8 DISPLACEMENT SENSOR

Precision Distance Measurement Using a Twyman­Green Interferometer

MODEL OEK-1 00

PROJECT #7

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8.1 Introduction

The displacement of one of the mirrors of an interferometer along the direction of the beam can be measured by counting the number of fringes that are moved. The agreement of the values calculated and the ones directly measured will be within 3 significant figures.

• Movement of one of the mirrors of a Twyman-Green interferometer is used as a demonstration of this method. •

..BE

M2

.. Screen

Figure 45

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8.2

L

BE

Figure 46

Equipment list

Part Number Description QTY

14768-01 Ball Driver Set 1

SK-08A Screw Kit 1

SK-25A Screw Kit 1

RG-23-4 2'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

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BS. Beamsplitter Assembly

20B20BS.1 2" Beamsplitter 1

U200-A2K Mirror Mount 1

SP-3 3" Post 1

VPH-3 3" Post Holder 1

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

ID-0.5 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

L. Laser Assembly

340-RC Clamp 1

40 Rod 1

ULM-TILT Laser Mount 1

R-30025 1mW HeNe Laser 1

MS. Steering Mirror Assembly

10D20ER.1 1" Mirror 1

COR-1 Cntr Of Rotatn Adaptr 1

P100-P Mirror l\IIount 1

UPA1 1" Mirror Holder 1

SP-3 3" Post 1

VPH-3 3" Post Holder 1

M1 and M2 Mirror Assemblies

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20D20ER. 1 2" Mirror 2

462-X-M Translation Stage 1

DM-13 Diff. Micrometer 1

U200-A2K Mirror Mount 2

SP-2 2" Post 1

VPH-2 2" Post Holder 1

SP-3 3" Post 1

VPH-3 3" Post Holder 1

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

8.3 Setup

8.3.1 Placement of the Breadboard Place the RG-23-4 breadboard on a fla t table 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.

8.3.2 Laser Setup Mount a 40 Rod on the RG-23-4 breadboard in location L as in Figure 47 Attach a ULM-TILT Laser Mount to a 340-RC Clamp. Slide the 340-RC onto the 40 Rod. Mount the R-30025 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).

8.3.3 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 47) with its aperture aligned with the laser beam. Move the iris to the other end of the breadboard (position 12 in Figure 47) 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 11 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.

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8.3.4 Iris Placement Affix ID-0.5 iris I in front of the laser as shown in Figure 48 and adjust the aperture to just allow the laser beam through. The iris will now be used as a reference for retroreflected beams.

8.3.5 Interferometer Setup Choose one of the setup configurations, Figure 45 or Figure 46 (Figure 46 is an alternative for the setup of Figure 45 which increases the cross section of the optical windows). Place the 20D20ER.I 2" diameter mirrors and the 20B20BS. l beamplitter into the U200-A2K mounts and post mount each in place as shown in Figure 46 or Figure 48, to construct the Twyman-Green Interferometer. Use 114-20 set screws on the SP-3 posts to connect to U200-A2K mirror mounts. Post mount each interferometer mirror 10" from the beamsplitter.

8.3.6 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.

8.3.7 Beam Expander Positioning Assemble the beam expander assembly BE and mount in the path of the laser beam as in Figure 49. 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 MAOX objective lens in its place and align so that the expanding beam is centered on the collimating lens of the LC-v. •

8.3.8 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.

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Place a screen (i.e. a 3" X 5" card) into a FC-I filter clamp and post mount on a P-2 post, VPH-2 post holder, at the output of the interferometer and adjust the tilt of the mirrors and beam splitter while looking at the retroreflection on the iris. When the points of light are superimposed on the iris, fringes can be observed on the screen.

--J2,II Figure 47

L

Screen

Ml~

Figure 48

Figure 49

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8.4 Procedure and Results

LARGE DISPLACEMENTS > 1 O~m.

1. Adjust the fine adjustment of the DM-13 differential micrometer on the 462-X-M stage to zero value.

2. Move the 462-X-M stage by turning the DM-13 micrometer and count the fringes. Obtain values of m between 50 and 100 full counts . Keep track of the displacement on the micrometer, x, and keep with corresponding m.

3. Repeat steps 1 and 2 a few times for the same value ofm to find a good average value for x.

4. Calculate the distance moved, ~x = rnA (where m is an integer and Athe wavelength), and compare with the value of the micrometer, x.

5. En"or analysis :

Find the standard deviation for repeated measurements to determine the certainty of the measurement.

SMALL DISPLACEMENTS < 10!-ill1

1. Adjust the fine adjustment of the DM-13 differential micrometer on the 462-X-M stage to zero value.

2. Adjust the fringe sizes on the screen to obtain 2 whole fringes. Mark the position of the center of the fringes on the screen and divide the space in between into ten spaces and mark. This wi II allow 1110 of a fringe count which will correspond to V10 sensitivity.

3. Move the stage by turning the micrometer and count the increment of fringes moved. Obtain values ofm between 5.0 and 10.0. Keep track of the displacement on the micrometer, x, and keep with corresponding m.

4. Repeat steps 1 and 2 a few times for the same value of m to find a good average value for x.

5. Calculate the distance moved, ~x = rnA (where m is an integer and Athe wavelength), and compare with the value of the micrometer, x.

6. Error analysis:

Find the standard deviation for repeated measurements to determine the certainty of the measurement.

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References [8.1] P. Hariharan, Optical Interferometry, Academic Press, Sydney (1985) .

[8.2] P. Hariharan, Basics ofInterferometry, Academic Press, San Diego (1992).

[8.3] F. A. Jenkins and H. E. White, Fundamentals a/Optics, McGraw Hill, New York (1976).

[8.4] E. Hecht, Optics, Addison-Wesley, Reading MA (1987).