Chapter 8: HOLOGRAPHY104 © Jeffrey Bokor, 2000, all rights reservedChapter 8HOLOGRAPHY [Reading Assignment, Hecht 13.3. For additional material, see Introduction to Fourier Optics, byJ. Goodman, 2nd ed., Chapter 9.Virtually all recording devices for light respond to light intensity.Problem: How to record, and then later reconstruct both the amplitude and phase of an optical wave.The same issue can also be raised for acoustic and seismic waves.The challenge is to figure out how to convert phase information to intensity. InterferometryCreate a second wavefront with known amplitude and phase that is coherent with the wave to berecorded (the object wave). Add this to the object wave. The intensity of the sum contains the interference patternlet A recording of this interference pattern is a hologram.The recording medium for holography is typically some type of film emulsion. The transmission ofthe developed film can be linear in absorbed energy over a limited dynamic range. Under these conditions, the transmittance of film can be writtenreferencewavereference A(x, y)object a(x, y)objectwave(x, y) planeIsxy A2a2AaAa++ +=Axy2axy22 Axyaxy xyxy–cos++=Chapter 8: HOLOGRAPHY105 © Jeffrey Bokor, 2000, all rights reservedWhere we assume that is constant and uniform, which gives the bias tb . is the sensitivityparameter of the film.Reconstruction: illuminate transparency by reconstruction wave .Transmitted light is: If B is a duplicate of A, B = A.Then . If is uniform, then is a duplication of a.We could also arrange that . Then the conjugate of the original wavefrontThis process is a two dimensional analog of amplitude modulation.Here we have three extraneous signals which lead to unwanted interference. If we want a or a*, wehave to filter out the other components.Real and virtual imagesA general principle in holography is linearity. A useful construct is to consider a point object. Thebehavior of a complex object can be found by superposition. The point source object is : position of the point sourceWhen the A* reconstruction wave is used:We get a converging spherical wave toward point . But we still have not specified how toexclude the three unwanted components.A2'BxyBxytAxyBtB' a2B 'ABa 'ABa++ +=U3' A2a=A2U3BA=U4' A2a=araoejk r ro–rro–---------------------------=roU4r ' A2ar ' A2aoejk r ro––rro–---------------------------------==ro–Chapter 8: HOLOGRAPHY106 © Jeffrey Bokor, 2000, all rights reservedOriginal Gabor Hologram (1948) The reference wave is a plane wave which comes from the to component of the object itself.The object wave is scattered by the variations The scattered wave is weak compared to the reference plane waveThus we can neglect the term.recordingmediumReference Apoint sourceobjectReconstructionbeam Adiverging beamrepresents a“virtual image”arealimagea*reconstructionA*objectrecordingmediumscatteredwavedirect transmittedwaverecordingobject must be highly transmissivetxoyoU2Chapter 8: HOLOGRAPHY107 © Jeffrey Bokor, 2000, all rights reserved In a Gabor hologram there are three overlapping components, the real image, the virtual image, andthe background. Leith-Upatnieks (offset reference) hologram (1962) The reference beam is tilted. This is a real “hero” experiment without a laser. Holography was madepractical after the invention of the laser.Now the field at the recording plate consists of a scattered wave from the object plus the ref-erence plane wave.The intensity at the plate isThe developed film transmittance has four terms:real image (U4)Background (U1)Hologramreconstructionvirtual image (U3)“twin” imageshologramobjectzo2reference plane waveaxyIxy A2axy2Aaxy jky 2sinexp Aaxy jky 2sin–exp++ +=tAtb' axy2'Aaxy jky 2sinexp 'Aaxy jky 2sin–exp+++=Chapter 8: HOLOGRAPHY108 © Jeffrey Bokor, 2000, all rights reservedReconstruction: The reconstruction beam is a plane wave at normal incidence, with amplitude B.Four components in the transmitted wave: U1: attenuated version of the reconstruction beamU2: scattered wave by object . It stays close to the axis.U3: original wave a, modulated by the exponential phase factor. This modulation causes deflec-tion by the angle 2. Proportionality to a causes the virtual image to be formed at the distance -zo.U4: a* is modulated. By a similar argument, we get the real image deflected by -2 at the dis-tance zo.The twin images (real and virtual) are now angularly separated from each other as well as from thebackground components of U1 and U2.22hologramU1U2U3U4zozoU1BtB=U2'Ba x y2=U3'BAaxy jky 2sinexp=U4'BAaxy jky 2sin–exp=axy2Chapter 8: HOLOGRAPHY109 © Jeffrey Bokor, 2000, all rights reserved The reference and object waves come from opposite sides of the recording medium. This can be viewed in white light since the Bragg condition is wavelength selective. More on thislater.Holographic Data StorageA current CD-ROM stores 640 megabytes. A dramatic improvement in CD-ROM technology is pos-sible with holographic techniques: The ~850 nm laser is focused using a high NA lens to read the pits.Rayleigh resolution: 1 m Reflection hologramsrecording planeobjectreferenceInterference fringesform standing wavesin emulsion. Theperiod is about and this is parallel tothe surface. 2observerhologramreconstructionThe virtual imageis formed by thelight Braggreflected by thehologramplastic filmembedded metal filmwith pits which rep-resent bits.current scheme0.6 NA 850nm=NA 0.5=Chapter 8: HOLOGRAPHY110 © Jeffrey Bokor, 2000, all rights reservedWith a shorter , and using a higher lens, we reach a resolution of 490nm. Withimproved coding, DVDs reach a storage density of 4.7 Gbytes. We use a small DOF to focus in on only one level at a time. Another factor of 3 - 5 is possible. TheDVD standard allows for using 2 levels, with recording on both sides of the disk, which makes it pos-sible to store up to 17 Gbytes.Holographic storage targets:Hundreds of Gbytes, in about 1 cm3, or possibly a disk format.About a 100