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# holographic interferometry

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holographic interferometry,scanners, optical element

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### holographic interferometry

1. 1. HOLOGRAPHIC- INTERFEROMETRY, SCANNERS AND OPTICAL ELEMENTS VINEETH KRISHNAN P.V S3.MSc.PHYSICS AM.AR.P2PHY12017
2. 2. CONTENTS INTRODUCTION HOLOGRAPHIC INTERFEROMETRY TYPES OF HOLOGRAPHIC INTERFEROMETRY MATHEMATICAL DESCRIPTION OF DOUBL EXPOSSURE METHOD MATHEMATICAL DESCRIPTION OF TIME -AVERAGING METHOD REAL TIME METHOD HOLOGRAPHIC OPTICAL ELEMENTS APPLICATION OF HOEโS HOLOGRAPHIC SCANNERS
3. 3. INTRODUCTION A photograph represents two dimensional recording of a three dimensional scene. What is recorded is the intensity distribution that prevailed at the plane of the photograph when it was exposed .the light sensitive medium is sensitive only to the intensity variations and hence while recording a phtograph, the phase distribution which prevailed at the plane of the photograph is lost. Since only the intensity pattern is has been recorded, the three dimensional character (e.g., parallax) of the object scene is lost. Thus one cannot change the perspective of the image in the photograph by viewing it from a different angle or one cannot refocus the unfocused part of the image in the photograph. Holography is a method evolved by Gabor in 1947, in which one not only records the amplitude but also the phase of the light wave; this is done by interferometric techniques. Because of this, the image produced by the technique of holography has a true three dimensional form. The idea of using of holograms for storage of information was first suggested by Van Heerden in 1963, who proposed to store data by recording the information carreing a light interference pattern in a holographic medium. The aesthetic appeal and commercial usefulness of holography are both related to the ability of a hologram to store a three-dimensional image. Unlike ordinary photographs, holograms record both phase and amplitude information. Because phase is a relative property, construction of a hologram requires a โreference beamโ in addition to the light reflected from an objectโs surface. Additional requirements include a powerful, coherent, monochromatic light source (e.g. a laser, whose workings you should understand);a vibration-free flat surface; some common optical devices; and photographic plates, chemicals, and a darkroom. A hologram can be made by exposing a photographic plate to the interference pattern made by the reference and object beams. The plate is then developed and dried.
4. 4. When illuminated by a reference beam similar to the original one, it recreates a three dimensional picture of the object. There is nothing mystical about this recreation, and you can understand how it works with the help of some Fourier transform mathematics. HOLOGRAPHIC INTERFEROMETRY Holographic interferometry is the technique of using classical interferometry and combining it with the technique of recording wavefronts from three dimensional diffusively reflecting object s with nonplanar surfaces in order to measure small optical path differences. The technique was first developed by Powell and Stetson in 1965. Their experiments were conducted over the period of October to December 1964, and they began with an investigation of the periodic coherence length of the HeNe laser being used. The compact laser beam was used to illuminate a spot on a small object was placed between two mirrors such that its image could be observed looking over one mirror into the tunnel of multiple reflections between the mirrors. Each image was 10 cm greater in path length than the one before it. Because these lasers had about three longitudinal modes, their coherence length was periodic, as described by the manufacturer, Spectra Physics in cooperation with the Perkin Elmer Corporation. This was demonstrated by recording a hologram of the view over one of the mirrors. In one of the holograms, however, a dark band was observed in the closest image to the hologram, and it was observed to shift position with perspective. This band was not observable in the original laser beam and had to be something created by the holographic process. The confocal laser cavity consisted of a spherical mirror at the output end with a flat mirror at the center of curvature at the other end. Adjustment of the longitudinal spacing controlled the number of off-axis modes of oscillation, and it was observed that the laser was oscillating in more than one of axis mode. The multiple laser modes were incoherent and did not interfere in the observable laser beam, so why did they interfere in the hologram reconstruction? Stetson put forth the idea that each mode existed in both the object and in the reference beam, and each pair recorded a separate hologram in the photographic plate. When these were reconstructed, both recordings reconstructed simultaneously from the same laser beam and the fields were then mutually coherent. Powell objected to this idea, because it implied that the hologram had the power to coherently reconstruct fields that were incoherent during its recording.
5. 5. The resulting arguments gave rise to a set of experiments that were later published in 1966. These consisted of: (1) Recording the reflection of a concentrated laser beam while capturing the entire reference beam on the hologram and adjusting the laser for combinations of off-axis modes. (2) Recording double-exposure holograms of an object where the object, the reference beam mirror, and the hologram itself were rotated slightly between exposures. (3) Recording holograms of the bottom of a 35 mm film can while it was vibrating. Later, in April 1965, Stetson and Powell obtained real-time interference patterns between a real object and its holographic reconstruction. TYPES OF HOLOGRAPHIC INTERFEROMETRY Stored beam /Real time holographic interferometry. The superposition of an object with the object itself (while being subjected to stress)is observed. Stroboscopic stored beam /stroboscopic real-time holography The wave front against which optical interferometric measurements are made is stored in the instant they occur. A variation is to vibrate the subject harmonically and then synchronously modulate the output of the laser. Double exposure In double exposure holographic interference both reference hologram and subject hologram are recorded in the same photographic plates. MATHEMATICAL DESCRIPTION OF DOUBL EXPOSSURE METHOD This method consists in recording two successive holographic exposure of an Object in two different positions. When the hologram is reconstructed it produces an interference pattern which is indicative of the object displacement between the two exposures. The mathematical description of double exposure holography is best setup
