holographic interferometry,scanners, optical element

1. HOLOGRAPHIC-
INTERFEROMETRY, SCANNERS
AND OPTICAL ELEMENTS
VINEETH KRISHNAN P.V
S3.MSc.PHYSICS
AM.AR.P2PHY12017

2. CONTENTS
INTRODUCTION
HOLOGRAPHIC INTERFEROMETRY
TYPES OF HOLOGRAPHIC INTERFEROMETRY
MATHEMATICAL DESCRIPTION OF DOUBL EXPOSSURE METHOD
MATHEMATICAL DESCRIPTION OF TIME -AVERAGING METHOD
REAL TIME METHOD
HOLOGRAPHIC OPTICAL ELEMENTS
APPLICATION OF HOE’S
HOLOGRAPHIC SCANNERS

3. INTRODUCTION
A photograph represents two dimensional recording of a three dimensional
scene. What is recorded is the intensity distribution that prevailed at the plane of
the photograph when it was exposed .the light sensitive medium is sensitive only
to the intensity variations and hence while recording a phtograph, the phase
distribution which prevailed at the plane of the photograph is lost. Since only the
intensity pattern is has been recorded, the three dimensional character (e.g.,
parallax) of the object scene is lost. Thus one cannot change the perspective of
the image in the photograph by viewing it from a different angle or one cannot
refocus the unfocused part of the image in the photograph. Holography is a
method evolved by Gabor in 1947, in which one not only records the amplitude
but also the phase of the light wave; this is done by interferometric techniques.
Because of this, the image produced by the technique of holography has a true
three dimensional form.
The idea of using of holograms for storage of information was first suggested by
Van Heerden in 1963, who proposed to store data by recording the information
carreing a light interference pattern in a holographic medium. The aesthetic appeal
and commercial usefulness of holography are both related to the ability of a hologram to
store a three-dimensional image. Unlike ordinary photographs, holograms record both
phase and amplitude information. Because phase is a relative property, construction of
a hologram requires a “reference beam” in addition to the light reflected from an object’s
surface.
Additional requirements include a powerful, coherent, monochromatic light source (e.g.
a laser, whose workings you should understand);a vibration-free flat surface; some
common optical devices; and photographic plates, chemicals, and a darkroom.
A hologram can be made by exposing a photographic plate to the interference pattern
made by the reference and object beams. The plate is then developed and dried.

4. When illuminated by a reference beam similar to the original one, it recreates a three
dimensional picture of the object. There is nothing mystical about this recreation, and
you can understand how it works with the help of some Fourier transform mathematics.
HOLOGRAPHIC INTERFEROMETRY
Holographic interferometry is the technique of using classical interferometry and
combining it with the technique of recording wavefronts from three dimensional
diffusively reflecting object s with nonplanar surfaces in order to measure small optical
path differences. The technique was first developed by Powell and Stetson in 1965.
Their experiments were conducted over the period of October to December 1964, and
they began with an investigation of the periodic coherence length of the HeNe laser
being used. The compact laser beam was used to illuminate a spot on a small object
was placed between two mirrors such that its image could be observed looking over one
mirror into the tunnel of multiple reflections between the mirrors. Each image was 10 cm
greater in path length than the one before it. Because these lasers had about three
longitudinal modes, their coherence length was periodic, as described by the
manufacturer, Spectra Physics in cooperation with the Perkin Elmer Corporation. This
was demonstrated by recording a hologram of the view over one of the mirrors.
In one of the holograms, however, a dark band was observed in the closest image to
the hologram, and it was observed to shift position with perspective. This band was not
observable in the original laser beam and had to be something created by the
holographic process. The confocal laser cavity consisted of a spherical mirror at the
output end with a flat mirror at the center of curvature at the other end. Adjustment of
the longitudinal spacing controlled the number of off-axis modes of oscillation, and it
was observed that the laser was oscillating in more than one of axis mode. The multiple
laser modes were incoherent and did not interfere in the observable laser beam, so why
did they interfere in the hologram reconstruction? Stetson put forth the idea that each
mode existed in both the object and in the reference beam, and each pair recorded a
separate hologram in the photographic plate. When these were reconstructed, both
recordings reconstructed simultaneously from the same laser beam and the fields were
then mutually coherent. Powell objected to this idea, because it implied that the
hologram had the power to coherently reconstruct fields that were incoherent during its
recording.

