16. Holography. Dennis Gabor (1947) Nobel Prize in Physics (1971)

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1 16. Holography Dennis Gabor (1947) Nobel Prize in Physics (1971) Photography Records intensity distribution of light. Does not record direction. Two-dimensional image. Holography = whole + writing Records intensity & direction of light. Information in interference pattern. Reconstruct image by passing original light through hologram. Need laser so that light interferes.

2 Recording Reconstructing Photograph of the recorded interference pattern in an amplitude-modulation hologram

3 Holography vs. photography (from Each point in the holographic recording includes light scattered from every point in the scene, whereas each point in a photograph has light scattered only from a single point in the scene. A hologram differs from a photograph in several ways: The hologram allows the recorded scene to be viewed from a wide range of angles. The photograph gives only a single view. The reproduced range of a hologram adds many of the same depth perception cues that were present in the original scene, which are again recognized by the human brain and translated into the same perception of a three-dimensional image as when the original scene might have been viewed. The photograph is a flat two-dimensional representation. The developed hologram surface itself consists of a very fine, seemingly random pattern, which appears to bear no relationship to the scene which it has recorded. A photograph clearly maps out the light field of the original scene. When a hologram is cut in pieces, the whole scene can still be seen in each piece. When a photograph is cut in pieces, each piece shows only part of the scene. Holograms can only be viewed with very specific forms of illumination, whereas a photograph can be viewed in a wide range of lighting conditions.

4 Recording Amplitude and Phase Object Beam ( x, y) = a( x, y) exp[ jφ( x y) ] a, Reference Beam (, ) = (, ) exp ψ (, ) A xy Axy j xy Interference (, ) = (, ) + (, ) I x y A x y a x y 2 2 * * = A + a + A a+ Aa (, ) (, ) 2 (, ) (, ) cos ψ (, ) ϕ(, ) = A x y + a x y + A x y a x y x y x y

5 Reconstruction of wavefront, ( ) ( 2 2, ) ta x y = β A + a + A a+ Aa ( x y) I( x y) t A, For the reading (probe) beam of B( x, y), * (, ) (, ) B x y t x y = βaa B + βaa B + βa Ba + βaba = U + U + U + U A For B = A U3 x, y = β A a x, y ( ) ( ) 2 For B = A U4 x, y = β A a x, y ( ) ( ) 2

6 Original Referencing & Conjugate Referencing For B = A Virtual image 2 ( ) = β ( ) U3 x, y A a x, y For B = A 2 ( ) = β ( ) U4 x, y A a x, y real image U ~ a * 4 Hologram

7 Simple Hologram

8 Simple Hologram Consider Two beams cross at an angle θ Photographic plate beam 1 θ x z

9 Simple Hologram beam 1 l θ z θ x Extra path of beam 2 is l = z sin θ Displacements of two beams are E = E cos( kx ωt ) 1 o E ( ) 2 = Eo cos k x + zsinθ ωt

10 Simple Hologram Thus displacement at film is: { ( ) ( [ l] )} E = E1+ E2 = Eo cos kx ω t + cos k x+ ωt Using the trig identity cos A+ cos B= 2cos A+ B cos A B ( ) ( ) ( ) ( 1 ) [ 1 l l] E = 2E cos k cos k x+ ωt o 2 2 Amplitude varies as Intensity varies as cos ( 1 kl) ( 1 ) ( 1 l ) I = E cos k = cos kzsin θ

11 Simple Hologram After the film is developed, lines (sinusoidal diffraction grating) appear on film. beam 1 z cos ( kz sin θ) 2 1 2

12 Simple Hologram When the beam 1 is shone on the developed film: ( 2 ) ( ) ( ) E E kz kx t 2 1 = o cos sin θ cos ω 1 2 { 1 cos sin } cos( ) = E + kz θ kx ωt o ( C) cos C = 1+ cos 2 ( ) o ( ) ( ) ( ) ( ( ) ) 1 + E cos k( x zsin θ) ωt E = E cos kx ω t + E cos kz sin θ cos kx ωt = E cos kx ω t + E cos k x+ zsin θ ωt ( ) ( ) cos Acos B = cos A+ B + cos A B ( ) beam 1?

13 Simple Hologram The three parts are: 1 E ( kx t) 2 0 cos ω Beam continuing in direction of beam 1 ( ) ( + θ ω ) E k x z t cos sin Beam in direction +θ. ( ) ( θ ω ) E k x z t cos sin Beam in direction -θ. Three beams emerge, one in direction 0, one at +θ and one at -θ.

14 You will get: Simple Hologram beam 1 Developed Photographic plate +θ θ virtual -θ θ +θ recreation of beam 2 (virtual image) -θ beam is real image real

15 Holography of 3D Scenes (a) (b)

16 Parallax in Holograms

17 Holography Many different optical arrangements. Recording requirements: Laser light source(coherent light) Holographic film needs small grains. Good stability (no movements during exposure) Reconstruction requirements: Much less strict. Some do not need laser.

18 Applications of Holography Artistic creations. Storing & transporting delicate images Russian icons are shown as holograms. Holographic Interferometry. Strain analysis of objects under stress Used for measuring shape of objects. Data storage. Contain large amount of visual information Similar technique for storing digital data.

19 Holographic Interferometery Double exposure holographic interferometry. Two holograms on photographic plate. Object is stressed between exposures. Movement of object appears as interference fringes Real time holographic interferometry. Standard hologram of image made. Reconstruct image on top of object. Stress object & interference fringes appear.

20 Holographic Interferometery From each point on two images, light will have the displacements. ( ) ( ) E1 = Eocos kx ω t E2 = Eocos k x +Δx ωt Δx is movement of that point when object was stressed. Resultant displacement is sum of the two: 1 2 ( ) cos ( ) { cos ( )} E = E + E = E kx ω t + k x+δx ωt o x +Δx kδx = Eo cos k ω 2 t cos 2 Intensity varies as I kδx 2 2 cos Intensity shows how much (Δx) object has moved.

21 Contour Generation Double exposure hologram at the same time

22 Vibration Analysis Double exposure hologram in sequence

23 Electronic Speckle Pattern Interferometry (ESPI)

24 Computer-generated hologram (CGH) 1. Detour-Phase CGH : amplitude pattern ( ) ( ) = = Δ + Δ = exp, X Y pq N p N q j pq f y q x up f j e a u U υ λ π υ φ

25 Computer-generated hologram (CGH) 2. Kinoform CGH: phase-only pattern

26 Aberration Compensation

27 Artificial Neural Networks (a) (b)

28 Holographic data storage

29 Holographic data storage From Lucent