5 TH ERMAL GRADIENT INTERFEROMETRIC MEASUREMENT

Transcription

1 5 TH ERMAL GRADIENT INTERFEROMETRIC MEASUREMENT Gradient Index Measurement with Temperature MODEL OEK-100 PROJECT #4

2 Introduction It is possible to measure the change in index of refraction of a material as a function of temperature by interferometric methods. I t is the purpose of this experiment to demonstrate the basic principals involved in such a measurement. However to obtain a high degree of accuracy for this measurement, better control of the ambient temperature and setup environment is necessary than is provided with this experimental setup. Some recommendations are available at the end of this experiment to increase the scope and accuracy of such a setup. For an interferometer, the path length difference in the two arms is related to the number of wavelengths rna = L2 - L I, where LI and L 2 are the path lengths for each arm, m is the number of whole fringes (it is possible to count fraction of fringes) and Iv is the wavelength of the laser light used. The test sample introduced in one of the arms of the interferometer will cause a path length difference related to the index of refraction of the material. The formula can be written as rna = 2n I t'+nt -t, where t is the thickness of the test sample (water), t' is the thickness of the cuvette walls, nl is the refractive index of the quartz, and n is the index of refraction of the test material (i.e. water). Solving for n and noting that the quartz path length change is negligible with temperature (see the procedure and setup section for the verification of this fact) we get, mjjt+ 1 =n. Taking a derivative of this last equation with respect to temperature will result in the following formula that will be used to measure the index of refraction change due to temperature change: (5.1) ~m A= ~n t Equation (5.1) can be used to calculate the change in index of refraction of the material contained in the test arm of the interferometer.

3 51 LA c:.r=j--~ MS ~ BE Figure 26 LA BE Figure 27

4 Equipment list Part Number Description QTY Ball Driver Set 1 SK-08A Screw Kit 1 SK-25A Screw Kit 1 RG 'x3' Breadboard 1 One Sheet of Aluminum Foil (Not included with kit) 1 BE. Beam Expander Assembly B-2SA Base Plate 1 LC-V Collimator Module 1 M-40X Objective Lens 1 MH-2PM Objective Mount 1 SP-3 3" Post 1 SP-4 4" Post 1 VPH-3 3" Post Holder 1 VPH-4 4" Post Holder 1 BS. Beamsplitter Assembly 20B20BS.1 2" Beamsplitter 2 U200-A2K Mirror Mount 2 SP-3 3" Post 2 VPH-3 3" Post Holder 2 CT. Collimation Tester Assembly 20QS20 2" Collimation Tester 1 AC-2A Lens Mount 1 B-2SA Base Plate 1 SP-3 3" Post 1 VPH-3 3" Post Holder 1 I. Iris Assembly Iris 2 MCF Flat Carrier 2 MH-2P Iris Mount 2 MSP-3 3" Post 2 MPH-3 3" Post Holder 2 MRL-3 Micro Optical Rail 1 MRL-18M Micro Optical Rail 1._---

5 L. Laser Assembly 340-RC Clamp 1 40 Rod 1 ULM-TILT Laser Mount 1 R mW HeNe Laser 1 MS. Steering Mirror Assembly 10D20ER.1 1" Mirror 1 COR-1 Cntr Of Rotatn Adaptr 1 P100-P Mirror Mount 1 UPA1 1" Mirror Holder 1 SP-3 3" Post 1 VPH-3 3" Post Holder 1 M1 and M2 Mirror Assemblies 20D20ER.1 2" Mirror 2 U200-A2K Mirror Mount 2 SP-3 3" Post 2 VPH-3 3" Post Holder 2 Screen Assembly B-2SA Base Plate 1 BC-5 Base Clamp 1 FC-1 Filter Clamp 1 SP-2 2" Post 1 VPH-2 2" Post Holder 1 T. Test Assembly 10BR08 BK-7 Prism Quartz Cuvette 1 FK Digital Thermometer 1 PT-1 Prism Table 1 SP-3 3" Post 1 VPH-3 3" Post Holder 1

