EXPERIMENT 25 HOLOGRAPHY Equipment List:- (a) (b) (c) (d) (e) (f) (g) Holography camera and plate holders Laser/beam lamp and assembly Shutter on stand Light meter Objects to make holographs of Holographic plates Pinhole for viewing References Jenkins and White, "Fundamentals of Optics", 4th ed., Chap. 31; Klein, "Optics", Section 8.3. Hecht and Zajac, "Optics", Section 14.3
2 AIM You will gain first hand experience in making a hologram. Measurements will be carried out that shows the hologram behaves in a similarly to lenses producing real and virtual images, depending on the viewing and orientation of the film. 1. DETAILS OF EQUIPMENT (a) Camera. The experiment uses an Optics Technology Model 177 Holographic Camera, a diagram of which is drawn below. The top of the box is removable - lift the back edge about 1 cm, draw the top backwards about 2 cm and lift off. Removable Neutral Density Filter Holder Beam Splitter Rear Mirror Front Mirror Film Plane Object Platform FIGURE 1 General layout of holographic camera. (b) (c) Laser. The source is a helium-neon laser (Lasertron) with a nominal output of 1 milliwatts in the TEM oo mode. Shutter. While taking the hologram, an electromagnetic shutter is placed so that it blocks the narrow laser beam except when activated. The period during which the shutter is open is varied by switches on the control box. (d) Light meter. A photoconductive cell is used to measure the light intensity. A switch gives 3 ranges, each differing by a factor of 10 from the one below. Be sure to have the switch in the least-sensitive (anti-clockwise) position before switching on the room lights or opening camera.
(e) 3 Beam expander. The beam is expanded so that the illuminated area of the object platform and the photographic plate is several square centimetres. This is accomplished by a 20 x (very short focal length) microscope objective. A 10 micrometre pinhole must be carefully adjusted to be at the focal point of this lens so that only the central maximum (the Airy disc) of the lens focal diffraction pattern is passed through to the camera. The beam (observed on a white card or paper placed at the entrance hole to the camera) should be free from structure due to diffraction at the edge of the pinhole. 2. SETTING UP Switch on the laser and check that the beam splitter is in place and clamped. Check that the main beam falls near the centre of the plate holder frame (i.e. the film plane) and that the object platform is well illuminated. Generally this should be aligned. However, if you find that this is not the case then call the technician or the demonstrator who will make slight adjustments to the laser orientation and the pinhole micrometer screws to allow only the central maximum of the lens diffraction pattern to pass into the camera. Place two or three of the white plastic letters on the object platform (plus a new coin or key if you wish). The required exposure for the films about 16 seconds. Finally, check that the beam entering the camera is still "cleanly" filtered. If not, then call the technician to readjust and check the light meter reading. Record the meter reading and exposure time selected. 3. TAKING A HOLOGRAM (a) Loading the film Holder The photographic film must be handled in the darkroom in TOTAL DARKNESS, there is no "safe" light; they are panchromatic and sensitive to all visible light. The film holder to be used for the first experiment is the one simply labelled sides 1 and 2 near the dark - slide handles. Try the following steps in daylight first, using old film:- Move the dark slide locking pin to the "open" position and pull out the dark slide (see NOTE 1 below); Place the film in the holder with the emulsion side up (see NOTE 2 below), fold the flap over to hold the bottom of the film down and push the dark slide GENTLY all the way across and into the flap. Turn the locking pin for safety. NOTE 1 - It is advisable not to remove the dark slide completely from the film holder (it can be difficult to find its slit in the dark!). Before switching off the light, simply draw it out until it clears the film area. NOTE 2 - The note on the side of the camera box tells you how to identify the emulsion side of the film. For the films moisten the ends of the thumb and forefinger and touch them on either side of the film in one corner. The emulsion side will be sticky. (b) Taking the hologram
4 The film is exposed by pulling back the dark side and using the electromagnetic shutter to expose for the correct time. N.B. It is imperative that you wait for 1 minute after you pull back the dark slide before exposing the film. This enables vibrations to die down. Also, do not bump the table while the film is being exposed since experiment is very sensitive to vibration. (c) Developing the film The solutions are contained in three processing tanks. Remove the lids and place each beside the corresponding tank so that they will not be replaced on the wrong tank at the end of the process. Expose the timing clock to bright light for a few minutes so that it will fluoresce strongly. Check that you can insert the film, in the dark, into the metal film holder used with the processing tanks. Switch off the light and transfer the film from the Riteway holder to the metal holder. Follow the developing schedule set out below, agitating the holder every 10 seconds or so. (1) Developer D19 (1/1 mixture) - 5 minutes. (2) Acetic Acid Stopbath - 1 minute. (3) Amfix - 3 minutes (known as the fixer). (4) Wash under running water for 15 minutes. Hang up to dry. 4. VIEWING A HOLOGRAM Back in the lab; insert the processed and dried photographic film in the viewing frame in the same position and orientation as when it was exposed. Only the reference beam is now required, so remove the beam splitter and the filters. The virtual image should clearly be seen in the same position as was the original object when the film is correctly orientated (see "V" in Figure 2). A real image may be found in two positions. Remember, a real image is one that can be projected onto a screen, so DO NOT use your eyes to see the image. Use the translucent screen. If the film is turned slightly so that it is perpendicular to the direction of the reference beam, the real image may be seen 25 cm beyond the film (off the edge of the bench, R1 in Figure 2). You may need to look for features of the image such a bright reflection off, say, the ball bearings.
