family techniques waves usually electromagnetic superimposed order extract information waves important investigative technique fields astronomy fiber engineering optical applications chemistry quantum mechanics nuclear particle physics physics remote sensing interactions surface mechanical stress strain measurement widely science industry measurement small index changes surface irregularities science continuous wave transform analyze light containing features absorption associated substance mixture astronomical consists separate combine signals offering resolution equivalent diameter equal largest separation individual elements basic principles makes use principle combine waves way cause result combination meaningful property original state waves works waves frequency combine resulting intensity pattern determined phase difference waves waves phase undergo interference waves phase undergo destructive interference waves completely phase completely phase intermediate intensity pattern determine relative phase difference use light form electromagnetic wave typically known configuration single incoming beam coherent light split identical beams beam partially reflecting mirror beams travels different route called path arriving path difference difference distance traveled beam creates phase difference introduced phase difference creates interference pattern initially identical waves single beam split paths phase difference changes phase paths physical change path length change index path seen observer direct view mirror seen beam sees reflected image mirror fringes interpreted result interference light coming virtual images original source characteristics interference pattern depend nature light source precise orientation mirrors beam optical elements oriented line observer resulting interference pattern consists circles centered normal respect interference fringes generally shape sections overlap fringes near axis straight parallel equally spaced extended source point source illustrated fringes observed set infinity fringes localized mirrors use white light result pattern colored fringes central fringe representing equal path length light dark depending number phase experienced beams traverse optical system discussion categories techniques categorized variety criteria versus detection detection interference occurs beams carrier frequency phase difference beams results change intensity light resulting intensity light mixing beams measured pattern interference fringes viewed recorded discussed article fall category technique shifting input signal new frequency range weak input signal assuming use active weak input signal frequency mixed strong reference frequency local combination input signals creates new signals sum frequencies difference new frequencies called typically new frequencies desired signal filtered output output signal intensity proportional product input signals important widely application technique receiver invented engineer circuit incoming radio frequency signal antenna mixed signal local converted technique lower fixed frequency signal called intermediate frequency filtered applied extracts audio signal sent optical detection extension technique higher visible frequencies double path versus common path double path reference beam sample beam travel paths examples include green interaction sample test sample beam reference beam create interference pattern interpreted common path class reference beam sample beam travel path illustrates point lateral examples common path include phase contrast microscope zero area splitting versus splitting splitting divides light emerging point narrow coherent light allowing parts travel different paths allows illustrates young interference experiment lloyd mirror examples splitting include lens young interference experiment played major role general acceptance wave theory light white light young experiment result white central band interference corresponding equal path length slits surrounded symmetrical pattern colored fringes diminishing intensity addition continuous electromagnetic radiation young experiment performed individual molecules large seen electron microscope lloyd mirror generates interference fringes combining direct light source blue lines light source reflected image red lines mirror held grazing result pattern fringes band equal path length nearest mirror dark bright interpreted effect proof phase surface reflected beam inverted splitting uses partial divide incident wave separate beams separated illustrates examples splitting include laser unequal path shown set test optical flat precisely figured reference flat placed flat tested separated narrow reference flat slightly fraction degree necessary prevent rear surface flat producing interference fringes separating test reference flats allows flats respect adjusting tilt adds controlled phase gradient fringe pattern control direction fringes obtain easily interpreted series nearly parallel fringes complex lines separating plates light shows beam light flats beam allowing fringes viewed axis versatile instrument separated light paths traversed fringes adjusted localized desired plane typically fringes adjusted lie plane test object fringes test object photographed decided produce fringes white light white light limited length order great care taken optical paths fringes visible illustrated cell placed path reference beam match test cell note precise orientation beam reflecting surfaces beam oriented test reference beams pass equal glass orientation test reference beams experience surface reflections resulting number phase result light traveling equal optical path length test reference beams produces white light fringe interference heart pair partially glass optical flats spaced millimeters centimeters apart surfaces facing alternatively uses transparent plate parallel