Edit Thu Oct 25 14:57:57 2018 (awade): Note that the LISO models here have wrong units.  They are supposed to be in units of power but were not converted from V/V.  Things listed as dB are correct but multiply the exponent of magnitude plots by two. This will be corrected in future posts.

I came across two interesting papers by Matt Morgan et al. on the subject of reflectionless RF filters.   

• Morgan, M. A. & Boyd, T. A. Synthesis of a New Class of Reflectionless Filter Prototypes. 8 (2010) (pre-print only arXiv: 1008.3502)
• IEEE Transactions on Microwave Theory and Techniques, Volume: 63 , Issue: 4 , April 2015 (arXiv: 1407.7825)

It seems like there wasn't a lot of thought put into optimal RF filter designs before this point that properly terminated the stop band elements. The Morgan filters are essentially diplexing filters arraignments, that has been done before. However, in the case of these reflectionless filters, there are additional symmetries that lower the inductor and capacitor values, reduce the requirements on component Q and widen the component tolerance requirements in general. The matched component design means that all circuit parts can be drawn from the same batch, improving the manufacture variation errors and also reducing the sensitivity to temperature. Together this means that we can more readly make custum filters with off-the-shelf discreet components with more confidence they will preform as designed and be relativity imune to thermal variations.

Comparisons to the equivalent Butterworth and Chebyshev designs suggest that it performs just slightly worst than Chebyshev but with a better complex gain slope, this means flatter phase in the passband and better stability of the filter for mismatch with component variation. It seems like these reflectionless filter structures are more directly comparable to the inverse Chebyshev filters or the elliptic (Cauer filter) topologies. These have minimal or no pass band ripple at the expense of slower roll off in the stop band some stronger stop band dips.  The bonus is that they are properly terminated at all frequencies and absorb all stopband by design.

The shape of the pass band response is much closer to the current elliptical filter installed in that there is a strong dip designed to coincide with the PDH modulation frequency. The dip corresponds to the first pole of the filter.  As documented previously in PSL: 2238 the stop band attenuation of the TTFSS elliptical filters is not much better than 14 dB. However, the attentuation at the critical modulation frequency is 58 dB and that is what really matters.  The problem with the current TTFSS RF demodulation design is that it does not have proper dumping the the stop band, much of the rejected ω and 2ω frequency components are reflected strait back into the mixer.  

The naive wisdom is that we add a terminating resistor at the input of the RF LP filter to quell backreflections to the mixer.  This is probably good enough for many configurations where we just don't care that much.  However, 50 Ω to ground isn't strictly impedance matched accross the whole frequency band and messes up the impedance in the passband. What we want is something that optimally dumps the higher order RF terms and presents the mixer with a well defined impedance at its output* accross the whole band: that way the mixer is loaded properly to its design specs.

Below is an schematic of a first order reflectionless filter with component values selected to achieve the pole dip at 36 MHz.

Here the optimal choice for passive component values is:

where Z_0 is the input terminating impedance of the filter.  It is also implicitly assumed that the output terminating impedance is matched to this Z_0 value.

I modeled the worst case filter design variations by performing a Monty Carlo simulation of the ideal circuit with LISO.  I Assumed a standard deviation of compoent values of 5.0% (this is what the spec sheets claim and set each component to normal random sample for each component about its ideal design value. Below is a plot of 500 samples (thin low alfa lines) along with computed median and 1σ band. In reality the component variation will be much less as they are drawn from the same batch and the manufactures probably leave a margin of error in the absolute value of components that they can deliver to.

What the model shows is that the tolerance to component variation is probably ok.  It doesn't show the impact of component Q on filter performace (especially about the deep notch around the pole is what we are really interested in).  I'm working on getting PySpice to simulate this with the coilcraft spice models.

Here also is the input impedance of the filter as a function of frequency:

This seems less good, as can be seen from the actuall mismatch for individual samples.  The real variation of inductors and caps drawn from the same batch probably isn't this bad.

*Its not clear to me what the output impedance of a naked mixer is supposed to be. In the TTFSS design a 22 Ω resistor is in series with a MAX333A switching chip before the RF filter (these 333A's have ~ 30 Ω series resistance): so it seems like that design assume that you need to add resistance in serieis to get to 50 Ω termination.  

Also attached is the notebook used to compute the plots in this post using pyliso.

Edit Thu Feb 21 19:30:48 2019 (awade): fixing unrendered laxex

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:

                                                                                                                                                               
Here, 
Z_AC,PD : Calculated RF Transimpedance
Z _AC,Ref : Known RF transimpedance of reference photodiode
R_PC : Photocurrent ratio at DC of reference PD to RFPD under test. This is calculated as:
                                       
: Extra phase delay in RFPD under test's light path due to the extra distance of light travel (). This is calculated as:
                                       
T_meas : 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 () 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 % 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.

Conclusions:

• All RFPDs have roughly the intended peaks in their transimpedance and the notches are close to 2 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.

I have mounted south PMC servo card on a 1U chassis with two acromag cards. The card should be ready to use.

Changes to Servo Card:
I switched resistor R44 with 39k (as we did in North PMC card) to create a 10Hz pole with PZT capacitance. The updated schematic is attached.

Acromag XT1541-000 Configuration:
Attached .zip file contains configuration file and the screenshot of configuration info.
IP Address: 10.0.1.49
Subnet Mask: 255.255.255.0
Gateway Address: 10.0.1.1
Host Name: XT1541-000-SPMC-DAC

XT1541-000-SPMC-DAC Pin Connections

Signal Name	Acromag Card Pin	Servo Card Pin	Notes
PMCSW1	DIO 0	P1-6A	Connected through resistor divider (see option D, attachment, PSL:2058 and PSL:2070) R1 = 3k || 4.3k ||150k  = 1746.55  R2 = 3.3k || 3.9k || 470k  = 1780.73  This gives Voff = 0.66 V , Von = 4.5 V with Vexc = 9 V on the DAC and Rpullup = 10k
PMCSW2	DIO 1	P1-7A	Connected through resistor divider (see option D, attachment, PSL:2058 and PSL:2070) R1 = 3k || 4.3k ||150k  = 1746.55  R2 = 3.3k || 3.9k || 470k  = 1780.73  This gives Voff = 0.66 V , Von = 4.5 V with Vexc = 9 V on the DAC and Rpullup = 10k
BLANKING	DIO 2	P1-9A	Connected through resistor divider (see option D, attachment, PSL:2058 and PSL:2070) R1 = 270 || 390 ||4.7k  = 154.31  R2 = 300 || 330 || 390k  = 157.08  This gives Voff = 0.66 V , Von = 4.5 V with Vexc = 9 V on the DAC and Rpullup = 1k
MGAIN2	OUT 00	P1-4A	-
INOFFSET2	OUT 01	P1-5A	-
PMCRAMP	OUT 02	P1-6A	-

Acromag XT1221-000 Configuration:
Attached .zip file contains configuration file and the screenshot of configuration info.
IP Address: 10.0.1.48
Subnet Mask: 255.255.255.0
Gateway Address: 10.0.1.1
Host Name: XT1221-000-SPMC-ADC
All channels are configured for range 10 V with averaging factor set to 200.

Temperature data in the ATF (QIL) lab has been collected for a month now.  Data is sampled at 0.1 s intervals and saved on WS2. I'm not attaching the full data here (its about 4 Gb/month in csv format) but the minute trend is included along side the plots below.

Plotted below is the hour trend from September 11th up until October 13th 2018* (UTC).  

The Thermostate trace shows temperature as measured at the AC control sensor.  EnvMon is the themerature at the center of the table (sensor is mounted to table directly). 

*Note that these sensors were never calibrated for their absolute offset (but they should be pretty close).  Drift of the transducer box is unknown.  It uses a LT1128 op amp to convert AD590 sense current into voltage.  This is not the right choices.  Also the resistors are the lower grade radial type thick film, which is also not the best choice for immunity to circuit induced drift.

Attached is the latest full noise budget we have. I generated it by rerunning current noise budget notebook. The aim of this post is to create a checkpoint of where we are, how the analysis was done and what we are going to do in the future.

Current Measurements:
There are 5 measurements of ASD of the beat note currently. 1 set (dark red) is from un-dated data (committed as ported from 40mSVN). Others have dates marked on them. These data sets are the spectrum of beat note frequency. No post-processing is done on these measurements and they are plotted as measured.