5 Removable Neutral Density Filter Holder Beam Rear Mirror Emulsion Front Mirror R2 V Object Platform R1 For For V emulsion on right hand For R2 emulsion on left hand FIGURE Arrangements for reconstructing the virtual and real images. The best real image is found 20 to 30 cm behind the film (R2) when the film is rotated 180 o about a vertical axis (emulsion facing out of the camera). The image may be located on the ground glass screen on a stand. It is easier to see if the large (grey painted) dark cover is placed at the camera exit aperture. There is also a metal shroud (a large black square tube) that can be placed outside the film plane in order to exclude the room lights. Describe the various images. NOTE - If the real image is poor or absent, you have another chance in section 7. So leave a large letter on the left hand side of the object platform, ensuring that neither it nor its shadow obstructs the right hand side of the slit. This film with the letter and its images may be used in place of the first plate, as well as for the purposes of section 7. Tutor checkpoint. Obtain tutor's signature before proceeding. 5. IMAGES FORMED WITH A HOLOGRAM Your film will give you real and virtual images of the letters (and key, coin, etc.). Locate these images, measure their distances from the film position and calculate the magnification using formulae from Section 9. Compare the values with those obtained from measuring the image:object size ratio. Also compare the theoretical positions of the image (determined from substituting s, s, o, in the formulae in Section 9) with your measured positions. Tutor checkpoint. Obtain tutor's signature before proceeding. 6. VIEWING IN NON-COHERENT LIGHT Holograms may be viewed using conventional light sources, provided the light is made spatially coherent by using a pinhole.
6 Examine the hologram in the light from a mercury lamp, which should be on the nearest table (do not look directly into the lamp, as the violet and near ultraviolet components are rather intense). Explain what you see. 7. HOLOGRAPHIC DETERMINATION OF DISPLACEMENT If two successive exposures are made on the same film and the object is moved from its original position before the second exposure, the image formed by the composite hologram will show a system of fringes related to the displacement. For a simple translation x of the object, the fringes are straight lines (as in Young's experiment) localized at infinity. Path difference ξ = xθ = nλ Angular fringe space dn/dθ = x/λ θ λ = 632.8 nm ξ θ x Displacement Image Plane FIGURE 3 Origin of path difference for two displaced images. Remove the plastic letters from the object platform. Turn the screw controlling the moving half of the adjustable slit out, and then back in so that the half-slit is moving smoothly and any backlash in the screw has been picked up. Note the screw reading, and take a hologram with an exposure time half that used previously. Very carefully turn the screwhead through 10 divisions (1 division is 0.005 mm). Do not touch the dark slide. Allow a few seconds for any mechanical vibrations to die down, and take a second exposure of equal time. Process the film and give a description of the image formed by the composite hologram. Note the effect of changing the eye position (for a report you might like to research the terms localized and non-localized fringes and discuss which is applicable to these fringes). Referring to Figure 4, find the angular spacing of the fringes (i.e. the number of fringes, dn, per subtended angle, dθ) dn/dθ using one of the following methods: (a) Count the fringes visible in the field of view of a telescope. The angular field of view is then calculated by measuring the linear size of the field at a known distance from the telescope.
7 dθ sin θ ta θ l/d dθ l d FIGURE 4 Definition of angular field of view for a telescope. (b) View the fringes by eye and measure dθ geometrically. As for (a), the angle required is the length over which the fringes are distributed divided by the distance at which they are viewed. Using the formula given in Figure 3, calculate the slit displacement x. Compare this with the value given by the rotation of the screwhead. Tutor checkpoint. Obtain tutor's signature before proceeding. 8. SUMMARY OF HOLOGRAM IMAGE FORMULAE The notation to be used is given in the two diagrams below. (a) Formation (b) Reconstruction x Source (s, θ s ) s θ s θ o o x Object (o,θo ) x Source (s, θs ) s θs θi i x Image ( i, θ i ) Film Film FIGURE 5 Definition of object image and source distances. In Figure 6, the Source is the source of our reference beam, and the object is the physical object that we used to obtain the hologram. In addition, s and o are their respective distances from the film. Similarly, when the film has been developed and we want to reconstruct the image of the original object then S ource is simply the source of a laser light that we shine on the film, and Image is the reconstructed holographic image. Again, s and i are their respective distances from film. Note that since in both cases our reference beam is used to make the hologram then view it,
8 then Source and S ource are the same. Moreover, their distances from the film, s and s, are also the same. It can be shown that a hologram combines the focussing properties of a (sinoidal) zone plate with the directional properties of a (sinoidal) diffraction grating. Thus for image location we have the zone plate formula 1 i - 1 = ± 1 s f = ± ( 1 0-1 s ) while for the image direction we have the diffraction grating formula sinθ i - sinθ s = ± (sinθ o - sinθ s ). The magnification is given by the standard formula m = ± i o In these equations, distances are positive on the object side of the hologram. The positive sign in the equations corresponds to the virtual image (i positive), the negative sign to the real image (i negative).