A Compact Orbital Angular Momentum Spectrometer Using Quantum Zeno Interrogation

0.79 MB·

by  Paul Bierdz

A Compact Orbital Angular Momentum
Spectrometer Using Quantum Zeno
Interrogation
PaulBierdz,HuiDeng*
4
DepartmentofPhysics,UniversityofMichigan,AnnArbor,USA
1
[email protected],[email protected]
0
2

n
Abstract: We present a scheme to measure the orbital angular momen-
a
J tum spectrum of light using a precisely timed optical loop and quantum
1 non-demolition measurements. We also discuss the influence of imperfect
1 opticalcomponents.

] © 2014 OpticalSocietyofAmerica
s
c OCIScodes:050.4865Opticalvortices,120.4290Nondestructivetesting.
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t
p
o Referencesandlinks
.
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i
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h Review2,299–313(2008).
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1 tons,”Nature412,313–316(2001).
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5 7. D.Kaszlikowski,P.Gnacinacuteski,M.Zdotukowski,W.Miklaszewski,andA.Zeilinger,“Violationsoflocal
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Xi 11. J.M.Hickmann, E.J.S.Fonseca,W.C.Soares,andS.Cha´vez-Cerda, “Unveiling atruncated optical lattice
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a
12. Z.Wang,Z.Zhang,andQ.Lin,“AnovelmethodtodeterminethehelicalphasestructureofLaguerre–Gaussian
beams,”JournalofOpticsA:PureandAppliedOptics11,085,702(2009).
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Letters52,429–431(1990).
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computer-generatedholograms,”OpticsLetters17,221–223(1992).
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computer-generatedholograms,”JournalofModernOptics45,1231(1998).
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tomeasureorbitalandspin,orthetotalangularmomentumofasinglephoton,”PhysicalReview Letters 92,
013,601(2004).
17. G.C.G.Berkhout,M.P.J.Lavery,J.Courtial, M.W.Beijersbergen, andM.J.Padgett,“Efficientsortingof
orbitalangularmomentumstatesoflight,”PhysicalReviewLetters105,153,601(2010).
18. A.Peres,“Zenoparadoxinquantumtheory,”AmericanJournalofPhysics48,931(1980).
19. A.C.ElitzurandL.Vaidman,“Quantummechanicalinteraction-freemeasurements,”FoundationsofPhysics7,
987–997(1993).
20. P.G.Kwiat,A.G.White,J.R.Mitchell,O.Nairz,G.Weihs,H.Weinfurter,andA.Zeilinger,“High-Efficiency
quantuminterrogationmeasurementsviathequantumZenoeffect,”PhysicalReviewLetters83,4725(1999).
21. S0andS1areopticalswitchesthatcanbeswitchedfrombeentransmittivetoreflective.S0needstotransmitthe
initialincidentlight,andbeswitchedtobereflectivebytheendofthefirstouter-loopcycle.Ahighrepetitionrate
isnotrequiredanditcanbeimplemetedeithermechanicallyoropto-electrically.Alternativelyitcouldalsobea
statichigh-reflectancemirror,iftheone-timetransmissionlossattheverybeginningcanbetolerated.S1needsto
beswitchedeveryQZIloopcycle(D T)andneedtobepolarizationinsensitive.ThefastestswitchesarePockels
cells,whichcanoperateat10-100GHzwith99%transmission.Onescheme,similartotheoneimplementedin
Ref.[20],istoaninterferometerwithPockelscellsinoneofthearms.ThePockelscellsintroducep phaseshift
inthearmwhenactivated,andthusswitchthebeambetweentwooutputportsoftheinterferometer.Usingtwo
Pockelscellsrotatedrelativetoeachotherwillcancelthebirefringenteffect.
22. M.W.Beijersbergen,R.P.C.Coerwinkel,M.Kristensen,andJ.P.Woerdman,“Helical-wavefrontlaserbeams
producedwithaspiralphaseplate,”OpticsCommunications112,321–327(1994).
23. B.MisraandE.C.G.Sudarshan,“TheZeno’sparadoxinquantumtheory,”JournalofMathematicalPhysics18,
756(1977).
