PHYS 3232 – Optics
Fall 2008
Optical Holography
-Ajeya Karajgikar
Georgia Institute of Technology
Topics covered:
• What is holography?
• History of holography – Timeline
• Basic terms and concepts in holography
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Interference
Fresnel Zone Lens
Visibility
Influence of polarization
Holographic recording and reconstruction
Fundamental Imaging Techniques in Holography
Formation of holograms in general
Basic holography equations
Holography in everyday life
Interesting articles to read on holography
What is holography?
Holography is a technique that allows the light scattered
from an object to be recorded and later reconstructed so that
it appears as if the object is in the same position relative to
the recording medium as it was when recorded. The image
changes as the position and orientation of the viewing
system changes in exactly the same way as if the object was
still present, thus making the recorded image (hologram)
appear three dimensional. Holograms can also be made
using other types of waves.
The technique of holography can also be used to optically
store, retrieve, and process information. While holography is
commonly used to display static 3-D pictures, it is not yet
possible to generate arbitrary scenes by a holographic
volumetric display.
History of Holography
Holography was invented in 1947 by
Hungarian physicist Dennis Gabor (1900–
1979), work for which he received the
Nobel Prize in Physics in 1971.
Gabor's research focused on electron optics, which led him to the
invention of holography. The basic idea was that for perfect optical
imaging, the total of all the information has to be used; not only the
amplitude, as in usual optical imaging, but also the phase. In this
manner a complete holo-spatial picture can be obtained.
History of Holography - Timeline
Dennis Gabor, inventor of
holography, stands
beside his 18"x24" laser
transmission, pulsed
portrait. The historic
portrait was recorded in
1971 by R. Rinehart,
McDonnell Douglas
Electronics Company, St.
Charles, MO to
commemorate Gabor's
winning of the Nobel
Prize that year.
History of Holography - Timeline
Dr. Dennis Gabor signs a copy of the Museum of
Holography's inaugural exhibition catalogue, "Through
The Looking Glass," during his historic visit to the
museum on March 17, 1977. (Photo by Paul D.
Barefoot)
At the time Gabor developed holography, coherent light sources were
not available, so the theory had to wait more than a decade until its first
practical applications were realized, though he experimented with a
heavily filtered mercury arc light source. The invention in 1960 of the
laser, the first coherent light source, was followed by the first hologram,
in 1963, after which holography became commercially available.
History of Holography – Timeline (1962)
"Train and Bird" is the first hologram
ever made with a laser using the offaxis technique. This pioneer image
was produced in 1964 by Emmett
Leith and Juris Upatnieks at the
University of Michigan only four years
after the invention of the laser
In 1962 Emmett Leith and Juris Upatnieks of the University of Michigan
recognized from their work in side-reading radar that holography could
be used as a 3-D visual medium. In 1962 they read Gabor's paper and
"simply out of curiosity" decided to duplicate Gabor's technique using
the laser and an "off-axis" technique borrowed from their work in the
development of side-reading radar. The result was the first laser
transmission hologram of 3-D objects (a toy train and bird). These
transmission holograms produced images with clarity and realistic depth
but required laser light to view the holographic image.
History of Holography – Timeline (1962)
Leith and
Upatnieks
preparing to
shoot a laser
transmission
hologram using
the "off-axis"
technique
borrowed from
their work in the
development of
side-reading
radar. (Photo by
Fritz Goro for Life
Magazine, 1967)
History of Holography – Timeline (1962)
Russian scientist Yuri N.
Denisyuk, State Optical
Institute in Leningrad, USSR,
signing a copy of his book,
Fundamentals of Holography.
(Photo by Dr. Stephen Benton,
1979)
Dr. Yuri N. Denisyuk of the U.S.S.R. combined holography
with 1908 Nobel Laureate Gabriel Lippmann's work in
natural color photography. Denisyuk's approach produced a
white-light reflection hologram which, for the first time, could
be viewed in light from an ordinary incandescent light bulb.
