16-Holography.Pdf

Dennis Gabor (1947) ••• Nobel Prize in Physics (1971)

Photography Ð Records intensity distribution of light . + Does not record direction. + Two-dimensional image.

Holography = “whole + writing” Ð Records intensity & direction of light. + Information in interference pattern. + Reconstruct image by passing original light through hologram. + Need laser so that light interferes.

http://en.wikipedia.org/wiki/Hologram Recording

Reconstructing

Photograph of the recorded interference pattern in an amplitude-modulation hologram Holography vs. photography (from http://en.wikipedia.org/wiki/Hologram)

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. Recording Amplitude and Phase

Object Beam a(x, y)()= a x, y exp[− jφ(x, y)]

Reference Beam

A()xy,,exp,=− Axy ()⎣⎡ jψ ( xy)⎦⎤

Interference

2 Ixy(),,,=+ Axy ()() axy =+++AaAaAa22**

22 =++A()x,,2,,cos,,y ax()y Ax()y ax()y ⎣⎡ψϕ()()x y −x y ⎦⎤ Reconstruction of wavefront

22∗ ∗ tA (x, y)∝ I(x, y) txyA (), =+++β ( A a AaAa)

For the reading (probe) beam of B()x, y ,

* ∗∗ ∗ B(x,y) txA ( ,y)= ββββAA B++ aa B A Ba + ABa =+++ U1234 U U U

2 For B = A Uxy3 (),,= β Aaxy()

∗ 2 ∗ For B = A Uxy4 (),,= β Aaxy() Original Referencing & Conjugate Referencing

Virtual image For B = A

2 Uxy3 (),,= β Aaxy()

For B = A∗ real image 2 ∗ Uxy4 (),,= β Aaxy()

* Ua4 ~ Hologram Simple Hologram Simple Hologram

Consider Two beams cross at an angle θ

Photographic plate

beam 1 z θ x Simple Hologram

l beam 1 θ z

θ x

Extra path of beam 2 is l = z sin θ Displacements of two beams are

E1 =−ω Eo cos( kx t ) () EE2 =+θ−ωo cos⎣⎡ kxz sin t⎦⎤ Simple Hologram

Thus displacement at film is:

EEE= 12+ = Eo {cos() kxt −ω + cos( kx[ +l] −ω t)} ÐUsing the trig identity 11 cosAB+= cos 2cos22( ABAB +) cos ( −) 11 EE= 2coso ()22 kll cos( kx[ +−ω] t)

1 ÐAmplitude varies as cos(2 kl) ÐIntensity varies as

2 2211 IE=∝cos(22 kl) = cos( kz sin θ) Simple Hologram After the film is developed, lines (sinusoidal diffraction grating) appear on film. z beam 1

2 1 cos(2 kz sin θ) Simple Hologram

When the beam 1 is shone on the developed film:

2 1 EE=θ−ωo cos(2 kz sin) cos( kxt) 1 = 2 Eo {}1+θ−ω cos()kz sin cos() kx t beam 1 ? 2 1 cosCC=+2 ( 1 cos 2 )

11 cosA cosBABAB=++−22 cos( ) cos( )

11 E= 22 E0 cos( kx−ω t) + Eo cos( kz sin θ) cos( kx −ω t) 11 =−ω++θ−ω24EkxtEkxz00cos() cos()() sin t

1 +−θ−ω4 Ekxz0 cos()() sin t Simple Hologram

The three parts are: 1 2 Ekxt0 cos( − ω ) ÐBeam continuing in direction of beam 1 1 4 Ekxz0 cos( ( + sin θ−ω) t) ÐBeam in direction +θ. 1 4 Ekxz0 cos( ( − sin θ−ω) t) ÐBeam in direction -θ. Three beams emerge, one in direction 0, one at +θ and one at -θ. Simple Hologram You will get:

virtual Developed +θ Photographic plate θ beam 1 θ -θ

real Ð+θ recreation of beam 2 (virtual image) Ð-θ beam is real image Holography of 3D Scenes

(a)

(b) Parallax in Holograms Holography

Many different optical arrangements. Recording requirements: ÐLaser light source(coherent light) ÐHolographic film needs small grains. ÐGood stability (no movements during exposure) Reconstruction requirements: ÐMuch less strict. ÐSome do not need laser. Applications of Holography

Artistic creations. Storing & transporting delicate images ÐRussian icons are shown as holograms. Holographic Interferometry. ÐStrain analysis of objects under stress ÐUsed for measuring shape of objects. Data storage. ÐContain large amount of visual information ÐSimilar technique for storing digital data. Holographic Interferometery

Double exposure holographic interferometry. ÐTwo holograms on photographic plate. ÐObject is stressed between exposures. ÐMovement of object appears as interference fringes Real time holographic interferometry. ÐStandard hologram of image made. ÐReconstruct image on top of object. ÐStress object & interference fringes appear. Holographic Interferometery

From each point on two images, light will have the displacements.

EE12=−ω=+Δ−ωoocos( kxt) EE cos ⎣⎡ kxx( ) t⎦⎤ Ð Δx is movement of that point when object was stressed. Ð Resultant displacement is sum of the two:

EEE=+=12 Eo {cos( kxt −ω+) cos( kxx( +Δ−ω) t)} ⎡⎤⎛⎞xx+Δ ⎛⎞ kx Δ =−ωEko cos⎢⎥⎜⎟ t cos ⎜⎟ ⎣⎦⎝⎠22 ⎝⎠

Intensity varies as

2 ⎛⎞kxΔ I ∝ cos ⎜⎟ ⎝⎠2 Ð Intensity shows how much (Δx) object has moved. Contour Generation Double exposure hologram at the same time Vibration Analysis Double exposure hologram in sequence Electronic Speckle Pattern Interferometry (ESPI) Computer-generatedυ hologram (CGH) 1. Detour-Phase CGH : amplitude pattern π

N XY−1 N −1 jφ pq ⎡ 2λ ⎤ U f ()u, = ∑∑apq e exp⎢ j ()upΔx +υqΔy ⎥ p=0 q=0 ⎣ f ⎦ Computer-generated hologram (CGH) 2. Kinoform CGH: phase-only pattern Aberration Compensation Artificial Neural Networks

(a) (b) Holographic data storage Holographic data storage

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