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N-slit interferometer for secure free-space optical communications: 527 m intra
interferometric path length
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4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
N-Slit interferometer for secure free-space optical communications: 527
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m intra interferometric path length
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Interferometric Optics,, , ,Rochester,NY,14626-0592 REPORT NUMBER
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This a US Army High Energy Laser Laboratory project funded through a subcontract to BAE Systems.
14. ABSTRACT
The N-slit interferometer is demonstrated to function with an intra interferometric propagation path
length of 527.33 m. Interferograms representing several interferometric characters, corresponding to N =
2, 3, 4, and 5, were recorded at the interferometric plane located at the end of an open air propagation
range. Interferometric computations, based on the application of Dirac?s notation, were successfully used
to predict the structure and divergence of the propagating interferograms. These measurements were
carried out during an unusual mild-temperature, low-humidity, summer night in northern Alabama. In the
laboratory, at an intra interferometric propagation path length of 7.235 m, the N-slit interferometer was
also used to successfully detect the intrusion of microscopic fibers into the intra interferometric
propagation path. These experiments led to the detection of diffraction patterns superimposed over the
interferograms.
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IOPPUBLISHING JOURNALOFOPTICS
J.Opt.13(2011)035710(5pp) doi:10.1088/2040-8978/13/3/035710
N
-slit interferometer for secure free-space
optical communications: 527 m intra
interferometric path length
FJDuarte1,2,TSTaylor3,A MBlack3,WEDavenport4 and
PGVarmette5
1InterferometricOptics,Rochester,NY14626-0592,USA
2DepartmentofElectricalandComputerEngineering,UniversityofNewMexico,
NM87131-0001,USA
3USArmySpaceandMissileDefenseCommand,TechnicalCenter,TechnologyDirectorate,
DirectedEnergyDivision,Huntsville,AL35807,USA
4USArmyAviationandMissileCommand,WeaponsSciencesDirectorate,RedstoneArsenal,
AL35898,USA
5ScienceApplicationsInternationalCorporation,Huntsville,AL35806,USA
Received5November2010,acceptedforpublication30December2010
Published3February2011
Onlineatstacks.iop.org/JOpt/13/035710
Abstract
The N-slitinterferometerisdemonstratedtofunctionwithanintrainterferometricpropagation
pathlengthof527.33m.Interferogramsrepresentingseveralinterferometriccharacters,
correspondingto N =2,3,4,and5,wererecordedattheinterferometricplanelocatedatthe
endofanopenairpropagationrange. Interferometriccomputations,basedontheapplicationof
Dirac’snotation,weresuccessfullyusedtopredictthestructureanddivergenceofthe
propagatinginterferograms. Thesemeasurementswerecarriedoutduringanunusual
mild-temperature,low-humidity,summernightinnorthernAlabama. Inthelaboratory,atan
intrainterferometricpropagationpathlengthof7.235m,the N-slitinterferometerwasalso
usedtosuccessfullydetecttheintrusionofmicroscopicfibersintotheintrainterferometric
propagationpath. Theseexperimentsledtothedetectionofdiffractionpatternssuperimposed
overtheinterferograms.
Keywords: aviation,beamexpansion,clearairturbulence,Diracnotation,free-space,
propagation,interferometriccharacter,interferometricimaging, N-slitinterference, N-slit
interferometer, N-slitinterferometry,naturalfibers
(Somefiguresinthisarticleareincolouronlyintheelectronicversion)
1. Introduction represent a significant development on this free-space optics
communications technique, originally demonstrated in the
Recently, we reported on an N-slit interferometer with an laboratory over a propagation distance of only 10 cm and
intra interferometric path length of 35 m [1]. In the envisionedprimarilyasaspace-to-spacesecureinterferometric
presentexperimentswehaveextendedtheintrainterferometric communicationstechnique[2].