History of Holography – Timeline (1967)
The 1967 World Book Encyclopedia Science Yearbook
contained what is arguably the first mass-distributed
hologram, a 4"x3" transmission view of chess pieces on a
board. An article describing the production of the hologram
and basic information about the history of holography
accompanied it. A .05 watt He-Ne laser was used on a nineton granite table in a 30-second exposure to make the
original from which all the copies were produced.
History of Holography – Timeline (1967)
Also in 1967, Larry Siebert of the Conductron Corporation
used a pulsed laser that he designed to make the first
hologram of a person. The Conductron Corporation (later
acquired by McDonnell Douglas Electronics Corporation)
played an important role in the early days of commercial
display holography. Their mass production and large plate
capabilities serviced a tentative but potentially large market.
Their gang-printed reflection holograms provided burgeoning
marketing organizations with an exciting new promotional
tool. Their large 18 x 24 inch plates made unusual trade
show displays. The trend continued for several years until
the recession in the early 1970s forced the company to close
the pulsed laser facility.
History of Holography – Timeline (1968)
Dr. Stephen A. Benton,
Massachusetts Institute of
Technology, seen through "Crystal
Beginning," a white light
transmission hologram produced at
the Polaroid Corporation in
1977.(Photo by Michael Lutch for
WGBH, Boston)
A major advance in display holography occurred in 1968 when
Dr. Stephen A. Benton invented white-light transmission
holography while researching holographic television at Polaroid
Research Laboratories. This type of hologram can be viewed in
ordinary white light creating a "rainbow" image from the seven
colors which make up white light. The depth and brilliance of
the image and its rainbow spectrum soon attracted artists who
adapted this technique to their work and brought holography
further into public awareness.
History of Holography – Timeline (1972)
This is a series of photographs taken of "Kiss II" (1974), an integral hologram
produced by Lloyd Cross, inventor of the process. The hologram -- which was
made from approximately 360 frames of motion picture footage -- was typically
mounted in a semi-circular, wall-mounted display and illuminated by a single light
bulb below. The floating, 3-dimensional image of Pam Brazier blows a kiss and
winks as the viewer walks by. (Photo by Daniel Quat, 1977)
In 1972, Lloyd Cross developed the integral hologram by
combining white-light transmission holography with conventional
cinematography to produce moving 3-dimensional images.
Sequential frames of 2-D motion-picture footage of a rotating
subject are recorded on holographic film. When viewed, the
composite images are synthesized by the human brain as a 3-D
image.
History of Holography – Timeline (1972)
18" x 24" laser transmission hologram, "Hand in Jewels," produced in 1972 by
Robert Schinella and the McDonnell Douglas Electronics Company, St. Louis,
MO for Cartier, Inc., New York. The hologram appeared in Cartier's window on
Fifth Avenue, projecting the hand out over the sidewalk to the astonishment of
passers by.
History of Holography – Timeline (1983)
In 1983 MasterCard International, Inc. became the first to
use hologram technology in bank card security.
The first credit cards to carry embossed holograms were produced by American Bank Note
Company, New York, for MasterCard International, Inc. The 2-channel holograms were the
widest distribution of holography in the world at that time.
History of Holography – Timeline (1984)
National Geographic magazine was the first major
publication to put a hologram on its cover. The March
1984 issue carried nearly 11 million holograms
throughout the world.
Volume 165, Number 3, March 1984 had the first hot stamped hologram embossed directly onto a
magazine cover, with an accompanying story, "The Wonder of Holography." The 2 1/2" x 4" embossed
hologram of an eagle was produced in 1983 by Kenneth A. Haines, Eidetic Images, Inc. Elmsford, NY, a
subsidiary of American Bank Note Company, New York, NY. (Photo by Paul D. Barefoot, 1999)
Basic terms and concepts in holography
Interference:
The superposition or interference of two light waves (with
same frequency) will emerge from the points R and O.