24. Technically,each a 2isslightlydifferent,butthedifferenceiswellwithin1%.The a 2thatmattersmostisthe
| | | |
onecorrespondingtotheQZIloop(includingS1),which,withoutanyoptimization,consistsof4beamsplitters,
5mirrors,1waveplateanduptothreePockelscells.Assumingallopticsareanti-reflectioncoatedsothatlossis
1%ateachPockelscelland0.1%ateachothercomponent,wehave a 2 0.96.
| | ≥
25. J.Jang,“Opticalinteraction-freemeasurementofsemitransparentobjects,”PhysicalReviewA59,2322(1999).
Lightcarriesquantizedorbitalangularmomentum(OAM)oflh¯ perphotonwhentheelectric
field has an overall azimuthal dependence on phase, e ilf , where f is the azimuthal angle
−
aboutthe beam propagationaxis [1, 2, 3]. The OAM quantumnumberl takes integervalues
from ¥ to +¥ . With an infinite number of states available, OAM can be utilized for qudit
−
(d-dimensional,d>2)systems[4]thatallow,forexample,higherdimensionalentanglement
[5], quantumcoin-tossing[6],increasedviolationsoflocalrealism[7], improvedsecurityfor
quantumkeydistribution[8],simplifiedquantumgates[9]andsuperdensecodingforquantum
communicationswithincreasedchannelcapacity[10].
Determining OAM of light in an unknown state, however, is more challenging than
measuring different polarizations or frequencies. Eigenstates of OAM can be deduced from
thediffractioninterferencepatternwithjudiciouslychosenapertures[11,12].Butthemethod
requires a large collection of photons to develop the pattern. Moreover it may become very
complicatedforsuperpositionsof OAM states. An l-fold forkdiffractiongrating[13, 14, 15]
can separate a pre-determined OAM component from others at the single photon level, but
cannotbereadilyappliedtodeterminearbitraryOAMstateoflight.AcascadeMach-Zehnder
interferometersetup,usingDoveprismstointroduceanl-dependentphaseshift,canseparate
differentOAM componentsof lightinto differentoutputportsof the interferometers,even at
thesingle-photonlevel[16].ButthesetuprequiresN 1mutuallystabilizedinterferometersto
−
detectNOAM-modes.Arecentlyproposedscheme[17]requiresonlyaspatiallightmodulator
(oraspeciallydesignedhologram),whichconvertsthetwistingphasestructureofOAMstates
intoalinearphasegradient,andalens,whichfocusesdifferentOAMcomponentstodifferent
spatiallocationsonthefocalplane.However,themethodreliesonintricatespatialmodulation
ofthephase,andthusmayhavelimitedapplicabilitytobroadbandultrafastpulses.Moreover,
theextinctionratiobetweendifferentOAMstatesislimitedtoabout10.Toincreasetheextinc-
tion ratio or to detect higher order OAM states will require larger and increasingly complex
holograms.
Inthispaper,wepresentacompactOAM-spectrometercomprisingofonlyoneinterferome-
ternestedwithinanopticalloop(Fig.1).ItusesaQuantumZenoInterrogator(QZI)[18,19,20]
Fig. 1. A schematic of the compact OAM spectrometer. The Quantum Zeno Interroga-
tor (shaded region) distinguishes betweenzero andnonzero OAM states.Theouter loop
decreasestheOAMvalueoflightbyoneperroundtrip.Allthebeamsplittersarepolariz-
ingbeamsplitters(PBSs)thattransmitshorizontallypolarizedlightandreflectsvertically
polarizedlight.TheOAMfiltertransmitsstateswithzeroOAM,butblocksstateswithnon-
zeroOAM.S0andS1areswitchingmirrorsthateithertransmitsorreflectsincidentlight
[21].R1andR2arefixedpolarizationrotators,whichcanbehalfwaveplates.P1andP2
arefastpolarizationswitches,suchasPockelscells.Whenactivated,P1andP2switches
horizontalpolarizationtoverticalandviceversa.Whende-activated,theyaretransparent
to light. The shaded region is a Quantum Zeno Interrogator [20] which separates OAM
componentswithl=0andl=0intodifferentpolarizations.HenceatPBS3,zeroOAM
6
component issenttothedetectorwhilethenone-zeroOAMcomponent issentbackinto
theouter-loop.TheouterloopdecreasedOAMbyoneperroundtripvia,forexample,a
vortexphaseplate(VPP)[22].
