Ghost Imaging: Open Secrets And Puzzles For Undergraduates

2y ago
19 Views
2 Downloads
1.42 MB
9 Pages
Last View : 21d ago
Last Download : 2m ago
Upload by : Mollie Blount
Transcription

Ghost imaging: Open secrets and puzzles for undergraduatesLorenzo Basanoa兲 and Pasquale OttonelloDipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Italy共Received 8 June 2006; accepted 5 January 2007兲Ghost imaging, a novel technique in which the object and the image system are on separate opticalpaths, was first demonstrated using entangled photon pairs. This demonstration caused it to beregarded as a purely quantum effect, but subsequent work gave wide support to a classicalexplanation. We provide an introduction to ghost imaging based more on intuition than onformalism and discuss several experiments that can be implemented in a university physicslaboratory. 2007 American Association of Physics Teachers.关DOI: 10.1119/1.2437745兴I. INTRODUCTIONThe history of ghost imaging began shortly after the birthof ghost interference. Although we will consider only theformer technique, our discussion will be clearer if we beginwith the latter. In 1995 Klyshko and co-workers published anintriguing paper on two-photon ghost interference anddiffraction.1 A pair of entangled photons 共conventionallycalled the signal and the idler兲 are produced by spontaneousparametric down conversion2,3 and sent along two differentpaths. A double slit is placed only in the signal arm, and thetwo photons of each pair are eventually revealed by twodistant pointlike detectors. As expected, no first order interference pattern can be detected behind the double slit, due tothe insufficient spatial coherence of the individual beams.Nevertheless, an interference pattern can be observed bycounting coincidences between the fixed detector and theidler detector as the latter is moved in a transverse direction.The amazing aspect of this result is that the interference pattern is revealed by moving the detector in the path that doesnot contain the double slit 共hence the name ghost兲. Becausethe explanation of this surprising result is related to the nonlocal correlations of entangled photons, the experiment wasclassified as a purely quantum effect belonging to the EPR共Einstein-Podolsky-Rosen兲 type.In ghost imaging4 the apparatus differs slightly from theinterference setup we just described. A double slit is placedin the signal arm, but now the purpose of the experiment is toretrieve a ghost image of the double slit rather than the interference pattern produced by it. To achieve this goal, allphotons passing through the double slit are conveyed onto a“bucket” detector located in the focal plane of a collectinglens. The bucket detector can only reveal photon arrivals andcannot gain any information on the aperture shape. The detector placed in the other arm 共the idler兲 cannot acquire anyinformation about the aperture because photons arriving at itfollowed the path where the double slit was absent. It isremarkable that an image of the double slit can be retrievedby correlating the outputs of two detectors, neither of whichconveys information about the shape of the aperture. In thiscase, too, the use of the term “ghost” is appropriate.More recently the results of these experiments on ghostinterference and ghost imaging were described as purelynonlocal quantum effects, not amenable to a classicalinterpretation.4,5Bennink et al.6 have realized a conceptually remarkableexperiment that satisfied the protocol of ghost imaging andwas based on a classical source of light. Their apparatus343Am. J. Phys. 75 共4兲, April 2007http://aapt.org/ajpcreates a pair of very thin rays whose propagation directionsare individually random but spatially correlated and thusmimic the spatial behavior of an entangled photon pair.7Their experiment is able to emulate the imaging capability ofthe spontaneous parametric down conversion apparatus because the latter exploits only the spatial correlation of thebeams 共while correlations linking other properties of entangled photons such as phase, energy, and polarization arenot used兲. Later, Lugiato and co-workers showed that classical ghost imaging can be produced not only by needlelikebeams but also by speckle beams of extended crosssection.8–10 This result confirmed that the essential nature ofghost imaging is in the mutual spatial correlation of thebeams, whose nature might be quantum 共entangled photonpairs兲 or classical 共correlated needlelike rays or pairs ofbeams endowed with random internal speckles兲. In eithercase a ghost image can be retrieved using a suitable dataprocessing technique.We begin our introduction to ghost imaging by discussingthe needlelike beam pair because it lets us use elementaryclassical reasoning without losing sight of the essential elements of ghost imaging. Although our description is initiallysimple, it later involves more complex ideas such as the statistical features of speckle patterns and the basic elements ofconvolution. We have tried to meet the needs of a wide readership by describing the main mathematical tools that willenable as many readers as possible to follow our presentation.The paper is organized as follows. In Sec. II we describehow a ghost image arises from the use of the apparatus inRef. 6. The discussion of this experiment is very informativebecause it emphasizes the fundamental role played in ghostimaging by the mutual spatial correlation of the beams. InSec. III we follow Refs. 8–10 and ask if needlelike rays arereally necessary and what the consequences are of usingbeam pairs of extended and internally structured cross section, such as those produced by quasi-thermal light sources.11We will see that two main cases, which require distinct treatments, should be considered according to whether the average speckle size is comparable to the details of the object tobe imaged 共Sec. III A兲 or much smaller 共Sec. III B兲. At thispoint, we will have described the relevant classical procedures for obtaining ghost imaging, but we will still lack aninterpretation of the original ghost imaging experimentsbased on entangled photon pairs. This gap is filled in Sec. IV.Appendix A is a brief primer on the main statistical featuresof speckle patterns, and Appendix B offers a detailed de 2007 American Association of Physics Teachers343