Taking an object wave and reference wave without
restriction to generality:
o = oe-iΦ
r and o are the field amplitudes of the respective
waves at the point of superposition P
r = re-iΨ
The phase Ψ = ΨR - 2π(r1/λ) is determined by the starting
phase of the wave at point R and the phase change at
distance r1. The same is valid for Φ = Φo- 2π(r2/λ).
At point P, the complex amplitudes add up: r + o
The intensity I is the square of the sum of the complex
amplitudes:
I = |r + o|2 = r.r* + o.o* + o.r* + r.o*
I = r2 + o2 + r.o.{e-i(Φ-Ψ) + ei(Φ-Ψ)}
I = r2 + o2 + 2. r.o.cos (Φ-Ψ)
Basic terms and concepts in holography
If the light sources are emitting completely independently
then the average of cos(Φ-Ψ) vanishes since the phases
vary statistically. This results in
I = r 2 + o2
or I = I1 + I2
In this case the waves are called “incoherent”. The
intensities of both waves add up and interference does not
occur.
If the value of ΨR-Φo does not change, the waves are
“coherent”. Locations in space exist where cos(Ψ-Φ)=+/-1. If
the field strengths oscillate in the same phase (+) this
results in
r + o and Imax = r2 + o2 + 2.r.o
If they oscillate in opposing cycles (-) the resulting
superposition is
r – o and Imin = r2 + o2 - 2.r.o
Basic terms and concepts in holography
Fresnel Zone Lens:
Points of objects close to the hologram reflect or emit spherical
waves. Holograms of such objects waves have been known as
“Fresnel zone lenses.”
The point P which represents the object is located at the distance
z0 from thr photographic layer. It emits a spherical wave.
Additionally a plane reference wave r falls onto the layer. The
interference pattern consists of concentric circles. For all points
that have the same distance from the center of the photographic
plate the incoming waves have the same phase. The path
difference between the two interfering waves increases by one
wavelength λ from one ring to the other (and the phase difference
increases by 2π). The path difference in the center can be taken to
be zero. For the kth ring this results in the path difference kλ, so
that the ring radius can be written as
rk2 = (z0 + kλ)2 – z02 = 2 z0kλ + k2λ2
Basic terms and concepts in holography
Basic terms and concepts in holography
The distance between the neighboring rings is:
z0  k2
1
rk 
( )
rk

Try deriving this
from the previous
equation
Basic terms and concepts in holography
Each small area of the zone lens can be interpreted as a regular
diffraction grating. The zeroth order diffraction is the weakened
illumination beam. Additionally, for a sie-like grating diffraction of
the order N = +/-1 occurs at the following angles
sin k  

rk

rk
z 0  k
The deflection angle increases with the distance from the
hologram axis. It can be proved that the hologram of a single point
represents a Fresnel zone lens by showing that the beams are
intersecting real and virtual at the distance z0 from the hologram
plane.
During reconstruction the first order of diffraction forms a spherical
wave which creates an image point at the distance z0 in front of
the hologram. The -1st order of diffraction is a divergent spherical
wave with a virtual image point at the distance z0 behind the
hologram.
Basic terms and concepts in holography
Visibility:
In holography r and o represent the reference and the
object wave, respectively. During the recording of the
hologram the visibility V in the interference field is given
by the ratio of the two waves I1=r2 and I2=o2. It is defined
by
V  I maxImin
I max Imin
For coherent waves, one gets
I1
I2
V 
I1
1
I2
2.
The visibility reaches a maximum of 1 at I1 = I2
Basic terms and concepts in holography
Influence of Polarization:
For the preceding considerations concerning interference it
was assumed that the polarization of the light waves is
parallel. From that it follows that the maximal visibility of V=1
holds for I1 = I2. If the polarization directions of the two linearly
polarized waves enclose an angle ψ the following equations
resultI = r2 + o2 + 2ro cos(Φ-ψ) cos ψ
and
I1
I2 cos
V
I1
1
I2
2.