reflecting surfaces flats slightly typical system illumination provided source set focal plane lens focusing lens produces inverted image source paired flats present absence paired flats light emitted point passing optical system focused point ray emitted point source traced ray passes paired flats reflected produce multiple transmitted rays collected focusing lens brought point screen complete interference pattern takes appearance set concentric rings rings depends flats high resulting high factor high light produces set narrow bright rings dark background low image corresponds surfaces versus high image early techniques attempt measure properties light initially setting equipment switching white light actual measurements reason measurements recorded visually light result uniform fringe pattern lacking modern means environmental temperature control struggled continual fringe drift set basement fringes occasionally disappear vibrations passing horse traffic distant thunderstorms like easy observer lost fringes returned visibility advantages white light produced distinctive colored fringe pattern far difficulties apparatus low length early example use white light resolve ambiguity applications physics astronomy physics important experiments late 19th century famous failed experiment provided evidence special recent experiment perform measurements beat frequencies crossed optical illustrates experiment performed optical constructed controlling frequencies set right angles frequency measured beat frequency combined precision speed light excluded experiments level narrow band optical filters core hardware component transform narrow band filter exhibit number advantages compared competing technologies filters largest field view specified relatively simple operation tuning mechanical rotation high voltage control crystals optical system compared filters use elements relatively low temperature sensitivity negative relatively restricted range require use restrict illustrates operation transform essentially mirror practical transform substitute corner cube flat mirrors conventional simplicity illustration generated making measurements signal positions moving mirror transform converts actual spectrum shows image solar recover solar number near green line picture color coded image shift line associated velocity away satellite camera thin film narrow filters capable selecting single line imaging example alpha line line sun stars shows extreme image sun corresponding line iron coated reflective mirrors coated alternate layers light element heavy element approximately layers type placed mirror thickness layer tightly controlled desired reflected layer interfered laser wave observatory uses detection waves application cavity store bounce mirrors increases time wave interact light results better sensitivity low frequencies smaller usually called mode spatial frequency main laser observation waves occurred september relatively large freely accessible working space flexibility locating fringes choice flow wind tunnels flow studies general frequently fields physics heat transfer measure pressure density temperature changes gases study predictions quantum mechanics phenomenon known quantum astronomical high resolution observations technique synthesis mixing signals cluster comparatively small single expensive early radio single measurement later astronomical large array illustrated arranged pattern ground limited number result insufficient coverage rotation earth rotate array relative sky single measure information multiple taking repeated measurements technique called earth rotation synthesis thousands kilometers long achieved long astronomical optical overcome number technical issues shared radio short light extreme precision stability construction example spatial resolution requires stability optical measurements require high sensitivity low noise available late 1990s astronomical seeing causes stars introduces rapid random phase changes incoming light requiring data collection rates faster rate despite technical difficulties roughly dozen astronomical optical operation offering resolutions range shows movie assembled synthesis images beta system star system approximately light years away observed array instrument brighter component primary star mass donor component thick disk surrounding secondary star mass components separated tidal mass donor mass clearly visible wave character matter exploited build examples matter electron later followed demonstrated later followed employing molecules electron imaging technique records electron interference pattern object reconstructed yield greatly image original object technique developed enable greater resolution electron possible conventional imaging techniques resolution conventional electron limited electron large electron lenses investigate effect examine effects gravity acting elementary particle demonstrate strange behavior basis exclusion principle unlike objects rotated axis return original state develop minus sign wave function words needs rotated returning original state techniques reaching sufficient precision allow laboratory scale tests general atmospheric physics high precision measurements trace gases remote sounding atmosphere examples utilize absorption features trace gases typical use continual monitoring column concentration trace gases carbon instrument engineering applied science newton test plate frequently optical industry testing quality surfaces shaped figured shows photos reference flats check test flats different stages completion showing different patterns interference fringes reference flats resting surfaces contact test flats illuminated light source light waves reflected surfaces interfere resulting pattern bright dark bands surface left photo nearly flat indicated pattern straight parallel interference fringes equal