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Message ID: 2247     Entry time: Mon Oct 8 15:10:17 2018
 Author: anchal Type: Summary Category: PD Subject: Transimpedance and Dark Noise measurement of all RFPDs in PSL

tl;dr:

Transimpedance measurements of all RFPDs in PSL were taken at the setup at 40m. All measurement results and data are in the git folder link below. Dark Noise measurement was also attempted but it turned out that the measurement is limited by Agilent 4395A's noise floor and hence this measurement needs to be done again using low noise preamplifiers.

Data:
Git folder containing data, plots, results and jupyter notebook.
https://git.ligo.org/cit-ctnlab/ctn_labdata/tree/master/data/20181005_CTN_Lab_All_RFPD_TF_Data

Measurement Method:
I used the transimpedance measurement setup at 40m to take these measurements. It includes a laser current driver which is modulated through a bias-tee. This, in turn, gives an amplitude modulated laser. The laser is then sent through 2 focusing lenses to fall on a beamsplitter. One output of this beam splitter is read by a reference photodiode whose transimpedance is known to good accuracy. The other output is read by the 'RFPD under test'. The DC outputs of the RFPDs are read through an oscilloscope with1 MOhm DC coupling and is averaged over 10s. The RF outputs of the reference photodiode (B) and RFPD under test (A) are connected to input ports B and A of an Agilent 4395A network analyzer. The length of these RF output cables is the same. The RF source from Agilent 4395A is split using an RF splitter with one half feeding back to R port and the other half feeding into the bias-tee connected with laser current driver. The splitting of the source wasn't necessary but is mentioned here as it was done for some other reason which is not used in the analysis. Then 25 separate runs of transfer function A/B are measured in 4395A in the range 10 kHz to 1 MHz with 801 points at 10kHz IFBW (saved as SNxxx_LF_*.txt) and 25 separate runs in range 1MHz to 100 MHz with 801 points at 30kHz IFBW (saved as SNxxx_HF_*.txt). These runs are then stitched together in the analysis to create 25 datafiles (saved as SNxxx_TF_*.txt).
From this point onwards, analysis mentioned in repo iris in file iris.py is used. I didn't explore any other methods of analyzing data and calculating transimpedance as it seemed that Craig had already worked on this and figured out a good method for doing so. I'll describe this analysis in my own words, however, the best description can be obtained from Craig himself. Each of the 25 transfer function is first converted into transimpedance with physical units. Following formula is used for doing so:

$Z_{AC,PD} = Z_{AC,Ref} R_{PC} e^{-i \delta \phi}} T_{meas}$
Here,
ZAC,PD : Calculated RF Transimpedance
Z AC,Ref : Known RF transimpedance of reference photodiode
RPC : Photocurrent ratio at DC of reference PD to RFPD under test. This is calculated as:
$R_{PC} = \frac{\frac{V_{DC,Ref}}{Z_{DC,Ref}}}{\frac{V_{DC,PD}}{Z_{DC,PD}}}$
$\delta \phi$: Extra phase delay in RFPD under test's light path due to the extra distance of light travel ($\Delta L$). This is calculated as:
$\delta \phi = \frac{\Delta L f}{c}$
Tmeas : Measured transfer function A/B from Agilent 4395A

