Towards spectral intensity interferometry - Technionphweb.technion.ac.il/~eribak/ShoulgaRibakTowardsSpectralIntensity... · Towards spectral intensity interferometry G EORGIY S HOULGA
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Towards spectral intensity interferometry
GEORGIY SHOULGA1 AND EREZ N. RIBAK1,* 1Department of Physics, Technion – Israel Institute of Technology, Technion City, Haifa 32000, Israel *Corresponding author: [email protected]
Received XX Month XXXX; revised XX Month, XXXX; accepted XX Month XXXX; posted XX Month XXXX (Doc. ID XXXXX); published XX Month XXX
solvingtheobjectbeyondthediffractionlimit4‐7,providedthefluxissuf‐ficient8, 9. However, cross‐spectral occasional correlations and singlephotoncountsmightscreenthesignal,weakasitis.Thusweproposeanopticalsystem,whichdispersesthelightintomultiplespectralbands.Thisdispersioncanbeusedtomeasurethecorrelationfunctionateachbandseparately,leadingtoanimagewithdifferentspectralregionsinasourcestructure.Asthisdispersioncanimprovethesignaltonoiseratio,weanticipatebeingabletodetectfinerdetailsofthesource.
3. OPTICAL SYSTEM TheschematicsetupoftheopticalsystemispresentedinFig.2.Lightproducedbya532nmgreenlaserwaspassedthroughaneutraldensityfilter(NDF)inordertoreducetheintensity,toavoiddamagetothepho‐tomultipliers(PMTs)andsignalamplifiers.Then,itwassentontoaro‐tatinggroundglass(GG)disk(Newport,100diffuser)poweredbyaDCmotor.TherotationspeedoftheDCmotorwasadjustedto500rpm,toreducethecoherenceofthescatteredlight.Thescatteredlight,thuscon‐sideredapseudo‐thermallight15,illuminated350μmpinholes,thuscre‐atingartificialstars.Thesetofpinholeswasplacedascloseaspossibleto the rotating ground glass, because the scattered light produces aspecklepatternwhoseaveragesizeshouldbelessthanareaofeachar‐tificialstar.Then,light(thespecklepattern)fromtheartificialasterismwassplittothedetectorsintheuvplane.ThecollectionareaofeachPMT(Hamamatsu,R7400UPMT)shouldbelessthantheaveragespecklesize,andthus,15μmpinholeswereplacedinfrontofeachPMTtolimittheircollectionarea.PhotoneventsfromthePMTwereaugmentedbyhighspeedamplifiers(Becker&HicklHFAC‐26DB‐10UA,poweredbyseparate12vbatteries)andtheirmutualcorrelationswasperformedinMATLAB.
speedcorrespondingtothecoherencetimeofabout35μs.ThiswasdonebymeasuringaHWHMofthebunchingpeakaftercrosssignalcor‐relationprocess.Thesinglepatchlengthshavebeenchosentobe2μs(muchshorterthanacoherencetime,BEstatisticswereexpected),160μs (much longer than a coherence time, Poisson statisticswere ex‐pected)and35μs(aboutthecoherencetime,anequalmixtureofPois‐sonandBEstatisticswereexpected).Overall,10 equallengthpatcheswereusedtoacquireeachofthestatisticsgraphs(Fig.3).