Coating Brownian Noise (Green):

• This is calculated using Harry et al. (2001) Eq 21 (written slightly differently here with only coating contribution)
                                            
• Here, d: Coating Thickness  =  
            w: Beam spot size on mirrors = 
            : Coating Dielectric Loss Angle assuming 
            : Substrate's Young modulus = 
            : Coating Young modulus =  
             : Substrate's Poisson ratio = 
             : Coating Poisson Ratio = 
• Noise from above formula is in displacement. It is converted into frequency noise using the conversion factor for the cavity, .
• It is the highest estimated source of noise in relevant frequency ranges.
• This is an oversimplified model and we are working on incorporating analysis due to Hong et al. (2013) for calculating this noise.

Coating Thermo-Optic Noise (Pink):

• This is calculated using analysis given in Evans et al. (2008). Particularly, Eq 4:
                                            
• Here, : Noise spectral density of displacement noise due to thermo-optic noises.

                    : Profile-weighted temperature fluctuation PSD, calculated using:
                                                                     with                
                       : Effective thermoelastic coefficient for coating, calculated using Evans et a. (2008) Eq A1 and A4:
                                                                        and        
                                          Here,  : Thermoelastic coefficient for the k-th layer.  and 
                                                      : Thickness of each layer. This is read from coatingLayers.csv which contains optimized. There are 57 layers in total.
                                                    Rest variables are the same as previously stated.
                      : Effective thermo-refractive coefficient for coating, calculated using Evans et a. (2008) Eq B3-B8. This is bit tedious calculations so I'll leave out the details.
                       : Wavelength of beam light = 1064 nm
                     : Effective heat capacity per unit volume of the coating, where  is the heat capacity of the kth layer.
                                                                                and       
                       : Heat capacity per unit volume of substrate = 
                      Rest variables are as stated before.

• Same as before, the calculated noise is displacement noise and is converted into frequency noise.
• This noise has been reduced significantly by making thermoelastic and thermorefractive noise cancel each other Its further analysis is at low priority as it is well below other noise sources.

Substrate Brownian Noise (Yellow):

• This is calculated using Cole et al. (2013) Eq.1.:
                                            
• Here all variables are as stated before.
• Note: This is less by a factor of 2 from expression in the paper because the expressions in papers are for 2 mirrors together. We in our calculation take into account the number of mirrors separately.
• This noise source is the third highest source of noise in relevant frequency ranges. It is hard to make any change other than changing substrate material itself to reduce this noise source.
• This is a much better-understood source of noise and there are no proposed changes in its analysis for now.

Substrate Thermo Elastic Noise (Sky Blue):

• This is calculated using Somiya et al (2010) Eq 3 and 8: (Analytical expression for the theory by Cerdonio et al. (2001))
                                     where       
• Here,  : Substrate Heat Conductivity = 
            : Thermal relaxation frequency calculated by Cerdonio et al. (2001) Eq 9, 
            
• Note: There is a difference of $\sqrt{2}$ factor from Somiya and Cerdonio's expression because w in Somiya et al. and r₀ are related as as explained in Black et al. PRL 93, 241101 (2004).
• This noise source is the highest noise source up to 90 Hz and is second to Coating Brownian Noise in the above frequencies.
• There no proposed changes in the analysis for this source for now.

PDH Shot Noise (Orange):

• This is calculates using (in ):
                                                           
• Here, : PDH modulation index of FSS = 
            : Cavity Visibility = 
          : Incident power on FSS EOM = 
• This is then converted into frequency noise spectral density by using PDH Slope (Also accounting for cavity pole):
                                                              
• Here,  : Cavity Pole = 
             :  PDH slope = 
• This is a fairly low noise source and is a straightforward calculation. No updates required here other than remeasuring  and  .

PLL Oscillation Noise (Grey):

• This is directly measured and the data on the attached graph is from 2012.
• This data should be taken again and if possible should be included in automated scripts.

PLL Readout Noise (Purple):

• This is calculated with what is referred to as "Tara's Magic Number":
  
• I have no idea how this formula emerged. It would be best to measure the noise from PLL again and dissect and measure all independent noise sources again.

Seismic Noise (Black):

• This was measured last in 2011 October with a seismometer on the table.
• This doesn't affect much our region of interest but should be updated as we are 7 years in the future now.

Photothermal Noise (Brown):

• This is the coupling mechanism of intensity noise into frequency noise.
• To calculate this, following conversion from incident power noise to photothermal noise is used:
                                         
• Here,   :  Photothermal Transfer function in (m/W)
             : Power absorbed by mirror calculated by 
                            Here,  : Coating absorptivity = 
                                      : Incident Power
                                       : Cavity finesse = 
              : Relative Intensity Noise Spectral Density
• Relative Intensity Noise is measured directly. For the plot attached, RIN was measured only on the south path and north path's RIN was assumed same.
• Photothermal Transfer Function is calculated due to Farsi et al. (2012) Eq. A51:
                            
• Here,  : is contribution through the coating, calculated using Eq. A44 (Details excluded)
             : is contribution through the substrate, calculated using Eq. A45 (Details excluded)
             : is contribution through the thermorefractive process, calculated using Eq. A49 (Details excluded)
• This noise, it turns out is quite low in the relevant frequency range. No further updates are required in the analysis.
• The RIN needs to be measured again though for both the paths.

Residual NPRO Noise (Green):

• This calculation requires free-running frequency noise of NPRO. It is assumed to be following which is taken from Wilke et al. Opt. Lett. 25, 14 1019-1021 (2000):
                                             .
• Open Loop Transfer Function of FSS was measured in 2004 (see PSL:1504). The measurements are fitted with model transfer functions to get zeros and poles which are then used to estimate OLTF at frequency points of interest.
• The assumed NPRO free-running noise is then suppressed by these OLTFs (north and south) and added in quadrature.
• We need to measure the OLTFs again and if possible, measure the true free-running frequency noise of the NPROs.

Near future plan:

We should be able to finish aligning South Path with the newly installed PMC by end of this week. Then if everything works fine, we should start taking beat note measurements every week and focus on updating old data in the estimate plots.
 

Changes:

• The PMC on the south path has been installed with the PMC servo card on the rack.

• I added sliders for setting max, min and step size of autolocker scanning in PMC interface medm windows.

• I used one PLCX-25.4-103.0-UV-1064 and three steering mirrors in front of EOM to mode match with PMC.

• I laid down new cables for PMC reflection RFPD signals and EOM.

• I removed the power supply providing 9V to PMC Servo Cards and made a voltage regulator box with LM7809CT which converts 3-pin 18V to two BNC 9V.

• We are now using external mini-circuits in-line mixers (ZFM-3-S+) and low pass filters (SLP-1.9+) instead of using onboard mixer and filter on PMC servo card and injecting signal through FP1Test input.

• I mounted the inline hanging mixers and splitters on the rack with LO delay lines inside the rack so there are no hanging parts now.

• I changed requirements in ALConfig_NPMC.ini and ALConfig_SPMC.ini so that we can inject the signal from FP1Test and autolocker still functions.

• The HV supply of PMC servo boards was found to be around 180V. We changed it to the designed 160V.

• Attaching few pics for above changes.

Few numbers:

South PMC Mode matching ~ 70%
Modulation frequency = 14.75 MHz
Modulation Index  rad
 

Few notes:

• When aligning to PMC, it is a good idea to keep a white screen infront of transmission and work in dark with IR viewer to get an idea of what is happening.
• A camera on the back side of PMC also helps when sufficient light starts building up in the cavity.
• While finding optimum LO delay using the SRS delay box DB64, use the rated 2.5 ns extra lag written in the datasheet.
• Once maximum swing in PDH error signal is found, check locking once and see if the transmission is good or not. You might be locking to the sideband as the servo locks to one kind of slope only. If you find feeble transmission, just add T/2 delay in the delay box where T is the time period of modulation frequency. This lands you to near right spot.
• While soldering an SMA connector to the cable, put the heat shrink in first and past it to the cable before proceeding. I made this mistake few times.

The South PMC is installed and the South FSS is running again. Attached is the beam path profile from ala mode used for the south path.
While aligning this beam into the cavity (which is a very difficult task apparently), I disturbed the north path by mistake. So I had to align both paths from scratch again.

