20121221234921_ApplPhysLett_89_091109

Experiment in lensless ghost imaging with thermal light Lorenzo Basano and Pasquale Ottonello

Citation: Appl. Phys. Lett. 89, 091109 (2006); doi: 10.1063/1.2338657

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Experiment in lensless ghost imaging with thermal light Lorenzo Basano and Pasquale Ottonello a?

Dipartimento di Fisica,Universitàdi Genova,Via Dodecaneso33,16146Genova,Italy

?Received12April2006;accepted3July2006;published online30August2006?

According to a recent experiment in lensless ghost imaging with thermal light,the image is unblurred only when the object and the image planes are equally distant from the source of light.

This result unambiguously supports the view that thermal light ghost imaging is basically a quantum effect.The authors present evidence?based on experiments as well as on simulation?that the blurring is nonexistent and no quantum explanation is necessary.?2006American Institute of Physics.?DOI:10.1063/1.2338657?

Recently,a remarkable result1in ghost imaging2–8pro-duced by thermal light9–14was reported in this jounal.For the bene?t of the readers,the experimental setup and the measuring procedure are brie?y summarized here.We also add that the apparatus used in the present letter is an exact replica of that employed in Ref.1;therefore,Fig.1below can be used as a guide for describing both works.

The object whose image is to be optically reconstructed consists of a double slit located in the X1plane of arm A,at a distance d A from the thermal light source.15A bucket de-tector D1,placed behind the object,collects all the light passing through the slits.In arm B?the alternative path cre-ated by the beam splitter?a point detector D2,located at a distance d B from the primary source,scans the X2plane perpendicularly to the light path.

The photocurrents output by D1and D2are?rst dc blocked?to remove the average background noise?and are then sent to a multiplier whose output,after low-pass?lter-ing?RC?60s?,is plotted versus the transverse position of detector D2.

The following results of Ref.1are relevant to the present letter.

?1?When d B=d A,i.e.,when the object and the detector D2 are equally distant from the source of light?the“in-focus”condition?a lensless,high visibility,equal-size ghost image of the object is obtained?Fig.3?a?of Ref.

1?.As we will see below,this result can be easily ex-plained in terms of classical intensity?uctuation corre-lations.

?2?When d B d A,i.e.,when D2is moved to a slightly dif-ferent distance?“out-of-focus”condition?the image ob-tained turns out to be severely blurred?Fig.3?b?of Ref.

1?.This position-sensitive blurring is the key result of that experiment as it supports the view that“lensless imaging with thermal light is a quantum two-photon in-terference effect.”1Of course this occurrence,like other remarkable experiments in which the effects of quantum mechanics come into view at the macroscopic level ?e.g.,the violations of Bell’s inequalities?,appears to be strikingly at variance with classical intuition.To appre-ciate more clearly this point and to prepare the ground for our?nal conclusions,we outline here the reasoning one would follow to predict the result of the same ex-

periment using only the classical intensity correlation of speckle patterns.

In our apparatus,when the ground glass disk is still and

the beam splitter is missing,a stationary and well developed

speckle pattern forms in the X2plane.When we insert the

beam splitter and set d B=d A,an exact copy of this stationary

speckle develops in the X1plane,where the double slit is

located.When d B d A the speckle patterns in the two arms are the same except for magni?cation.16The total intensity of

the light passing through the slit pair is measured by the

bucket detector D1.

Now let us set the ground glass disk in motion,after

accurately verifying that d B=d A.The speckle patterns lying

on X1and X2begin changing with time but,at any given

instant,they are identical to one another.The?rst part of the

experiment consists in plotting the correlation of the photo-

currents output by D1and D2versus the transverse position

of D2in the X2plane.The result of our measurement,shown

in Fig.2?a?,is a well contrasted equal-size reproduction of

the double slit,in perfect agreement with Ref.1.The classi-

cal explanation of this imaging is that we perform the cross

correlation by multiplying each intensity pro?le in arm B by

the total intensity passing through the slits in arm A;this

procedure is statistically biased in favor of speckle patterns

a?Electronic mail:

ottonello@ge.infn.it

FIG.1.Schematic of our experimental apparatus.X1—object plane,X2—

image plane,D1—bucket detector,D2—point detector,thermal source—

He–Ne laser impinging on ground glass disk,and dc block—remover of

constant noise level.The details of the experimental apparatus are the fol-

lowing:width of each slit=300?m;interslit distance?center to center?