propagationdistanceto527.33m.Theexperimentwascarried Previously,theintegrityofthisfree-space interferometric
out,atnight,usingthefullavailablelengthofanexistingopen communications technique has been demonstrated via the
air propagation range. These experiments were performed catastrophic collapse of the interferometric characters, or
usingseveraltheoreticallypredictedinterferometriccharacters signal,resultingfromattemptstoinsertthinbeamsplittersinto
corresponding to a, b, c, d (N = 2, 3, 4, 5, respectively) [2] the propagation path [1–3]. A refinement in the interception
under night-time atmospheric conditions. The successful technique consists in the subtle insertion of microscopic
completion of these open air propagation experiments fibers into exact positions in the intra interferometric
2040-8978/11/035710+05$33.00 1 ©2011IOPPublishingLtd PrintedintheUK&theUSA
J.Opt.13(2011)035710 FJDuarteetal
path. Experiments performed in the laboratory, at an intra
interferometric distance of D(cid:2)x|j(cid:3) = 7.235 m, demonstrate
that the interferograms easily detect the presence of very
thin natural fibers, thus upholding the integrity of this
interferometricapproach forfree-space communications. The
detectionofthefibersoccursviathesuperimpositionofdistinct
Figure1.TopviewschematicsoftheN-slitinterferometeras
diffractionpatternsovertheinterferometriccharacters. describedin[1]. N slitsareilluminatedatatransmissiongrating(j)
So far, N-slit interferometers have been used in various thusallowingthepropagationofanN-slitinterferencesignal,along
industrial metrology tasks including microdensitometry, D(cid:2)x|j(cid:3),towardtheinterferometricplanex,atwhichislocatedaCCD
microscopy, and optical modulation measurements of thin detectorarray.ForD(cid:2)x|j(cid:3) =527.33m,theCCDdetectorisreplaced
byaflatsurfacedeployedatx.TBEisatelescopicbeamexpander
film gratings generated from a variety of manufacturing providinganexpansionfactorofM ≈10.TheMPBEisa
processes [4]. The present experiments demonstrate that N- one-dimensionalmultiple-prismbeamexpanderwithM ≈5
slitinterferometersarealsoapplicabletosecureterrestrialfree- (from[1]).
space optical communications over propagation distances of
practicalinterest.Additionalapplicationsincludethedetection
of even mild clear air turbulence [1] over various distances
of practical interest without fundamental limitations on its 3. Experiments
propagationrange.
Experimental details describing the N-slit interferometer,
shown in figure 1, are given in [1]. It is however necessary
2. Theory
to mentionthat the illuminationsource is a single-transverse-
As mentioned in [1], light propagation through N-slit arrays mode narrow-linewidth He–Ne laser (λ = 632.8 nm) and
was studied by Newton [5] and N-slit diffraction was the two gratings used were: one grating with 570 μm slits
discussed by Michelson [6]. In a more contemporaneous separated by 570 μm isles and a grating with 1000 μm
setting, Feynman [7] applied Dirac’s quantum notation [8] slits separated by 1000 μm isles. The tolerances in the slit
to perform double-slit thought experiments on electrons. dimensions are quoted by the manufacturer as 0.5 μm, with
This approach was applied to the N-slit interferometer furtherdetailsgivenin[1].
(see figure 1), for narrow-linewidth laser illumination, thus The 570 μm grating was employed in the experiments
yieldingthegeneralized, one-dimensional, N-slit interference designed for the detection of thin natural fibers at D(cid:2)x|j(cid:3) =
equation[9,10] 7.235 m, while the 1000 μm grating was used to obtain the
(cid:2)N (cid:2)N resultswiththe D(cid:2)x|j(cid:3) =527.33mconfiguration.
|(cid:2)x|s(cid:3)|2 = (cid:2)(rj) (cid:2)(rm)ei((cid:3)m−(cid:3)j) (1a) As discussed in [2], for both gratings a series of
j=1 m=1 interferometric characters were created by illuminating an
increasing number of slits. That is, a, b, c, and d,
or
interferometriccharactersweregeneratedbythecorresponding
(cid:2)N (cid:2)N illuminationof N =2,3,4,and5slitsrespectively.