Few notes for aligning beam into cavities in future:

• The only way to know if the beam is reflecting off the mirror, not the enclosure or something else inside the tank, is to bend and look through an IR viewer. So my first step would be to do this and ensure the beam is at least hitting the mirror. This step requires the removal of the thermal shield.
• After this, it takes a while to actually start seeing the reflection from the mirror. I bend to see into the cavity to see if the reflection from the mirror is hitting something else and change angles accordingly.
• At this stage, once we get the reflection, we very nicely just match it with the incident beam. BUT, make sure you are not seeing anything in the transmission. It is possible that the beam is simply going through the spacer. A way to check if the transmitted light is through the cavity or spacer is by changing laser frequency (Slow input to laser) slightly.
• Once we get the coincident reflection with no transmission, scan the slow input about 0.75 V to see if any of the modes are excited. If you get lucky, some lower order mode gets excited to give some information about how wrong the incident beam is.
• From this point onwards, it is just walking of beam all over the mirror of the cavity and scanning laser frequency to get any glimpse of the fundamental mode.
• Once the fundamental mode is caught, we actuate the fast input to the laser with ~3 Vpp sinusoidal signal at around 4 Hz. Adjust the periscope to get some tangible transmission and then just do the usual optimization by walking the beam.

Important things to remember:

• Make the autolock condition of PMC less hard so that it remains locked with the fluctuating laser frequency.
• Every time you are moving a knob, double check if you are moving the right one. This is how I fucked up a perfectly good alignment on the North side.

Also, I have made correct length cables for FSS LO delays for both paths and both cavities are getting locked nicely. At North cavity, I see ~70% mode matching and at South cavity ~60%. These were measured with laser power meter.

Future steps are to align ouput of the cavities onto Beat note detector and start measuring noisebudget weekly. After that, we'll concentrate on increasing mode matching and reducing noise sources in the paths.

I soldered a prototype board implementing the transimpedance circuit I, Andrew and Rana discussed earlier.

PFA the schematic and picture of the board.

Some numbers:

Voltage rail: +- 15V
Transimpedance: Rated:16.549 kOhms (15k+1.05k+499)
                             Measured: 16.99 kOhms
Vol Ref; LT 1021DCS8-5 (Actual circuit would have ADR4550ARZ)
Measured voltage at Vol Ref Output: 5.003 V
Measured output at Room Temperature: 8.48 V
Temperature from the measured output: 299.005 K (25.9 )
                                                           It was certainly colder than that. I had no other good temperature reference.
Highest output on waving a hot air gun above circuit: 9.15V
Error in temperature perception from that: 358.5 mK

Possible sources of error:

• No bypassing capacitors were used. So some voltage noise from power supply must have crept into the circuit.
• Transimpedance resistor is made up of thin film resistors of 25ppm/K TCR. This translates to approximately 7.5 mK/K (change in perceived temperature per kelvin change in circuit temperature)
• The resistors in the adder circuit are thick film resistors however their effect should be minimal with even 200ppm/K translating to 1 mK/K.
• Voltage reference used was LT1021DCS8-5 with 3ppm/K TCR. This translated to 0.8 mK/K, so we should be good with this.

Methods:

For measuring room temperature, I first dabbed the AD590 with little-wet tissue to cool it down. This was done to make sure no remnant heat from previous runs is remaining. Then I put the AD590 inside a shallow metal drawer opposite the soldering bench and waited for some time to let the reading settle. I assumed the metal drawer must be in equilibrium with room temperature and must have high heat capacity to work as a good room temperature bath for AD590.

When seeing the changes due to circuit temperature change, I waved a hot air gun over the circuit so that hot air blows over the circuit and not onto it. The temperature of the hot air gun was 110  with the highest speed setting. I have no exact knowledge of how much circuit temperature I increased but it got pretty hot to touch by the time I reached a ceiling in how much output value is changing (about 9.15 V)

Conclusions:

I think I should go ahead with designing a layout of the circuit. There is only so much we can do in the design of the circuit itself. I have chosen 0.2ppm/K resistors for transimpedance to reduce our major source of drift. For voltage reference, since we are getting more precise ones in the same cost, I chose ADR4550ARZ (BRZ version on Digikey was out of stock) which has lower output voltage noise than LT1021. I have also ordered thin film resistors for the adder stage to completely eliminate the effect of drift from them.

• Since we are working on temperature control of cavities, we worked out a hack to still take beat note spectrum meanwhile.

Method of measurement:

• Spectrum is measured by SR785 at 800 points from 0 Hz to 6392 Hz.
• No averaging is used and autorange is switched on.
• Units of V_rms/sqrt(Hz) are used in the measurement.
• I wrote a script, measBNnoise.py which is in Git, which continuously saves data from SR785 which is set as stated above.
• Saving data takes from 90s to 120s, so data is being saved stroboscopically.
• We are hoping that as the beatnote frequency is drifting slowly, Marconi will follow it almost always nicely except when it re-ranges.
• So taking data in this way will mostly take data when Marconi is not re-ranging.
• Data was taken for 12 hours in which total 381 measurements were made. 346 were filtered and used as described below.
• Then I used another script I wrote, BNspectrum.py which does following:
  1) Reads all data files and computes the area under the curve. (We are using it as a figure of merit to filter out instances when Marconi was re-ranging)
  2) Throws away data sets which have this area above 2*sigma from the mean value of the whole set.
  3) Computes median at each frequency bin of remaining data set.
  4) Computes standard deviation from the median at each frequency bin.
  5) )Plots this data like iris (plot attached) and saves it in a .txt file to be used by noisebudget.ipynb later.

Present state of the experiment:

• FSS on both paths has been upgraded to higher modulation frequencies (36 MHz on North, 37 MHz on South) (see PSL:2242 and PSL:2247)
• PMC is installed on the South Path. (see PSL:2251)
• See alignment details at PSL:2253.
• ISS is not installed at this point.
• Wideband NewFocus 1811 (DC-125MHz) RF Photodetector is used.
• Temperature control on cavity shields was not on. They were put in a known almost stable heating state of 0.3871W Common and 0.7742W differential heating.

Conclusions:

• This beatnote is as good as Feb 2018 measurement only.
• In my opinion, ISS will help in reducing the noise further.
• Presently, I have not optimized polarization of light going into EOM according to amplitude modulation produced by it. This in absence of ISS must be putting in more noise then we think.
• Lens positions have not been optimized and are at there eyeballed positions where I put them after ala mode calculations. They might be off in order of cms.
• The older elliptical filters in FSS boxes have not been replaced yet.
• I'm not sure how big this is a factor, but in absence of temperature control, the frequency must be picking up more noise through drift in cavity lengths due to uncontrolled heating.
• We are not using lower noise narrowband RF detector as we are presently not controlling BN frequency.
• I also think we should have had taken data for a longer time. I will do this over the weekend.
• I'll over the weekend write a script so that this hacked measurement will start happening every weekend. This way we can see any changes in our measurement from new things we work on during the week.

Over the break, the test of Vacuum Can Temperature Sensors transimpedance circuit was running and fb4 has logged the values. PFA time series data from fb4. See PSL:2270 for experiment details.

To reiterate:

• Channel 0 and 1 are from the same board (Circuit 1) which is enclosed inside an aluminum box which is sitting inside a thermacol box. So this circuit should be well insulated from environmental fluctuations
• Channel 2 and 3 are on another board (Circuit 2) which is in the open.

As seen in timeseries data, something is wrong in Ch2 data as it is fluctuating too much arbitrarily. I'll see what went worng in this particular circuit. Thankfully, I had an extra circuit on same board which is recorded in channel 3 so that we can compare the channels.

Inferences:

• In terms of fluctuations over small periods, it seems both circuits perform similarly with no noticeable drift.
• The EPICs channels are updating at 10 Hz while I found that fb4 records channels at 16 Hz. Due to this, I think we can not really do fft properly.
• Standard deviation of a 1minute time series data for the three channels came out to be, Ch0 -> 22.5 mV , Ch1 -> 18.0 mV and Ch3 -> 15.0 mV
• The boards are designed to have a response of 1.625 mV/mK. So either temperature is fluctuating by around 20-30 mK or the boards are 20 times worse than the design.
• Also, clearly the offsets of each board are very different. This could be because of the difference in thin film resistor values at the adder stage or reference voltage chips.
• There are visible offset jumps in the time series data. I'm not sure this is due to any gap in the recording which fb4 didn't understand or something actually happened. But these are periodic themselves with a period of about 2 hrs.
• Since fb4 is running again properly now, I'll check back timeseries data of tonight.
• Next, I'll try to make some controlled heating environment and a precise temperature sensor so that we can see if different AD590s have different slopes for temperature changes.

