[Kevin, Rana, Koji]

I calculated the dark noise of POX and POY due to Johnson noise and voltage and current noise from the MAX4107 op-amp using nominal values for the circuit components found in their data sheets. I found that the dark noise should be approximately 15.5 nV/rtHz. The measured dark noise values are 18.35 nV/rtHz and 98.5 nV/rtHz for POX and POY respectively. The shot noise plots on the wiki have been updated to show these calculated dark noise sources.

The measured dark noise for POY is too high. I will look into the cause of this large noise. It is possible that the shot noise measurement for POY was bad so I will start by redoing the measurement.

  Calculation for the input mode cleaner

I have been working on the calculation for the input mode cleaner. I have come out with a new optical setup that will allow us increase the Gouy phase different between the WFS to 90 degrees. I use a la mode to calculate it. The a la mode solution :

   label            z (m)      type             parameters         
    -----            -----      ----             ----------         
    MC1                    0    flat mirror      none:            
    MC3               0.1753    flat mirror      none:            
    MC2              13.4587    curved mirror    ROC: 17.8700       
    Lens1            29.6300    lens             focalLength: 1.7183
    BS2              29.9475    flat mirror      none:            
    First Mirror     30.0237    flat mirror      none:            
    WFS1             30.2269    flat mirror      none:            
    Second Mirror    30.2650    flat mirror      none:            
    Third Mirror     30.5698    flat mirror      none:            
    Lens2            30.9885    lens             focalLength: 1     
    Fourth Mirror    31.0778    flat mirror      none:            
    Lens3            31.4604    lens             focalLength: 0.1000
    Fifth Mirror     31.5350    flat mirror      none:            
    Sixth Mirror     31.9414    flat mirror      none:            
    WFS2             31.9922    flat mirror      none:      

I attached a pictures how the new setup is supposed to look like. 

Can you please give us some more details on how this design was decided upon? What were the design considerations?

It would be nice to have a shorter path length for WFS2. What is the desired spot size on the WFS? How sensitive are they going to be to IMC input alignment? Are we still going to be recentering the WFS all the time?

Nic, Andres, and I discussed some more about the MC WFS project today. We want to shorten the proposed WFS2 path. Andres is going to explore moving the 2" diameter lens in coming up with layouts. We also want the WFS to face west so that we can see the diode face with an IR viewer easily and dump the reflected beams in the razor dumps.

We wondered about fixing the power levels and optical gain:

1. What is the MC modulations depth? What would happen if we increase it a little? Does anyone know how to set it? Will this help the MC frequency noise?
2. What is the max power on the WFS? I guess it should be set so that the power dissipation of the detector is less than 1 W with the MC unlocked. So P_diss = (100 V)*(I_tot), means that we should have less than 10 mA or ~50 mW when the MC is unlocked.
3. Another consideration is saturation. The RF signals are tiny, but maybe the DC will saturate if we use any more power. The quadrants are saturated when unlocked and ~200 mV locked. According to D990249, the DC gain in the head is 1000 V/A. The measured power levels going into the heads (w/ MC unlocked) are: P_WFS1 = 4.9 mW and P_WFS2 = 7.7 mW. We don't have control of the DC gain, but there is a 10x and 100x switch available inside the demod board (D980233). From these numbers, I figure that we're in the 100x position and so the effective DC gain between photocurrent and the DC readback voltages is 100 kOhm. Therefore, we are in no danger of optical or electronics saturation. And the unlocked photocurrent of ~40/100000=0.4 mA => 0.04 W heat generated in the diode, so we're OK to increase the power level by another factor of 2-4 if we want.
4.  We noticed that the ADC inputs are moving by ~50 counts out of 65000, so we're doing a really bad job of signal conditioning. This was previously noticed 6 years ago but we failed to follow up on it. Feh.

While checking this out, I converted the McWFS DC offsets script from csh to bash and committed it to the SVN. We need to remove the prefix 'feature' that Jamie has introduced to cdsutils so that we can use C1 again.

 I did the calculation, and I reduced the beam Path. In my calculation, I restricted the waist size at the WFSs to be between 1mm-2mm also the other parameter is that the Gouy Phase different between the WFSs have to be 90 degrees. I also try to minimize the amount of mirrors used. I found the Gouy phase to be 89.0622 degrees between the WFSs and the following table shows the solution that I got from a la mode:

  label                         z (m)                   type               parameters         
    -----                         -----                    ----                  ----------         
    MC1                    0                        flat mirror           none:            
    MC3                    0.1753               flat mirror           none:            
    MC2                   13.4587              curved mirror    ROC: 17.8700 (m)       
    Lens1                 28.8172              lens                   focalLength: 1.7183(m)
    BS2                    29.9475              flat mirror           none:            
    First Mirror         30.0237              flat mirror           none:            
    Lens3                 30.1253              lens                  focalLength: -0.100 (m)
    Lens2                 30.1635              lens                 focalLength: 0.1250(m)
    WFS1                 30.2269              flat mirror         none:            
    Second Mirror    30.2650              flat mirror         none:            
    Third Mirror       30.5698              flat mirror         none:            
    Lens4                30.8113              lens                  focalLength: -0.075 (m)
    WFS2                31.0778              flat mirror         none:            

In the first image attached below is the a la mode solution that show the waist size in the first WFS, and I used that solution to calculate the solution of the waist size for the second WFS, which is shown in figure 2. I photoshop a picture to illustrate how the new setup it supposed to look like. 