Fig. 1. Schematic of the experimental setup used with a needlelike source.PB: primary beam; ROM: randomly oscillating mirror; BS: 50% beam splitter; B1: image beam; CCD: camera; B2: object beam; OM: object mask;BD: bucket detector for measuring the total intensity going through themask; and G: gate allowing the camera to record the images.scription of the experimental apparatus. Appendix C explainsthe much debated case of ghost imaging produced by quasithermal light.II. AN ELEMENTARY IMPLEMENTATIONOF GHOST IMAGING (RANDOMLY DEFLECTEDNEEDLELIKE CLASSICAL BEAMS)As mentioned in Sec. I, the apparatus described in Ref. 6created a true ghost image of a mask and required only aclassical description. Ghost imaging was described as “anovel imaging method in which the object and imaging system are on different optical paths and are illuminated separately by correlated optical fields.”6Figure 1 illustrates the setup used in Ref. 6. In the following we do not use the terms “idler” and “signal,” which areused for quantum entangled photons, and refer to the twobeams as “image” and “object.” The chopped primary beam共PB兲 is first randomly deflected about the forward directionby the randomly oscillating mirror 共ROM兲 and is then divided by the beam splitter BS into two identical beams B1and B2. The image beam B1 is sent to the CCD camera. Theobject beam B2 is passed through the transparent mask OM共the object to be reconstructed兲. Suppose that OM consists ofan opaque mask pierced by three circular holes of equalsizes, H1, H2, and H3 共see Fig. 2兲. The total intensity of B2exiting the mask is measured by the bucket detector BD,which is activated by the arrival of photons that have crossedthe mask’s openings. The activation of BD does not dependon which hole the photons have gone through 共photons re-vealed by the bucket detector convey no information aboutthe shape of the mask兲. The gate G provides an enable signalto the CCD camera, depending on the value of the bucketdetector output. In this experiment the travel directions ofbeams B1 and B2 are individually random but strongly correlated. If, at a certain instant, we know where one beam isgoing, we can tell exactly where the other one is heading.Let’s now see how a faithful copy of the mask can beobtained and why it can be called a ghost image. By theproper control of the mirror oscillations, the object ray B2can be made to hit the mask OM at some random positionwith almost uniform probability. This position may lie eitherwithin one of the holes or in the opaque part of the mask. Forexample, consider the two cases shown in Fig. 2. In the first,the object ray B2 goes right through the center of H1, andthen proceeds past the mask until it reaches the bucket detector which, in turn, enables the CCD camera to record theevent. Because of the strict angular correlation of the tworays, image ray B1 will hit the CCD camera 共and be recordedby it兲 at a position that corresponds to the center of H1. Forthe case that B2 does not meet a hole, the ray is absorbed bythe opaque portion of the mask, and no gate pulse is delivered to the CCD camera and no event is recorded. Thus, asthe images are acquired and summed in the video boardmemory, a clear image of the three holes will emerge after alarge number of trials. Note that there is no quantum elementin this process, nor are photons necessary to implement it.For example, bullet pairs fired against a metal mask by properly correlated guns would produce an equivalent effect. Inthis setup all the CCD images are formed only by photonsthat travel in the arm where there is no mask, and hence theapparatus satisfies the definition of ghost imaging given inRef. 6.In the simplest form described here, a ghost-image apparatus can be interpreted as the optical version of the keyduplicator at a hardware store. A faithful copy of a key isobtained because the position of the milling head 共in our caseray B1兲 is strongly correlated with the position of the tipsensing the object profile 共in our case ray B2兲. Nobodywould maintain that the key duplicator is a nonclassical device because the milling head does not interact locally withthe original object. It is the spatial correlation between thesensing tip and the milling head that allows us to create afaithful copy of the original key.The logic of the needlelike rays experiment performed inRef. 6 is strikingly similar to that of the quantum experiment,which employed entangled photons.4 More general questionsnaturally arise. For example, to what extent can the true nature of ghost imaging be regarded as a quantum effect?III. GHOST IMAGING WITH THERMAL LIGHT:PRELIMINARY COMMENTSFig. 2. Object mask consisting of three holes of equal size pierced in anopaque material. The symbols and exemplify two points at which thebeam B2 may hit the mask. In our experiment the hole diameter is 1 mmand the hole-to-hole distance is 4 mm.344Am. J. Phys., Vol. 75, No. 4, April 2007In this section some knowledge of speckles and their mainstatistical features12 is required. Appendix A describes thephysical origin of speckles and their relevant properties.The idea that the crucial element in ghost imaging is thespatial correlation of two beams received an important confirmation in Refs. 8–10 in which it was shown that ghostimaging can also be obtained classically when the crosssectional area of each beam is not negligible and exhibitsrandom intensity fluctuations that render the illumination ofthe mask completely incoherent. Even though no first orderinterference effect is detectable behind the object, the correLorenzo Basano and Pasquale Ottonello344