Edit: Fri Jan 11 11:24:11 2019

Added lighter plots. The plots now have mean value (averaged over 1 minute of data) with the shaded region showing one sigma uncertainty region. I've added the jupyter notebook in .zip file.

I wanted to take a direct spectrum noise measurement of the circuit. However, if I have simply hooked the output of the circuit to SR785, I wouldn't know if the noise is coming due to temperature fluctuations or due to circuit noise itself. So I made a quick subtraction circuit of unity gain with an OP27 and subtracted different pairs of channels and then took their spectrum using SR785.

Method:

• First I shorted the input to the subtraction circuit and measured the spectrum. This gave me an estimate of output noise due to this additional circuit and SR785 measurement.

• I assumed the gain of the subtraction circuit is just 1 so, the output noise of the circuit under test wasn't assumed to get amplified from subtraction circuit.

• Then I took measurements of the difference of signals for each pair from CH0, CH1, and CH3 in both permutations. All measured spectrums are plotted in the first plot.

• I used both permutations to nullify any effect of different gains in positive and negative inputs of the subtraction circuit due to slightly different resistor values.

• Then I averaged the spectrum from the 2 permutations of difference and subtracted output noise of the subtraction circuit measured earlier in quadrature. These are plotted in 2nd plot.

• Then for the Circuit 1 which was insulated from the environment, assuming the two circuits have identical noise, I divided by sqrt(2) to get individual channels output noise.

• I subtracted this insulated individual channels output noise from the difference noise with 'open to environment' channel in quadrature to get an estimate of noise when the circuit is open to the environment.

• The individual channel output noises are plotted in Plot 3.

Conclusions:

• There is a high peak at 60 Hz because of AC frequency. I am not sure about the origin of the 7 Hz peak. Other peaks look like reflections during the measurement.

• There is about a factor of 2 improvement by insulating the box.

• The circuit is designed for 1.625 mV/mK transduction.

• Since EPICS channels are read at 16 Hz rate, we should be interested in the 0-16 Hz bandwidth. In this bandwidth, voltage output noise for the insulated channel is 0.79 mVrms and 'open to environment' channel is 1.74 mVrms.

• So the noise wouldn't harm the designed 1mK sensitivity. In practice, even if these estimates are bad, the circuit should be ok for our needs.

• So the only thing that can endanger our precision really would be temperature drift of circuit components on which we have already invested enough money and time during design.

• So agreeing with Andrew, I'm going to go ahead and install these new circuits and directly see their performance towards improving BN spectrum as we think the Vacuum Can temperature is oscillating more than lab temperature due to poor circuits presently employed.

I'm attaching the first results of the transfer function from liso model of complete TTFSS box. I've also attached the jupyter notebook with some important formulas used.

Both files are present in git/cit_ctnlab/ctn_electronics/TTFSS_lisomodel/ git repo.

I'm just posting results for the analysis I did so far. I'll be able to make better inferences with some more work I intend to do tomorrow.

Edit: Wed Feb 6 16:59:59 2019

The updated plot is at git. Added analysis of variation of crossover frequency and phase margin with changing Fast gain.

I added some more graphs to our FSS analysis.

• I modeled AD602 variable gain amplifier with a circuit similar to how it actually works internally. The resultant circuit now has a right input resistance of 100 Ohm and capacitance of 2 pF. It is slightly noisier than AD602.
• I calculated the total suppression function and suppressed laser frequency noise.
• I did a parametric analysis by varying the PZT gain and obtained a range of cross over frequencies and phase margin we can attain.
• Everything looked awesome so far, but the real problem is EOM railing.
• So I calculated that if the said suppression is achieved, what is the actuation signal that is sent to EOM.
• The last plot is the spectral density of this actuation signal. Since only, we clearly are going to rail the EOM and the said suppression will never actually happen.
• We need to shift actuation region of EOM to even higher frequencies so that it doesn't rail. But at the same time, we need to keep the crossover frequency and phase margin of crossover decent. And to top it off, we need to do all this making sure we get at least  suppression at 100 Hz.
• So from here, I guess we need to work on shifting the poles and zeros and tune in the gain values right to get point.
• I'm not 100% sure about this analysis, please let me know if I am doing something wrong here. The latest notebook and pdf are on git.

Edit Thu Feb 7 11:32:13 2019 :

Last plot in the attachment is wrong. See following discussion in PSL:2306 and PSL:2307

Hmm... Last estimate of V_rms applied to EOM can't be true.  

If laser frequency noise is 

Total frequency noise down to 1 kHz should then be 316 Hz_rms. As you've noted in your jupyter notebook the EOM frequency domain response to actuation signal goes as f, i.e.

where ms is EOM phase slope (15 mrad/V) and V_EOM is the applied actuation voltage. As you wrote, that leads to

If we assume that the EOM is taking 100% of the load for canceling laser frequency noise at a given frequency then it follows that the applied voltage to exactly cancel laser frequency noise is 

This would indicate that the burden on the EOM becomes 1/f heavier in frequency because of the laser noise roll up and 1/f heaver because the EOM responds as f to signals in the Fourier domain.  The above puts an upper bound on the ASD curve of load that the EOM is absorbing to cancel laser frequency noise.

Integrating the above V_EOM PSD down from high frequency will give the total V_rms load that the loop would need to apply to suppress laser frequency noise:

or  

I've plotted this below and attached the notebook used for the calculation.  It kind of looks like the maximum load at 1 kHz hits about 200 Vrms.  Maybe I've gotten some factors wrong here but you can sort of see the scaling of how the maximum load on the EOM will look.  

One thing to note is that the above estimates are an upper bound assuming that the EOM is taking all of the load down to that frequency point and that the PZT path isn't fighting or out of phase with EOM.  To correctly compute the load on the EOM you are going to have to break down the EOM only portion of the loop from the laser frequency to the point of voltage injected into the EOM.  This can be done by effectively nesting the PZT loop into the round trip gain in a way similar to that described in Josh Smith's Thesis section 2.6.2.  Finding the actuation signal should be similar to finding the PLL actuation signal, at this point in the loop it is the G/(1-G)/A copy of the sensor noise.  In the high gain regime the applied EOM control signal should just be the laser frequency  divided by the EOM frequency slope. Of course you can compute for G_EOM OLG to get a true value with a bunch of algebra.

This actually has units of Hz/Hz. Note, that  is just Fourier transform of frequency actuation, so it is unitless. I used this to get the transfer function of EOM actuation, from applied signal in V to resulting actuation in Hz, which is the prefactor of  above having units of Hz/V.

So, if EOM is taking the whole load of frequency noise, actuation signal ASD would be:

But obviously, this is wrong because this just assume that we are not feeding back the actuation signal at all. So instead, I assumed that if everything is 'ideally' working and we actually have the frequency noise suppressed by a teamwork of PZT and EOM, the incoming noise signal to EOM path's transfer function is:

So, the actuation signal generated for EOM by EOM path's transfer function in an ideally working loop is:

The error in the last plot in PSL:2305. is that I forgot to divide by  since transfer functions in the code are from Hz to Hz. So I think this is the real error.

But on reading section 2.6.2 of Josh Smith's Thesis (which btw has a typo in Eq. 2.33 and 2.34), I did the thing of nesting the PZT path with the plant. So as per Eq. 2.31:

is the transfer fucntion of Plant for the simplified loop with just EOM as the actuator. Then the actuation signal ASD would be (note is free running laser frequency noise ASD):

which turns out to:

Which is exactly the same as above. But still my model has this error. I'll fix it and post it soon. For readers in the future, the last set of equations are the only correct equations to the best of my knowledge.