6 Setup Placement of the Breadboard Place the RG-23-4 breadboard on a flat stable surface. Make sure that there is enough surface area near the breadboard to place the power supply units and other items that need not be mounted Laser Setup Mount a 40 Rod on the RG-23-4 breadboard in location L as in Figure 28 Attach a ULM-TILT Laser Mount to a 340-RC Clamp. Slide the 340-RC onto the 40 Rod. Mount the R laser head in the ULM-TILT mount and align the laser tube so that the polarization plane is perpendicular to the table top ("S" polarization) Laser Beam Alignment Post mount the Iris Assembly I on the MRL-3 Rail. Tum on the laser, point the beam along the long side of the breadboard and adjust the laser height to 6 inches. Place the ID-0.5 iris directly in front of the laser head (position I. in Figure 28) with its aperture aligned with the laser beam. Move the iris to the other end of the breadboard (position 12 in Figure 28) and adjust tilt and vertical position of the laser on the post to align the beam with the iris aperture. Move the Iris back and forth between positions II and h to ensure that the beam is parallel to the surface of the breadboard. Once the tilt of the laser is set the height can be varied by the 340-RC clamp and the beam will still be parallel to the surface of the breadboard Iris Placement Affix ID-0.5 iris I in front of the laser as shown in Figure 29 and adjust the aperture to just allow the laser beam through. The iris will now be used as a reference for retroreflected beams Interferometer Setup Choose one of the setup configurations, Figure 26 or Figure 27 (Figure 27 is an alternative for the setup of Figure 26 which increases the cross section of the optical windows). Place the 20D20ER.l 2" diameter mirrors and the 20B20BS.l beamplitter into the U200-A2K mounts and post mount each in place as shown in Figure 27 or Figure 29, to construct the Mach-Zehnder Interferometer. Use set screws on the SP-3 posts to connect to U200 A2K mirror mounts. Post mount each interferometer mirror 10" from the beamsplitter Interferometer Alignment Center the beam on BS optic and on MI by adjusting their post heights. Check the beam height in front of mirror MI. If beam height is not the same before and after the beamsplitter, adjust the tilt of the beam splitter until the beam is horizontal. Place the iris assembly I in front of mirror M2, match the height of the beam by adjusting the beamsplitter and MI respectively.

7 Beam Expander Positioning Assemble the beam expander assembly BE and mount in the path of the laser beam as in Figure 30. Attach the SP-3 post to the B-2SA base and mount the LC-V collimating lens directly onto the B-2SA base. Place the VPH-3 post holder on the breadboard so that when the LC-V is put in place there will be some room left to mount the M-40X objective lens. Mount the M-40X objective lens directly behind the LC-V. Turn on the laser and adjust the height of the LC-V until the beam is centered on the lens. Insert the M-40X objective lens in its place and align so that the expanding beam is centered on the collimating lens of the LC-V Collimation Calibration Place the collimation tester (model No 20QS20) in an AC-2A optics mount (use proper support stud tips in the AC-2A). NOTE The collimation tester is a wedged plate with its thicker side marked on the edge. It is desirable to have the thick edge of the plate pointing to the top of the AC-2A. Place the Collimation Tester Assembly CT at a 45 angle in the path of the expanded beam and look for fringes in the reflection. Adjust the position of the collimating lens in the beam expander until horizontal fringes are observed in the reflection. There should be three to five fringes visible in the reflection when fringes are horizontal. At this stage the expanded beam is well collimated. D L - 11 Figure 28

8 56 L Screer1'-=- Figure 29 I MS Figure Procedure and Results 1. Post mount the PT-1 mount with its face normal to the horizontal direction in the path of one of the anus of the interferometer between mirror M2 and BS2 beamsplitter. Fill the cuvette with distilled water and place cuvette sample in PT-l mount as shown in Figure 31. Adjust the interferometer to find fringes produced by light traversed through the cuvette.

