ees.mae oe ssemac xermens uo evauaee va anerormance oenrouceroceure,s aeoe smua avsee seeonw cnonnuc.eannra ansmsosnono m reoaeana amromenwo ar wz-wo exeerremnenesa. sea eexse ormenes oneea saeossesses a ssemacea error.or annrouconoe wc e reaers reerreo11.e exermena seus sownn.: rnces oz-, nm connuous-wave ame sonaneous emsson s re-coueroaans useoro zeneraon aneecon.e sourcesourceoxroncs-an arms, wereeaen erenceeweene arms snowonereromercre ase ea un.ne arms coueo aase canoeo ccoonroe are srecer zeneraon ane secon arms coueo a useonucve anenna useor correaon sna nasoomxers.e emersr meoeunceon oez cross ea saeaer sucaeea cannseaeeneraen oen az-recsonnear usene secon oewo exermens.ezeams comae usn reraa, wcs ensureeeamroeoes no cane sncan, wene ocaaen ecve ocso anennass cane. weenenrozeen.rse ex sreercme ann, ceonrarec sorne oc aersas uese aeszea un aneoson oeea saes racca reasonss moee as a oeecrc eemeneneraeseea, wcor ea uns caae o crea nearuncon oe ae voae.ns manner,e emoe srecer uns no oernme wnows sn sze.ne secon exermen,ere ea sae. ae, aneeas soe creae e morerecse an accuraenear o o comaree exermens,enearea saes useoenerae ame wnowne eruaao snzem.e omereera sceecso anres a.cure near sweeneearomo sor aoa esus anscusson“eeoeresccraeonrsoceeraureonaseen aeoe smuae sameuseresenene seconw m = conr s” w =. ane ssemac errorarameer^se aezer curveaon w eroevoounss. snown. sama,ee s reseucrunm re^sacmonsrreuce an sreucer sumecrreucomot^rueeasc soowrn c eosmmaarson.oseoe asoronnes,e reconsruce secrums a sncan eernses.e oerue secrum, wen comare w e same secrum as mos cear seenne snecr.um,ree aosoeuer vaue oe rao oe reconsruce secrumoe an e same sows anm ue secrum are sown.cross areuences,e reconsruce secrum un.overovezm,ene, wen comareoe same secrum, asncae raos cosero ra ase same sueacrum o.e reconsruce secrumensoerae,owever no asruee r sessuemna scsemac error esmaes sownn cre aon w erevous sown reconsrucon errorac. ee cosenarameersaon o σ^ oes no aowor aerec an scae oe oerueea error,e error esmae cane seeno caureeenera sae snce mere corrure error we. ona,e secrumsnvarano a consan osen σ, e euaoerueesonso aransaon oeuse, meann aerec reconsrucon on aso eweene reconsruecaon er aronr uo an a ve consan.eacaearesevaons sownn .a aane smaeesru ma anreu seeesn a aoovvee sssueoeacaeuses canes, wc ereoreave mnmanuence oneuse, s weceru nmo. conann an aru ae aunses re,c roerse usn ewo erenea uns aon w er secra are sownn s. useac.oeecave,oereeaaer reerreo asere srecerusere an enear sae enca excerom sascaucu uanosns w sereeerec,euses an er secra sou e sreceruseres seeno aear commmnrom measuremen nose.owever,ere srecene seconar oeme wnorwes csoemnareeorseane oareme wnow an s exece waer vaour asoronnes are noresennere s saeuse.urermore,e vsenenear saeuse asncae eoe vercanersecnerenussee,s wne.e are oservaons are conssen w e execaonaere srecer unas a ssemac e.rese semmnromsezo eecrc core. ror rorecceonusreruwcon o=.e,r=e sraencaereuzseer cuorveewams=eenccornearoeonas, wncsesnrouce a ans secrumn . .e esmaeea eownn .re sre rror, sownn .c,s conssen w e ar oecemreu wsneowen as cnomcressenersa oeme wnow an sreceneaer neave soenenervaa,e se oose evrero sr.oeunenerva, s oe