where and areintroducedtimedelays(aphasecosineambiguityremains,seeAppendix).Therefore,triplecorrelation,incontrasttothesecondordercorrelation,isatwodimensionalstructure,whereeachaxisrepresentsadifferenttimedelay.Themethodispresented,asde‐velopedoriginally,fortemporalcorrelations,butthesamelogicappliestoourcaseoftwo‐dimensionalspatialcorrelations.Itisverydifficultandtimeconsumingtocalculatethetriplecorrela‐
tiondirectly,pointbypoint,withthefullsetoftimedelays and .Themethodwehaveusedinsteaddoesnotcalculatethetriplecorrelation
6. SIMULATIONS AND LABORATORY MEASUREMENTS Anartificiallymadeasterismofthreestarswasmeasuredinthelabora‐torywiththreesinglephotondetectors.Suchanasterismwasamask
withthreepinholes,withnon‐redundantdistancesbetweeneachtwocomponentsofthetriplestarsystem(Fig.6,right).Themaskwasmadebydrillingthree350μmholesinasheetofaluminum.ThenweranaMATLABsimulationtocomputetheintensitydistributionofthesameasterisminthefarfieldandfromitreconstructedanimageintwocases:withandwithoutphaseinformation.TheintensitydistributioninthefarfieldwascalculatedbyFouriertransformofthemask(orcouldbedonebyusingFraunhoferdiffractionintegral).TheimagereconstructionwasobtainedbyaninverseFouriertransformappliedtotheuvimage(Fig.6,left)containingtheamplitudeandphaseateachpoint(Fig.6,right)andtotheuvimagewithabsolutevaluesoftheamplitudeateachpoint(Fig.6,center),thuslosingthephaseinformation.Alreadyfromthelat‐terreconstructionwecandeducethattheobjectconsistsofthreepin‐holes, but the orientation of these three pinholes (the phase infor‐mation)willbesuppliedbythedegreeofthethirdordercoherence.
Tocheckhowthearea,illuminatedbyphotonsofthesamewavelength,increasesasafunctionofdeviationangle,wetakesimilarimagesaspre‐sentedabove,butacquiredforfourwavelengths:400nm,500nm,600nmand700nm,atnegligiblebandwidth.Thenweplottheirradianceasafunctionofthelateralaxisofeachpic‐ture(Fig.13).Inotherwords,wemeasuretheverticalsmearofthedis‐persedspotsinFig.11.Aswecansee, thenumberofdetectorsthatmeasuredifferent spectral bands canbe evaluated according to themaximumdeviationangleallowedinthesystem.
References 1. R. H. Brown, The Intensity Interferometer (Taylor & Francis, London,
1974). 2. A. Labeyrie, S. G. Lipson, and P. Niesenson, An Introduction to Optical
Stellar Interferometry (Cambridge, 2006). 3. T. Sato, S. Wakada, J. Yamamoto and J. Ishii, "Imaging System Using an
Intensity Triple Correlator". Appl. Opt. 17, 2047‐2052 (1978). 4. S. Oppel, T. Buettner, P. Kok and J. von Zanthier, “Superresolving Mul‐
tiphoton Interferences with In‐dependent Light Sources”, Phys. Rev. Lett. 109, 233603 (2012).
5. M. E. Pearce, T. Mehringer, J. von Zanthier, and P. Kok, “Precision esti‐mation of source dimensions from higher‐order intensity correlations”, Phys. Rev. A 92 043831 (2015).
6. A. Kellerer, “Beating the diffraction limit in astronomy via quantum clon‐ing”, Astron. Astroph. 561, A118 (2014), Corrigendum, Astron. Astroph 582, C3 (2015).
7. A. Kellerer and E. N. Ribak, “Beyond the diffraction limit via optical ampli‐fication”, Optics Letters 41, 3181‐3184 (2016).
8. T. Wentz and P. Saha, “Feasibility of observing Hanbury Brown and Twiss phase”, Mon. Not. R. Astr. Soc. 446, 2065–2072 (2015).
9. P. D. Nuñez and A. D. de Souza, “Capabilities of future intensity interfer‐ometers for observing fast‐rotating stars: imaging with two‐ and three‐telescope correlations”, Mon. Not. R. Astr. Soc. 453, 1999–2005 (2015).
10. A. Ofir and E. N. Ribak, “Offline, Multidetector intensity interferometers – I. Theory”, Mon. Not. R. Astron. Soc. 368, 1646‐1651 (2006a).
11. A. Ofir and E. N. Ribak, “Offline, Multidetector intensity interferometers – II. Implications and Applications”, Mon. Not. R. Astron. Soc. 368, 1652‐1656 (2006b).
12. I. Klein, M. Guelman, and S. G. Lipson, “Space‐Based Intensity Interfer‐ometer”, Applied Optics 46, 4237‐4242 (2007).
