Analysis of the data on August 3th ~ Part 1
From the measurement of the 5 FSRs, the FSR frequency for the Yarm cavity was estimated as
f_FSR = 3878678 Hz +/- 30 Hz
and the Yarm length is
L_yarm = 38.6462 m +/- 0.0003 m
This is the precision of 8ppm. In my opinion, this is a satisfactory result for our purpose.Y-arm length
e-log length [m]
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556(2008-Jun-24) 38.70 +/- 0.08 Cavity swinging measurement
556(2008-Jun-24) 38.67 +/- 0.03 Tape & photo
776(2008-Jul-31) 38.640 +/- 0.007 Beam injection, poor PLL, Transmitted DC
782(2008-Aug-02) 38.6455 +/- 0.0012 Beam injection, independent PLL, Transmitted DC
787(2008-Aug-04) 38.64575 +/- 0.00037 Beam injection, independent PLL, Transmitted RF
this(2008-Aug-04) 38.6462 +/- 0.0003 Beam injection, independent PLL, Transmitted RF, five FSRs, freq calibrated
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o According to the entry 795, all of the scan frequency was calibrated.
o The five peaks of the scanned data for TEM00 were fitted. Each peak was fitted by the following formula:
V(f) = A / Sqrt(1 - ((f-f0)/fc)^2)
Variable
f: scan frequency
Parameters
A: peak amplitude
f0: center frequency
fc: half bandwidth of the peak for -3dB
o The results are shown in the attached figure 1. They look very similar each other but they are different plot! The fittings were extremely good. The center frequencies estimated were as follows:
FSR1: 3879251.9 Hz +/- 8.8 Hz
FSR2: 7757968.1 Hz +/- 10.8 Hz
FSR3: 11636612.9 Hz +/- 10.2 Hz
FSR4: 15515308.1 Hz +/- 8.7 Hz
FSR5: 19393968.7 Hz +/- 8.4 Hz
o The FSR frequencies were fitted by a line. The fitting and the residuals are shown in the attached figure 2.
The fitting results were
f_FSR(n) = 586.4 + 3878678 * n
This means that:
o FSR frequency was 3878678 [Hz].
o The lock of the carrier had detuning of 586 [Hz].
The detuning of the carrier from the resonance can be explained by the alignment drift. In deed, at the end of the measurement, decrease of the transmitted power by -15% was found. Then, the frequency of the 1st FSR was measured before and after the alignment adjustment. This changed the frequency of the FSR1 by 350Hz. This change could not be explained by the cavity length change as this is too big (~3.5mm).
Actually, the spacing of the cavity length is more stable. The residual is rather scattered with in 20-30Hz. So, I took the error of 30Hz as the whole precision of the frequency measurement that includes the fluctuation of the alignment, the cavity length itself, and so on. This yields the FSR and the cavity length of
f_FSR = 3878678 Hz +/- 30 Hz
L_yarm = 38.6462 m +/- 0.0003 m . |