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Entry  Fri Jul 25 10:48:13 2008, Koji, Update, General, Abs. Len. Meas. ~ Realignment / beating / PLL trial 
    Reply  Mon Jul 28 15:54:04 2008, Koji, Update, General, Abs. Len. Meas. ~ More on the beat / the PLL setup PLL_setup.pngbeat_at_8MHz.jpg
       Reply  Thu Jul 31 11:19:30 2008, Koji, Update, General, Abs. Len. Meas. ~ Resonance search trial 
          Reply  Sat Aug 2 12:53:43 2008, Koji, Update, General, Abs. Len. Meas. ~ New PLL at the PSL table yarm_dc.png
             Reply  Mon Aug 4 00:37:58 2008, Koji, Update, General, Abs. Len. Meas. ~ RF PD at the Y end / Manual frequency scan YEND_LAYOUT.png4th_FSR1.png4th_FSR2.png
                Reply  Mon Aug 4 05:23:57 2008, Koji, Update, General, Abs. Len. Meas. ~ Measurement for Y-arm completed 
                Reply  Mon Aug 4 21:48:24 2008, Koji, Update, General, Abs. Len. Meas. ~ Scan for TEM00/01/10 TEM00.pngTEM01.pngknife_edge.png
                   Reply  Mon Aug 4 22:31:10 2008, Koji, Update, General, Abs. Len. Meas. ~ Simple Test for TEM01/10 split TEM01_10.png
                   Reply  Tue Aug 5 00:05:57 2008, Koji, Update, General, Abs. Len. Meas. ~ IFR2023A calibration 
                      Reply  Wed Aug 6 11:10:34 2008, Koji, Update, General, Abs. Len. Meas. ~ analysis of the TEM00 scan TEM00fit.pngTEM00FSRfit.png
                         Reply  Wed Aug 6 11:43:52 2008, Koji, Update, General, Abs. Len. Meas. ~ analysis of the TEM01 scan TEM01fit.png
                            Reply  Thu Aug 14 21:52:51 2008, Koji, Summary, General, Abs. Len. Meas. ~ summary of my Summer mode_spacing_measurement_080816_v2.pdf
Message ID: 801     Entry time: Wed Aug 6 11:10:34 2008     In reply to: 795     Reply to this: 802
Author: Koji 
Type: Update 
Category: General 
Subject: Abs. Len. Meas. ~ analysis of the TEM00 scan 
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]
-----------------------------
 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
-----------------------------
----------------
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 .
Attachment 1: TEM00fit.png  64 kB  | Hide | Hide all
TEM00fit.png
Attachment 2: TEM00FSRfit.png  31 kB  | Hide | Hide all
TEM00FSRfit.png
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