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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 Interference Fresnel Zone Lens Visibility Influence of polarization

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Optical holography

PHYS 3232 – Optics

Fall 2008

Optical Holography

  • Ajeya Karajgikar

    Georgia Institute of Technology

Topics covered
Topics covered:

  • What is holography?

  • History of holography – Timeline

  • Basic terms and concepts in holography

    • 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
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
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
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 timeline1
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
History of Holography – Timeline (1962)

"Train and Bird" is the first hologram ever made with a laser using the off-axis 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 19621
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 19622
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
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 nine-ton granite table in a 30-second exposure to make the original from which all the copies were produced.

History of holography timeline 19671
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
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
History of Holography – Timeline (1972)

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.

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)

History of holography timeline 19721
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
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
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
Basic terms and concepts in holography


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 = 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*

r and o are the field amplitudes of the respective waves at the point of superposition P

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 holography1
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 = r2 + 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 holography2
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 holography4
Basic terms and concepts in holography

The distance between the neighboring rings is:

Try deriving this from the previous equation

Basic terms and concepts in holography5
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

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 holography6
Basic terms and concepts in holography


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

For coherent waves, one gets

The visibility reaches a maximum of 1 at I1 = I2

Basic terms and concepts in holography7
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 result-

I = r2 + o2 + 2ro cos(Φ-ψ) cos ψ


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 holography8
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 holography9
Basic terms and concepts in holography


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 holography10
Basic terms and concepts in holography


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.

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.

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.

In line hologram gabor
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.

Off axis hologram leith upatnieks
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
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
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 hologram1
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
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 denisyuk1
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.”

Formation of a hologram
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 hologram1
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
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 a1and a2 will be designated a1* and a2*.

Basic holography equations1
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 a1and 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

Holography in every day life
Holography in every day life


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 life1
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

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 life2
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 life3
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 life4
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 life5
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 life6
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
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