(shadedregioninFig.1)toperformcounterfactualmeasurementsontheOAMstate,andthus
mapsdifferentOAMcomponentsofanarbitraryinputlightpulseintodifferenttimebinsatthe
output.ItcanachieveveryhighextinctionratiosbetweendifferentOAMstatesandcanwork
forarbitrarilyhighOAMorderslimitedmainlybyopticallosses.
We illustrate now how the spectrometer works by tracing, as an example, a horizontally
polarized input pulse with an OAM value l = l 0, noted as y (0) = H,l . The input
0 0
≥ | i | i
pulse first transmits through optical switches S0 and S1 [21], and enters the QZI. The po-
larizationrotatorR1rotatesitspolarizationbyD q =p /(2N),andthestatebecomes y (0) =
| 1 i
cos p H,l +sin p V,l . If l = 0, the horizontal and vertical components of y (0)
2N | 0i 2N | 0i | 1 i
passes throughthe lower andupper armsof the interferometer,respectively.Theyrecombine
(cid:0) (cid:1) (cid:0) (cid:1)
into the same state y (0) at the polarizing beam splitter PBS2 (neglecting an overall phase
| 1 i
factor).S1isswitchedtobereflectiveattheendofthefirstQZIloop,andthecombinedbeam
continuestoloopintheQZI.ThepolarizationisrotatedbyD q =p /(2N)eachloop.AfterN
loops,thelightbecomesverticallypolarizedandentersonlytheupperpathoftheinterferom-
eter. At this point, the polarization switch P1 is activated and switches the polarization into
horizontal.HencethelighttransmitsthroughbothPBS2andPBS3,andarrivesatthedetector
attimeT .
0
If l =0, however, the vertical component is sent to the upper path at PBS1, and is then
0
6
blockedbytheOAMfilter.OnlythehorizontalcomponentemergesafterPBS2,thestatecol-
lapsesinto H,l withaprobabilitycos2 p .AfterNloops,afractionp=cos(p /(2N))2N of
| 0i 2N
thelightremainsinthehorizontalpolarizationinthelowerarmoftheinterferometer,whilea
(cid:0) (cid:1)
(babilitya) 111000--042 æìàòô æìçàòô æìçàòô æìçàòô æìçàòô æìçàòô æìçàòôOAæìçàòôMæìçàòô æìçàòô ìæçàòô æìçàòô æìçàòô æìçàòô (babilityb) 111000--042 æìàò æìçàòô æìçàòô æìçàòô æìçàòô æìçàòô æìçàòôOAæìçàòôMæìçàòô æìçàòô æìçàòô æìçàòô æìçàòô æìçàòô
o o ô
Pr 10-6 ç 0 2 4 6 8 10 Pr 10-6 0 2 4 6 8 10
æ à ì ò ô ç ç æ à ì ò ô ç
10-8 10-8
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
Number of Loops HNL Number of Loops HNL
Fig. 2. The probability of detecting the correct OAM value as a function of the number
of loops(N)intheQZIusingaperfect OAMfilter.(a)Neglect opticalloss.(b) Assume
a 2=0.96basedoncommerciallyavailableoptics.Whenopticallossisincluded,there
| |
exists an optimal N for higher order OAM states, due to the compromise between the
quantumZenoenhancementandopticalloss.
fraction1 pofthelightislost(blockedbyOAMfilter).Atthispoint,thepolarizationswitch
−
P2 is activated and switches the polarization to vertical, and the light reflects off both PBS2
andPBS3,andenterstheouterloop.Bythistime,S0isswitchedtobereflective.Asthelight
cycles in the outer loop, the polarization in rotated back to horizontal by R2, and the OAM
value is decreased by D l =1 per cycle by a vortex phase plate (VPP) [22]. After l cycles,
0
l=0.WhenthelightenterstheQZIagain,itwillexitthespectrometertothedetector,atatime
T(l )=T +l (NL +L )/c. Here L and L are the optical path lengths of the QZI
0 0 0 QZI out QZI out
loop(fromS1toPBS2backtoS1)andtheouter-loop(fromS1toPBS2,toPBS3,toS0,back
toS1).ThedetectedfractionofthelightintensityisP(l0)=pl0 =cos 2pN 2Nl0.