• The migration of all EPICS channel hosting and all python programmes has been done from Acromag1 to C3IOCServer. Now Acromag1 is neither hosting anything nor running any codes.
• All channels are hosted in C3IOCServer through docker services. The channels are grouped into 5 groups which can be independently stopped or restarted now. This will allow to cahnge any channels or add channels without disrupting everything else.
• All python programmes (Autolockers, PID scripts etc) are also running as separate services.
• All these services are run inside a container which is utilizing an IP address in our local netwrok. Addresses 10.0.1.96-127 are reserved for such services.
• At any time, to see the list of services, ssh into C3IOCserver (ssh 10.0.1.36) and run sudo docker ps.
• Using the container names, the services can be stopped (sudo docker stop container name), started (sudo docker start container name) or restarted (sudo docker restart container name)
• To shut down all the python programmes, go to /home/controls/Git/cit_ctnlab/ctn_scripts and run sudo docker-compose down.   To start them again, run  sudo docker-compose up. To run it in background, use flag -d.
• To shut down all the channels, go to /home/controls/modbus and run sudo docker-compose down. Rest instructions are as above.
• For adding a new python script as a service, you would need to add any additional packages in /home/controls/Git/pyEPICSDocker/requirement.txt and run "sudo docker build -t pyep ." at the same directory. Delete any previous instance of the image to save space.
• After this, add the service in Git/cit_ctnlab/ctn_scripts/docker-compose.yml following the examples of existing services.
• If the packages are LIGO propietary, you would need to mount the cloned git dir into "/dev" folder in the docker-compose.yml file and add sys.path.append('/dep') in your python script. Follow example of netgpibpackage used in PLLautolocker.py.

Wandered into the PSL just now.  Slow controls were going wild.  Traced it back to the fact that acromag1 and its auto-restarting services were still live. The new dockerized python script services on C3IOCServer were fighting the Acromag1 machine processes.  I've copied the service scripts into the ~/Downloads/ folder of acromag1 and deleted them from /etc/init/.   I then rebooted acromag1 and the problems went away. 

We should achieve whatever is on Acromag1 and probably rebuild that machine with an operating system that is still in long term support 

This week on 19th March in the evening, I was working on replacing the GND connections of the power supply with thicker wires and checking out any AC rms voltage between different ground points to look for ground loops. During this, I found that the high voltage power supply for PMCs wasn't directly grounded with the rest of the power supplies. These are Kepco PCX 200-0.1 MAT power supplies. From here onwards, I'll tell about this incident chronologically:

Before the incident:

• Pins 4 (Sensing -) and 5 (Output -) were not shorted with a shorting clip to keep voltage regulation good.
• Pins 8 and 9 were shorted. These pins are for the external resistor for voltage control. At this point, my understanding from the manual was that front panel voltage knob overrides this external voltage control.
• Pin 5 was GND terminal for two such power supplies connected in series and operated at 80V each, totaling to 160 V for the single-sided rail of PA85 in the PMC servo boards.

The incident:

• I removed the shirt between PIN 8 and PIN 9 leaving it open and used this clip to short PIN 4 and PIN 5. I also connected PIN 4 to the rest of the GND of other power supplies which is GND for the rest of the lab.
• Then to test this, I switched on all power supplies, leaving one pair of +-24V power supplies at the bottom. I left them as at this point already, +18 V supply used for FSS boxes showed me a trip (it became a current source limiting to 3 A with about 3V voltage). Also, the Kepco power supplies for PMC where I did the changes shot to maximum 200V (instead of set 80V).
• I shut down everything and rewired everything as before.

My understanding of what happened here:

• Since short between PIN 8 and PIN 9 were removed, the external voltage control of Kepco power supply got activated and rose to maximum 200V making rail of PA85 in PMC servo card +280 V (Maximum allowed +450V).
• This allowed the PMC PZTs to be driven to upto 280V (Maximum allowed being 200V) if the control signal required it to. So far after all the tests, I came to the conclusion that this didn't happen and PZTs are healthy.
• The +18V power supply simply tripped because the FSS boxes use 18V rails to power 24V rail circuits as well in absence of power at 24V rails (which I didn't switch on yet). So the lesson here is that always switch on 24V rails power supply first for the FSS boxes.
• Finally, this is just a guess, the sudden rise of Kepco power supplies to 200V might have sent a surge of charge to rest of the GND. It doesn't really make sense, but something must have happened because I found RF amplifier of PMC reflection RFPD dead after all of this.

Current state:

• I replaced the MAX4107 RF amplifier in SN020 RFPD (and actually after doing this twice), this RFPD became as before with same transfer function as measured in PSL:2247.
• I noticed that PDH error signal for South FSS was too low. Later I found this was just because Andrew added a microwave amplifier in the RF output which mismatched the phase matching of FSS PDH.
• There are more findings on the South reflection RFPD and FSS of South path. I'll report this in a future post with some numbers.
• I have tested all FSS boxes and PMC Servo cards as well as EOM drivers. Everything else in the lab seems ok at this point. The lasers are locking nicely and following Slow PID as well.
• Regarding the ground loop issue which was the start point of all this, everything is status quo, so it is also there.

I borrowed a small isopropanol glass bottle from CTN to OMC (Apr 17, 2019)

I borrowed a small acetone glass bottle, which was in the yellow solvent cabinet, from CTN to OMC (Apr 19, 2019)

Today I made a standalone Adjustable TTL Trigger generator box. Following are some features:

• The rising edge of output can be used to trigger all TTL compliant external trigger enabled equipment (oscilloscopes, HP4395A, SR785 etc.)
• Uses AD620 at very high gain (G=5k) to create a comparator. Positive input is the signal and negative input is controlled with a 100 kOhm potentiometer.
• The threshold can be set anywhere between +18V and -18V.
• Powered internally with four 9V Alkaline batteries and has a switch to turn ON/OFF. Should last really long.
• The output is through a 4.7 V Zener Diode which activates in reverse bias when the signal becomes 140 uV higher than the set threshold.
• Input impedance equivalent to AD620.
• The trigger is not latched and output goes to -0.7 as soon as the signal falls below the threshold.
• Has a window port for checking the threshold.
• The practical way of operating would be to see the signal and output of the box together in an oscilloscope first and fine tune the potentiometer to see triggers at the right point.

not all amps are good for use as a comparator

https://www.analogictips.com/faq-use-op-amp-comparator/

But I used AD620 which is an instrumentation amplifier, not opamp. I thought comparators are made with differential amplifiers (from Horowitz & Hill Sec 4.23) and since AD620 was a nice available instrumentation amplifier, I thought it would work (and it does work).

But this particular circuit that I made seems to be less general than I thought. 100 kOhm potentiometer makes it hard to fine tune the threshold. Also, I think I should have buffered the threshold voltage divider circuit because I see the threshold level changing with the incoming signal when the signal is more than the threshold. It doesn't affect my particular application, but I think that makes this a crappy TTL generator. But since my purpose has been served, I'll push optimizing and generalizing this box to some other day. Maybe my new SMD prototype boards would be handy.

I borrowed the following components from PSL lab to QIL lab 

1. Mixer (Minicircuit, ZFM-3-S+)

2. RF amplifier (Minicircuit, ZFL-500LN)

3. IFR/Marconi 2023 A (# BD9020)

I have made a SMA cable of length 1.952m after optimizing phase delay of LO. This is giving the maximum PDH error signal.

For future reference, I'm saving present setup details:

• Off-resonance South Reflection RFPD SN010: 3.34 V
• Resonance dip in South Reflection RFPD SN010: 2.98 V
• Cavity Transmission Peak: 3.6 V
• OUT1 peak-to-peak signal: 230 +- 5 mV

From the ratio of off-resonance value and error signal pk-pk at OUT1, we can check in future if everything is same as right now. From ratio of off-resonance value and dip value, we can check cavity  mode matching in future.

I today shifted our modbus (db files for EPICS channels, ioc command files and docker-compose file to run the services) over to this git repo.

Through this, we would have version control now so that we can revert back to a working stage if something causes an error in the hosting of the channels. All db files are updated every 5 minutes by dbFilesUpdate.py in ctn_scripts. So we should try to commit the changes manually once in a while to the repo. This is there so that locally the files track changes in the settings and parameter values but we also have version controlled history in git for long reverts.

