Review of Ghost Imaging

Abstract

Ghost Imaging, a novel technique in which the object and the image system are on separate optical paths, was first demonstrated using entangled photon pairs. Quantum imaging is one of the important exciting areas in practical engineering applications. Quantum imaging was first demonstrated experimentally by Pittman et al in 1995, following by the idea of Klyshko. The first part of the report presents an overview of the physics of ghost imaging. The second part of the report also deals with the various techniques for ghost imaging namely lensless thermal ghost imaging, differential ghost imaging
and multi wavelength ghost imaging. The third part of the report contains numerical analysis of diffraction pattern on a screen using Huygens’ principle. The ghost imaging techniques have a wide range of applications, such as fluorescence imaging, lidar detector, optical coherence tomography, in satellites, and also in defence systems.

Full text

Review of Ghost Imaging
Project Report of work done from June-July, 2015
Under the supervision of
Prof. Hema Ramachandran
Raman Research Institute
Bengaluru
Submitted by
Debapriya Pal
1st Yr. under 5 Yr. BS-MS Dual Degree Programme
INSPIRE FELLOW
IISER Kolkata
24th July 2015

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ACKNOWLEDGMENT
It gives me immense pleasure to express my gratitude to all those who have
been associated with me and helped me in completing this work. I would
like to thank Prof. Hema Ramachandran for the priceless guidance and
knowledge which helped me take my first steps in the field of optical physics.

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Abstract
Ghost Imaging, a novel technique in which the object and the image system
are on separate optical paths, was first demonstrated using entangled photon
pairs. Quantum imaging is one of the important exciting areas in practical
engineering applications. Quantum imaging was first demonstrated experi-
mentally by Pittman et al in 1995, following by the idea of Klyshko.
Ghost images are obtained by correlating the output of a signal-pixel pho-
todetector with the output from a high spatial-resolution scanning photode-
tector array whose illumination has not been interacted with that of the
object. This demonstration caused it to be regarded as a purely quantum
effect. The term “ghost image” is apt because neither detector’s output
alone can yield an image: the bucket detector has no spatial resolution,
while the high spatial-resolution detector has not viewed the object. Sub-
sequent theory and work gave wide support of forming ghost images with
classical correlations. The first part of the report presents an overview of
the physics of ghost imaging.
The second part of the report also deals with the various techniques for ghost
imaging namely lensless thermal ghost imaging, differential ghost imaging
and multi wavelength ghost imaging. The benefits of the various types of
ghost imaging techniques in different situations are also discussed.
The third part of the report contains numerical analysis of diffraction pat-
tern on a screen using Huygens’ principle. The coding used in the analysis
is done in python interface.
The ghost imaging techniques have a wide range of applications, such as
fluorescence imaging, lidar detector, optical coherence tomography, in satel-
lites, and also in defence systems.

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Contents
1 History and the Basics of Ghost Imaging. 4
1.1 Introduction............................ 4
1.2 The Optics behind Ghost Imaging . . . . . . . . . . . . . . . 5
1.3 Does Ghost Imaging at all need Quantum Entanglement? . . 7
1.4 Ghost Imaging using Spatial Light Modulator . . . . . . . . . 9
2 Overview of Some Papers on Ghost Imaging 11
2.1 Lensless Ghost Imaging with Sunlight . . . . . . . . . . . . . 11
2.2 Differential Ghost Imaging . . . . . . . . . . . . . . . . . . . . 14
2.3 Multiwavelength Ghost Imaging . . . . . . . . . . . . . . . . . 16
3 Diffraction Pattern on a Screen for Double Slit. 19
3.1 Introduction............................ 19
3.2 Mathematical Expression of the Principle . . . . . . . . . . . 20
3.3 Python code used for generating Diffraction Pattern . . . . . 20
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Chapter 1
History and the Basics of
Ghost Imaging.
