### Abstract

I measured the PZT and EOM efficiency from each efficiency ratio between PZT and MCE and between EOM and PZT. Also, I estimated the optical gain of IMC from PZT efficiency and the result from the cavity pole measurement. 

PZT efficiency = 4.50 MHz/V

EOM efficiency = 0.34 rad/V

IMC Optical gain = 17.9 V/MHz

The efficiency of PZT is in order of magnitude with the results of previous measurements (klog16678), On the other hands, I could not found the klog about the previous EOM efficiency measurement.

The optical gain seems to be significantly larger than in the previous measurement (klog14569), but I do not know the reason for this at this time.

### What I did

#### PZT efficiency measurement

1. I measured three TFs in the same procedure in klog16678 locking IMC without three common boost filters.
   • Measured TF1 from K1:VIS-MCE_TM_TEST_L_EXC to K1:IMC-SERVO_OUT2_OUT [= A_mce * C_imc / (1 + G_imc) [V/cnts] ] (See Fig.1)
   • Measured TF2 from K1:IMC-SERVO_NPRO_TEMP_BIAS_EXC to K1:IMC-SERVO_OUT2_OUT [= - A_temp * C_imc / (1 + G_imc) [V/cnts]] (See Fig.2)
   • Measured TF3 from K1:IMC-SERVO_NPRO_TEMP_BIAS_OUT to K1:IMC-SERVO_SLOW_DAQ_OUT [~= - A_temp / A_pzt [V/cnts]] (See Fig.2)
2. Computed A_pzt/A_mce = TF2 / TF1 / TF3 [cnt/V] and fit it with the inverse function of the TF of MCE_L (Fig. 3). We obtained the A_pzt/A_mce@DC ~ 102 cnt/V
3. According to klog29702, I obtained the A_pzt = A_pzt/A_mce * A_mce ~ 102 cnts/V * 4.39 x 10^4 Hz/cnts = 4.5 MHz/V @DC

This value seems to be in order of magnitude with the results of previous measurements (klog16678 (5.56 MHz/V), klog2853 (1.48 MHz/V), klog13012 (3 MHz/V))

#### EOM efficiecy meausrement

1. I measued the TF from FAST OUT to SLOW OUT with Moku:lab. (Fig.4)
2. Since the EOM moves the phase of the light, it acts as a derivative element in terms of the frequency actuator, so I devided the frequency response of the gain by 2πf to bring the response back into phase.
3. As the A_eom/A_pzt, I took the average of the values between 4kHz and 6kHz, where the phase is around 90 degrees and the gain variation is likely to be within 10%. A_eom/A_pzt = 7.6 x 10^-8.
4. Finally, by multiplying the obtained A_eom/A_pzt by A_pzt obtained earlier, the efficiency of the EOM was found to be 0.34 rad/V.

I could not find the klog about the previous measurement for the EOM efficiency... (The EOM in klog2810 is supposed to be different from the EOM used today, according to JGW-G1707105.). 

Looking at the current EOM model number (NIR-MPX-LN-0.1) and looking at the spec values, it seems that this EOM can run at 1.5 V for half a wavelength, so the efficiency is roughly pi/1.5 = 2.1 rad/V. Compared to this spec, the current EOM is 2pi smaller.

#### IMC optical gain

I derived the from the DC gain of cavity pole measurement in klog29193 (80.41) and the PZT efficiency = 4.50 MHz/V. the optical gain is 80.41/4.50 = 17.9 V/MHz. This value is about 20 times larger than the results of previous measurements. The past measurements were apparently made at IN1 of CMS, not OUT2 of CMS, but even if we take this into account and include the -20dB attenuator in front of IN1 and the 14dB of INPUTGAIN, this magnitude difference cannot be explained.