During the last few days, we took some data which contains more than one TEM00 and also 87.6MHz sideband. We also extrapulate some more information from the data we have already have. From the analysis we did for them, I found

1. Extrapulate more information.

For the fit of only one peak, we found the fit can give more than one result. This is reasonable, since there is couple between finesse and fsr. For example, we can have two totally different result for the same measurement we did for TEM00(as in attached figure 1, you need to zoom in to see the detail). In this picture, the finesse 75, fsr 4.54GHz can give a perfect fit while the finesse 57, fsr 3.44GHz can give as well. The difference of these two fit is only that I give two different initial range of Finesse. For the first one, I give the Finesse range around 50. However, for the second one, I give the Finesse range around 70. However, the good news is that we can have FSR we expect if we fix the finesse around 70.

For the measurement of TEM00 and sideband. I also found the fit can give more than one set of result. If I give the original Finesse around 70, means around our expected value. We can get a reasonable result of cavity length. This agrees with the fit of bandwidth. See attached figure 2. The finesse now is 72 while cavity length is 39mm. Besides, this fit result give the similar calibration factor with the former fit.

However, all the fit with a finesse value around 70 give FSR around 4GHz, while the direct measurement of FSR gives 2.8GHz. The reason can be PZT cannot response linearly with our driving HV signal.

2. Measurement with TEM00(two) and sideband together

The whole measurement and fit is attached in figure 3. You can see even visually that the distance between twoTEM00 and sidebands are totally different. That is the reason why you can see the fit cannot give a result. But anyway, I tried to fit these two peaks seperately, the result is in the attached figure 4 and 5.  This time, the calibration factor becomes ridiculously different while the fit result of FSR and cavity length becomes also quite different. You can see from the seperate fit, the time difference in the first peak is 0.000501 while 0.000340 in the second peak.

3. Measurement with TEM00(three) and sideband together

The whole measurement is shown in attached figure 6. In this figure, you can see the difference of 0.2GHz in FSR causes the displacement of the peak away from the standard position. Also this causes the fit failed. I also choosed these peaks and fit them seperately. Firstly, the calibration factor is fitted around 1200, 1300, 1100 (MHz/V) seperately.  From this point of view, we can deduce the PZT scanning velocity firstly increase and then decrease. And the fit of the finesse and FSR of the first and third peak give a similar result(first: FSR = 4.9GHz, Finesse = 75  third: FSR = 3.9GHz, Finesse = 61 ). However, the fit of the second has a very large error.