Fig. 3. Same setup as in Fig. 1, with the needlelike source replaced byquasi-thermal light. A threshold control has been added in the object channelto improve the visibility of the final image.lation of the two beams lets a faithful image of the apertureemerge by properly designed processing, as explained in thefollowing.At first sight, the goal of obtaining a ghost image usingextended incoherent beams might seem hopeless. Recall thatthe success of the experiment in Ref. 6 relies on the fact thatthe beam pairs in their apparatus are pointlike and correlated.So even though the CCD camera does not receive photonsthat went through the mask, it records the position of theirtwins that are translated with respect to the former by a fixedamount 共which is also the secret of ghost imaging producedby entangled photon pairs兲. This explanation of ghost imaging is simple as the key duplicator analogy reveals. If theneedlelike rays of Sec. II are replaced by beams of nonzerocross section, each beam’s cross section exhibits a randomintensity structure 共speckles兲, and the beam cross sections arelarger than the object to be copied. In this case the pointreconstruction of the image that is justified in Ref. 6 can nolonger be invoked.We emphasize the essential change that takes place whenwe shift from needlelike rays to extended speckle beams.With needlelike rays, each frame contributes to the final image with a single bright dot whose position is inside an areathat corresponds geometrically to one of the holes. Brightdots falling outside the three hole areas cannot activate thecamera gate 共see Fig. 2兲. Ideally, the camera accumulatesbright dots according to a noiseless reconstruction, that is,there will be light inside the hole images and dark outsidethem.With speckle beams, each frame grabbed by the CCDcamera is a random collection of bright and dark patches共speckles兲 covering an area larger than the mask. In eachframe there may be light where the mask image necessitatesdark, which implies the occurrence of a large amount ofnoise; it is difficult to visualize how the sum of such randomand noisy images will be able to reproduce the ordered pattern of the mask. An explanation of this successful reproduction requires subtle statistical considerations that we willnow describe.In Fig. 3 beams B1 and B2 create 共on any plane theyintersect兲 two random speckle patterns whose average granularity is much smaller than the beam cross section; each ofthe beams is then spatially incoherent. Because B1 and B2are generated from a single beam that divides at a 50%–50%beam splitter, they are mutually coherent and generate a pairof identical speckle patterns in the object and in the imageplanes 共see Fig. 4兲. This description can explain many results345Am. J. Phys., Vol. 75, No. 4, April 2007Fig. 4. Sample of a twin speckle pair: one impinges on the CCD camera, theother one on the object mask.of ghost imaging that were often ascribed to quantum behavior. But quantum mechanics is not needed, nor is it needed toexplain the famous Hanbury-Brown and Twiss spatialcorrelations.13 The goal of ghost imaging with random lightis to reconstruct an image of the mask under the followingconditions:共1兲 The instantaneous speckle pattern falling on the CCDcamera is produced by B1, that is, by the beam thatnever interacts with the object. If we would simply sumall the speckle patterns falling on the CCD camera, wewould not obtain anything but noise.共2兲 The instantaneous speckle pattern falling on the maskis identical to the pattern falling on the CCD camera共Fig. 4兲.共3兲 The response of the bucket detector BD is the value ofthe total intensity that passes through the mask. According to the conventional procedure used in ghost imaging,the BD’s response is the statistical weight of each patternin the final average.The first condition tells us that we should not treat allimages reaching the CCD camera on an equal footing. Certain images are to be weighted more than others. Althoughthe choice of a particular selection criterion is essential inghost imaging, it is evident that, according to conditions 共2兲and 共3兲, a selection criterion should be based only on theresponse of the bucket detector, because this response is theonly parameter possessing a memory of the presence of amask. An important issue is that there is not a universal rulefor attributing a statistical weight to the useful images. Recall, for example, that a binary selection method was employed in Sec. II: the needlelike beam falling on the camerawas either recorded or discarded. As we will see, more flexible rules can be adopted when the beam sections contain arandom structure, as in ghost imaging with thermal light.A. Ghost imaging with thermal light: Intermediate-sizespeckleWe describe here how we can reconstruct the image of amask when the average size of the speckles produced by thetwin beams is comparable to the dimensions of the apertures.A similar problem involving a double slit was solved theoretically and demonstrated experimentally in Ref. 14.To assess the efficiency of speckle imaging it is essentialto understand why the relative size of the speckle granularityaffects the results. To this end we use a mask pierced byLorenzo Basano and Pasquale Ottonello345