|(cid:2)x|s(cid:3)|2 = (cid:2)(rj)2+2 (cid:2)(rj) Asinthepreviousindoorexperiment(at T ≈ 22◦C)the
(cid:3) (cid:2)jN=1 j=1 (cid:4) detectorfortheD(cid:2)x|j(cid:3) =7.235mmeasurementsisaPrinceton
× (cid:2)(r )cos((cid:3) −(cid:3) ) . (1b) Instrument (Pixis 100) CCD array composed of 1340 pixels
m m j each ∼20 μm in width. This CCD array is deployed at the
m=j+1
interferometric plane (x). Two types of natural fibers were
In either equation, s represents the photon source, j refers
used: initially, fine human hair with a diameter of ∼50 μm,
to the jth slit in the transmission grating, x represents the
and subsequently, a spider web fiber with a diameter in the
interference plane, (cid:2)(r ) are wavefunction amplitudes of
j 25–30μmrange.
‘ordinary wave optics’ [8, 11], and the term in parenthesis
For the experiment on the extended configuration, at
represents the phase which describes the exact geometry
of the N-slit interferometer [10, 11]. As discussed D(cid:2)x|j(cid:3) = 527.33 m, the interferometric plane (x) was
in [1], this equation was originally derived for single- comprised of a calibrated screen and the interferograms were
photon propagation, albeit in practice it also applies to an recorded using digital photography. The illumination-grating
ensemble of indistinguishable photons [12], as in the case part of the interferometer was mounted on a small optical
of narrow-linewidth laser emission. This approach [10, 12] table [1] and deployed at an elevation of 15.17 m, whilst the
is consistent with van Kampen’s quantum theorems [13]. interferometric plane was deployed on a small hill at an intra
The nexus between the probability distribution |(cid:2)x|s(cid:3)|2 and interferometric distance of D(cid:2)x|j(cid:3) = 527.33 m, as measured
measured interferometric profiles is also described in [12]. with a calibrated laser range finder. These experiments were
As previously emphasized, an important advantage of this performed during a clear summer night with atmospheric
quantuminterferenceequationisthecontinuousdescriptionof conditions characterized by an ambient temperature of T ≈
measuredinterferogramsfromthenear-tothefar-field[10]. 24◦Candahumidityof∼66%.
2
J.Opt.13(2011)035710 FJDuarteetal
Figure2.Interferogramregisteredatx,forD(cid:2)x|j(cid:3) =527.33m,
λ=632.8nm,andN =4(1000μmslitsseparatedby1000μm),
recordedinopenairatT ≈24◦Candahumidityof66%.This
interferogramcorrespondstotheinterferometriccharacterc.The
horizontalscaleatthebaseofthefigureis5cm/div(whilsttheless
visibleupperscaleis1cm/div).
Figure5.Interferogramregisteredatx,forD(cid:2)x|j(cid:3) =7.235m,
λ=632.8nm,andN =2(570μmslitsseparatedby570μm)with
aspiderwebfiberdeployedorthogonallytothepropagationplane
(thatis,paralleltotheslits,orperpendiculartotheplaneoffigure1)
atadistanceof15cmfromx.Thediffractionpattern,generatedby
Figure3.Interferogramregisteredatx,forD(cid:2)x|j(cid:3) =527.33m, thefiber,issuperimposedoverthecentralorderoftheinterferogram.
λ=632.8nm,andN =5(1000μmslitsseparatedby1000μm),
recordedinopenairatT ≈24◦Candahumidityof66%.This
interferogramcorrespondstotheinterferometriccharacterd.The
horizontalscaleatthebaseofthefigureis5cm/div(whilsttheless
visibleupperscaleis1cm/div).