No interference occurs if the directions of polarization are
perpendicular to each other; the visibility is 0. For optimal
visibility object and reference wave have to polarized parallel
each other. Even by using linearly polarized light radiation this
cannot always be achieved in practice since light is being partly
depolarized when scattered at an object.
Basic terms and concepts in holography
Holographic Recording and Reconstruction:
The difference between photography and holography lies
in the ability of holography to record the intensity as well
as the phase of the object wave. It may seem almost
incredible that the information of a three dimensional
object, can be recorded into a two dimensional
photographic layer. A look at the lectures on
electrodynamics can help understand this principle: if the
amplitude and the phase of a wave are known in one
(infinite) plane, the wave field is entirely defined in space.
Basic terms and concepts in holography
Recording:
The amplitudes of the object and reference wave on the
photographic layer are given by o and r, respectively. These
variables describe the intensity of the EM field of the light
wave which impinges on the photosensitive layer. Both waves
superpose, i.e. they form o+r. The intensity I is calculated as
the square of the amplitude:
I = |r + o|2 = (r+o)(r+o)*
I = |r|2 + |o|2 + ro* + r*o
The last term containing the object wave o is important for
holography. The darkening of the holographic film is
dependent on the intensity I. Thus the information about the
object wave o is stored in the photographic layer.
Basic terms and concepts in holography
Reconstruction:
The reconstruction is performed by illuminating the hologram
with the reference wave r. We will assume that the amplitude of
transmission of the film material is proportional to I which is
contrary to usual film processing. Therefore, the reconstruction
yields the light amplitude u directly behind the hologram:
u ~ r.I = r (|r|2 + |o|2) + rro* + |r|2o
= u0 + u-1 + u+1.
Governs the
reference wave
which is weakened
by the darkening
of the hologram by
a factor of (|r|2 +
|o|2) (zeroth
diffraction order)
Describes the
conjugate
complex object
wave o*.
Corresponds to
the -1st diffraction
order.
The object wave is itself
reconstructed with amplitude of
the reference wave |r|2 being
constant over the whole
hologram. This proves that the
object wave o can be completely
reconstructed. It represents the
1st diffraction order.
In-line Hologram (Gabor)
The technique of straightforward holography developed by
Gabor places the light source and the object on the axis
perpendicular to the holographic layer. Only transparent
objects can be considered. If an axial point O is chosen
as an object emitting a spherical wave the resulting
hologram for a plane reference wave is a Fresnel zone
lens. The disadvantage of in-line or straightforward
holograms is obvious: during reconstruction the hologram
is illuminated with a plane reference wave as shown in
part (b) of the image. Since it represents a zone lens a
virtual point appears at the same distance to the right of
the hologram. During observation the two images lying on
the same axis interfere which leads to image
disturbances (shown in (b)). Moreover, the observer
looks directly into the reconstruction wave. Because of
these disadvantages this form of holography is only of
historical interest.
In-line Hologram (Gabor)
Off-axis Hologram (Leith-Upatnieks)
It turns out that it is more favorable to shift either the
holographic layer or the object sideways. Laser beam,
object, and hologram are not on the same axis anymore.
The hologram represents the outer area of a fresnel zone
lens. Again a virtual and a real image are formed during
construction. The advantage of off-axis holography is that
both images do not interfere during observation and
image disturbances are avoided. By tilting the reference
wave (or shifting the object) it is achieved that the three
diffraction orders, namely the image, the conjugated
image, and the illumination wave, are spatially separated.
This has the advantage that also holograms of opaque
objects can be produced since the reference wave is not
obstructed by the object. In principle, a single beam or a
multiple beam technique can be used.