Inshort,theOAMspectrometersortsdifferentOAMcomponentsintodifferenttimeintervals
separated by D T = (NL +L )/c with a perfect extinction ratio.(cid:0)Th(cid:1)e total transmission
QZI out
efficiencyofthespectrometerisP(l )forthecomponentwithOAMofl h¯.P(l ) 1foralll
0 0 0 0
asN ¥ duetothequantumZenoeffect[23],asshownintheFig.2(a). →
→
In practice, optical components introduce loss. Assuming high quality, but commercially
available optical components, we estimate a round trip transmission of a 2 0.96 [24]
per cycle for both the outer loop (a ), the QZI loop (a ) and initial| a|nd∼final optics
out QZI
(a ).HencethetotaltransmissionefficiencyoftheOAMspectrometerbecomesP(l )
init,final 0
≈
a (2N+2)(l0+1)cos 2pN 2Nl0 forthe l0-thorderOAM component.We plotinFig. 2(b)theP(l0)
vs.N forOAMcomponentsl =0 10.WithincreasingN,thequantumZenoeffectleadsto
0
(cid:0) (cid:1) −
anincreaseinP(l ),whilelossleadstoadecreaseinP(l ).Asaresult,anoptimalN isfound
0 0
atabout7 8forhighorderOAMcomponents.Notethattheextinctionratiobetweendifferent
−
OAMstatesremainsinfiniteeveninthepresenceofloss.Crosstalkwouldonlytakeplacewhen
theOAMfilterisnotcompletelyopaquetononzeroOAMstates.
To take into account imperfect OAM filters, we derive below the general expression for
thetransmissionefficiencyandextinctionratio,withfiniteN andopticalloss.Weconsiderthe
OAMfilterhavingacomplextransmissioncoefficient T(l)eif (l)forthelthOAMcomponent.
Ifthestate y = H,l enterstheQZI,afterN cycles,itexitstheQZIloopinapolarization
0
| i | i p
superpositionstate p H +p V [25],where p and p aregivenby:
H V H V
| i | i
p p N
p 1 0 cos sin 1
(cid:18) pHV (cid:19)=a QNZI(cid:20)(cid:18) 0 T(l)eif (l) (cid:19)(cid:18) sin(cid:0)22pNN(cid:1) −co(cid:0)s2N2pN(cid:1) (cid:19)(cid:21) (cid:18) 0 (cid:19). (1)
p (cid:0) (cid:1) (cid:0) (cid:1)
1.000 (b)
(a)
0.500
y 0.100
bilit 0.050
a
b
o 0.010
Pr 0.005
0.001
0.0 0.2 0.4 0.6 0.8 1.0
Transmission
Fig.3.TheprobabilitiesofdifferentoutcomesofaQZIinterrogationasafunctionofthe
transmissionoftheOAMfilter,neglectingopticalloss.Thebluesolidlinerepresentsde-
tectingOAM=0,thereddashedlineisdetectingOAM=0,andtheorangedottedline,loss.
6
(a)N=8.(b)N=2 10.
−
Thepulsere-enterstheouterloopatPBS3withprobability p 2,correspondingtoasuccessful
H
interrogationbythe QZI (if l =0).With probably p 2,|the|pulse exitstowardthe detector,
0 V
correspondingto an error(if l6 =0). The total loss|of t|his QZI interrogationis loss2 =1
0
6 | | −
p 2 p 2.Intheouterloop,theOAMvalueofthepulseisloweredby1viatheVPP,and
H V
t|he|int−en|sity| ofthepulseisreducedbya factor a 2 perloop.Therefore,theprobabilityof
out
| |
detectingtheOAMeigenstatel inthelthtimeinterval(or,measuredaswithOAMlh¯)isgiven
0
by:
P(l;l )= a 2 p (l l)2 (cid:213) l0 a 2 p (m)2 . (2)
0 init,final V 0 out H
| | | − | | | | |
m=l0−l+1(cid:0) (cid:1)
Andwedefinetheextinctionratioh as:
h (l )=P(l ;l )/(cid:229) P(l;l ). (3)
0 0 0 0
l6=l0
WithanimperfectOAMfilter,lightwithnonzeroOAMhasafiniteprobabilityoftransmit-
tingthroughthefilter inverticalpolarizationaftertheNth QZI-loop.Itwillthenbeswitched
tohorizontalpolarizationbyP1andexitata timeintervalcorrespondingtocomponentswith
alowerOAM.Consequently,theextinctionratioisreduced.Ifthelightistransmittedthrough
thefilterbeforetheNthloop,itwillresultsinalargerloss.AnimperfectOAMfiltermayalso
partiallyblocklightwithzeroOAM,whichwhichalsoresultsinloss.