1.1 Introduction
The history of ghost imaging began shortly after the birth of ghost inter-
ference. In the year 1995, Klyshko and co-worker published an intriguing
paper on two-photon ghost interference and diffraction. A pair of entangled
photons (conventionally called the signal and idler) are produced by spon-
taneous parametric down conversion and sent along two different paths. A
double slit placed only in the single arm, and the two photons of each pair
are eventually revealed by two distant point like detectors. As expected, no
first order interference pattern can be detected behind the double slit, due to
the insufficient spatial coherence of the individual beams. Nevertheless, an
interference pattern can be observed by counting the coincidences between
the fixed detector and the idler detector as the latter is moved in a trans-
verse direction. The amazing aspect of this result is that the interference
pattern is revealed by moving the detector in the path that doesn’t contain
the double slit. Hence the name ghost is being used.
In ghost imaging, the apparatus differs slightly from the interference setup
described above. A double slit is placed in the signal arm, but now the pur-
pose of the experiment is to retrieve a ghost image of the double slit rather
than the interference pattern produced by it. To achieve this goal, all pho-
tons passing through the double slit are conveyed onto a ‘bucket’ detector
located in the focal plane of the collecting or converging lens. The bucket
detector can only reveal photon arrivals and cannot gain any information on
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the aperture shape. The detector placed in the other arm (the idler) cannot
acquire any information about the aperture because photons arriving at it
followed the path where the double slit was absent. It is correlating the
outputs of the two detectors, neither of which conveys information about
the shape of the aperture. In this case, too, the use of the term ‘ghost’ is
appropriate.
1.2 The Optics behind Ghost Imaging
The first experiments on what would be eventually be referred to as ghost
imaging were reported in 1995 in a paper titled , ‘Optical imaging by means
of two-photon quantum entanglement’. The schematic representation of the
setup is given below in Figure 1. Laser light falls onto a nonlinear optical
Figure 1.1: Ghost image setup used in 1995 experiment. ( Figure from
reference [1] ).
crystal named Beta Barium Crystal (BBO crystal). This crystal splits each
photon into two quantum mechanically entangled photons of orthogonal po-
larization; referred to as signal and idler photons. In other words, light
undergoes spontaneous parametric down conversion inside the crystal.
Then these two photons pass through a polarizing beam splitter which sends
the signal photon up towards the object to be imagined, and the idler to-
wards the CCD camera.
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The object is an absorbing screen with a pattern of apertures to be imag-
ined. The signal photons either hit the screen and is absorbed, or it passes
through an aperture and is detected by a bucket detector or single pixel
detector.
Bucket detector only measures whether or not a photon hit, and doesn’t
give any information about where it hit. The bucket detector cannot by
itself produce any image of the object.
The CCD camera is an ordinary camera which detects the position of the
idler photon. It has a number of pixels having high spatial resolution. CCD
stands for Charge Coupled Device. This device is for the movement of elec-
trical charge, usually from within the device to an area where the charge
can be manipulated, for example conversion into a digital value.
The information from the CCD and the bucket detector passes through a
coincidence circuit, which only records the data from the CCD camera if the
photons hit both the detector at the same time. The data that survives the
coincidence circuit is collected on computer and, after a sufficient number
of photons have been accumulated, an image of the object is built up. An
image is recorded by the CCD, even though the CCD doesn’t see the object!
The key to this imaging is because of the photons produced by the BBO
crystal, which are quantum-mechanically entangled. ‘Entanglement’ refers
to the fact that the particles are inextricably connected to one another, even
though they may be separated by some distance. Quantum entanglement
is a physical phenomenon that occurs where pairs or group of particles are
generated or interact in such a way that the quantum state of each par-
ticle cannot be described independently; instead, a quantum state maybe
given for the system as a whole.Entanglement occurs within the BBO crys-
tal, where the incoming single photon breaks into two photons, undergoing
spontaneous parametric down conversion. Because energy and momentum
must be conserved in this decay, there is a definite relationship between the
behavior of the signal and idler photons. If one photon is deflected ‘up’, the
other must be deflected ‘down’; if one photon is deflected ‘left’ the other
must be deflected ‘right’.
For the purpose of our experiment, the entanglement of the photons means
that the position that the signal photon hits the object is directly related
to the position that the idler photons hit the CCD camera. The positions
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at which the two photons hit their respective targets are correlated. If a
signal photon has made it past the object, the net result is that the CCD
camera only records the idler photons which are in positions which mirror
the aperture of the object.