error an eoowenear saeuse cose oneme anareauevne,e reconsruceuses seeno vaue oe rao oe reconsruce secrumoe an ecreo smraenc.enr. ,e asoue near sae secrums sown.e secrum oe reconsrucon mos cos secrumreoe secrumeow z, wereaere raoseno var more ase noseeooroowsnear sae soram oe reconsruce raosas anneruare rane o anse asrooarcame o.ee ere re ssreeccveer rauossesa asre a an mos o an, meannearene manues oa oereuencns o wcuanave veresae reconsrucons more comenarceaooeenneeaarr s saaeeruesuee.nc, sse scrouwmn onoe recoen ssreuccruomn o oee rerceon ssrerucon oe smuaeusen.a ane noeen overesmae as sown e raosc aereu resseonnance.re,uenec aess.ors sonneesave sameuse secrums anear comnaon o ownn.,e ereore noe ase-se an scaerue secra, an can nees.oweuvaerra,neee exaecee mnnemuem osn.own,oe.s no caronve an overesmaon oe *- -e moeowor waemtrurae - − −aerroex vaosneourvneruneneamen. ar, caneeum ae a.nee exezceaneene- =arse c-onu,own e...eeermne ora .uacn,e.,azc,me.,-omnaern,.,ecoronsc,.aznse,.ra-roaan an -namc- ransmsso o semase onrancrsamer aneecorn .em,ec.o-r.,n oreo a ann s,.-e ea.e s,c uremon m,en.-e.ome o aar en. r,a.v e-. r.o zuoo svn eecses ..oc. rea,eanesn. aoananar .auser,.,ausc,.,osumus,.. ans.oc., – . z reeon raeerasers.nommseornc,a. anecroonmceaca conroceao onsc oa sarmaasn usn vo. asers . vaxeor,r.. va.n,e.a–ner,.,rsc.ows,.eraerzme-oman secrosco o waer .earaaer,z.,meu-oem,, an. s.– ecroemceeerr,...n eaon-ase meoorreuenc caraon o .en,.,an,.,azer,..soc,z...ommun., – . measure eroc samn errorsneraerzme-oman .oron,m.en. es. a..exress, m–oecuar se. aa.rans., . croscocaaase..uan.ecrosc. .raoeer veersr,us.o.renzos,c.auanavevauaon onraresoranceecra –orenz.orn,.rce,. or.emsem,– . overonnuous erenavouon –me an ceneurscoroa mzaon .eer.,..eaac,es...moe.xem.o,oru–nconnm.zaon.omu..,– .rave,ne..e.n eso a.eraerzross-orreaonecrosco anman oare-rea ..esen,.oorse, a,n.oc,. acaons:z sec eraerz secrosco anman -oernecnues an ooncsev., rosco. anman -oernecnues an acaons,aser

Claims

. meooreermnn aea error curveor aeaevce,e meo comrsn roerco arunsm aenme o- aomeaan sen awa seoe o rn a a sam onzne se u wnsn a zme-oman seu uzn eeaevce sameavn aeas one an an a aanw sn oa oeverazmne-no amanz s reecuever,e eenneerraann a a c reacnonsaruecea error curveoreeaevce recor eme-oman sna a n e canaeea error curveoe caeceurmae nnm n ae- onreom e ourea mnnc s ore sn aeacsorurmo onnee reecaonusrersucneem caec-uoameanr senuaenc secrum r aen oeamnz saeons a -or mmu coneumrees uosnn a cearnen caaeneaae ereroar c eurrrvoer c courrvesn conuncon w exremumn an oecveuncon comrsn e on resonno an e oecveuncon e or moreeermne asoronneeaures, asoronneeaurese ann a co mrreeassuorne on a reeaseumresan oceee aweeeans oen oen ae osro mroroeneneer omnee same. ca.cue meo accorno cam, wereneermnn one or more asoronneeauresne an asaoerorenuneencn see ccarucuma ceomrreseusenceermnn ane-e anor a resonancereuenc o ene-e. secrum, an werene oecveuncon comrses n.eeea muereson aceco cracnuaoe anre ouenecr seceen cams, wereneermnn one or more asoron cacuaereue crum comrses n a curveo ars secon oe more asoronnnce seaeucrreusmro commresne an cu arvseo.ronne oe same aneermnn one or .eee me curove a ccocmorrsnesoe cearmmn,n