6. 6. by first considering the recording of two object wavefront fields ๐01 and ๐02 in the same emulsion using a wave ๐ ๐ .since these wavefronts are all additive in the plane of the emulsion the resulting irradiance distribution I recorded in the hologram will expressed as I = โธ๐01 โธ2 + โธ๐02 โธ2 +2 โธ๐ ๐ โธ2 +๐ ๐ โ (๐01 + ๐02 )+( ๐01 โ +๐02 โ ) ๐ ๐ The image wave front Where, and . In the double exposure case, the reconstructed image is then Using trigonometric identity this may be expressed as This describes the geometry of the interference fringes found on the surface of the image as reconstructed from a double exposure hologram. MATHEMATICAL DESCRIPTION OF TIME -AVERAGING METHOD This technique consists in making a single holographic recording of an object while it is subjected to a cyclic vibratory motion and assume that the exposure time in recording the hologram is long compared to one period of the vibration cycle. In this manner the hologram effectively stores an ensemble of images corresponding to the time average of all positions of the object during its vibration.
7. 7. On their reconstruction, the interference of the ensemble images, or the vector sum of individual wavefronts, produces an interference pattern which is weighted towards the formation extremes of the object If the vibration frequency is โต and the amplitude z then the object light field can be represented as This equation can be further simplified using Bessel function n=0 we may be written This variation is characterized by being maximum when decrease In value. In summary, it can be seen that time-average holographic interferometry is a unique tool for studying sinusoidal vibration patterns using only one holographic exposure.
8. 8. REAL TIME METHOD The superposition of an object with the object itself (while being subjected to stress)is observed. The technique consist in taking a single holographic exposure of an object in an unstressed state ,processing the plate and replacing it in exactly the same position in which was recorded. HOLOGRAPHIC OPTICAL ELEMENTS H.O.E stands for Holographic optical element and it is a hologram that consists of a diffraction pattern rendered as a surface relief, or a thin film containing an index modulation throughout the thickness of the film. For our purposes, holograms can be divided into two categories: reflection holograms, in which incident and diffracted light are on the same side of the HOE, and transmission holograms, in which incident and diffracted light are on opposite sides. HOEs are produced on a glass plate coated with a film of dichromated gelatin emulsion by exposing it to two mutually coherent laser beams, referred to as object and reference beams. The object beam emanates from a pinhole placed on the normal center line of the plate wave fronts interfere in the gelatin with plane waves of a collimated reference beam, forming molecular cross-links in the film in proportion to the light intensity due to the absorption of the light by the dye. The interference fringes are registered in the film as variations in hardness and index of refraction. The photo- sensitive dichromate is then removed from the gelatin during post- exposure chemical processing, and the resulting hologram is relatively free of absorption. The HOE is then dried and hermetically sealed with a glass cover cemented to the substrate and sealed around the edges. When the completed HOE is illuminated with the photo-conjugate to the construction reference wave, it reconstructs the conjugate of the original object beam, thus forming a real image of the original point source.
9. 9. ๏ A holographic optical element is a hologram of point source. ๏ HOEโs are wave length sensitive. ๏ Single HOEโs can serve multiple, function, it can be used as lens ,beam splitter simultaneously. ๏ The HOEโs are relatively thin and light-weight. ๏ Production cost is less. ๏ with the availability of real time recyclable recording media any desired system function can be recorded, erased and when needed ๏ท HOEโs are being recorded in dichromated gelatin emulsion. APPLICATION OF HOEโS ๏ Beam combiner ๏ Laser scanners ๏ In optical signal processing ๏ท Fiber guiding and optical waveguide components HOEโs today have a matured stage. Holographic night vision goggles and holographic head up display system have already been introduced now. HOLOGRAPHIC SCANNERS
10. 10. Holography was has not remained merely a technique for recording 3D images but has grown into a new subject having applications in diverse fields. The recording medium has to convert the original interference pattern into an optical element that modifies either the amplitude or the phase of an incident light beam in proportion to the intensity of the original light field. The recording medium should be able to resolve fully all the fringes arising from interference between object and reference beam. These fringe spacingโs can range from tens of micrometers to less than one micrometer, i.e. spatial frequencies ranging from a few hundred to several thousand cycles/mm, and ideally, the recording medium should have a response which is flat over this range. If the response of the medium to these spatial frequencies is low, the diffraction efficiency of the hologram will be poor, and a dim image will be obtained. Standard photographic film has a very low or even zero response at the frequencies involved and cannot be used to make a hologram - see, for example, Kodak's professional black and white film whose resolution starts falling off at 20 lines/mm โ it is unlikely that any reconstructed beam could be obtained using this film. If the response is not flat over the range of spatial frequencies in the interference pattern, then the resolution of the reconstructed image may also be degraded. The table below shows the principal materials used for holographic recording. Note that these do not include the materials used in the mass replication of an existing hologram, which are discussed in the next section. The resolution limit given in the table indicates the maximal number of interference lines/mm of the gratings. The required exposure, expressed as millijoules (mJ) of photon energy impacting the surface area, is for a long exposure time. Short exposure times (less than 1/1000 of a second, such as with a pulsed laser) require much higher exposure energies, due to reciprocity failure. Holographic scanners are moving detectors, like rotating mirrors. Focusing in addition to deflection can be combined in a single hologram. Resolution enhancement beyond the limits set by the numerical aperture of the scanning beam becomes possible by detector plane filtering.
11. 11. SCANNER TYPES Single hologram scanners are the following types Rotating gratings Rotating holographic lenses Rotating general holograms Translating gratings Translating holographic lenses Translating general holograms Practical system The concept of using holographic scanning has been around for more than two decades and during this time many differentApplications have been suggested, but only a few have been demonstrated it like IBM,Nippon Electric company.