On another note, it is important to start the docker processes in a particular order. To ease with this, I have added a restartAll command in the .bashrc of ioc3server which looks like this:

#Restarts all teh EPICS channels and python scripts in the correct manner.
restartAll() {
        cd /home/controls/Git/cit_ctnlab/ctn_scripts
        sudo docker-compose start dbFilesUpdateOneTime
        echo 'Updating db files before restarting...'
        while true; do
                sleep 1
                if [ -z `sudo docker ps -q --no-trunc | sudo grep $(sudo docker-compose ps -q dbFilesUpdateOneTime)` ]; then
                        break
                fi
        done
        echo 'dB files updated. Shutting down python scripts...'
        sudo docker-compose down
        cd /home/controls/Git/cit_ctnlab/modbus
        echo 'Now restarting the EPICS channels...'
        sudo docker-compose down
        sudo docker-compose up -d
        cd /home/controls/Git/cit_ctnlab/ctn_scripts
        echo 'Checking if the python scripts are down...'
        sudo docker-compose down --remove-orphans
        echo 'Starting python scripts...'
        sudo docker-compose up -d
        echo 'Done!'
}

So every time a new channel is added. After doing git pull, one should use this command or the commands listed above in order to make sure the channels and python scripts boot up in the right fashion.

Edit Mon May 13 12:17:23 2019: Updated restartAll() function to do a last time db files update before restarting.

We have changed the logbook name from PSL_Lab to CTN. To keep all the links working, I ran the attached script in a local copy of the log files and then copies them back to the server. The script essentially just changes PSL_Lab from all hyperlinks to CTN. Now, all such links are working. However, the front text of the links was not changed to avoid unnecessary tweaking. So in most of them, the front test still says PSL:XXXX but the links are correct.

Awesome. Can you do the same for crosslinks to the old ATF_lab logbook name (ATF_Lab-> QIL)?

1. Fix the temperature control so that the fluctuation over hours time scale is low as Tara/Evan had it. This will allow for using the Marconi with a low FM range (or potentially none; we could just demod with a fixed frequency and directly digitize the IF signal in the CYMAC).
2. Debug and fix the FSS misbehavior. Circuit creep in the last few years has degraded its performance relative to the in-loop performance achieved back in 2015.
3. Recalculate the Brownian noise.

I had aligned the North Cavity before the weekend and was about to align south one today when I saw that the modematching on the North Cavity has fallen to 20%. This is a tell-tale sign of vacuum can temperature changing too much. When I checked, indeed the temperature sensors were railing to their lower most value of 26.599 Celcius. Same for both in-loop and out of loop sensors. While the table top temperature sensor was giving a meaningful value.

Investigation begins

I first checked point by point the temperature sensor board LIGO-D1800304. From ADC all the way back to the AD590s.The two sensors were indeed giving a voltage of 4.8 V through a transimpeadance of 16.25k  which meant 295.385 uA of current corresponding to 22.23 Celcius. So indeed the sensors were telling me that the can had cooled down to almost room temperature over the past 2 days.

Framebuilder logs

I checked the framebuilder logs to figure out what has happened. The temperature was being stabalized at 34.38 Celcius by the PID script. At around 15;20:25 Aug 16, 2019 PDT, the temperature starts decaying. Infact, I should use this data in future to calculate current time constant of temperature decay of the can through the insulation. The table temperature was around 19 Celcius all this time. I found out that FB4 is not recording the channels that I have added later. I need to look into this as well.

Attached is the decay plot of the temperature

Possible points of problem

After a deep search through elog, CTN:2043 and CTN:2045 are the most relevant latest post. Kira and Kevin worked on this heater drier circuit and I'm doubting that something blew up in this circuit CTN:1903. I guess this would be my first point of attack.

Another possibility is that the heater load got disconnected. Well, I just checked the resistances and I get values of 38, 70, 70 and 38 Ohms. These are the right values according to CTN:1750. This is not the issue.

Lastly, the worst possible issue would be that the temperature sensors are reporting wrong temperature. But looking at the the properexponential decay of temperature reported by them, I would first assume that they are working fine.

Code and Data

I updated ctn_scripts\channelFramebuilderConfigFileCreator.py to work with the new format of modbus hosting through docker (and cleaned it a bit). Also, from now on, C3CTN.ini will stay in the ctn_scripts repo to have version control.

I have run this once and followed instructions from CTN:2014 to restart frambuilder daqd process so that all new channels are logged as well.

Utilizing the fact that the heater stopped last Friday, I fitted the day to extract out a time constant for cooling down of the Vacuum Can through the present insulation. Attached is the fit. The time constant has come out to 2.298 +/- 0.001 hr.

Code and Data

We need to switch out normal flat-faced beam dumps with triangular cavity beam dumps in all places where they are not present. Following is a summary of beam dump status

Total Normal Beam Dumps behind PMCs: 12

There's an error here. The factor of 2 should not be there. Correct equation would be:

as mentioned in the quoted post CTN:1874 as well.

I have added these parameters to this wiki page.

Present understanding

• CTN:2035 was the last measurement of cavity shield heater resistances. These were reported as 85.6 Ohm and 156.8 Ohm.
• So Andrew, undestandably, configured the EPICs channel such that to put in 1 W power on the south heater, more current was driven through it in comparison to North heater.
• This should have worked well, but over the past year atleast, I have been noticing that south heater is much more effective than the north one.

My hypothesis

• I remeasured the resistances and they came almost same: South 88.4 Ohm and North was 159.7 Ohm.
• It could have been the case that North side was some parasitic resistance (due to bad connection with the heater) in series, increasing its effective resistance to 159.7 Ohm.
• This would mean that the heating part of the resistance is still almost same as South, but because we sense it larger, we send less current on this coil.
• I assume Tara or whoever put on these heaters, they made sure the length of the wires were almost same, so it is a fairly good assumption that the heating part of resistance is same.
• This also matches with the observation. North side is less effective in heating, because we send less current to it.

Changes made today

• I changed the dB files for the EPICs channels, so that same 88.4 Ohm resistance is assumed for both North and South heaters.
• From the performance so far, and looking at the second derivative of the beatnote signal, I feel the heaters are more balanced now.
• This should help the PID as the actuation is not biased now.
• I have made the hard actuation limits same on both ends of PID at 1.1 W.
• We might need to retune the PID to get new PID constants.

Over the weekend, I ran Relay Tuning method for the PID of beatnote frequency control. After CTN:2426 this needed to be done to fix the PID constants to appropriate value. The results of the tuning were:

Critical period Tc = 45.900000000000006
Critical gain Kc = 18.382414309527164
Suggested kp, ki, kd are 3.676482861905433, 0.16019533167343933, 56.25018778715313

RXA: Wah!  precision help here

The relay amplitude was set to 0.5 W and I could see very good sustained oscillations which the code used to get above calculated values.

Testing performance

I tested the performance of PID today. Attached is the convergence of beatnote frequency, which happened in about 20 minutes only to 40 kHz offset value. After that point, the proportional gain of the PID is so high, that the actuator response essentially copies the fluctuations in the beatnote frequency itself. So no more stabilization happens. The integral constant is very low (I think it is required for quick convergence with no overshoot), so to travel this 40 kHz distance, it will probably take hours. But that's fine with us as our photodetectors work well enough with this offset too.

If you see the second plot, the beatnote did not drift beyond +/- 2kHz for over 40 min. I want to see if tonights beatnote will get any better due to this good stabilization.

Code And Data

For the convenience of others, I'm summarizing the open questions I asked on elog in December. Comments on the posts, advice or answers to my questions would be nice.

• CTN:2492 Why are output powers of these lasers much lower than rated power when diode current is maximum? And why do I see a maxima in South Laser Power when diode current is increased, shouldn't it just increase with diode current monotonically?
• CTN:2495 Comments on beatnote noise differences with different laser power and modulation depth. Can I infer some good choice of laser power and modulation index from this? Suggestions for more tests on this line?
• CTN:2496 Rana asked for the latest available photos of FSS RFPDS. We want to add an active notch in the final RF amplifier stage.
• CTN:2497 There is indeed actual DC offsets at the output of FSS RFPDs RF out. Please cross-verify my measurement method and does this mean the MAX4107s are busted. Should I replace them?
• CTN:2499 Time series measurement of the signal before and after the summing stage in FSS on Northside. There is significant leftover 1-Omega frequency even after the elliptical filter. I think I need to make the input end lossy to absorb back reflections from the elliptical filter. Need permission to modify the circuit and test if this helps.
• CTN:2501 There is a logged event of South Laser losing about 20% of its output power with the same diode current. Is this laser dying? What is happening?
• CTN:2505 As instructed, I have taken transfer functions through FSS from PZT path and EOm path to RIN before and after the PMC. I need validation on method used. My conclusion is the noise in FSS is due to RIN and not the other way round (FSS causing RIN).  I tried taking an OLTF of the PMC loop but the NPMC Loop unlocks as soon as I connect the source port of AG4395A to an excitation port in a summing stage. So I've been unable to verify the source of this RIN yet, but previous measurement (CTN:2502) suggests it is PMC.

