Borrowed From [1] the University of Washington,

Electrical Engineering Dept.,

[1] Excellent Senior work that was the subject of our LINK TO UW; which was subsequently dropped by them.

From Doppler Shift to Off Axis Movement

Final Report: "Where is the Doppler Shift?"
by Nathan Horton

Andrew Lundberg

EE 488

Winter 1996

Introduction:
The purpose of our project was to investigate the theory and workings of the past optical microphone projects. From the outset, we believed that the succuss of past projects could not be attributed to Doppler Shift, as was reported.

Where is the Doppler Shift? was an appropriate question that proved to be somewhat rhetorical. Much was learned and hypothesized during our investigation. The importance and resulting foundation for our project was the substantiation of our theory that the optical microphone described in the past should not work for the reasons presented. The following will detail our final setup, method, observations, analysis, and conclusions.

Setup:
The majority of our research centered around two different setups:

The first was a traditional Michaelson Interferometer (Figure 1a). This was setup with two fixed mirrors, a beam splitter, a beam expander, a photo-detector and a 1mW HeNe laser. The photo-detector was fed into a pre-amp box and then out to a spectrum analyzer. The system was driven by a speaker with an amplifier connected to a signal generator. An audio microphone was used as a reference and was placed near the speaker.

The second setup was almost identical to the first (Figure 1b). The only difference was the substitution of a 2 in. diameter mylar diaphragm for one of the fixed mirrors. A polarizer was also used on the reference beam to help equal out the relative intensities.

Revised parts list:

1 Laser (1mW)
1 Polarizing Beam Splitter
1 Beam Expander
2 Front Surface Flat Mirrors
1 Mylar Diaphragm and Mount
1 Photo-detector (Newport 815)
1 Photodiode (photo-detector)
1 Audio Microphone
1 Speaker
1 Amplifier
1 Function Generator
1 Spectrum Analyzer
1 Polarizer
1 Headphones

Method:
The general approach used was the analyzing of the Michaelson Interferometer setup. As stated above, we ran two sets of tests; one with a second mirror placed at the test arm and one with a round, mylar diaphragm placed at the test arm. For most of our testing, we used the microphone to obtain a reference signal.

For the two mirror setup, we placed the expanding lens between the laser and the beam splitter to produce a clear, circular fringe pattern at the photo-detector. We drove the mirror at the test arm with the speaker and analyzed the frequency response. According to our hypothesis about the Doppler effect's lack of responsibility for the results that were expected, we attempted to run experiments that would show what was responsible. We analyzed the spectrum response with the photodiode at two different spots in the airy pattern. First at the very center and then out on the edge fringes. A photodiode was used to vary the number of fringes that would be read. We ran experiments displaying many fringes, a few fringes, and a single fringe in the photo-detector area (the photodiode enabled us to get a few and single fringe coverage of the detector area).

To run our second set of tests, we replaced the second mirror at the test arm with the mylar diaphragm. For this setup we placed the expanding lens between the beam splitter and the photo-detector so that the reflection off of the mylar would be a point instead of a large spot. We also placed a polarizer between the reference mirror and the beam splitter to equalize the intensity of the reference beam. With this setup the fringes appeared straight, so we didn't move the location of the photo-detector in the pattern as done previously. However, we did drive the diaphragm with the speaker and use the photodiode to obtain the different number of fringes across the area of the photo-detector as done with the first setup. We obtained variation on this setup almost by accident. One of us ran the laser test while the other cleaned the reference mirror and got a working setup. Further testing with this `one arm' setup was done and results due to "off axis movement" were obtained. Finally, we ran the photo-detector into the speaker and drove the diaphragm with our voice to produce a microphone.

Observations:
Michaelson two mirror setup:

must be driven very hard
poor signal results (Figure 2)
no signal if one arm is blocked (Figure 3)
lots of noise
aperture effects

many fringes (Figure 2) and one fringe (Figure 4)

signal better at center of pattern
weaker on edge (Figure 5)

several fringes

no signal

harmonic addition
minimal amplitude control
no frequency shifting with increase in volume
direct correlation to test frequency

Figure 2. (Top) Response from middle of airy pattern setup (a). (Bottom) Reference signal from microphone.

Figure 3. (Top) Response from setup (a) with no reference arm. (Bottom) Reference signal from microphone.

Figure 4. (Top) Response for single fringe measurement. (Bottom) Reference signal from microphone.

Figure 5. (Top) Response from edge of airy pattern setup (a). (Bottom) Reference signal from microphone.

Michaelson with one reference mirror and one mylar diaphragm

good signal (Figure 6)
very sensitive (better than microphone)
good amplitude control (Figure 6 and 7)
works best when slightly missaligned
limited high frequency response

two inch mylar diaphragm 5 kHz
mylar directly on speaker 10 kHz

lots of harmonic addition (increases with volume) (Figure 8)
least noise when reference beam at minimum intensity
no bands, all frequency spikes
direct correlation to test frequency
no frequency shift with increase in volume

Figure 6. (Top) Response for measurement setup (b). (Bottom) Reference signal from microphone.