Figure6.Interferogramregisteredatx,forD(cid:2)x|j(cid:3) =7.235m,
λ=632.8nm,andN =2(570μmslitsseparatedby570μm)with
aspiderwebfiberdeployedorthogonallytothepropagationplane
(thatis,paralleltotheslits,orperpendiculartotheplaneoffigure1)
atadistanceof15cmfromx.Thediffractionpattern,generatedby
Figure4.Controlinterferogramregisteredatx,for
bDy(cid:2)x5|j7(cid:3)0=μ7m.2)3a5tTm,≈λ2=2◦6C3.2.T8hnismi,natenrdfeNrog=ra2m(5co7r0reμsmposnlditsstsoetphaerated itnhteefirfbeeror,girsasmu.perimposedovertheouterrightwingofthe
interferometriccharactera.
bythediffraction pattern superimposedoverthecentral order
4. Results
of the interferogram in figure 5. For comparison purposes
the fiber is displaced to intersect the outer right wing of
A measured interferogram, resulting from the illuminationof
the interferogram, as demonstrated by the diffraction pattern
N = 4 slits of the 1000 μm grating, at D(cid:2)x|j(cid:3) = 527.33 m, superimposed over the right secondary maximum of the
through the open atmosphere at T ≈ 24◦C and a humidity
interferograminfigure6.
of66%,isshowninfigure2. Thecorrespondingmeasurement
under nearly identical propagation conditions, for N = 5, is Ameasuredinterferogram,resultingfromtheillumination
showninfigure3. of N = 3slitsofthe570μmgrating,at D(cid:2)x|j(cid:3) = 7.235m,in
thelaboratoryand in theabsenceofturbulence at T ≈ 22◦C
Ameasuredinterferogram,resultingfromtheillumination
of N = 2slitsofthe570μmgrating,at D(cid:2)x|j(cid:3) = 7.235m,in is shown in figure 7. The corresponding measurement under
thelaboratoryandintheabsenceofturbulenceat T ≈ 22◦C, identicalpropagationconditions,for N =3,withaspiderweb
is shown in figure 4. The corresponding measurement under fiber deployed orthogonally to the propagation plane (that is,
identicalpropagationconditions,for N =2,withaspiderweb parallel to the grooves of the grating) is shown in figure 8.
fiber deployed orthogonally to the propagation plane (that is, The fiber is positioned 15 cm from the detection plane (x)
paralleltothegroovesofthegrating)isshowninfigure5. and intersects the outer right wing of the interferogram, as
The fiber is positioned 15 cm from the detection plane demonstratedbythediffractionpatternsuperimposedoverthe
(x)andintersectsthemaininterferenceorder,asdemonstrated outerrightwingoftheinterferograminfigure8.
3
J.Opt.13(2011)035710 FJDuarteetal
Figure7.Controlinterferogramregisteredatx,for Figure8.Interferogramregisteredatx,forD(cid:2)x|j(cid:3) =7.235m,
D(cid:2)x|j(cid:3)=7.235m,λ=632.8nm,andN =3(570μmslitsseparated λ=632.8nm,andN =3(570μmslitsseparatedby570μm)with
by570μm)atT ≈22◦C.Thisinterferogramcorrespondstothe aspiderwebfiberdeployedorthogonallytothepropagationplane
interferometriccharacterb. (thatis,paralleltotheslits,orperpendiculartotheplaneoffigure1)
atadistanceof15cmfromx.Thediffractionpattern,generatedby
thefiber,issuperimposedovertheouterrightwingofthe
interferogram.
5. Discussion
The atmospheric propagation experiments using an intra
interferometric path length of D(cid:2)x|j(cid:3) = 527.33 m consisted tells us that any attempt to observe the intra interferometric
in propagating the interferometric characters a, b, c, d, signal will distort or destroy the signal. Indeed, the use of
corresponding to N = 2, 3, 4, 5, using the 1000 μm ultrathin transparent beam splitters deployed near Brewster’s
grating. Therecorded interferograms, for c and d, are shown angle, its least disruptive configuration, causes the collapse
in figures 2 and 3. Planning for these experiments was of the propagating interferometric characters [1–3]. In order
facilitated by the accurate prediction of the interferograms to empirically investigate the effect of finer methods of
via the interferometric equation. Predicted and recorded intersection in these experiments we used spider web fibers.
