This document discusses regenerating an original hologram from a slice of the hologram. It begins with an introduction to holography, including how holograms are recorded and reconstructed. It then discusses the history of holography and the fringe structure and shape that results from the interference pattern. The document focuses on how the original hologram can be regenerated from a small slice by analyzing the number of fringes in the slice and how the parameters like amplitude may change. It concludes that holograms have applications in security, data storage, and medicine and discusses future directions for holography.

1. Cognizance
The Technical Extravaganza
18th-20th March, 2016
IIT, ROORKEE
Regenerating original hologram from a slice
Dheeraj, Devanshi Chaudhary
Department of Electronics and Communication Engineering
DIT University Dehradun: 248009, India
yadavdheeraj129@gmail.com,devanshi0114@gmail.com

2. Contents
• Introduction
• Holography?
• History
• Hologram Recording
• Hologram Reconstruction
• Fringe Structure
• Fringe Shape
• Regeneration of Hologram from a slice and parameter affected during change
• Conclusion
• Future of Holography!
• Interested articles on holography
• References
• Feedback and Questions

3. Introduction
• Holography is a 3-D imaging method where the complex light wavefront reflected by
objects is recorded.
• Unlike photography, it records both amplitude as well as phase of the light wave.
• It is simply an interference phenomenon. During the recording process reference beam
and object beam interfere within the recording layer. When the waves interfere we get
the pattern of fringes on the recording media.
• Our work reflects the key idea of regenerating the original hologram from its small part
(slice), the amount of information loss with the area of slice available is also presented.

4. Holography?
• Lens-less imaging process.
• Information about both the
amplitude and phase of the
diffracted or scattered waves can be
recorded.[1]
• It is an encoding of the light field as
an interference pattern of seemingly
random variations in the opacity,
density, or surface profile of the
photographic medium.
• The technique of holography can
also be used to optically store,
retrieve, and process information.
Fig-1(Holography Technology)

5. History
Dennis Gabor (1900–1979), developed holography while working
to improve the resolution of electron microscope. He later received
the Nobel Prize in Physics in 1971.[2]
Produced moving 3-D image.[2]
Developed first laser transmission
hologram of 3-D object (using a toy
train)[2]
Produced a white light hologram.[2]
Fig-2(3-D hologram of train)

6. Hologram Recording
• Interferometry.
Object wave  a(x,y) = |a(x,y)| exp[-jФ(x,y)]
Reference wave  A(x,y) = |A(x,y)| exp[-jѰ(x,y)]
• On recording media , we get the interference of both wave i.e. object wave and reference
wave.
Mathematically,
I(x,y) = |a(x,y)|2 +|A(x,y)| 2 + 2|a(x,y)||A(x,y)| cos[Ѱ(x,y)-Ф(x,y)]
Fig-3(Recording of hologram)

7. Hologram Reconstruction
• Use reconstruction beam for reconstruction of hologram.
• The hologram acts as a diffraction grating.
• The reconstruction beam after passing through the hologram produces a real as well as
virtual image of the object.
Then on recording medium, we get,
BtA = BtB+ β΄B|a(x, y)|2 + β΄A*Ba(x, y) + β΄ABa*(x, y).
Fourth term, this component is directly proportional to original scattered wave
a*(x , y). It leads to originate real image located at zo from opposite side of object.
Fig-4(Reconstruction of hologram)

8. Fringe Structure
The fringe pattern’s orientation or fringe angle is described by
θf = θobj+ θref/ 2
For 2-D Plane:
Y || S1S2.
S1(0, D) ,S2(0, -D).
where D is the distance between slits
and recording media.
Now, path difference (Δ) will be
S2P – S1P = Δ =
[x2 + (y-d/2)2 + D2]1/2 – [x2 + (y +
d/2)2 +D2]1/2 . [11]
Optical Holography by Robert J. Collier, Christopher B.
Burckhardt, Lawrence H. Lin
Fig-5(YDSE)