HAPPY HOLIDAYS

I set up Red Pitaya, Wenzel Crystal, and Moku at my apartment and took frequency noise measurements of Red Pitaya and Wenzel Crystal with Moku.

Method:

• Wenzel Crystal was powered on for more than 5 hours when the data was taken and has an output of roughly 24483493 Hz. This was fed to Input 2 of Moku with a 10dB attenuator at front.
• Red pitaya was on signal generator mode set to 244833644 Hz with 410 mV amplitude. This was fed to Input 1 of Moku.
• Measurement files RedPitayaAndWenzelCrystalFreqTS_20201002_163902* were taken with 10 kHz PLL bandwidth for 40 seconds at 125 kHz sampling rate. So the noise values are trustworthy upto 10 kHz only.
• Measurement files RedPitayaAndWenzelCrystalFreqTS_20201002_165417* were taken with 2.5 kHz PLL bandwidth for 400 seconds at 15.625 kHz sampling rate. So the noise values are trustworthy upto 2.5 kHz only.
• Measurement MokuSelfFreqNoiseLongCablePhasemeterData_20190617_180030_ASD.txt was taken by feeding the output of Moku signal generator to its own phase meter through a long cable. Measurement details can be found at CTN:2357.
• All measurement files have headers to indicate any other parameter about the measurement.

Plots:

The plots in RedPitayaAndWenzelCrystalNoiseComp.pdf show the comparison of frequency noise of Red Pitaya and Wenzel Crystal measured with different bandwidths. Last two plots show all measurements at once where the last plot is shown for phase noise with integrated rms noise also plotted as dashed curves.

Large time-series data files are stored here: https://drive.google.com/drive/folders/1Y1JndCos8-cW4TQETRNVNybFcZhrVUCz?usp=sharing

Attachment 2 contains the calculated ASD data.

Update Thu Oct 22 21:47:21 2020

Attachment 3: Moku phasemeter block diagram sent to me by Liquid Instruments folks.

Measurement and estimation method:

• 125N-1064 Thermal continuous tuning coefficient is 5 GHz/V
• The south cavity is locked with nominal settings with slow PID switched on.
• The cavity was first allowed to equilibrate at the nominal setpoint of cavity heater currents of 0.5 W common power and -0.09358 W Differential power.
• After more than 9 hours, the cavity heaters are switched off and the cavities are allowed to reach equilibrium with the vacuum can.
• The slow voltage control of the south cavity moves slowly in response to the temperature change of the cavity.
• Cavity frequency change to length change factor is  m/Hz.
• Cavity spacer is made out of fused silica whose coefficient of expansion is  [from Accuratus SiO2 datasheet]
• Therefore, NPRO temperature tuning slow voltage to cavity temperature conversion factor is:

• After waiting for 60 hours, the cavity finally cooled down to equilibrium with the vacuum can. The out-of-loop temperature of the vacuum can at this point is used as the equilibrium temperature of the cold cavity.
• The voltage change in slow voltage control of south laser from this point to setpoint is used to estimate the cavity temperature at beatnote measurement which came out to be around 37 degrees Celcius. I'm taking a generous uncertainty of  during noise budget calculations to account for miscalibration of the vacuum can temperature sensor and other errors in this method.
• The noise budget calculation was updated, Bayesian inference updated and the results in the paper draft have been updated.

Code

I transferred two Gold Box RFPDs labeled SN002 and SN004 (both resonant at 14.75 MHz) to 40m. I handed them to Gautam on Oct 22, 2020. This elog post is late. The last measurement of their transimpedance was at CTN/2232.

[Anchal, Paco]

CTN was raided today afternoon between 2 pm and 3 pm by 40m tribes. They have taken away precious Acromag units which are a very scarce resource these days. Following units were taken (Attachment 1):

• 1 XT1111 from blue cabinet.
• 4 XT1221 which were used at following places (see network):
  • |10.0.1.42  | 00:01:C3:00:98:59  | CTN Lab  | Acromag XT1221: 8-Channel Differential Analog Voltage Input Module  (CTN Slow controls)|
  • |10.0.1.50  | ?  | CTN Lab  | Acromag XT1221 8-Channel Differential Analog Voltage Input Module (Temperature Sensor monitor channels)  |
  • | 10.0.1.46 | 00:01:C3:00:98:55  | CTN Lab  | Acromag XT1221: 8-Channel Differential Analog Voltage Input Module  (PMC North remote controls)|
  • | 10.0.1.48  | 00:01:C3:01:12:FF  | CTN Lab  | Acromag XT1221: 8-Channel Differential Analog Voltage Input Module  (PMC South remote controls)|

3 rack mount units were affected:

CTN Slow Controls chassis:

• 2 XT1221 were removed from here. These can be installed back if Acromags become available and we need this experiment again
• 1 XT1541 is still mounted on this chassis.

PMC Servo Card Chassis:

• 1 XT1221 was removed from each servo card chassis (see attachment 2(North) -3 (South)).
• These chassis are otherwise functional and one can repopulate the XT1221 to make them function again (see CTN/2248 for instructions).

All these units are stored in the flowbench side wire rack (see attachment 4).

I followed the analysis of this recently published paper Jan Meyer et al 2022 Class. Quantum Grav. 39 135001 to calculate the birefringence noise in the CTN experiment. Interestingly, the contribution from birefringence noise after my first attempt at this calculation looks very close to what we were calculating as coating thermo-refractive noise before. If this were true, our experiment would have seen it much before. In fact, we wouldn't have seen thermo-optic cancellation as Tara experimentally verified here. So something is missing

What is birefringence noise?

After going through some literature and reading properly Meyer et al, I have the following understanding of the birefringence noise (and why it is called so).

• The temperature fluctuations cause length fluctuations in the coating layers (through the coefficient of thermal expansion)
• The length fluctuations cause stress fluctuations in the coating layers (through Young's modulus Y).
• The stress fluctuations get converted into refractive index fluctuations through the photoelastic effect (through photoelastic tensor)
• The photoelastic tensor for cubic crystals like GaAs has 3 independent values, P11, P12 and P44. (Section 12: Table 1. Elasto-Optic Coefficients: Cubic Crystals (43m, 432, m3m))
• This induces refractive index fluctuations that are different for the fast and slow axes. The difference between the two fluctuations causes a phase shift in reflected light from each layer. That's why this can be birefringence noise. In an unstressed isotropic material, this pathway should not exist.

Is this different from thermo-refractive noise?

This is a question I am still not sure how to answer. My understanding is that the common mode change in refractive indices of both axes drives the thermo-refractive noise. This means I should be able to derive the coefficient of thermo-refraction using the same formalism.

Calculation:

Both thermo-refractive noise and thermo-photoelastic noise show up as dn/dT terms in the thermo-optic noise summation, just through different physical processes. This could mean that experimentally measured coefficients of thermo-refraction already include birefringent contribution if any. In my calculations for the plots presented here, I got the following values of the two coefficients:

Coefficient of thermo-refraction (Effective for coating): 8.289e-05

Coefficient of thermo-photoelastic effect (Effective for coating, using Eq.11 of Meyer et al.): 8.290e-05

It was very surprising to me to see that both these coefficients came out to be within 1% of each other.

Because of this, when we add the noise sources coherently (since they are all driven by the same thermal fluctuations), the thermo-optic cancellation that we have experimentally proved does not work anymore. So something must be wrong with my calculation.

Possible explanations:

• Calculaiton error in my code. I'll double check tomorrow.
• Somehow the thermorefractive noise already takes into account the birefringent noise, through the coefficient of thermo-refraciton that we use as seed in our thermo-refractive noise calculation. This would explain how the witnessed themo-optic cancellation was achieved.
• Meyer et al. is calculating birefringent noise for the substrate. Maybe the tensorial calculations are different for coatings.