9 57 Post'md ~ Post Holder Figure 31 CAUTION Boiling water needed for this experiment. Use insulated tongs to remove the cuvette from the boiling water. 2. Remove the cuvette from the boiling water and empty the water, then place immediately in the interferometer. You can observe that the fringes found will not move as the cuvette is cooling, therefore there will be no error introduced in the fringe count due to the container. 3. Remove the cuvette and boil in distilled water (with distilled water also on the inside). Remove from hot water and place on PT-l in the same position where fringes were previously found. 4. Wait up to a minute for the water to cool to a temperature lower than 70 C and place the thermometer probe into the cuvette. Stir the water with the probe of the thermometer and watch the temperature increase in the thermometer. When the temperature reading of the thermometer levels off and then starts to drop, continue to stir the water with the thermometer probe until the temperature starts nearing 40 C. At this point the temperature starts to vary slower with time; you may easily keep track of the fringe movements. Adjust one mirror of the interferometer to get a central fringe, see Figure 32, and immediately start counting the fringes. The thermometer has a typical settling time of 15 seconds; therefore it is desirable to have the fringe count to be at a rate close to 1 fringe count for every 15 seconds.

10 58 Toward,-_., i:= Cen~, center I ~ fringe fringe \ movement Fringe ::::I Figure The number of fringes moved is directly proportional to the index of refraction change of water due to temperature change as seen in equation Take a few data points by counting the fringes and the associated temperature change and make a table as shown in the sample calculation below. Sample Calculation Am T 1, T2 AT Ancalc Anactual %error , xlO-4 2.8xl0-4 10% , x xlO- 3 8% , xl0 J 2.8xl0- J 4% , xl0- J 4.9xlO- J 6% The values calculated here are compared with data from a table found in a handbook of chemistry or physics. 7. Index Change of Air- Remove quartz cuvette and mount from the interferometer. Place a lighter or a lit match in one arm of the interferometer and observe fringe distortion, place match in the other arm and observe fringes. (180 out of phase from the fringes observed in the other arm). 8. Index change ofbk7 Prism- Place the10br08 prism on the PT-l mount and place assembly in the interferometer. Locate fringes. Place a cube of ice in a sheet of aluminum foil and wrap so that as the ice melts the water will be contained in the foil. Place the foil directly on the prism. As the prism contracts due to the temperature change, and also due to the temperature dependence of the index of refraction, the fringes resulting from the prism will move closer together.

11 59 NOTE The prism may fog up a little as the ice is placed on it. You may wipe the prism faces with an optical paper to maintain clear fringes. 9. Recommendation for increasing the accuracy of this experiment- To improve the results of this experiment, it is necessary to have better control over the ambient temperature of the environment. One source of error is the thermometer that has a IS-second settling time for the final temperature reading, where in this experiment the temperature is constantly changing and so an error is introduced in this fashion. To solve this problem, a larger container could be used for the water so that the temperature will change more slowly. It is possible to construct a Michelson interferometer with one of the mirrors submerged in a bucket of water and the rest of the interferometer on the outside, allowing for a much larger body of water with a slower changing temperature for more accurate measurement. Another area where it wi II be possible to improve the accuracy of the experiment would be to have a larger window with a flat surface of less than one wavelength to be able to follow the fringes easier and reduce chances of miscounting the fringe movement. 5.5 References [5.1] P. Hariharan, Opticallnteljerometly, Academic Press, Sydney (1985). [5.2] P. Hariharan, Basics ofinter/erometry, Acaden 1 ic Press, San Diego (1992). [5.3] F. A. Jenkins and H. E. White, Fundamentals o/optics, McGraw Hill, New York (1976). [5.4] E. Hecht, Optics, Addison-Wesley, Reading MA (1987). [5.5] Weast, Handbook o/chemistry and Physics, CRC Press, 61st Edition ( ).