Fig. 5. Reconstruction of the object for a single hole mask; the threshold is kept at a low level. In Figs. 5–7 the average speckle size is about 300 m.three 1 mm holes, each of which can be closed if desired.The speckle size is about one-third of the hole dimensionsand is significantly smaller than the hole-to-hole separation共4 mm兲. For completeness, we recorded the images thatformed when one, two, or three holes were open.According to point 共3兲 of Sec. III, the image of the mask isrecovered by summing the speckle patterns falling on theCCD camera 共none of which interacts with the mask beforebeing summed兲. Each CCD speckle pattern is multiplied bythe output of the bucket detector produced in the other armby the twin pattern impinging on the mask. We again emphasize that the value of this multiplier is unrelated to the shapeof the mask and acts as a statistical weight assigned to eachimage in the final sum. The mathematics of this proceduregiven in Eq. 共C5兲 is that a faithful image of the mask isobtained by the convolution of the mask transparency function with the autocorrelation function of the speckle pattern.This procedure has been successfully employed to comparetheory to experiments on ghost imaging produced by thermallight.9 In these experiments10 the gate circuit G was notpresent, and the statistical weight assigned to each specklepattern impinging on the CCD camera was provided by thevalue of the bucket output.Before discussing some practical consequences of Eq.共C5兲, we ask if we can find a better method for improving thevisibility of the reconstructed image; that is, a method moreefficient than that of merely multiplying each speckle patternby the value of the corresponding bucket detector output. Wefound that the efficiency can be improved; the explanation issimplest for the one-hole mask.Suppose that the gate threshold has been set at a valuebelow which a speckle pattern is rejected. In other words, aCCD pattern is admitted to the final summation only whenthe corresponding bucket detector output is sufficiently large,that is, when the mask aperture is sufficiently illuminated. Inthe one-hole case, each time the speckle pattern B1 is recorded by the camera, its twin pattern B2 must exhibit abright speckle at the hole’s position; otherwise, the bucketdetector would not be able to send a gate pulse. Thus, themain effect produced by a proper setting of the threshold is346Am. J. Phys., Vol. 75, No. 4, April 2007that the speckle patterns summed by the CCD camera 共andcontributing to the final image兲 must all contain a bright spotat the hole’s position. The consequence of this selection isthat an enhanced image of the hole will emerge above thesurrounding background noise 共see Fig. 5兲. By proper settingwe mean that the threshold level should be neither too low共no selection would be made兲 nor too high 共only very fewpatterns would be summed and the statistical a