This formula can be derived easily by first taking the ratio of light powers on the two photodiodes at DC and then taking ratio at AC and using photocurrent ratio at DC to substitute for unknown values like power attenuation, the fraction of power falling on PD and ratio of responsivity of the two photodiodes. Note that this circumvents any differences due to the different focusing of light on photodiodes, losses due to mirror and beamsplitter and different responsivities of the two photodiodes. The extra path length ($\Delta L$) is measured using a ruler. The uncertainty in this measurement and all other measurements are carried forward and described later.
After this conversion, the median values of real and imaginary parts of the complex transimpedance is taken out of the 25 traces separately at each frequency point. These median values are used to create a complex median transimpedance representing the estimate of the analysis. Covariance of the real and imaginary parts of the 25 transfer function is used to create a covariance matrix at each frequency point. This is transformed into covariance of magnitude and phase basis. From this, the variance in magnitude and phase of the transimpedance is extracted. This variance is added with other noise sources (Uncertainties in DC voltage levels and known DC and AC transimpedances) in quadrature to get an estimate of the uncertainty of transimpedance at each frequency point.
Apart from transimpedance, dark noise measurement was also attempted. I took the spectrum of RF out when a beam dump is placed in front of the RFPD under test. The spectrum is taken from 10kHz to 100 MHz with 801 points and 10 kHz bandwidth. To estimate noise of 4395A, I took the same spectrum with input port A shorted. The two spectrums are then subtracted in quadrature to get an estimate of the dark noise. However, it is found that these measurements are in fact limited by the noise of 4395A itself. So we have decided to take dark noise measurements separately with low noise preamplifiers later. The data files of this attempt are still in the data folder with the analysis in the jupyter notebook.

Uncertainty handling:

The uncertainty in transfer function measurement is estimated using the method described above. Othe sources of uncertainties are the following:

• RFPD DC transimpedance: These are read off from the resistor values in the actual circuit. I have assumed 2% uncertainty in each resistor value in the DC transimpedance circuit. Since transimpedance is created through 3 resistors, the uncertainty is $2\sqrt{3}$% in the calculated transimpedance.
• Reference Photodiode: Reference Photodiode's marked dc and ac transimpedance are assumed to have 1% error in them. This number came in a discussion with Gautum.
• DC Voltage level: Uncertainty in this value was simply eye-balled during the measurement. Without any amplitude modulation, I just saw how much the 10s averaged value fluctuate and used at as the uncertainty.
• Extra Path Length: Since extra path length of light was measured quite crudely with a ruler, I took uncertainty in this measurement as 1 cm.

Plots and results:
In the attached folder, plots for each RFPD are there. The *TI_Four_Squares.pdf plots show median transimpedance with each TF sweep also plotted in red on left. The right 2 boxes are residuals of TF sweep from the median transimpedance calculated.
Further, for comparison, RFPD counterparts of north and south paths taking reflection measurements from the cavity and PMC are plotted together.
All the characteristic results are tabulated in CTN_Lab_All_RFPD_Characteristics.xlsx file in the data folder.

PSL All RFPD Characterisitics
SN Position Peak Freq. (MHz) TI at Peak (V/A) Notch Freq. (MHz) TI at Notch (V/A) DC TI (V/A)
SN009 North Cavity Refl 36.036 2594 +/- 191 73.109 77.8 +/- 9.2 2020 +/- 68
SN010 South Cavity Refl 36.67 1529 +/- 99 74.237 76.8 +/- 8.5 2222 +/- 75
SN020 North PMC Refl 21.692 2891 +/- 248 42.413 137.6 +/- 12.0 2222 +/- 75
SN001 South PMC Refl 15.107 14430 +/- 1256 29.402 558.0 +/ 37.2 2222 +/- 75
SN101 Beat Note 27.34 1178 +/- 77 No Notch No Notch 2222 +/- 75

Conclusions:

• All RFPDs have roughly the intended peaks in their transimpedance and the notches are close to 2$\omega$ value.
• North and South Cavity Relfection PDs have an almost similar response. This is good to have equivalent paths. So I think we solved the problem which initiated this whole project.
• North and South PMC Reflection PDs are quite different primarily dude to different frequencies at which they will be operated at. The low peak frequency in South path has resulted in a very high transimpedance at the peak. But since PMCs only affect the mode shape, this should not affect the equivalency of the two paths.

Edit Tue Oct 9 09:54:40 2018 (awade): Narrowed table width to prevent horizontal scrolling.

Edit Wed May 15 19:48:20 2019:

See https://nodus.ligo.caltech.edu:30889/ATFWiki/doku.php?id=main:experiments:psl:rfpd for the latest changes in RFPD.

 Attachment 1: All_RFPD_TI_and_Dark_Noise_Measurements.pdf  4.021 MB  Uploaded Mon Oct 8 19:24:00 2018
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