Abstract:

I calculated IMMT1T QPD fundamental noise.
In the current condition, IMMT1T QPD noise should be limited by shot noise, so SNR will be improved if we increase the laser power to 10W.

Detail:

To investigate the better parameter for IMMT1T QPDs, I calculated the fundamental noise level with current parameter.
What I used for the calcuation is following documents:
QPD circuit: JGW-D1402411-v3
QPD characteristic: S5981 datasheet
OPamp characteristic: LT1114 datasheet

Total output noise of the transimpedance amplifier can be calculated as the summation of the following 5 noises:
1. Voltage noise of OP amp
2. Current noise of OP amp
3. Thermal noise of transimpedance resistance
4. Dark noise of QPD
5. Shot noise of QPD

Voltage noise of OP amp:

According to the datasheet of LT1114, maximum input voltage noise is 2.8e-8 V/rtHz above 10Hz.

Current noise of OP amp:

According to the datasheet of LT1114, maximum input voltage noise is 0.03 pA/rtHz above 10Hz.
Since curret transimpedance resistance is 20k Ohms, output voltage noise due to OP amp current noise is 0.03 pA/rtHz * 20k Ohms = 6.0e-10 V/rtHz

Thermal noise of transimpedance resistance:

The transimpedance resistance (R) is 20k Ohmas and temperature is about 300 K, so the thermal noise of the resistance is sqrt(4*k_B*T*R) = 1.8e-8 V/rtHz, where k_B and T are the Boltzman constant and absolute temperature of the resistance, respectively.

Dark current noise of QPD:

According to the datasheet of LT1114, maximum dark current (Id) of QPD is 4 nA, so the shot noise of the dark current is sqrt(2*e*Id) = 3.6e-14 A/rtHz, where e is an elementary charge.
So, the output voltage noise due to the dark current is 3.6e-14 A/rtHz * 20k Ohms = 7.2e-10 V/rtHz.

Shot noise of QPDs with the current (future) configuration:

If we use 1W (10W) input, IMMT1T trans QPD2 obtained 1W (10W) * 3000 ppm (IMMT1 transmission) * 0.1 (IMMT1T POM transmission) * 0.5 (BS before IMMT1T QPDs) = 1.5e-4 (1.5e-3) W.
According to the datasheet of LT1114, optical efficiency of the QPD is about 0.25 A/W @ 1064nm.
So, the photocurrent (Ip) of the QPD is 0.25 A/W * 1.5e-4 (1.5e-3) W = 8.75e-5 (8.75e-4) A.
Therefore, the shot noise of photocurrent is sqrt(2*e*Ip) = 3.5e-12 (1.1 e-11) A/rtHz.
Since the transimpedance resistance is 20k Ohms, output voltage due to the shot noise of photo current is 3.5e-12 (1.1e-11) A/rtHz * 20k Ohms = 6.9e-8 (2.2e-7) V/rtHz.

Summary:

	Noise (1W) [V/rtHz]	Noise (10W) [V/rtHz]
OP amp voltage	2.8e-8	2.8e-8
OP amp current	6.0e-10	6.0e-10
Thermal noise	1.8e-8	1.8e-8
Dark current	7.2e-10	7.2e-10
Photo current	6.9e-8	2.2e-7

Since photo current shot noise is the largest in both cases, current IMMT1T QPD noise seems to be limited by shot noise.
So, if we increase the laser power, SNR wll improve by sqrt(10).

Comments to this report:

tomotada.akutsu - 13:51 Thursday 30 January 2025 (32505)

Thank you for the revisiting calculation. If the IMMT1T QPD is calibrated, the real readout noise spectral density could be compared with your calculation to confirm if limited by shot noise or not! Maybe RIN would be sufficiently suppressed when ISS on.

takafumi.ushiba - 13:40 Friday 31 January 2025 (32527)

I noticed the mistake of my calculation.
Since the noises except for photo current shot noise are calculated for each segment, laser power for calculating photo current shot noise should be devided by 4.
So, the final shot noise results should be a half of the previous post.
Following table is the correct summary of the noise level at each segment.

	Noise (1W) [V/rtHz]	Noise (10W) [V/rtHz]
OP amp voltage	2.8e-8	2.8e-8
OP amp current	6.0e-10	6.0e-10
Thermal noise	1.8e-8	1.8e-8
Dark current	7.2e-10	7.2e-10
Photo current	3.5e-8	1.1e-7

Though shot noise has the largest contribution for both cases, OP amp voltage noise and thermal noise also have contributions of 34% and 14% in the case of 1W operation.

takafumi.ushiba - 15:46 Friday 31 January 2025 (32529)

To compare the calculated noise with the measurement, I converted the calculated noise into the equivalent values at K1:IMC-IMMT1_TRANS_QPDA2_DC_{PIT,YAW}_OUT_DQ.
According to the table, summation of the fundamental noise is 4.8e-8 V/rtHz and 1.1e-7 V/rtHz in the case of 1W and 10W, respectively.

Since the calculated noise will be changed from single-end signals to differential signals, the noise level at ADC is 2 times larger.
A conversion factor from voltage at ADC to DGS cnts is 1/610e-6 cnt/V.
Assuming that noise of each segment have no correlation, summation of the noise of four segments are sqrt(4) of noise at each segment.
PIT and YAW signals are devided by SUM of QPDs, so the signals at K1:IMC-IMMT1_TRANS_QPDA2_DC_{PIT,YAW}_IN1 is noise of 4 segments devided by 3300 * (Pin/1.2W).
Since K1:IMC-IMMT1_TRANS_QPDA2_DC_{PIT,YAW}_GAIN is 1.6, this value should be multiplied.

So, the fundamental noise measured at K1:IMC-IMMT1_TRANS_QPDA2_DC_{PIT,YAW}_OUT_DQ is as follows:
1W: 4.8e-8 * 2 * 1/610e-6 * sqrt(4) / {3300 * (1/1.2)} * 1.6 = 1.8e-7 cnt/rtHz
10W: 1.1e-7 * 2 * 1/610e-6 * sqrt(4) / {3300 * (1/1.2)} * 1.6 = 4.4e-8 cnt/rtHz

takafumi.ushiba - 19:24 Monday 03 February 2025 (32562)

I measured the IMMT1T QPD2 spectra when PRFPMI was locked with 1W and 10W (fig1).
Red and blue lines represent the spectra when PRFPMI was locked with 10W and 1W, respectively.

Measured noise floors are about 1.4e-7 and 1.8e-8 with 1W and 10W, respectively.
So, my calculation for 1W (1.8e-7) seems close to the measured value while that for 10W (4.4e-8) seems about 2.5 times larger than the measurement.
I'm not so sure the reason but we ca obtain better SNR by increasing the laser power, anyway.

Images attached to this comment

32562_1738577927_Screenshot from 2025-02-03 19-17-40.png

tomotada.akutsu - 21:35 Monday 03 February 2025 (32565)

ISS can be turned on for the RF lock??

takafumi.ushiba - 9:01 Tuesday 04 February 2025 (32570)

Yes, and in fact I turned on ISS during the measurement for 10W, posted in the previous post.