intervals surface right photo uneven resulting pattern curved fringes pair adjacent fringes represents difference surface elevation half light differences elevation measured counting fringes surfaces measured inch method determine surface tested concave convex respect reference optical flat procedures adopted observe fringes displaced presses gently flat observes fringes white light sequence colors familiar experience aids interpretation finally compare appearance fringes moves ones head normal oblique viewing position sorts maneuvers common optical shop suitable formal testing environment flats ready sale typically mounted formal testing certification widely telecommunications control measure light filters multiple layer thin film telecommunications division technology enables use multiple light single optical fiber depends devices thin film single mode employ suppress optical cavity modes single interest green invented green variant widely test optical components basic characteristics distinguishing configuration use point light source interesting note criticized configuration unsuitable testing large optical components light sources available time limited length pointed constraints geometry forced limited length required use reference mirror equal size test mirror making green impractical purposes decades later advent laser light sources answered objections green laser light source unequal path length known laser unequal path illustrates set test lens light point source expanded lens shown parallel beam convex spherical mirror positioned center focus lens tested beam recorded imaging system analysis integrated optical circuits light branches externally vary relative phase slight tilt beam result path difference change interference pattern basis wide variety devices sensors optical switches latest proposed extremely large astronomical thirty design primary mirrors built hundreds mirror segments highly non mirror segments presents major challenge traditional means optical testing compares surface spherical reference aid recent years computer generated begun supplement test complex surfaces illustrates unlike figure actual line order laser light passed zero order beam experiences modification order beam modified match desired shape test surface illustrated test setup zero order beam directed spherical reference surface order beam directed test surface way reflected beams combine form interference fringes test setup mirrors needing exchanged ring laser navigation systems operate principle effect distinction entire ring laser fog external laser counter beams optical fiber ring rotation system causes relative phase shift beams observed phase shift proportional accumulated rotation fog observed phase shift proportional angular velocity networks frequencies individual signals different channels share single physical transmission line called frequency division example cable cable television system carry television channels time given different frequency don interfere continuous wave radar basically detection devices compare transmitted reflected beams optical detection coherent measurements capable detecting weak light scattered atmosphere monitoring wind speeds high accuracy application optical fiber communications high resolution techniques self method measure laser optical detection essential technique high accuracy measurements frequencies optical sources frequencies relatively years ago lengthy frequency chains needed connect microwave frequency atomic time source optical frequencies step chain frequency produce frequency step compared detection step output microwave source far infrared laser infrared laser visible laser measurement single line required years effort construction custom frequency chain currently optical frequency provided simpler method measuring optical frequencies mode locked laser form train spectrum seen consist carrier frequency surrounded closely spaced optical frequencies equal pulse repetition frequency pulse repetition frequency locked frequency standard frequencies elements red end spectrum doubled frequencies elements blue end spectrum allowing serve reference manner locking frequency output atomic standard performed single step measure unknown frequency frequency output dispersed spectrum unknown frequency overlapped appropriate segment frequency resultant beats measured common industrial applications optical versatile measurement tool high precision examination surface topography popular measurement techniques include psi vertical scanning known scanning white light term csi csi exploits extend range capabilities interference techniques widely micro electronic micro psi uses light provides precise measurements usable surfaces smooth csi uses white light high numerical looking phase fringes psi looks best position maximum fringe contrast feature overall fringe pattern simplest form csi provides precise measurements psi rough surfaces configurations csi variously known enhanced high resolution use effects combination interference phase enhance precision addresses issues associated classical analysis static measures positions fringe centers seen fringe equal provide measure errors determining location fringe centers provide inherent limit precision classical analysis intensity variations introduce error trade precision number data points closely spaced fringes provide data points low precision widely spaced fringes provide low number high precision data points fringe center data uses classical analysis information theoretically obtained detailed analysis intensity variations thrown away finally static additional information needed determine tested surface right tell single image concave convex traditionally information obtained non automated means observing direction fringes reference surface pushed phase shifting limitations relying finding fringe centers