13. E. N. Ribak, P. Gurfil and C. Moreno, “Spaceborne intensity interferome‐try via spacecraft formation flight”, SPIE 8445‐8 (2012).
14. E. N. Ribak and Y. Shulami, “Compression of intensity interferometry sig‐nals”, Experimental Astrono‐my 41, 145‐157 (2016).
15. W. Martienssen and E. Spieler, "Coherence and Fluctuations in Light Beams". Am. J. Phys. 32, 919‐926 (1964).
16. D. Dravins, T. Lagadec, and P. D. Nuñez. "Long‐Baseline Optical Intensity Interferometry". Astronomy & Astrophysics 580, A99 (2015).
17. A. W. Lohmann and B. Wirnitzer, "Triple correlations," Proc. IEEE 72, 889‐901 (1984).
18. Bartelt, A. Lohmann, and B. Wirnitzer, "Phase and amplitude recovery from bispectra," Appl. Opt. 23, 3121‐3129 (1984).
19. A. Lohmann, G. Weigelt, and B. Wirnitzer, "Speckle masking in astron‐omy: triple correlation theory and applications," Appl. Opt. 22, 4028‐4037 (1983).
20. A. J. F. Siegert, MIT Radiation Laboratory Report 463 (1943). 21. E. N. Ribak, A. Laor, D. Faiman, S. Biryukov, N. Brosch, “Converting
PETAL, the 25m solar collector, into an astronomical research facility”, SPIE 4838‐172 (2002).
22. C. Barbieri , D. Dravins , T. Occhipinti , F. Tamburini , G. Naletto , V. Da deppo , S. Fornasier , M. D'Onofrio, R. A. E. Fosbury , R. Nilsson and H. Uthas, “Astronomical applications of quantum optics for extremely large telescopes”, Journal of Modern Optics 54, 191‐197 (2007).
23. D. Dravins, S. LeBohec, H. Jensen and P. D. Nunez, “Optical Intensity In‐terferometry with the Cherenekov Telescope Array”, Astroparticle Phys‐ics 43, 331‐347 (2013).
24. P.H. van Cittert, “Die Wahrscheinliche Schwingungsverteilung In Einer Von Einer Lichtquelle Direkt Oder Mittels Einer Linse Beleuchteten Ebene“. Physica 1.1‐6 201‐210 (1934).
25. F. Zernike, “The Concept of Degree of Coherence and its Application to Optical Problems“. Physica 785‐795 5.8 (1938).
26. J. Nam and J. Rubinstein, “Numerical reconstruction of optical surfaces” J. Opt. Soc. Am. A 25, 1697‐1709 (2008).
Appendix: 2nd and 3rd order coherence functions Weconsiderafinitequasi‐monochromaticlightsourceSofsizeb,locatedatdistancezfromtheobservationplane(Fig.15).
Thereisaspecialcase,whenallthreedetectorsarelocatedonthesameline3.Ifnowdetectors2and3arefixedinplaceandseparated by a distance∆ , and detector 1 is free tomove instepsofsamedistanceinaline,wehavetheintensityateachoneofthedetectorsas ∆ , , , and ∆ , ,re‐spectively.Thetriplecorrelationisthen
Eq. (12)Error!Reference sourcenot found. tells us that bymeasuringthethirdordercorrelationfunctionandtheabsolutevalueofthefirstordercorrelationfunction(fromtheSiegertre‐lation)thephasecanbefoundby
Φ ∆ ≜ 1 ∆ ∆ ∆
cos, , 1 ∆ 1 ∆ ∆
2| 1 ∆ || ∆ || ∆ |(13)
Solving Error!Reference source not found. as a differenceequationwecanobtainthephaseby
ingfourdetectors.Threearefixedinplacewithbaselines∆ and∆ andthefourthistheonlyonewhichismovingandmappingtheplane.Then,the intensity at each one of the detectors is , y , , ∆ , , , , ∆ , and ∆ , ∆ , . Then,Eq.(13)becomesasetoftwoequationsfordetectors1,2,4and1,3,4,re‐spectively,