Figure3(a)shows,perquantumZenointerrogationoflightwithOAMoflh¯,theprobabilities
ofthelightexitingtowardthedetector( p 2),re-enteringtheouter-loop( p 2)andbeinglost
V H
| | | |
(1 p 2 p 2). These probabilitiesare plottedas a functionof transmissionT(l,a ) and
V H 0
N.−Th|ec|ro−ssi|ng|of p 2 and p 2 separatestheregimeswhentheinterrogationresultismore
H V
| | | |
likely(totherightside)orlesslikely(totheleftside)tobecorrectthanincorrect.
AsapracticalexampleofanimperfectOAMfilter,weconsiderapinholespatialfilter.Light
with OAM of lh¯ =0 has zero intensity at the center of the beam, while light without OAM
6
hasmaximumintensityatthecenter.Henceaverysimplepinholeefficientlydistinguisheslight
with and without OAM. The intensity distribution of a Laguerre-Gaussian beam, a paraxial
beampossessingOAMlh¯,isgivenby[1]:
I √2r |l| 2r r2
ILG(l;r )= 0¥ duu|l|e0−uLl(u) w0 ! L|l|(cid:18)w20(cid:19)e−w20 (4)
||
R
1.000 1æ
(a) 0.500 (b) æ
æ
10-4 æ
mission 00..015000 mission 10-8 æ æ æ
ans 0.010 0 ans 10-12 æ æ
Tr 0.005 12 Tr 10-16 æ æ
3
0.001 10-20
0.0 0.5 1.0 1.5 2.0 0 1 2 3 4 5 6 7 8 9 10
ApertureSizeHa0L OAMHlL
Fig.4.Transmissionofthepinholespatialfilter(a)asafunctionofthenormalizedaperture
sizea0,forOAMcomponentswithl0=0 3and(b)asafunctionofl0witha0=0.8.
−
500 107
(a) |a|2 (b)
450
1.00 106
400 0.96
)350 0.95* )105
h 0.90 h
( (
atio300 atio104
R R
250
n n
ctio200 ctio103
n n
Exti150 Exti102
100
101
Dl
50
1 2 3
0 100
5 10 15 20 25 30 0.4 0.6 0.8 1
Number of Loops (N) Aperture Size (a )
0
Fig. 5. (a) Extinction ratio h as a function of the number of loops N for various losses
a 2.Solidsymbolsareforl0=1andopensymbolsareforl0=3.l0>3areessentially
| |
indistinguishablefroml0=3.Forthel0=0case,theextinctionratioisovera1000forall
a 2valuesbecausenoprematuremeasurementsarepossible.Theadditionalgreencrosses
|lab|eled as a 2=0.95 represents a 2=0.96 but including misalignment of the OAM
∗
filterandV|PP|asdiscussedinthetex|t.(|b)Extinctionratioh asafunctionofthenormalized
aperture size a0 for l0=6, D l =1 3, N =8, and a 2 =0.96. Skipping OAM states
− | |
increasestheextinctionratiobyordersofmagnitude.
WhereL(x)isthelthorderLaguerrePolynomial.ThusthetransmissionT(l)throughapinhole
l
witharadiusa (normalizedbythewaistofthel =0Gaussianbeam)is:
0 0
T(l,a )= a0 2p r dr df I (l;r ) ¥ 2p r dr df I (l;r ) (5)
0 LG LG
0 0 0 0
Z Z (cid:30)Z Z
Figure 4(a) shows T(l,a ) vs. a for l =0 3. The transmission decreases sharply with
0 0
−
increasinglwhena issmallerthan 0.8.Choosinga =0.8,weshowinFig.4(b)thenearly
0 0
∼
exponentialdecreaseofT(l,a )withl.Thesevaluesarealsomarkedbytheredverticallines
0
inFig.3(a).DuetothefastdecreaseofT(l,a )froml=0tol 1,alargeextinctionratiois
0
≥
100
(a) 100 (b)
10-2
10-3
y
ability1100-05 8910 10-6 Probabilit 10-4
Prob10-10 67 10-9 10-6
10-15 45 l0 10-12 OAM
0 3
1 0 2 4 6 8 10
2 3 4 5 6 12 10-15 10-8 2 4 6 8 10 12 14 16
l 7 8 0 Number of Loops (N)
9
10
Fig.6.(a)TheprobabilityofmeasuringanOAMvaluel foragiveninputstatel (Equa-
0
tion 2), using pinhole as the OAM filter, N =8, a 2=0.96, and misalignment of 10%
| |
and1%,respectively,atthepinholefilterandVPP.Despitethedecreaseinprobabilityfor
thediagonal elementsatlargel ,theoff diagonal elementsdecreasemuch faster,asim-
0
pliedbythelargeextinctionratios.(b)Thediagonalelementsof(a)asafunctionofNfor
l0=0 10.