interferograms, in regard to the overall divergence of the Theexperimentswereconductedinthelaboratory,at D(cid:2)x|j(cid:3) =
interferometricpatternsandthepositionofthespatialfeatures 7.235m,for N =2,3,4,5.
oftheinterferograms,agreewithin1–2%. Improvedaccuracy The results for N = 2, and 3 are shown in figures 5, 6,
shouldbeavailablebyreplacingtheinterference planescreen and 8. The beautiful diffraction patterns superimposed over
with tiled CCD detectors, which for this class of intra the interferometric characters a and b, either at the central
interferometricdistance shouldprovidea40–50 cm detection orderoroutlyingpositions,clearlydemonstratethatfree-space
width. communications using N-slit interferometry can detect even
Digital movie recordings of the interferograms reveal verysubtlemethodsofintrusion.
mainly slight variations in the intensity domain of the inter-
ferograms, which are consistent with incipient atmospheric
6. Conclusion
turbulence conditions[1, 4], mostlikely due to amild breeze
present during the experiments, even though the temperature
(T ≈ 24◦C) and humidity (∼66%) were very favorable for In this paper we report on the N-slit interferometer
unperturbed propagation. Previously [1], slight variations in with the largest intra interferometric path length to date,
theinterferograms, for D(cid:2)x|j(cid:3) = 35 m, were detected even in D(cid:2)x|j(cid:3) = 527.33 m. Thus, we have proven that the
anenclosedenvironmentatT ≈30◦C. N-slit interferometer is a viable interferometric tool over
The results disclosed in this paper, with D(cid:2)x|j(cid:3) = long free-space propagation paths under fair atmospheric
527.33 m, represent a significant advance in interferometric conditions. It has also been demonstrated, in a laboratory
free-space optics communications, which were initially environment, that even very subtle attempts to intercept the
demonstrated in the laboratory over a propagation distance interferometric characters, using microscopic natural fibers,
of only 10 cm and mainly envisioned as a space-to-space arereadilydetected viatheobservationofdiffractionpatterns
secure optics communications alternative [2]. Certainly, superimposed over the interferometric signal. This is a new
the propagation path demonstrated here opens the realm interferometric effect, which to our knowledge has not been
of application for free-space interferometric communications previouslyreported.
via the terrestrial atmosphere over propagation distances of These experimental observations, plus the data collected
practical interest. Further applications include the detection in previous experiments [1–3], lead us to conclude that N-
of even mild clear air turbulence [1] over various distances slitinterferometerswithlargeintrainterferometricpathlengths
applicabletocommercialaviationrunways. are ready for the next stage of development into practical
In previous publications [1–3] it has been indicated that configurations, either for secure free-space communication
the integrity of the interferometric characters is protected systemsor interferometric detection of clear air turbulence in
by the fundamental physics of interference [2, 7], which airfields.
4
J.Opt.13(2011)035710 FJDuarteetal
Acknowledgment [3] DuarteFJ2005J.Opt.A:PureAppl.Opt.773
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throughasubcontracttoBAESystems. [5] NewtonI1704Opticks(London:RoyalSociety)
[6] MichelsonAA1927StudiesinOptics(Chicago:The
UniversityofChicago)
Note added in proof. The interferograms with superimposed diffraction [7] FeynmanRP,LeightonRBandSandsM1965TheFeynman
patterns, as in figures 5, 6, and 8, can betheoretically described using the LecturesonPhysicsvol3(Reading,MA:AddisonWesley)
methoddisclosedin[10]thatallowsthecharacterizationofinterferenceviaa
[8] DiracPAM1978ThePrinciplesofQuantumMechanics
seriesofN-slitarraysalongthepropagationaxis[10].
4thedn(Oxford:OxfordUniversityPress)
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