9. Fringe Shape
Let us take an isotropic point source .
• Amplitude of wave ‘A’.
• since 3-D plane P(x, y, o), so z-axis = 0
Complex amplitude of a wave
A(r, t) = (a/r)ei(wt-kr)
where, r = (x2+y2+z2)
From the above amplitude equation we observe amplitude decreases as r increases.
[x2 + (y + d/2)2 + D2] = {Δ+[x2+(y-d/2)2 + D2]1/2}2
On solving the above equation we get,
Y= Δ2/(d2-Δ2) [D2 + (d2-Δ2)] ……… (1)
Eq. (1) represents a HYPERBOLA fringes.
*x2<<D2 STRAIGHT LINE
Fig-6(Fringe shape)

10. We can decide number of fringes in a small part of hologram by calculating fringe
width.[12]
• Recording plate of dimension n*n.
• Next, we take a small part of
recording plate of dimension (say)a*a.
• Thereby, we can calculate fringe
width by using formula:
W = λD/2d
(for both bright and dark fringes).
•With the amount of number of
countable integer fringes we can then
estimate the number of fringes in area
a*a and later in whole n*n.
Fringe Count in small part of the hologram
Fig-7(Fringe shape)

11. After finding the change in parameter we can regenerate the hologram from
a slice of a*a dimension without much loss of data.
n
n
a
a
Hologram Regeneration from a slice

12. Hologram Regeneration from a slice
 In a small part of area (slice) with dimensions a*a we’re able to detect following:
Fringe count,
Structure & Shape of fringe
 Now we can find the change in parameters of hologram when we cut/slice into small
part of dimension a*a from n*n .
 The time period of wave remains unaffected. T = 2π/ Ѡ
 Hence, frequency remains unaffected.
 With established wave number, K= 2π/ λ we find change in amplitude
Complex amplitude of a wave
E(r, t) = (A/r)exp i(wt-kr)
r = (x2+y2+z2)1/2
 Amplitude decreases as (1/r) distances of energy conservation .
Where Ʌϕ = ϕ1 – ϕ2
Ʌϕ = 2π/λ (m)λ
Ʌϕ = 2π/λ(m+1/2)λ
Ʌϕ= 2π/ λ* Ʌx=k*Ʌx
 Ʌϕ Amplitude wave number

13. Conclusion
In this presentation , we have presented a related key aspect to count number of
fringes in a given holographic recording medium of certain area by assuming a
linear shape of fringes which is obtained when the distance between the recording
medium and the slits is quite long. We regenerate a hologram from a slice of a*a
dimension.
The application of the finding can be stretched out in lossless/lossy coding of data
by saving the data as holograms and further using the dictionary technique to store
the linear interference patterns.

14. Future of Holography!
• Holography as a measure to increase security.
• Pattern recognition.
• Holographic data storage.
• Holographic video game Console.
• Microsoft Hololens.
• Medical
Fig-8(Microsoft Hololens)
Fig-9(Medical holography)

15. Interesting Articles 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
Fig-10(Quantum holography system)

16. References
1. Introduction to Fourier Optics 2nd J.Goodman
2. http://hologram.org/.
3. https://www.youtube.com/watch?v=AXhGfkGh4vM
4. https://www.youtube.com/watch?v=aThCr0PsyuA
5. https://www.youtube.com/watch?v=iaaHcH9nQmI
6. slashdot.org
7. Andrew Chan "Digital hologram".
8. Guy E.blelloch "Introduction to optics."
9. HC-Verma "Concepts of physics volume-1".
10. Tung H.Jeong "Fundamental of photonics"(Module 1.10--Basic principal and application
of holography).
11. E. S. Maniloff, D. Vacar, D. McBranch, et al., OpticalHolography (Academic, New
York, 1971).
12. Huai M. Shang, Cheng Quan, Cho J. Tay, and Yua Y. Hung“Generation of carrier
fringes in holography and shearography”, Vol. 39, Issue 16, pp. 2638-2645 (2000),
doi: 10.1364/AO.39.002638

17. Feedback & Questions?

18. THANK YOU