EDIT: The calculation of the modulation depth was corrected in response to Daniel's comment (shown below).

[Summary]

• Modulation depth@118MHz ~ 1 mard 0.2 mrad.
• Signal-to-noise ratio of the demod signals is worse than those of AS36 by some factor (depending on the PSL power).
• With this SNR, the SRC alignment can be sensed in frequencies up to 5 Hz which should be good enough to make a slow ASC control loop.

[Setup]

In the CER, we have two IFR units for this measurement (36354). One is configured for 118 MHz, providing the modulation, and the other is configured for 72 MHz, providing the demodulation RF source. We unplugged the RF source for the 90 MHz system in the ISC R3 rack (the one by HAM6) and plugged the 72 MHz source. This means that we use the 90 MHz demodulation system for demodulating the RF components at 72 MHz. This allows us for a minimum hardware modification at the cost of losing the ASAIRB_RF90 signals. Currently, ASAIRB_RF90 is used only once in the locking sequence where the ISC_DRMI guardian checks whether the DRMI is locked on a hopped mode or not. During this test, we have commented out this action from the ISC_DRMI guardian so that it doesn't stop at this point.

We cranked up the RF power of the 118 MHz unit from -10 dBm to 10 dBm. Note that the RF amplifier that is directly connected to this IFR unit has a input rate of +10 dBm. According to the previous measurement (36354), this should provide 30 dBm at the input of the EOM. The RF power of the 72 MHz unit was set to 13 dBm which gave reasonable RF powers in all the 90 MHz demodulator systems.

BTW, the Triplexer doesn't give appreciable loss at 72 MHz (see table.2 of E1600027).

[Measurement concept: frequency-offset demodulation]

Today we introduced an intentional frequency offset of 205 Hz to the 72 MHz unit. This results in the demod signals rotating in the I-Q phase space at the offset frequency. The main motivation for doing this frequency-offset technique is that it allows us for relatively accurate measurement of the relative RF phase between the two IFR units and the main RF source (Wentzel OCXO).

Looking at the raw RF signals with an oscilloscope, we confirmed that the RF phase of the IFR units with respect to the Wentzel OCXO slips at a rate of roughly 2 pi / 10 seconds even though the IFR units are synchronized to the 10 MHz source which is locked to the GPS 1 pps signal. Not surprisingly the relative phase between the two IFR units don't seem to slip by appreciable amount. In future, we will get an harmonic generator so that the 72 and 118 MHz RF signals are synchronized to the main OCXO.

Regardless of whether the RF phase slips or not, the idea is to have a look at the ASC-AS_WFS_A(B)_RF118 signals in frequency domain so that the peak height at the offset frequency gives us a measure of the modulation depth.

[Modulation depth]

We estimated the modulation depth of the 118 MHz RF sidebands to be 1 mrad 0.22 mrad, much smaller than the others (15661).

Our measurement is essentially comparison of the signal strength between the 36 and 72 MHz demodulated signals given that we know the modulation depth for 9 MHz. The below shows the derivation.

• DRMI was locked with both arm cavities set to off resonant point. PSL was set to 2 W.
• Measuring the rms of the 205 Hz peak produced in the ASC-AS_A_RF90_I1_OUT, we determined the rms to be about 7 counts.
  • This corresponds to an amplitude of 10 counts or peak-to-peak amplitude of 20 counts at 205 Hz
• Measuring the DC value of AS_A(B)_RF36_I(Q)_SUM, we found the quadrature sum  to be about 2000 counts.
• Taking out the gain difference (a factor of 40 from the whitening gain, a factor of 1/5 1/16 from PD response and difference in the interferometer transmissivity by a factor of 11) from the 72 MHz calculation, we get a signal amplitude in the unit equivalent to the 36 MHz to be 5 cnts ( = 10 cnts x 4 segments x 1/40 whitening gain x 5 PD response 16 PD response x 1/11 ifo trans).
• Therefore Gamma_118 / Gamma_9 = 1.45 cnts/ 2000 cnts.
• Assuming Gamma_9 to be 0.3 rad, we get Gamma_118 = 0.75 mrad ~ 1 mrad 0.22 mrad.

[Signal to noise ratio]

In the current freqeuncy-offset scheme, the ASC signals are upconverted to frequencies around 205 Hz. Looking at the spectrum of the demodulated signals when the interferometer was locked with a 2W PSL, we saw that the signal-to-noise ratio of the 72 MHz signals are worse than that of the 36 MHz by a factor of 10. See the attached dtt session.

After we reached a state equivalent to NOMINAL_LOW_NOISE, we took a look at the spectrum again to see how much the signal-to-noise ratio has improved. It seem to have improved by a factor of 5 or so even though the PSL power increased by a factor of 15  (2 W -> 30 W). See the second attachment. Some fraction can be explained by the 3 dB reduction of 45 MHz RF source power that takes place during the locking sequence.

It seems that we can sense the ASC signals up to 5 Hz before diving into some white noise.

[Future direction]

• If allowed, modify h1asc and place a PLL block for measuring the RF phase.
• If allowed, place a phase correction functionality for individual segments of AS118.
• If allowed, record some relevant channels.

The difference between the transimpedance gains at 36 and 72 MHz is taken from LIGO-T1300488. Looking at Figs. 5 and 6 on page 3, we read the response as +2 dB at 36 MHz (Q3 trace in Fig. 5) against –22 dB at 72 MHz (Q3 trace in Fig. 6). The gain difference is then estimated to be 24 dB, or a factor of ~16.

The transmission ratio towards the antisymmetric port between the 9 and 118 MHz sidebands is around ~1/10, see Hang's presentation LIGO-T1700215.