Figure 7. (Top) Response for reduced amplitude from figure 6. (Bottom) Reference signal from microphone.

Figure 8. (Top) Response for setup (b) driven to show increase in harmonics. (Bottom) Reference signal from microphone.

Off axis movement (one arm results)

no signal when spot is centered in detector
best signal if spot is placed directly on the edge of the detector

Analysis:
Doppler Shift
The Doppler Shift has been accredited as the reason for the frequency correlation in laser microphones in the past. However, our understanding of the Doppler Shift gives it some very particular properties that will make it identifiable. The main property and the one that most clearly contradicts past claims is the increase and decrease of Doppler frequency due to increase and decrease in volume. In effect this means that a frequency spike in the frequency domain would shift up and down in frequency when the amplitude of the test signal is increased. Nowhere in our experiment was this behavior recognized. The other possible sign that Doppler is at play would be found in frequency bands that increase and decrease in width (Doppler Shift riding on another effect). Although frequency bands were found at higher frequencies this behavior was not present either. We have attributed the existence of the bands to diaphragm characteristics.

Optical Path Length
Our original theory on the past success of optical microphones was based on the effect of phase shifting due to change in optical path length of one arm in relation to the other. This phase shifting causes the fringes in the interference pattern to run back and forth due to the movement on the mirror. However, the exact reason for an output signal was not apparent at first. The first setup allowed us to isolate this effect. We know that it was an interference phenomenon, because if one arm was removed then the output signal went away.

From our findings we have come to the following hypothesis as to the reason for the correlation between the change in optical path length and the output signal seen on the spectrum analyzer. There are two approaches that lead to the same result.

The first is an effect of isolating a single fringe over the photo-detector. This gives rise to a possible intensity differential of a dark fringe compared to a light fringe. As the fringes run back and forth across the detector the intensity changes up and down with each passing fringe. The movement of the fringes is proportional to the movement of the diaphragm. The period of this movement is the frequency (Figure 9).

Figure 9. Relationship between diaphram movement and fringe movement.

Each intensity peak is a fringe and as they are moving they are close together and when they are changing direction the fringes are spread out. This creates an envelope frequency on the signal that is the same as the frequency of the input signal.

The second approach is one of considering many fringes over the surface of a photo-detector. Our explanation of this effect is based on the following assumption. As a fringe moves, its intensity changes non-linearly (sinc distribution) as shown in Figure 10.

Figure 10. Non linear change of intensity between fringes.

If this is true then the difference of intensity over the diaphragm ranges from some minimum to some maximum. These minimum and maximum intensities are a result of different fringe placement over the area of the detector. This intensity distribution explains the findings of better response at the center of the airy patter than at the edges, since the center is the least linear portion. This gives rise to a bigger intensity difference. The extraction of the signal is the same as describe for the single fringe above.

One interesting side note was realized when trying to read a signal from a couple of fringes. No output was found for this setup. To explain this we make the assumption that the difference between just two fringes is not large enough to differentiate it from the noise.

Off Axis Movement
Off axis movement of the diaphragm was not some thing that we anticipated. However, it proved to be the best way to reproduce the test signal. This effect is easily differentiated from the change in optical path length by removing the reference arm. This will actually improve the response of the off axis movement by eliminating the effects of interference (OPL). Off axis movement is due to the fact that the diaphragm does not move with a flat front. This causes the reflection angle of the beam to change slightly. The result is that the beam partially moves in and out of the photo-detector area (Figure 11), thus varying the intensity directly proportional the frequency of the

Figure 11. Off axis movement causing intensity difference on photo-detector.

diaphragm. Off axis movement explains why this setup with the reference arm gave better results when slightly missaligned. This allows the place of highest intensity to move in and out of the detector area. Good amplitude control is found here too, due to the fact that the larger the signal, the more the diaphragm bows and moves the beam in or out of the photo-detector. It is easy to see that this effect is not present when a flat mirror is used at the test arm as in the first setup.

Conclusion:
The Doppler Effect was never found, and to our knowledge, it has never been found in this manner. We believe it is there, but that it is buried in the noise and would require extensive signal processing to separate. The change in optical path length is the dominant interference effect and can be partially attributed to the success of the past optical microphone. Increased use of signal processing could greatly improve the performance of the optical microphone due to changes in the optical path length. However, if we were to build an optical microphone, we would utilize the result from off-axis movement theory because it gave us our clearest signal reproduction.

DISCLAIMER:
Borrowed Work product of U of W EE department.
Excellent Senior work that was the subject of our LINK TO UW; which was subsequently dropped by them.