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

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

͑Received12April2006;accepted3July2006;published online30August2006͒

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 evidence͑based on experiments as well as on simulation͒that the blurring is nonexistent and no quantum explanation is necessary.©2006American Institute of Physics.͓DOI:10.1063/1.2338657͔

Recently,a remarkable result1in ghost imaging2–8pro-duced by thermal light9–14was reported in this jounal.For the benefit of the readers,the experimental setup and the measuring procedure are briefly 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 B͑the alternative path cre-ated by the beam splitter͒a 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 D2arefirst dc blocked͑to remove the average background noise͒and are then sent to a multiplier whose output,after low-passfilter-ing͑RCϷ60s͒,is plotted versus the transverse position of detector D2.

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

͑1͒When d B=d A,i.e.,when the object and the detector D2 are equally distant from the source of light͑the“in-focus”condition͒a lensless,high visibility,equal-size ghost image of the object is obtained͓Fig.3͑a͒of Ref.

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

͑2͒When d B d A,i.e.,when D2is moved to a slightly dif-ferent distance͑“out-of-focus”condition͒the image ob-tained turns out to be severely blurred͓Fig.3͑b͒of Ref.

1͔.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 inequalities͒,appears to be strikingly at variance with classical intuition.To appre-ciate more clearly this point and to prepare the ground for ourfinal 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 magnification.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.Thefirst 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.2͑a͒,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 profile in arm B by

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

procedure is statistically biased in favor of speckle patterns

a͒Electronic mail:



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 distance͑center to center͒

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

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


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


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