Fourier Hologram (Lensless)
If the object O and the light source R are within the same
plane parallel to the hologram, Fourier holograms are
generated. This geometric condition can only be satisfied
for plane objects. In a Fourier hologram the interference
fringes appear as a set of hyperbolas whilst especially in
in-line holograms circular sets in the form of Fresnel zone
lenses appear. Like in all thin holograms two (real)
images appear during reconstruction. The regular image
is at the position of the original object; the conjugated one
appears in the same plane parallel to the hologram. The
point light source R is the center of the point symmetry for
the two images.
Fraunhofer Hologram
Fourier holograms are formed by the superposition of
spherical waves whose centers have the same distance
from the holographic layer. If the layer is moved far away
the center depart and in the limit plane waves are
created.
This hologram type is especially used for the
measurement and investigation of aerosols. The object
with radius r0 has to be so small that a diffraction pattern
will appear in the far field. The condition for the distance
object/hologram is z0 >> r02/λ
Fraunhofer Hologram
This figure represents the Gabor holography with the condition of diffraction
being present in the far field. The light of the primary image is spead over such
a large area in the conjugated image that is appears as a weak even
background.
Reflection Hologram (Denisyuk)
Until now holographs were presented at which the object
and the reference wave impinge from the same side on
the photographic layer. Holograms whose images are
reconstructed in the reflection are of large importance
especially in the field of graphics and art. In this case, the
reference wave- and later the reconstruction wave- has to
impinge from the observer’s side onto the hologram. The
object wave in this type of recording impinges on the
hologram from the opposite side.
Of importance is the setup after Denisyuk in which the
holographic layer is positioned across between the light
source and the object. This results in the interference
planes being almost parallel to the light sensitive layer.
Reflection Hologram (Denisyuk)
The distance of the grating planes when using a He-Ne or
ruby laser is λ/2 ~ 0.3μm.
Therefore, for a typical layer thickness of around 6μm,
almost 20 grating planes fit into the light sensitive layer.
So this system behaves like a thick grating.
During reconstruction the illumination wave which is
ideally identical to the reference wave is reflected at the
grating planes. The virtual image of the object appears in
the reflected light. Interference effects appear during the
mirroring which lead to Bragg reflection. If white light is
used for illumination only the wavelength used for the
recording is reflected due to the Bragg effect. Therefore a
sharp monochromatic image appears although white light
is used for reconstruction. This is the advantage of thick
reflection holograms which are called “white light
holograms.”
Reflection Hologram (Denisyuk)
Summary of the holographs
Formation of a hologram
The basic technique of holograph formation is to divide
the coherent light coming from a laser into two beams:
one to illustrate a subject and one to act as a reference.
Formation of a hologram
Reference wavefronts are often (but not necessarily)
unmodulated spherical or plane fronts. The reference
beam is directed so as to intersect the light transmitted or
reflected by the subject. Assuming the two beams to be
perfectly coherent, an interference pattern will form in the
volume of space where the beams overlap. A
photosensitive medium, placed in the overlap region, will
undergo certain chemical or physical changes due to
exposure to light intensity. After removal from the light
and after any processing required to record these
changes as an alteration of the optical transmission of the
medium, the medium becomes the hologram.
Basic holography equations
The complex amplitude of light arriving at the plate from
Object 1 can be expressed as a1= a1exp(iφ1) where a1 and φ1
are both functions of the spatial coordinates at the plate.
Similarly, the complex amplitude of light arriving at the plate
from Object 2 can be expressed as a2= a2exp(iφ2)
The complex conjugates of a1 and a2 will be designated a1*
and a2*.
Basic holography equations
We find that the transmittance t of the completed hologram (the ratio of
light transmitted by the hologram to that incident on it) contains a term tE
proportional to the exposure E = IPτe and hence proportional to the
intensity I.