I made a few changes in my calculations today, which changed the noise contribution of this photoelastic noise (coatTPE) to roughly half of the individual contribution from coating thermo-refractive (coatTR). If this was true, it would significantly affect thermo-optic optimization, although not totally destroying it. I admit there is an outcome bias in this statement, but this noise estimate fits very well with the noise floor measured by CTN lab.

Changes in the calculation:

I made two changes in total:

• I'm using original coefficients of thermal expansion for each layer instead of the "effective" coefficients used in calculations of thermo-optic noise as per Evans et al. PRD 78, 102003 (2008)
• I removed the use of young's modulus and the crystal's elasticity tensor.

So now, the noise calculation is as follows:

• The temperature fluctuations cause isotropic strain fluctuations in the coating layers related through coefficient of thermal expansion
  
• The strain fluctuations cause changes in the refractive index of the layers through photoelastic tensor
  
  In the last step above, I assumed isotropic bulk strain in the layers (which is expected for this cubic lattice), thus
  
• The product of the above two numbers give the coefficient of thermo-photoelastic effect as:
  
  I averaged this coefficient over all coating layers weighted by their thicknesses.
• The noise contribution comes same as coatTR term as they both are channels causing dn/dT.

Notes:

• The above calculation does not take into account any birefringence in the layers that could be caused by this effect. In fact, the cubic crystal symmetry of GaAs does not allow for birefringence to occur in usual formalism and the only way it could happen is due to a large strain in one direction breaking the symmetries. Thus, I would not call this noise "birefringence noise", but it is a credible noise source in it's own right.
• Note that the themo-optic cancellation is only partially happening now, but the thermo-optic noise is still much less than the simple quadrature sum of the noises. We can maybe check back our measurements in our previous paper if the measured photothermal transfer function allows this.
• Maybe this noise source is not perfectly coherent with coatTE and coatTR and needs to be added a bit differently.

About the plot:

• The trace marked "Coating Thermo-Optic" is a coherently summed noise of coatTR, coatTE, and coatTPE.
• The trace marked "Coating Thermo-elastic + Thermo-refractive" is what we previously used to calculate as thermo-optic noise.
• "Measured Beat" is the best measurement we made and is a median over 50 lowest noise measurements made in June of 2020.
• "Coating Brownian" trace is calculated using bulk loss angle value of 4.878e-5 which was measured by Penn et al. in indirect measurement.

I think we need to regroup and discuss this further.

Interesting.

The obvious go to measurment here would be two-lasers-one-cavity to measure the residual between the two polarisaiton modes of one of the cavities. Is the experiment in a state where this could be done easily?

If I recall correctly Tara had this set up with an optical circulator on the input side which Antonio and I switched to linear polarisasion with Faraday isolator.  The mode splitting of the AlGaAs coatings would take care of only selecting one polarisation mode, but is it posisble that the latter measurments sampled a different polarisation to the original thermo-optic measurment? Just a thought.

The photothermal transfer function measurement made back in 2014 showed some cancellation of thermo-optic noise, but there were some irregularities with the modelled transfer function even back then. Here in attachment 1, I have plotted the measured photothermal transfer function, along with the estimated transfer function with and without adding a term for thermal photoelastic (TPE) channel.

Notes:

• The estimated transfer function without TPE (as was estimated back then) does match well with the measured transfer function on the south cavity below 200 Hz.
• However, the north cavity measurement did not match well.
• The estimated transfer function with TPE (green) is in between south and north measurements at least in magnitude above 200 Hz.
• However, the phase of estimated transfer functions (with or without TPE) do not match well with any of the measurements. This phase discrepancy is worrisome.
• Looking at these estimated transfer functions and measured transfer functions, which model do you think explains the measured data better?

Updated noise budget:

I was wondering if photothermal noise would get amplified due to the TPE effect. We were not using a measured photothermal transfer function in our noise budget for this noise contribution and relied on a theoretical model instead. For comparison, I added noise traces for three cases, Estimated photothermal noise with and without PTE, and photothermal noise using measured TF. In all these cases though, the ISS in the experiment suppressed RIN enough that photothermal noise did not matter to beatnote frequency noise.

Not easily, but it is doable if we resurrect the south path only. I estimate ~1 month of work for that if things go fine.

With circularly polarized light, Tara could be addressing any of the two possible resonances, with only effect of suffering in modematching with the cavity. So it should be a 50/50 chance that they measured it in a different polarization. However, the nature of thermal photoelastic measurement is same in both polarizations. The photoelastic tensor for GaAs (cubic symmetry), in theroy, does not create birefringence, or afect different polarizations differently. The source of birefringence in these coatings is not known.

Martin Fejer recently gave two talks in a coatings workshop where he showed calculations regarding the thermal photoelastic channel. I have not been able to under the logic behind some of the calculations yet, nevertheless, I used his formulas for our coatings to get an alternative idea of this noise coupling.

Major difference

• Fejer argues that free body thermal expansion does not generate any strain, and it is only when the substrate is present to counteract with it, that such strain is generated.
• Hence, the calculation goes as: thermal expansion -> stress in presence of substrate -> strain -> photoelastic effect.
• So instead of the simple contribution for photoelastic tensor and thermal expansion that I take, the term is:
  
• This gives an effective (averaged with layer thickness weighting) coefficient of thermal photoelasticity of 1.45e-5 K^-1 instead of 4.30e-5 K^-1 from my calculations. That's a reduction by a factor of roughly 3.

Updates

• Attached is the photothermal transfer function calculated with TPE contribution as calculated by Fejer. This makes the situation bit more messy on what to trust.
• I updated the noise budget with two new noise traces, the thermo-photoelastic contribution as calculated by Fejer and the total thermo-optic noise as calculated by Fejer.

I just received more calculation notes of Fejer (through Yuta) which I'll study and try to make more sense of this calculation. It also contains the calculations of sough-after birefringence noise.. But in his presentation as well, he stated that birefringence noise is not sourced through termperature fluctuations and is not part of thermo-optic noise (something I didn't understand again).

Rueben from Technical Safety Services installed and calibrated an Apex 1000 airflow monitor for the fume hood in CTN. Its power supply should remain plugged in to the outlet directly below the unit. Attachment 1 is the testing certificate. We can contact Shelley in H&S tomorrow to receive their report on the work.

in order to improve the stability of the chamber temperature the current plan is to add a heater and insulation for the second chamber. room temperature changes were about 2K_pp over the last couple of days. I already ordered flexible insulating foam for the chamber (the round parts). What we need is one or more heaters. We could somehow add half of the original heater to that chamber but i would like to go for a more final solution as we need one for the other chamber in the ATF as well. The plan is to buy standard heaters with adhesive backside and stick them to the chamber.  Price is about $70 for a 10"x10" heater (MINCO). The chamber surface is about 22"x25" in total, cut into smaller areas by the 4 vaccum tubes and 2 legs. I think we can cover most of it with a total amount of 4 to 6 heaters of different sizes.

I think its important to think of a good solution, since we may want to retrofit some other chambers.

For the electronics to drive the heater, let's make sure not to use the power supply solution that is in use now in LIGO and at the 40m. We should make sure to make the design such that the residual temperature noise from the heater is below what we expect for coating thermal noise, assuming we use Fused Silica spacer of 1m length.

This should be quite easy in principle, especially with the radiative shields on the inside.

 What is a "good" solution for you? A custom-made heater fitting the whole thing like the ones at the sites? They are expensive and it will take several weeks/month  to get them. The only advantage i see is that you can remove them from the chamber but do we need this feature? The other heaters are standard parts and you just stick them to the chamber, so you have a good thermal contact to it. As we only have two of the "other" chambers with a different layout for the small CF flanges i think this is good enough for our tests. For a new super-cavity chamber we can choose a different design. I think it does not make a big difference in stability. The design of the insulation is more important..

Yeah, i'm currently thinking off designing a first prototype for such a low-noise driver. As i think we will use the DAQ for temp controll thats the only part we need (and the power supply for the supply, but we have one of those). The current heaters i want to use have enough heating power when used with up to 24V, which is a good value as easy to buy. The noise can be easy as low as a couple of 10nV/sqrt(Hz) with standard parts..