6 THICKNESS MEASUREMENT OF TRANSPARENT MEDIA

Transcription

1 6 THICKNESS MEASUREMENT OF TRANSPARENT MEDIA Measure the Thickness of Transparent Media Using the Mach-Zehnder Interferometer MODEL OEK-100 PROJECT #5

2 Introduction The thickness of a transparent media with known geometry and index of refraction can be measured by interferometric methods. The value measured in this experiment is within 2 significant figures of the accepted value. A quartz plate placed in a Mach-Zehnder interferometer is used as a demonstration of this method. The aim is to rotate the sample through an angle 8 measured from the original direction of the beam and count ~m fringes. The movement of the fringes is caused by a changing optical path length and is related to the thickness of the transparent medium. Equation (6.1) is the basic relationship between path length difference and the change in the number of fringes in a Mach-Zehnder interferometer. A ~L =~m- (6.1) 2 -, ~_~_----IJ t Figure 33 Ray trace ofa beam path inside the slab before and after a rotation e. A formula is generated to calculate the index of refraction of the material by taking advantage of the special geometry of the plate. The optical path length difference is:

3 63 Using the geometry and trigonometric relationships, the three terms in the equation are rewritten as: AL = nt (_1_ - coss - si ns tancp ) (6.2) coscp Relating equations (6.1) and (6.2) and solving for n we get: 1 2n 1. t rna coscp - = - ( coss - SInS tancp ) (6.3) 6.2 Definitions of Terms 81 The physical path length traveled by the beam in the air before window is rotated (see Figure 33) 82 The physical path length the bean 1 traverses inside the medium before rotation (see Figure 33) L1L A L1m n Effective path length change due to physical path length difference or change in index of refraction or both combined Refracted angle of the beam inside the material measured from the normal to the surface Wavelength of the laser light used Number of fringes passing a certain point on the screen due to change in effective path length difference caused in one of the arms of the interferometer Index of refraction of the medium under consideration 8 Incident angle of the beam measured in reference to the normal of the surface Z Thickness of the plate Path length traveled by the beam inside the material of index n

4 64,. LA I=::J---~ MS BE Screen Figure 34 I '~ MS BE BS ] Figure 35

5 Equipment list Part Number Description QTY Ball Driver Set 1 SK-08A Screw Kit 1 SK-25A Screw Kit 1 RG 'x3' Breadboard 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 SPA 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

6 MRL-3 Micro Optical Rail 1 MRL-18M Micro Optical Rail 1 L. Laser Assembly 340-RC Clamp 1 40 Rod 1 ULM-TIL T 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 200S20 2" Collimation Tester A Rotary Stage 1 AC-2A Lens Mount 1 SP-3 3" Post 1 VPH-3 3" Post Holder 1

7 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 36. 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 iris directly in front of the laser head (position II in Figure 36) with its aperture aligned with the laser beam. Move the iris to the other end of the breadboard (position 12 in Figure 36) 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 1\ and 12 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 37 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 34 or Figure 35 (Figure 35 is an alternative for the setup of Figure 34 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 35 or Figure 37, 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. Ifbeam 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.

8 Beam Expander Positioning Assemble the beam expander assembly BE and mount in the path of the laser beam. 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. Tum 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. --II W Figure 36

9 69 L Figure 37 Figure Procedure CAUTION Handle the optics with care. Do not place finger on the smooth transmissive surface of the prism. If the surface gets dusty. use acetone and soft tissue paper to wipe surface. refer to full cleaning instructions in the Newport Catalog. 1. Sample plate positioning- Place the 20QS20 quartz plate in AC-2A optic mount and mount on a SP-3 post in the vertical plane. 2. Mount a VPH-3 post holder on a 481 -A rotation stage and place the mounted optic in the post holder. 3. Place the Assembly S in the path of one of the arms of the interferometer as shown in Figure 34 and adjust the tilt ofthe plate to obtain the fringes again. It may be necessary to adjust the min ors and beam splitters to obtain satisfying fringes.

10 70 4. Plate alignment- Observe the fringes as the 481-A stage is rotated. When the surface nonnal of the plate is parallel with the beam, the fringes will stop moving for an instant and then move in reverse direction as the plate is still rotated in the same direction as started. Use this fact to align the plate with the beam by watching for this phenomenon as the stage is rotated back and forth a few times. 6.6 Expected Resu Its 1. Record the first angle reading on the 481-A rotational stage for the aligned plate. 2. Rotate the plate and record the number of fringes, m, that roll by, counts of larger than Record the second angle and find the difference of the two angles. This value will be used as ein equation (6.3). 4. Calculate value of t using equation (6.3). 5. Repeat steps 1 through 4 a few times for various values of m. 6. Error analysis: 6.7 Sample Data Find the average value of the thickness t and the standard deviation to detennine the certainty of the value obtained. m 0 tcalc (mm) tact (mm) A% % ) % 6.8 References [6.1] P. Hariharan, Optical Interferometry, Academic Press, Sydney (1985). [6.2] P. Hariharan, Basics ofinterferometly, Academic Press, San Diego (1992). [6.3] F. A. Jenkins and H. E. White, Fundamentals ofoptics, McGraw Hill, New York (1976). [6.4] E. Hecht, Optics, Addison-Wesley, Reading MA (1987)