1.3 Does Ghost Imaging at all need Quantum En-
tanglement?
From the discussion earlier, it is clear that for ghost imaging only a strong
correlation is need between the signal and the idler photons. Now, it is nat-
ural to ask, then, if quantum entanglement is required to produce a ghost
image.
In 2002, this question was answered in the negative in a paper titled, “‘Two-
photon’ coincidence imaging with a classical source.” The experimental sys-
tem is very similar to the original imaging experiment, the only difference
being the change from photons which are entangled to other photons which
are simply correlated.
Figure 1.2: Ghost image setup with random, rapid tilts. ( Figure from
reference [2] ).
A laser producing very narrow pulses is reflected off of a mirror which has
random, rapid tilts. Because of the mirror, each pulse travels through the
optical system in a slightly different direction. Because the photons in the
laser pulse were originally travelling more or less in the same direction, the
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photons travelling are correlated in direction. The laser light is reflected
from a mirror to minimize the unwanted passing of the laser light to the
detectors. Then like the previous setup, part of the beam is sent to the
object and the other part is sent towards the CCD camera. The distance of
the bucket detector and the CCD camera from the beam splitter in order to
obtain the coherence length. The detector behind the object is also moved
in transverse direction to cover the full length of the object. Even though,
there is no correlation between the photons travelling to the two detectors,
there is a enough of a correlation to result in an image from the CCD again.
Figure 1.3: Ghost image setup with random, rapid tilts.
We can visualize this setup in such a manner where a blindfolded person
attempts to paint a picture with the help of a friend.
The painter selects a color and a canvas to paint on. In this sense, he acts
as an optical source, throwing random stuff against the ‘detector’(the blank
canvas). The friend who can see the painting, and tells the painter whether
or not his planned brush stroke is an appropriate match to the object. The
friend plays the role of the coincidence circuit, only allowing to be saved
those strokes that are consistent with the object. In this highly inefficient
way, an image which matches the object is eventually built up on the canvas.
So the ghost imaging can be done without using entangled photons.
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What is the difference between the two images obtained using
quantum mechanically entangled photons and that with random,
rapid tilting mirror?
The classical ghost image is produced by correlating the photons in a very in-
efficient way. The correlation between the photons is not perfectly matched.
In quantum entangled ghost imaging, the entangled photons can produce
a perfect correspondence between the photons on the bucket detector and
the CCD, therefore corresponding image with perfect visibility and contrast
is formed.
1.4 Ghost Imaging using Spatial Light Modulator
The ghost imaging systems described so far is highly complicated. In the
paper “Ghost imaging with a single detector”, the CCD camera was elimi-
nated from the setup. Instead of a CCD camera, a spatial light modulator
was used.
SLM or Spatial light modulator is a device which allows us to control the
phase of the laser field reflected from it. The SLM can be manipulated to
produce any sort of illumination upon the object which is desired, and thus
illumination can be predicted and calculated.
Figure 1.4: Ghost image setup with the spatial light modulator.
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Then by correlating the amount of light which is actually measured by the
bucket detector with the light expected to be illuminating the object due
to the behavior of the SLM, and repeating the process for multiple SLM
configurations, we can again obtain an image of the object without using a
CCD camera.
We can visualize this setup also as a person with a laser pointer stand-
ing on the opposite side of the object from the bucket detector. The person
moves the laser pointer side to side, up and down, and keeps track of those
positions for which the bucket detector receives a signal. By mapping that
positions for which the detector gets a signal, we can make a map of the
object (!!first letter of my name!!) itself.
Figure 1.5: Here, the motion of the laser pointer is analogous to the SLM.
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Chapter 2
Overview of Some Papers on
Ghost Imaging
2.1 Lensless Ghost Imaging with Sunlight
Here, only single pixel detector is needed to collect the object information
without any imaging lens (for converging the light), which makes imaging
setup much simpler and more adaptable.
In the experiment measuring the intensity correlation of the thermal light
performed by Hanbury Brown and Twiss (HBT), it was found that only
when the coherence time of the light field is close to or longer than the time
resolution of the detector, can the intensity correlation be observed.
