Fourier Spectroscopy with the Michelson Interferometer

Procedure

The procedure for this laboratory consist of taking several interferograms for several different light sources. For this experiment, I used five different light sources as listed:

1. HeNe Laser. Wavelength:=632.8 nm
2. Sodium lamp
3. Cadmium lamp
4. White light filtered at 632.8 nm
5. White light

The procedure for each light is similar so I will outline the general procedure and then make comments regarding any special circumstances regarding individual light sources.

Setup

The setup from this lab is perhaps the most time consuming portion, however proper setup pays large dividends later in the lab. A stepper motor must be used to move the mobile mirror on the interferometer at a constant speed for all interferograms. It is essential that this motor move slowly enough such that the interference patterns move past the PMT at a slow rate, less than 1 Hz. Moving the stepper motor too quickly will result in a large 60 Hz component in the data resulting from the alternating current frequency in the lamp. For my experiment, I used a gear setup that moved the caliper adjustment 1/16^th of a degree for each step of the motor. I also used a low pass filter to filter out the higher frequency 60 Hz noise. The motor was then driven at 20 Hz.

The PMT voltage was sampled with the computer at a rate of 20 Hz. This ensured one sample per turn of the stepper motor. Sampling at a higher frequency would have shown the quantized nature of the stepper motor in the data.

Each light source must be set up so that a minimum of light diverges out of the lamp and onto the interferometer making the interference pattern difficult to see. A piece of black construction paper with a 0.5 cm radius whole cut in it placed between the light source and the interferometer works nicely for this. Once the lamp source is in place and the computer interface and PMT are in place, it is time to begin taking the interferograms.

Taking the Interferogram

The interference pattern of the light should be visible on the PMT aperture. If not, adjust the mirrors such that the two split beams re-converge on the same spot. For any light source other than the laser, this can be done by placing your eye in the place of the PMT and looking directly into the beams as they exit the interferometer. Once the pattern is found, it will be necessary to center the pattern on the PMT aperture. This is difficult but essential for accurate data as the fringes get much closer together as you move away from the center of the pattern.

For each lamp, the computer is used to take a series of data monitoring the fringes as they pass the PMT. The more time monitored, the better the accuracy of the final results. Remember than the true Fourier transform assumes that the path difference began at zero and moved to infinity with time. This is obviously not possible, however a large yet reasonable amount of data should be taken. Due to computer problems, I was only able to take 180 seconds of data for each lamp. Had I been able to take more data, the peaks in the resulting spectrums would have been narrower.

Once the data for a series is taken, it needs to be analyzed with a spreadsheet or computational mathematics program. For my purposes, I used Mathematica and found it easy to use. Using Mathematica, I was able to perform the Fourier transform of each data series. Once this is finished, the data must be scaled to reflect the actual wavelengths present in the source. This is done by identifying the peak in the HeNe laser data as begin 632.8 nm. The rest of the data is then scaled accordingly.

Special Considerations for Each Lamp

Each light source used in this experiment behaves differently. Consequently, it is useful to discuss the idiosyncrasies of each lamp

1. The HeNe laser provides the calibration element for the experiment. Consequently, it is especially important to take accurate data with this source. Especially here, the more data taken, the narrower the peak given by the transform. Also, it is necessary to use a diverging lens with this light source since the laser beam alone is not nearly wide enough to view the interference fringes.
2. The Sodium source, for our experiment, was the least stable of all the sources. Watching the PMT output while the interference pattern is stationery will show how stable and consistent the intensity of your lamp is.
3. The Cadmium source behaves very nicely and gave possibly the best data of the experiment.
4. The filtered white light fringes are only visible in a small region around where the path difference for the two beams is zero. In order to see these fringes, it will be necessary to find this point. Using the HeNe laser setup, watch the interference pattern move as the mirror moves. At the zero path difference point, the fringes will switch directions. At this point, place your filtered white light source in place an look for the interference pattern.
5. The white light source is the extreme of the above mentioned problem with the filtered white light. The interference pattern is only evident for a small range right around the zero path difference point. Using the filtered white light source above, move the mirror to the point where there is the most amplitude on the interferogram. At this point, the path difference is zero and removing the filter should reveal multicolored white light fringes.