CognizanceThe Technical Extravaganza

18th-20th March, 2016IIT, 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

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

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.

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)

HistoryDennis 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)

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)

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)

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 beS2P – 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)

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)

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)

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

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

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.

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)

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)

References1. Introduction to Fourier Optics 2nd J.Goodman 2. http://hologram.org/.3. https://www.youtube.com/watch?v=AXhGfkGh4vM4. https://www.youtube.com/watch?v=aThCr0PsyuA5. https://www.youtube.com/watch?v=iaaHcH9nQmI6. slashdot.org7. 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

Feedback & Questions?

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