To obtain a source with sufficiently long coherence time, a Faraday anoma-
lous dispersion optical filter (FADOF) to filter the sunlight down to a narrow
spectral width is used.
Figure 2.1: Narrow band filter setup consisting of IF, interference filter;
Glan1 and Glan2, Glan prisms; FADOF, Faraday anomalous dispersion op-
tical filter. ( Figure from reference [7] )
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An interference filter is an optical filter that reflects one or more spectral
bands or lines and transmits other spectral bands or lines and transmit oth-
ers, while maintaining a zero coefficient of absorption for all wavelengths
of interest. An interference filter can be high pass, low pass or band pass.
In, this experiment an interference filter IF with a transmission wavelength
centered at 780 nm is used to pre filter the light in front of the system in
order to decrease the noise caused by the leakage.
A Faraday anomalous dispersion optical filter(FADOF) is implemented to
filter the sunlight down to narrow spectral width having long coherence time.
A Glan-Thompson prism is a type of polarizing prism. It consists of two
right-angled calcite prisms that are cemented together by their long faces
with no gap. Birefrengence splits light entering the prism into two rays, ex-
periencing different refractive indices; the p-polarized ordinary ray is totally
internally reflected from the interface, leaving the s-polarized extraordinary
ray to be transmitted. The filter setup shown in Fig. 2.1 Glan1 and Glan2
are two Glan prisms with extinction ratio(signal to noise ratio) of 10−5.
With the help of this filtering setup, a 780 nm beam of sunlight with a
bandwidth close to 0.01 nm was obtained.
Figure 2.2: Experimental setup of lensless ghost imaging with sunlight. (
Figure from reference [7] ).
Sunlight is collected by the Meade astronomical telescope and multimode
fibers in the HBT experiment. BS: 50:50 beam splitter. Obj: object shown
in bottom left, consisting of a mask with two holes. The distances from
the secondary source, S, to the collimator and the object are both z = 31
12

cm. Pinhole is placed before the detector for ensuring coherence area. Lens
L2 behind the object focuses the light passing through the object to the
collimator, which has no spatial resolution.
A collimator is a device that narrows a beam of particles or waves. To
”narrow” can mean either to cause the directions of motion to become more
aligned in a specific direction (i.e., make collimated light or parallel rays),
or to cause the spatial cross section of the beam to become smaller (beam
limiting device). To image the object, the collimator C1 is scanned in the
direction transverse to the beam and the coincidence counts of the detectors
are recorded as a function of the transverse distance x.
The object in the experiment is a mask consisting of two round holes, 2.2
mm apart as shown in the bottom left of the Figure 2.2 . The two holes
have unequal diameters of approximately 0.5 and 0.4 mm.
The 1D ghost image of a horizontal cross section of the object was obtained
from the second-order intensity correlation function g(2)(x) and is plotted
as the below graph.
Figure 2.3: Lensless Ghost image of the two-hole mask illuminated with
sunlight. Horizontal axis: distance xscanned by collimator C1. Vertical
axis: intensity correlation function g(2)(x). Black points, experimental data;
solid curve, Guassian fit. ( Figure from reference [7] ).
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The FWHMs (Full width at half maxima) of the two peaks are 0.89 and
0.71 mm, respectively. The diameters cant be measured very precisely, but
the distance between the two peaks is 2.2 mm, which is exactly the distance
between the two holes.
It should be noted that the visibility of the image is only 1.2%.
Among the reasons for the low visibility in the experiment, the most crucial
physical restriction is the relatively short coherence time of the source and
the limited time resolution of the detection system.
The image visibility can be improved in this setup by the means of us-
ing bandwidths in both the arms of the setup which are sufficiently narrow.
The image visibility can be improved by using a filter with less noise leakage
such as high finesse Fabrey-Perot filter.
Benefits and Application of this Technique :-
•In the thermal light ghost imaging, only a single pixel detector is
needed to collect the object information without any imaging lens,
which makes the image setup much simpler and more adaptable.
•Ghost imaging with sunlight has wide applications in situations, where
the direct observation of a target with imaging resolution is difficult.