−
readilyachieved,whichisverywellapproximatedby:
h (l0)=P(l0;l0)/(cid:229) P(l6=l0;l0)≈ a out|pVp(V0)(|12)|p2H(1)|2. (6)
| |
h is essentially the same for all OAM components,and it is mainly determinedby how well
theQZIcandistinguishbetweenstateswithOAMvaluesl =0andl =1.WeplotinFig.5(a)
0 0
h vs.N for a 2=0.9 1.Ingeneral,h increaseswithN butdecreaseswith a 2,resultingin
anoptimalN| f|oreach−a 2 <1.Evenfor a 2=0.9,h >70canbereached|wi|thN =7.For
a 2=0.96,h peaksat| |180. | |
| | ∼
An additional source of error is due to the misalignment of the beam through two OAM-
sensitivecomponents:theOAMfilter(e.g.apinhole)andtheVPP.Misalignmentatthepinhole
filter leads to reduced coupling efficiency of the zero OAM state, increased transmission of
non-zeroOAMstates,andthusreducedextinctionratio.MisalignmentontheVPPchangesthe
desiredOAMstateintoasuperpositionwithneighboringOAMorders.However,theseneigh-
boringordershaveverysmallamplitudes(e.g.<1%with1%misalignment)[4],andtheyare
furtherfilteredoutthroughtheQZIloop,resultinginnegligiblereductionintheextinctionratio.
ThemaineffectofmisalignmentatVPPistheslightlyreducedtransmissionofthecorrectOAM
state,hencereducedoveralldetectionprobability.Weillustratetheeffectsofmisalignmenton
theextinctionratioinFig.5(a)(thegreencrosses),assumingconservatively10%misalignment
ofthefocusedbeamwaistatthepinholeand1%misalignmentofthecollimatedbeamwaistat
theVPP.Extinctionratiosover100arestillreadilyachieved.
Theextinctionratiocanbeincreasedbymanyordersofmagnitudeifweonlyneedtomea-
sure every other order, or every third order of OAM (Figure 5(b)). Correspondingly,we can
choose smaller aperture sizes and a VPP that reduces the l by D l = 2 or 3 per passing. A
smaller aperture size also introduces extra loss, but only in the final QZI on the zero OAM
state,andthusonlydecreasesthedetectionprobabilitybyaboutafactoroftwo.
To evaluatetheoverallperformanceofthe OAM spectrometer,we plotinFig. 6(a)P(l;l )
0
vs.l andl onthelogscale,includinglossandmisalignment.ThediagonalelementsP(l ;l )
0 0 0
correspondtocorrectlydetectinganOAMcomponent.Theyaretwoordersofmagnitudehigher
than neighboring off diagonal elements, consistent with the high extinction ratios calculated
before.InFig.6(b),weshowP(l ;l )asafunctionofNfordifferentl .N 8givesthehighest
0 0 0
∼
probability for detecting high order OAM components, while still maintaining an extinction
ratioofabove100.
Insummary,wepresentacompactOAMspectrometerthatdisperseslightofdifferentOAM
valuesintime.LossissignificantforhighorderOAMcomponentswithcommerciallyavailable
optical components. However, the high loss doesn’t have an appreciable effect on the signal
to noise ratio; extinction ratios of >100 are readily achieved even after taking into account
opticallossandmisalignments.Theextinctionratiocanbefurtherimprovedbymanyordersof
magnitudebyskippingOAMorders,orbyusingabetterOAMfilterthanasimplepinhole.