(Alexa Daniel)
We went to EX to try to make a more precise measurement of the cavity length. For this measurement we use the fact that in reflection of a locked cavity a phase-modulated RF sideband will not convert into AM, if it is exactly on a free-spectral-range even in the presence of length locking offset. The setup is as follows:
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We split the RF signal coming from the PDH locking diode into the second demodulator channel. (The first channel is used for the PDH locking as usual.)
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We used the ifr to generate a second RF modulation. Its output was split between an LO and a modulator path.
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The LO path was connected to a spare line on the RF patch panel and was hooked up to the LO input of the second demodulator channel on the other side.
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The modulator path was combined with the main modulator signal using a splitter in reverse.
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The SR785 was set up to excite the error point of the PDH servo using the first excitation input of the CM servo board. The B channel was hooked up to the I-phase monitor of the second demodulator channel, whereas the A channel was the readback of the excitation.
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The ifr was set to 13 dBm at a frequency near 666 times the free-spectral-range.
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The ifr frequency was then scanned around this FSR to find the minimum in the response using a 1-2 kHz dither through the SR785.
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After, the measurement we connected the ifr to a spare frequency input of the comparator to measure the exact frequency.
At first glance the accuracy of this method seems to be about 5 Hz, maybe even 2 Hz. We will repeat the measurement in the afternoon to see how repeatable it is.
To measure the arm cavity length we measured transfer functions while adusting the IFR frequency. The data includes the magnitude and phase at 1.3kHz for the several frequencies. The ArmCavityLength.m script computes the projection of these TFs at the various frequencies to determine the zero crossing.
The ZeroCrossing.pdf is a plot of the result. The x-axis is the frequency scaled by 24.992271MHz. Notably, the IFR frequency has an offset of 12Hz which has been adjusted for in this plot. Clearly, the zero crossing is at 24.9922709MHz, which gives an arm cavity length of L = 3994.4704m /pm .3mm assuming a zero crossing accuracy of 2Hz.
As built numbers can be found in alog 9385.
A previous measurement with less accuracy can be found in alog 9386.
We repeated the measurement again this afternoon. I have attached the data, graph, and new matlab script. Again we find that the zero crossing is at 24.992271 MHz /pm 2Hz. This gives an arm cavity length of L = 3994.4704 m /pm .3mm.
Note: the 12 Hz offset between the IFR and timing comparator was consistent.