Ghost imaging: Open secrets and puzzles for undergraduates Lorenzo Basanoa and Pasquale Ottonello Dipartimento di Fis

Related Documents:

are a stupid ghost. The least a ghost can do is to read a man’s thoughts. However , a worthless ghost like you is better than no ghost. The fact is, I am tired of wrestling with men. I want to fight a ghost”. The ghost was speechle

Nov 07, 2021 · Tues. & Thurs. 5:30 pm Holy Ghost Wed. & Fri. 8:30 am Holy Ghost Weekend Saturday 5:00 pm Holy Ghost Sunday 8:00 am Holy Ghost 9:30 am St. Bridget 11:00 am Holy Ghost

COUNTY Archery Season Firearms Season Muzzleloader Season Lands Open Sept. 13 Sept.20 Sept. 27 Oct. 4 Oct. 11 Oct. 18 Oct. 25 Nov. 1 Nov. 8 Nov. 15 Nov. 22 Jan. 3 Jan. 10 Jan. 17 Jan. 24 Nov. 15 (jJr. Hunt) Nov. 29 Dec. 6 Jan. 10 Dec. 20 Dec. 27 ALLEGANY Open Open Open Open Open Open Open Open Open Open Open Open Open Open Open Open Open Open .

The term "ghost kitchen" has surged in popularity over the past year. In this rst section of The Beginner's Guide to Ghost Kitchens, we outline what a ghost kitchen is and what sets it apart from the rest of the dining industry. A ghost kitchen is a food facility that operates exclusively for online and delivery orders.

Green: ghost solid. 4 The Ghost SPH Method 4.1 Algorithm Overview We solve the particle deficiency at boundaries and eliminate arti-facts by (1) dynamically seeding ghost particles in a layer of air around the liquid with a blue noise distribution, (2) extrapolating the right quantities from the liquid to the air and solid ghost parti-

the term Ghost Schedule. It is prudent to discuss what a Ghost Schedule is not. A contractor's Ghost Schedule is not a schedule maintained in lieu of submitting a baseline schedule and schedule updates per the contract. Even if the contractor is using a Ghost Schedule, it still must comply with the contract's scheduling requirements. An .

Gerald Massey's “ Book of.the Beginnings,” 338, 415 Ghost at Noon-day, 321 Ghost—The Gwenap, 268 Ghost—The Micklegate, 23, 60 Ghost-seeing, in North American Review, 307 Ghost, Solitary Visit by a, 367 Ghosts by Day, 350 Ghosts in Africa, 33 Ghosts, The Truth about, 325, 343 Ghosts,

Required Texts: Harris, Ann Sutherland. Seventeenth Century Art and Architecture, 1st or 2nd edition will work, only 2nd edition available in book store Harr, Jonathan. The Lost Painting: The Quest for a Caravaggio Masterpiece. Optional Text: Scotti, R.A. Basilica: The Splendor and the Scandal: The Building of St. Peters’s; Barnett, Sylvan.