w aereunae-earmramnn one or more asoronneeauresrom an werene oecveuncon comrseseuae-era orameee cur.rve- aroun e asoronne, .e meo accorno an oerecen cams, weren cuernveeran a canaeea error curve comrsesrovn aaramerzaon o aea errorw newer ceann eacae reeeao enrr oor s cue comrseseneran a new se oarameers aneneran a an rverome se oarameers as a reazaon oearamerzaon wereneenerae se oarameers are use as varaes oe oecveuncon. .e meo accorno cam, wereneneran a new se oarameers comrses caenneraaneeaaram eerroerrs curavsee. one one or more asoronneeaureseermneor arevous .e meo accorno an oerecen cams, weren - see rseconraen amme-oumea on s annas s an sea oeeacaeonse,s,z w r esnanemoraea an - e canaeea error curvesven s, w s ecever aea ore reresenn an error oeeaevce - w erroerrea cunrveen a oenraen re aco rreceonsmruec-eomamne- sonman sna comrses a n e canaeea s anneroan e aoorm a reconsruce se oaaonss, sna w eusan reecaon vsaruuecse. se oaaonsoenerae a reconsruceme-oman a.sore moenones acncorenzo r aanne o, ane wreecreenn se cams c,o wmerrseens ree sameaswo or more or more asoronneeauresorwo or more secons oereueenacn seecrueme,r emancaon o one comrsn an asoronne, an comnn eeermn seconrom eac semenn e one or more asoronneeauresuncon comrseseo o onnee o orr m moorere c coommnnee a assoorroonnnneeeeaauureress., an werene oecve m.oree o m aeo accorno an oerecen cams, wereneeaevce comrses one or coeaeevrc se,recezeor-,eencearrcraenasa unon. sae, so saeeane, roan scea sae, voce com.rese mse:o accorno an oerecen cams, werene zme-oman seu - a sourceor ouun a sna- a c aonzurraensmo eer oca coueoe source va ars ocaa,ezransmer - m az sna wen exce e sna enz reocseovenre ooc raece cvoeueeoz senar soomurcee vaz a srecon ocaa,ez recever recevez sna eneran a ansmer an conureoeec ewee n eecrceecon snaas a resu o anneracon - a sa smamn ee s seacez sosnoan aenoree sz snana receve ez receveroassroue -eeaace an receveevcee sez u receorve ar.usmen o aeaeweene sna anez sna . zme-oman ssem comrsn: - - a az sroaunrscmeoerr o oucuan c aou sna conureo e eoe source va ars ocaa,ezransmer - az receverm o acaz co sunae wen mouae e sna enoso oe source va a secon ocaa,ez recever recevezne snoa receveeneraenz a sn eneacrrcomeeeconz srannasmaers an conureoeec ew a resu o anneracon - a sa sameene seacez sosnoan aenoree sz snana receve ez receveroassroue - ameae seavccee se uor ausmen o aeaeweene sna anez sna - r aeceve ez recever an wne ereecnronec eeecvrcoen ccomrsn a memor crcur, arocessor crcur, an annerace, o con evces conureo: o recervoe aemeaevce oeermne aee-aom earrnor s cunrave re ucsonree meeo azc rceocrevnero an o cams-. rec.ore amze-moem-aonm sann s eas a oe e am rr s a oac rmcor cureve anno cam, werene eecroncevces conureo aneeermne oeen reercaoer ae recmones-roumcaen smen-a.oman sna w.erenn eecer eoneccroenvccee cvocmerssn a memor crcur, arocessor crcur, an annerace, -. conureoerorm an oe meos accorno an o camscom.r csomnunserru recaoans,e w socra we mene exuemcu seorn a onne e oerc mroonrecreovrcaem csa,usee onee e oerc mroornecrorams erorm an oe meos o cams-. evceo rec.onsseru oc a aemae- eorrmora cnur svenaor r aecoeraee uvscneeeermeaneevc aen. oe meos o cams- o

Images