5. The resulting arguments gave rise to a set of experiments that were later published in
1966.
These consisted of:
(1) Recording the reflection of a concentrated laser beam while capturing the entire
reference beam on the hologram and adjusting the laser for combinations of off-axis
modes.
(2) Recording double-exposure holograms of an object where the object, the reference
beam mirror, and the hologram itself were rotated slightly between exposures.
(3) Recording holograms of the bottom of a 35 mm film can while it was vibrating. Later,
in April 1965, Stetson and Powell obtained real-time interference patterns between a
real object and its holographic reconstruction.
TYPES OF HOLOGRAPHIC INTERFEROMETRY
Stored beam /Real time holographic interferometry.
The superposition of an object with the object itself (while being subjected to stress)is
observed.
Stroboscopic stored beam /stroboscopic real-time holography
The wave front against which optical interferometric measurements are made is stored
in the instant they occur. A variation is to vibrate the subject harmonically and then
synchronously modulate the output of the laser.
Double exposure
In double exposure holographic interference both reference hologram and subject
hologram are recorded in the same photographic plates.
MATHEMATICAL DESCRIPTION OF DOUBL EXPOSSURE METHOD
This method consists in recording two successive holographic exposure of an Object
in two different positions. When the hologram is reconstructed it produces an
interference pattern which is indicative of the object displacement between the two
exposures. The mathematical description of double exposure holography is best setup

6. by first considering the recording of two object wavefront fields 𝑈01 and 𝑈02 in the same
emulsion using a wave 𝑈 𝑅 .since these wavefronts are all additive in the
plane of the emulsion the resulting irradiance distribution I recorded in the
hologram will expressed as
I = ⎸𝑈01 ⎸2
+ ⎸𝑈02 ⎸2
+2 ⎸𝑈 𝑅 ⎸2
+𝑈 𝑅
∗
(𝑈01 + 𝑈02 )+( 𝑈01
∗
+𝑈02
∗
) 𝑈 𝑅
The image wave front
Where, and .
In the double exposure case, the reconstructed image is then
Using trigonometric identity
this may be expressed as
This describes the geometry of the interference fringes found on the surface of
the image as reconstructed from a double exposure hologram.
MATHEMATICAL DESCRIPTION OF TIME -AVERAGING METHOD
This technique consists in making a single holographic recording of an object
while it is subjected to a cyclic vibratory motion and assume that the exposure
time in recording the hologram is long compared to one period of the
vibration cycle.
In this manner the hologram effectively stores an ensemble of images
corresponding to the time average of all positions of the object during its
vibration.

7. On their reconstruction, the interference of the ensemble images, or the
vector sum of individual wavefronts, produces an interference pattern which
is weighted towards the formation extremes of the object
If the vibration frequency is ⍵ and the amplitude z then the object
light field can be represented as
This equation can be further simplified using Bessel function
n=0 we may be written
This variation is characterized by being maximum when decrease In
value.
In summary, it can be seen that time-average holographic interferometry is a
unique tool for studying sinusoidal vibration patterns using only one
holographic exposure.