•The thermal light ghost imaging has been widely demonstrated in the
fields, such as fluorescence imaging (visualization of fluorescent dyes or
proteins as labels for molecular processes or structures), lidar detection
(It is designed to detect the infrared emissions of law enforcement law
agencies, warn the motorists that their speed is being measured) and
optical coherence tomography (it is an established medical imaging
that uses the ghost imaging method to make a picture of the cross
section of our tissues.)
2.2 Differential Ghost Imaging
When it comes to real sensing and/or imaging applications, such as the
imaging of a low contrast object or the location and possibly sizing of a
small absorbing obstacle in a large beam, the Signal to Noise ratio (SNR)
of conventional ghost imaging methods is remarkably low, and very long
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measurement times would be necessary.
The signal-to-noise ratio (SNR) shows how well the image of the object
is distinguishable from the contrast and the resolution.
Differential ghost imaging(DGI) overcomes this limitation and helps to apply
the ghost imaging technique to realistic and potentially interesting problems.
The technique can measure the transmission function of an object in abso-
lute units, with a SNR that, depending on the object in absolute units, with
a SNR that, depending on the object transmission relative variance, can be
orders of magnitude higher than the one achievable with conventional ghost
imaging.
Figure 2.4: Schematic diagram of the experimental setup. ( Figure from
reference [9] ).
The pseudo-thermal source operates at λ= 0:532 µm and produces a col-
limated beam of deepF resnel speckles whose size δ0v84:7 µm does not
change upon propagation. The area of the beam is Abeamis approx 32:9
mm2and contains Nspeckle= Abeam /Acoh v4590 speckles. The speckle beam
is divided by a cube beam splitter in two spatially correlated beams, the ob-
ject and the reference beams, whose intensity distributions are I1(x1) and
I2(x2), respectively. The object beam hits the object at a distance z1= 130
mm from the source, and the bucket signal S1is collected with a photodiode.
The reference beam I2(x2)is detected at the same distance z1= z2with a
CCD sensor whose square pixels have a size 6:67 m very less than Fresnel
speckles. The reference bucket S2is obtained by summing the signals out
from all the CCD pixels.
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Benefits of this Technique :-
•For highly transparent object, the differential ghost imaging technique
works much better than the conventional ghost imaging one. Con-
versely, for highly absorbing object the two techniques perform quite
similarly.
•Differential ghost imaging dramatically enhances the signal to noise
ratio.
•Both the techniques act quite similarly when the object is a small
aperture, but if the object is a small obstacle, conventional ghost imag-
ing becomes highly inefficient while differential ghost imaging remains
quite performing.
•In all the situations where standard techniques appear not to be ade-
quate, such as when the object to be imagined is located in optically
harsh or noisy environments, differential ghost imaging will pave the
way for better imaging.
2.3 Multiwavelength Ghost Imaging
The earlier described ghost imaging techniques used only single wavelength
and thus we can only obtain a monochromatic ghost imaging (SGI).The
colour ghost image obtained by ghost imaging with a multiwavelength source
is better than the monochromatic ghost image in observation.
Figure 2.5: Setup for multi wavelength thermal ghost imaging with SLMS.
DM: dichroic mirror; PBS: polarizing beam splitter. ( Figure from reference
[10] ).
Two laser beams pass through the SLMS and then generate two light beams
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by a 50:50 beam splitter. The spatial correlations between the two beams
can be produced by the amplitude mask that generates random spatial pat-
terns following the Gaussian statistics. Thus, two light fields are rendered
spatially incoherent but in a correlated fashion.
Two light beams are the signal, which interacts with the object and then
is measured by a bucket detector, and the reference, which is directly mea-
sured by the CCD camera.
The ghost imaging comes from the average intensities of light received by the
bucket detector and the CCD camera, from the intensity cross-correlation
function.
The intensity cross correlation function looks at the correlation between
two different colors rather than just the same color. In other words, coinci-
dent green and red intensity fluctuations correlate if green and red labelled
particles are moving together.
Striking Results of this Experiment
•Two wavelength ghost imaging with SLMS produces four ghost images
(i.e., one red ghost image, one green ghost image, and two blue ghost
images). Each ghost image is the same as the ghost image achieved
by the single-wavelength ghost imaging.
