Procedure

1. Start by building the interferometer in Figure 1 from the Introduction.  The laser, two steering mirrors before the interferometer, 50/50 beam splitter, and the two interferometer mirrors should already be on the table and not-too-poorly aligned.
2. Use the white alignment paddles that insert into the mirror stands to make sure the beams inside the interferometer are perfectly overlapping.
3. Look at the output from the interferometer.  You may need to make some small adjustments to the interferometer mirrors to get the output beams to overlap, but once they do you should be able to see a fringe pattern in the output beam.
4. Place one of the photodiodes into the path of the output beam. You should see a non-zero signal on the oscilloscope that changes when you cover the face of the photodiode.
5. It’s time to start changing something so that we have an interesting signal.  The motor should already be connected to the differential micrometer, so you should be ready to turn on the motor to start moving the stage and seeing the fringe pattern change.  The signal on the oscilloscope should start tracing out a sinusoid.
6. Use the DC offset knob on the apparatus instrument box to force the sinusoid to oscillate about 0 V.  Now the counter should start increasing as it counts each wavelength.  The circuit here is called a comparitor, and it’s a very useful one.
7. Stop the motor.  It’s time to start taking data.  Look at the differential micrometer and determine the current position value.  Restart the counter on the instrument box and start the motor.  You’ll be making a plot of fringe counts as a function of distance.  Take as many data points as you need to be confident in your measured slope, and try to take data with as large a change in distance as possible.  You will use this data to determine the wavelength of the HeNe laser.
8. Before you move on, keep the motor off, reset the counts on the instrumentation box, set the time constant on the low pass filter to 0.1 ms, and bounce the tennis ball on the optics board from about 10 cm high.  Record the number of counts.  Repeat these steps enough times such that you have an average value and a standard deviation that you trust.

Quadrature Interferometry

1. Add the metal film beam splitter after the steering mirrors but before the 50/50 mirror of the interferometer.  Insert it in the same orientation as the 50/50 – the “wasted” input beam should hit the wall behind the apparatus.  You may need to make slight adjustments to the optics components to realign the beams.
2. Start the motor again and look at the two outputs.  If the interferometer is well aligned then you should see two outputs (one from the 50/50 and one from the metal film beam splitters) and they should be complimentary – one dim while the other is bright and vice versa.
3. Once the quadrature interferometer is working well, set up the other photodiode to record the new output.  Set the instrumentation box to ‘quadrature mode’. Look at the scope while the motor is on and you should see two complimentary sine waves.  Use the DC offset to make sure they are oscillating about 0 V. You should start getting counts much in the same way as you did for the MM interferometer (but that’s not the data we’re here for).
4. Set the oscilloscope to XY mode in the ‘Display’ menu.  You will likely see a line being traced back and forth. Your goal here is to adjust the beam position and angle with the various mirrors such that the oscilloscope traces a near-circular path with the origin at the center.  The dielectric mirror is dissipative and the lost energy there leads to this circular signal as opposed to a straight line.
5. Drop the tennis ball from the same height as before and note the number of fringes detected.  Take enough data to get an average value and standard deviation that you trust.

Sagnac Interferometer

1. We are going to have to completely rebuild the interferometer for this part so buckle up!
2. Leave the two mirrors that guide the laser into the interferometer, but remove everything else.  Place the beam cube splitter where you would like the interferometer to start.  Use three mirrors to complete the apparatus as shown in Figure 3.  You maybe have to remove the 50/50 beam splitter in order to use its mount.  And you may have o get creative with how you bolt the mirror stands into the optical board.  Use the alignment paddles to make sure that the counterpropagating beams are colinear.
3. With the beams overlapping, the interferometer is immune to even surface defects in the mirrors and incredibly small vibrations.
4. Use the crazy-looking stand that has a beam cube splitter on an angle.  This piece separates the overlapped output beams so that they can each enter their own detector.  But don’t place the photodiodes just yet
5. Now use the translation stage of the very first mirror after the laser to translate the beams away from eachother.  You need a large enough gap to fit the gas cell.

Index of Refraction Measurement

1. Place the gas cell in one of the beams in the square of the interferometer.
2. Talk to the TA or lab technician about how to operate the vacuum pump and gas valve system.
3. Make sure you can see the outputs of the angled beam cube splitter on a piece of paper or on the wall on the other side of the room. Start slowly evacuating the glass cylinder.  You should see the outputs of the angled beam cube splitter slowly blink.
4. Install the photodiodes so that the output of the angled beam cube splitter show up on the oscilloscope.  Adjust the resistor setting on the photodiode and DC offset to get the oscillating signal centered on 0 V.  The count on the instrument should increase as you change the pressure in the gas cell.
5. If everything is working, completely evacuate the gas cylinder, reset the counts on the instrument to zero, and slowly let the gas cylinder come back up to atmospheric pressure by opening the appropriate valve.  You should get something between 50 and 100 counts for one atmosphere of air.  So if you were used to taking index of refraction of air to be unity, you now know better!