collecting intensity data point image seen multiple analyzed reference optical surface shifted precise fraction exposure alternatively precise phase shifts introduced laser frequency captured images processed computer optical errors precision psi far greater possible static analysis measurement routine phase shifting technology adapted variety types laser common path configurations point lateral generally phase shifting techniques adapted system uses fringes measurement scanning interference achieved path length delays matched time light source csi monitors fringe contrast phase fringes illustrates csi microscope objective forms white light include low objectives reference mirror objective high objectives limited working distance sample alternatively objective moved vertically height range sample position maximum fringe contrast found chief benefit scanning systems designed suffer ambiguity coherent seen volume suited steps rough surfaces resolution system determined length light source industrial applications include process surface measurement surface hard reach spaces hostile environments surfaces high aspect ratio features grooves channels holes film thickness measurement semi conductor optical industries etc illustrates green set white light scanning object technique uses monitor small single multi perform dimensional large parts assemblies detect larger surface defects discovered accident result mistakes committed making early relatively weak photographic plates necessitating long vibrations minute shifts occur optical system resultant showed subject covered fringes considered ruined eventually independent groups realized fringes important information dimensional changes occurring subject began intentionally producing double main article covers disputes priority discovery occurred issuance patent method exposure methods create exposure records object state subsequent photographic plate object subjected stress composite image depicts difference stressed states real time second method creating object created illuminated reference beam generate image object directly superimposed original object object subjected stress object waves image interfere new waves coming object technique allows real time monitoring shape changes method time average involves creating object subjected periodic stress vibration yields visual image vibration pattern synthetic radar radar technique remote sensing satellite synthetic radar images geographic feature taken separate days changes taken place radar images taken separate days recorded fringes similar obtained technique monitor millimeter scale resulting earthquakes landslides uses structural engineering particular monitoring structural stability shows active volcano hawaii data acquired space shuttle synthetic radar april october generate fringes image electronic pattern known uses video detection recording produce image object superimposed fringe pattern represents displacement object recordings fringes similar obtained invented laser considered severe objects particularly imaging image produced later realized patterns carry information object surface developed technique pattern exploited variety applications photograph pattern second photograph pattern digital images results fringe pattern fringes represent lines equal short laser range capture fast events phase problem exists absence information tell difference lines indicating peak versus lines indicating trough resolve issue phase ambiguity combined phase shifting methods method establishing precise invented exploited low length white light initially white light split reference beam folded bouncing forth times mirror pair spaced precisely apart test path precisely times reference path fringes seen repeated applications procedure allowed precise measurement distances meters established distance measurement equipment leading scale networks measured instruments method superseded gps uses study materials measurement complex thermal properties dimensional motion mapping including mapping patterns structures biology medicine optical medical imaging technique low provide internal tissue seen core typical system arm focused tissue sample sample longitudinal pattern arm bounced reference mirror reflected light tissue sample combined reflected light reference low light source signal observed limited depth sample scanning records thin optical slice sample time performing multiple moving reference mirror scan entire dimensional image tissue reconstructed recent advances combine phase coherent ranging capability low phase contrast differential interference contrast important tools biology medicine animal cells single organisms little color totally invisible simple bright field illumination structures visible specimens procedures time consuming kill cells seen phase contrast allow living cells studied non biological applications example analysis processing angle resolved low uses scattered light measure sizes objects including cell allows depth measurements combined density measurements found state tissue health measurements objects example found tissue changes normal average cell size increases phase contrast ray imaging refers variety techniques use phase information coherent ray beam image soft tissues elementary discussion phase contrast ray imaging introduction depth review phase contrast ray imaging important method cellular structures wide range biological medical studies technologies ray phase contrast imaging utilizing different principles convert phase variations rays emerging object intensity variations include propagation based phase contrast based far field enhanced imaging ray methods provide higher contrast compared normal absorption contrast ray imaging making possible smaller details disadvantage methods require sophisticated equipment ray sources ray high resolution ray
Interferometry