8. REAL TIME METHOD
The superposition of an object with the object itself (while being subjected
to stress)is observed. The technique consist in taking a single holographic
exposure of an object in an unstressed state ,processing the plate and
replacing it in exactly the same position in which was recorded.
HOLOGRAPHIC OPTICAL ELEMENTS
H.O.E stands for Holographic optical element and it is
a hologram that consists of a diffraction pattern rendered as a surface
relief, or a thin film containing an index modulation throughout the
thickness of the film. For our purposes, holograms can be divided into
two categories: reflection holograms, in which incident and diffracted
light are on the same side of the HOE, and transmission holograms,
in which incident and diffracted light are on opposite sides. HOEs are
produced on a glass plate coated with a film of dichromated gelatin
emulsion by exposing it to two mutually coherent laser beams,
referred to as object and reference beams. The object beam
emanates from a pinhole placed on the normal center line of the
plate wave fronts interfere in the gelatin with plane waves of
a collimated reference beam, forming molecular cross-links in the film
in proportion to the light intensity due to the absorption of the light by
the dye. The interference fringes are registered in the film as
variations in hardness and index of refraction. The photo-
sensitive dichromate is then removed from the gelatin during post-
exposure chemical processing, and the resulting hologram is
relatively free of absorption. The HOE is then dried and hermetically
sealed with a glass cover cemented to the substrate and sealed
around the edges. When the completed HOE is illuminated with the
photo-conjugate to the construction reference wave, it reconstructs
the conjugate of the original object beam, thus forming a real image
of the original point source.

9.  A holographic optical element is a hologram of point source.
 HOE’s are wave length sensitive.
 Single HOE’s can serve multiple, function, it can be used as lens ,beam
splitter simultaneously.
 The HOE’s are relatively thin and light-weight.
 Production cost is less.
 with the availability of real time recyclable recording media
any desired system function can be recorded, erased and when needed
 HOE’s are being recorded in dichromated gelatin emulsion.
APPLICATION OF HOE’S
 Beam combiner
 Laser scanners
 In optical signal processing
 Fiber guiding and optical waveguide components
HOE’s today have a matured stage. Holographic night vision goggles
and holographic head up display system have already been introduced
now.
HOLOGRAPHIC SCANNERS

10. Holography was has not remained merely a technique for recording 3D
images but has grown into a new subject having applications in diverse fields.
The recording medium has to convert the original interference pattern into
an optical element that modifies either the amplitude or the phase of an
incident light beam in proportion to the intensity of the original light field.
The recording medium should be able to resolve fully all the fringes arising
from interference between object and reference beam. These fringe
spacing’s can range from tens of micrometers to less than one micrometer,
i.e. spatial frequencies ranging from a few hundred to several thousand
cycles/mm, and ideally, the recording medium should have a response
which is flat over this range. If the response of the medium to these spatial
frequencies is low, the diffraction efficiency of the hologram will be poor,
and a dim image will be obtained. Standard photographic film has a very
low or even zero response at the frequencies involved and cannot be used
to make a hologram - see, for example, Kodak's professional black and
white film whose resolution starts falling off at 20 lines/mm — it is unlikely
that any reconstructed beam could be obtained using this film.
If the response is not flat over the range of spatial frequencies in the
interference pattern, then the resolution of the reconstructed image may
also be degraded. The table below shows the principal materials used for
holographic recording. Note that these do not include the materials used in
the mass replication of an existing hologram, which are discussed in the
next section. The resolution limit given in the table indicates the maximal
number of interference lines/mm of the gratings. The required exposure,
expressed as millijoules (mJ) of photon energy impacting the surface area,
is for a long exposure time. Short exposure times (less than 1/1000 of a
second, such as with a pulsed laser) require much higher exposure
energies, due to reciprocity failure.
Holographic scanners are moving detectors, like rotating mirrors.
Focusing in addition to deflection can be combined in a single hologram.
Resolution enhancement beyond the limits set by the numerical aperture of
the scanning beam becomes possible by detector plane filtering.

11. SCANNER TYPES
Single hologram scanners are the following types
Rotating gratings
Rotating holographic lenses
Rotating general holograms
Translating gratings
Translating holographic lenses
Translating general holograms
Practical system
The concept of using holographic scanning has been around for more
than two decades and during this time many differentApplications have
been suggested, but only a few have been demonstrated it like
IBM,Nippon Electric company.