Keita, Kiwamu, Daniel, Elli

We have measured the SRC length to be 56.013+/-0.0035m.  This is 4.8+/-3.5mm longer than the design SRC length of 56.008m.   
This result is consistent with an earlier measurement of the LHO SRC length of 56.015(+/-.005)m (alog17451).  (This earlier measurement which was considered questionable due to signal-to noise issues and a lack of SRMI angular control.)

Method:
See alog 18263 DRMI was locked with wavefront sensors on for alignment control.  An auxiliary NPRO on IOT2R was sent into the interferometer through the back of IM4.  The Aux laser was coaligned with the PSL using the PSL transmission through IM4 onto IOT2R, and the prompt reflection of the Aux laser onto IM4. The auxiliary laser frequency was locked at a frequency offsets to the PSL using a PLL, and this frequency offset was swept to measure the Aux laser power reflected from DRMI as a function of frequency.

The DRMI reflection coefficient is a function of frequency because Mich reflectivivty varies with frequency. This is due to the 8.9cm Schnupp asymmetry, and Michelson reflectiviy = cos(2*pi*f//c*ScnuppAsymmetry). When DRMI is locked, the PSL light is totally reflected from Mich, and DRMI reflectivity looks the same as the PRC reflectivity.  At 842.7 MHz offset from the PSL frequency, Mich transmissivity is 100%, and DRMI looks like a cavity between the PRM and SRM mirrors and with the length of SRC+PRC combined.  As the PRC length is already known (alog 10642), we can measure the DRMI reflectivity around 842.7MHz by sweeping the Aux laser through +/-842.7MHz offset from the PSL frequency.

The reflected  beatnote of the PSL and the Aux laser read out at relfair path. The frequencies of the transmission dips closest to +/-842MHz were fitted using a lorentzian function. The number of fsrs (N) between peaks at ~+842MHz and -842MHz were determined.  This determines the fsr and the length of the combined PRC/SRC cavity.

df=positive_peak_frequency-negative_peak_frequency
vfsr=N*df
LSRC=c/2/vfsr-LPRC;

Analysis:

Graphs of the reflected beatnote power vs aux laser frequecy offset are attached.  There is an 11MHz osciallation in the reflected power which is not yet explained.   The phase has had a linear phase term removed, but is not continous from sweep to sweep, perhapse due to small changes in the alignment of the aux laser to the psl over time.  There are peaks which appear every fsr, which I am assuming ar ehigher order modes, but I haven't looked closely at these yet.
Peaks were fitted at -842.14(0.02)MHz and +841.933(0.02)MHz, graphs attached.  
The number of fsrs between these peak frequencies is 1277.  (If the number of fsrs wer off by +/-1, the cavity length would differ by +/-10cm.  We had already estabilished from previous measurements that the SRC length is not off by this much.)
This corresponds to a combined PRC/SRC cavity vsfr=1.319MHz, and length=113.664(0.0027)m.  The PRC length was already measured by Evan et al (alog 10642) to 57.6508+/-0.0007m, so the SRC length is 56.013+/-0.0035m.