=1.0mm,average speckle size at a distance of500mm from the

source=200?m,and size of detector D2=100?m.

APPLIED PHYSICS LETTERS89,091109?2006?

0003-6951/2006/89?9?/091109/3/$23.00?2006American Institute of Physics

89,091109-1

that have intense bright spots at the slit positions and pro-duces,in the long run,a smoothed but distinct image of the object.

It is now easy to predict classically how the result shown in Fig.2?a ?is expected to change when D2is progressively separated from the primary source:d B ??d B =d A .This can be done on the following grounds.?1?The total intensity mea-sured by detector D1does not change when we alter the distance of detector D2from the source.?2?As the X2plane is taken away from the source ?by increasing d B to d B ??,the speckle pattern lying on X2suffers only a magni?cation by the factor d B ?/d B .

Therefore,in view of points ?1?and ?2?above,the clas-sical intensity correlation of speckle patterns predicts that,when d B ??d A ,we should obtain an unblurred image of the object,magni?ed by the factor d B ?/d B .

This conclusion is also nicely supported by the results ?Fig.3?of a MATLAB program that realizes a one-

dimensional ?1D ?simulation of the experiment,in which the relevant distances are the same as those listed in the caption to Fig.2.The thermal light source is simulated by a string of random-phase independent emitters.The intensity pro?le ?“1D speckle pattern,”see Fig.3?a ??of the light generated by a certain distribution of the random phases is ?rst computed at two distances from the source:d A ?plane X1?and d B ?plane X2?;the program ?nds the total value ?M ?of the X1intensity lying within a pair of segments which simulate the double slit;this value of M ?which stands for the “output of the bucket detector”?is then used as a statistical weight for multiplying the intensity pro?le computed on X2;the result of this multiplication is summed to the corresponding value that was obtained in the previous trial ?using a different set of random phases ?.The procedure is repeated N times before displaying the ?nal average ?Fig.3?b ??.This computation could be equivalently,and perhaps more clearly,described as the correlation of each intensity pro?le ?Fig.3?a ??with the area ?below the pro?le itself ?contained within the slits.The mathematical de?nition of the ?nal output O ?x ?is

O ?x ?=

?

I B ?x ?

?

double slit

I A ?y ?dy

?

where I A ?·?and I B ?·?are the light intensity pro?les at dis-tances d A and d B ,respectively,from the light source,x is the transverse coordinate of detector D2,and the angular brack-ets denote an ensemble average.Of course the simulation must produce a classical result for no element of quantum mechanics is introduced into it.

At this point we must emphasize that the “out-of-focus blurring”reported in Fig.3?b ?of Ref.1contradicts both the classical prediction and our computer simulation;moreover,this effect is extremely position sensitive since a complete blurring was obtained when the distance of the X2plane from the source was increased by a mere 10%.This is the sense of our previous statement that the out-of-focus blurring de?es a classical explanation and represents a remarkable result in ghost imaging.

The interesting point is that,on repeating the experiment a large number of times,we always obtained results ?Fig.2?b ??that did not reveal any blurring of the image when d B was increased;in addition to this,the distance between the two maxima was found to increase with d B ?according to the ratio d B ?/d B ,i.e.,as predicted by the MATLAB simulation as well as by classical intuition.

Since we have no reasons for doubting the reliability of our experiment,we must conclude that the result reported above con?rms the purely classical explanation of ghost im-aging with thermal light,as indicated,e.g.,in Ref.10.

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FIG.2.Experimental results.?a ?Plot of correlation between the outputs of detectors D1and D2obtained when they are equally distant from the light source ?d A =d B =484mm ?.?b ?Same as in ?a ?when the distance of detector D2has been increased to d B ?=534mm,while leaving the position of D1unchanged ?d A =484mm ?

.

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