Summing the amplitudes a1 and a2 and multiplying the complex
conjugate of the sum, we may write for the intensity
I = (a1 + a2) (a1 + a2)*
= a1a1* + a2a2* + a1a2* + a2a1*
= I1 + I2 + a1a2* + a2a1*
We assume a linear relation between t and E, and consequently
between t and I, of the form
light amplitudetransmitted
t
light amplitudeincident
Holography in every day life
Microscopy:
When specimens of cells or microscopic particles are viewed
conventionally under high magnification, the depth of field is
correspondingly small. A photograph that freezes motion of
the specimen captures in a focused image a very limited
depth of field within the specimen. The disadvantages of this
restriction can be overcome if the photograph is a hologram,
which in a single snapshot contains potentially all the
ordinary photographs that could be made after successive
refocusings throughout the depth of the living specimen. The
image provided by the hologram may be viewed by focusing
at leisure on any depth of an unchanging field. In making a
hologram with a microscope, the specimen is illuminated by
laser light, part of which is first split off outside the
microscope and routed independently to the photographic
plate, where it rejoins the subject beam processed by the
microscope optics.
Holography in every day life
It can be shown that, if reconstructing light of
wavelength λr is longer than the wavelength of
light λs used in “holographing” the subject, a
magnification is given by
 q  r 
M    
 p  s 
where p is the object distance (subject from film)
and q is the image distance (image from
hologram).
Object and image distances are equal when the
reference and reconstructing wavefronts are both
plane wave. However, if the hologram were made
with laser X-radiation and viewed with visible light,
magnifications as large as 106 could be achieved
without deterioration in resolution.
Holography in every day life
Holograms that simply redirect light may be used as
inexpensive optical elements, serving in place of lenses
and mirrors. To cite one popular application, laser
readers of the universal product code on groceries use a
spinning disc outfitted with a number of holographic
lenses. By continuously providing many angles of laser
scanning, the product code can be identified even when
the item is passed casually over the scanner.
Holography in every day life
Holographic data storage also offers tremendous
potential. Because data can be reduced by the
holographic technique to dimensions of the order of the
wavelength of light, volume holograms can be used to
record vast quantities of information. As the hologram is
rotated, new exposures can be made. Photosensitive
crystals, such as potassium bromide crystals with color
centers or the lithium niobate crystal, can be used in
place pf thick-layered photoemulsions.
Because information can be reduced to such tiny
dimensions and crystal can be repeatedly exposed after
small rotations that take place of turning pages, it is said
that all the information in the Library of Congress could
theoretically be recorded on a crystal the size of a sugar
cube!
Holography in every day life
A telephone credit card used in Europe has embossed
surface holograms which carry a monetary value. When
the card is inserted into the telephone, a card reader
discerns the amount due and deducts (erases) the
appropriate amount to cover the cost of the call.
Supermarket scanners read the bar codes on
merchandise for the store's computer by using a
holographic lens system to direct laser light onto the
product labels during checkout.
Holography in every day life
Another area in which holograms maybe very useful is in
pattern recognition. Briefly, the procedure is as follows. A text
is scanned, for example, for the presence of a particular word
or letter to be identified in an appropriate optical system. The
presence of the letter is indicated by the formation of a bright
spot in a location that indicates the position if the letter in the
text. The hologram acts as a matched filter, recognizing and
transmitting only that spatial spectrum similar to the one
recorded on it. The technique can be applied to holographic
reading of microfilms, for example. Military applications of
include the use of a memory bank of holograms of particular
objects or targets constructed from aerial photographs.
Weapons could, by pattern recognition, select proper targets.
It has also been suggested that robots could identify and be
directed toward appropriate objects in the same way.
Holography in every day life
CNN Holograms Debut With Jessica Yellin Figure (must
watch!!!)
CNN Will I Am Hologram, First time on TV
Just for fun!
Holography as a measure to increase security
Interesting articles to read on holography:
The Brightest, Sharpest, Fastest X-Ray Holograms Yet
NTT Develops Stamp-Size 1GB Hologram Memory
Quantum holography system
Holographic Storage Overview at CNET
Laser Pointer Holograms
How Holographic Storage Works