•The second-order thermal ghost imaging with two-wavelength yields
four ghost images, whose nature is the correlations of degenerate-
wavelength and non-degenerate-wavelength.
•N wavelength ghost imaging with SLMS, N2ghost images could be
obtained.
•Since the red, green and blue are the three primary colours, according
to the colour additive law, the red, green, and the blue ghost images
are incoherently added together to form one colour ghost image.
Benefits of this Technique :-
•The SNR of two-wavelength ghost imaging with SLMS is four times
the SNR of the single-wavelength ghost imaging.
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•The SNR of N wavelength ghost imaging with SLMS is N2times the
one of the single-wavelength ghost imaging, which is very useful in
application.
•This method is very effective for all types of objects including the
highly transparent and highly absorbing objects, as the ratio between
the SNR of the multi wavelength ghost imaging and single-wavelength
ghost imaging is a constant that is independent of the object.
•The coloured ghost image produced will be more conductive to ob-
servation in practice than the monochromatic ghost image. It will
improve the quality of the ghost image.
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Chapter 3
Diffraction Pattern on a
Screen for Double Slit.
3.1 Introduction
According to Huygens’ Principle,
“ Every point on a wave-front may be considered a source of secondary
spherical wavelets which spread out in the forward direction at the speed of
light. The new wave-front is the tangential surface to all of these secondary
wavelets. ”
Every point on a circular wave front are in phase and is a source of a
Figure 3.1: Huygens principle setup used for the diffraction pattern.
19

secondary wave fronts. Therefore the point awill act as a source for a new
wavefront. Every point of a particular wavefront will be coherent. The holes
band care at the same distance from the hole a. When that wave front
reaches the holes band c, then these two holes will act as a source of sec-
ondary wavefronts. The intensity at any position dwill be the superposition
of the intensity contributions from both the holes.
3.2 Mathematical Expression of the Principle
Consider the case of a point source located at a point P0, vibrating at a
frequency f. The disturbance may be described by a complex variable U0,
known as the complex amplitude. It produces a spherical wave with wave-
length λ, wave-number k = 2π/λ. The complex amplitude of the primary
wave at the point Q located at a distance r0from P0is given by:
U(r0) = U0eikr0
r0
since the magnitude decreases in inverse proportion to the distance trav-
elled, and the phase changes as k times the distance travelled.
Using Huygens’ theory and the principle of superposition of waves, the com-
plex amplitude at a further point P is found by summing the contributions
from each point on the sphere of radius r0.
3.3 Python code used for generating Diffraction
Pattern
from math import*
f=open(‘diff.out’,‘w’)
b=input(‘wavelength :’)
k=(2*pi)/b
xi=-10000.0
xf=10000.0
yi=-10000.0
yf=10000.0
dx=0.05
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dy=0.05
e0=input(‘initial value of electric field :’)
z=input(‘distance of the two slits from the screen :’)
x2=input(‘x-coordinate of slit w.r.t the central line, x=0 :’)
y2=input(‘y-coordinate of slit w.r.t the central line, y=0 :’)
x3=input(‘x-coordinate of other slit w.r.t the central line, x=0 :’)
y3=input(‘y-coordinate of other slit w.r.t the central line, y=0 :’)
while xi<xf and yi<yf:
r1=sqrt((xi-x2)**2 + (yi-y2)**2 + z**2)
r2=sqrt((xi-x3)**2 + (yi-y3)**2 + z**2)
e1=(e0/r1)*complex(cos(k*r1),sin(k*r1))
e2=(e0/r2)*complex(cos(k*r2),sin(k*r2))
E=e1+e2
xi=xi+dx
yi=yi+dy
print>>f,xi,yi,sqrt((E.imag)**2 + (E.real)**2)
The input value given for generating the data points are b = 0.005, e0
= 1, z = 5000, x2 = 0.1, y2 = 0, x3 = -0.1, y3 = 0.
Using the generated data points and plotting it using qtiplot, we get the
Figure(3.3).
Figure 3.2: Diffraction pattern obtained on the screen, generated by using
the python code and plotting it using qti plot.
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