Torrey asks here whether the Output Filter Cavity Offset Frequency can fluctuate from the Nominal Value of 17.6 MHz. If we assume 4 cavities have the same single cavity bandwidth of \Delta epsilon_1 and the same frequency offset, then the integrated transmission is around \Delta epsilon_1 / 2 (see section A.9 in our GQuEST paper). If we assume that 3 cavities have the same frequency offset and assume an allowable additional 5% signal transmission loss due to this mechanism, then the frequency can shift 16% of the bandwidth away from the nominal offset.

I derived this by integrating 4 Lorentizans, once with all 4 with the same offset and once with one with a deviated offset. I then figure out the deviation required so that the transmitted bandwidth is 95% of the no deviation case. For our bandwidth of 42 kHz, this is a value of 6.6 kHz.

If this single cavity had a fluctuating offset, then the RMS discrepancy between this cavity could probably be \sqrt{2} larger because it spends time near no offset deviation. I am assuming there are no dynamic effects of changing the offset when the round trip time in the cavity times the frequency fluctuation is much less than 1, which is the case becuase t_cav*f_bandwidth = 1/2pi.

If I make an assumption that at any given time the 4 cavities are randomly distributed, let's say "equally spaced" on a gaussian with z-scores of -0.84, -0.25, 0.25, and 0.84 (the integral from one value to the next, including +/- infinity, is 0.2), then the 1 sigma error for 95% transmission is 11% of the bandwidth away from the nominal offset, or 4.6 kHz. This is only a rough estimate and more sophisticated methods should be used if we want a more exact answer, but a good sanity check is that it is below the 1 cavity answer.