Skip to final thought ...

Kiwamu and I have set about measuring the contrast of the signal on the RF PD. We can only do this when the end green laser is locked to the cavity. This is because the green transmission through the cavity, when unlocked, is too low. Unfortunately, once we lock the green beam to the cavity, we can't keep the beatnote on the RF PD stable to within a few hundred Hz of DC (remember that the cavity is swinging around by a couple of FSRs). So we also lock the PSL to cavity.

At this point we're stuck because we can't get both of these beams resonant within the cavity AND have the frequency difference between them be less 1kHz - when the lasers are locked to the cavity, their frequencies are separated by an integer number of FSRs + a fixed frequency offset, f_offset, that is set by the phase difference on reflection from the coating between the two wavelengths (532nm and 1064nm). We can never get the frequency difference between the lasers to be less than this offset frequency AND still have them both locked to the cavity.

So our contrast measuring method will have to use the RF signal.

So this is our method. We know the incident power from each beam on the RF PD (see Kiwamu's elog entry here), but to recap,

P_green_PSL = 72 uW (as measured today)

P_green_XARM = 560 uW (as measured by Kiwamu last week).

The trans-impedance of the RF PD is 240 Ohms. We'll assume a responsitivity of 0.25 A/W. So, if the XARM transmission and PSL green beams are perfectly matched then the maximum value of the RF beat note should be:

RF_amplitude_max = 2* SQRT(P_green_PSL*P_green_XARM) * responsivity * transimpedance = 240*0.25*2*(72E-6*560E-6)^(1/2) (volts)

= 24 mV = -19.5 dBm (or 27.5dBm after the +47 dB from the two  ZFL-1000LN+ amplifiers - with +15V in - that protrude from the top of the PD)

The maximum RF strength of the beat-note that we measure is around -75 dBm (at the RF output of the PD). This means the contrast is down nearly 600x from optimal. Or it means something is broken.

Final thought: at the end of this procedure we found that the RF beat note amplitude would jump to a different and much higher amplitude state. This renders a lot of the above useless until we discover the cause.

The calendar tab now displays calendars with weeks that run from Sunday to Saturday (as opposed to Monday to Sunday). However, the frame on the left hand side of the main page still has 'incorrect' calendars.

                TP3 noise
noise in m/s = -------------------
                 10 * 802(V/(m/s))

Using the numbers from the sensing measurement, I calibrated the measured in-loop MICH spectrum from Tuesday night into free-running displacement noise. For convenience, I used the noise-budgeting utilities to make this plot, but I omitted all the technical noise curves as the coupling has probably changed and I did not measure these. The overall noise seems ~x3  higher everywhere from the best I had last year, but this is hardly surprising as I haven't optimized anything for low noise recently. To summarize:

• DRMI was locked using 1f error signals.
• MICH was controlled using AS55_Q.
• Main difference is that we have a little less (supposedly 10%) light on the AS55 PD now because of the AUX laser injection setup. But the AUX laser was shuttered.
• 1f LSC PDs (REFL11, REFL55 and AS55) had ADC whitening filters engaged in while this data was taken.
• ITM and BS coils were not de-whitened.

I will do a more thorough careful characterization and add in the technical noises in the coming days. The dominant uncertainty in the sensing matrix measurement, and hence this free-running noise spectrum, is that I haven't calibrated the actuators in a while.

[Yuta, Jenne, Koji]

We stabilized the Xarm using the ALS and took a spectrum of POX as our out of loop sensor.  We used the calibration from elog 6841 to go from counts to meters.

We find (see attached pdf) that the RMS is around 60pm, dominated by 1Hz motion.

In other, related, news, I took out the beam pipe connecting the AP and PSL tables and covered the holes with foil.  This makes it much easier and faster to get to the X beat setup for alignment.  Eventually we'll have to put it back, but while the AUX laser on the AP table is not being used for beating against the PSL it'll be nice to have it out of the way.

I calibrated the REFL signals to meters from counts.  The I-phase signals all line up very nicely, but the Q-phase signals do not at all.  I'm not sure what the deal is.

 I locked  the PRMI on sidebands, and drove the PRM.  I looked at the peak values at the drive frequency in the REFL signals, and used that as my "COUNTS" value for each PD. 

I know the PRM actuator calibration is 19.6e-9 (Hz/f)^2 m/ct , so if I plug in my drive frequency (564 Hz, with the notch in the PRC loop enabled), and multiply by my drive amplitude in counts, I know how many meters I am pushing the PRM.  Then, to get a meters per count calibration, I divide this calibration number (common for every PD) by the peak value in each PD, to get each signal's calibration.

As a side note, I also drove MICH, and tried to use this technique for the Q-phase calibrations, but neither calibration (using the PRCL drive nor the MICH drive) made the Q-phase signals line up at all.

At least for the I-phase signals, it's clear that REFL33 has more noise than REFL11 or REFL165, and that REFL55 has even more noise than REFL33. 

Here are the calibration values that I used:

We usually want to remove PRCL from the Q quadrature for each PD.
Therefore, you are not supposed to see any PRCL in Q assuming the tuning of the demod phases are perfect.
Of curse we are not perfect but close to this regime. Namely, the PRCL in Qs are JUNK.

In the condition where MICH is supressed by the servo, it is difficult to make all of the Qs line up because of the above PRCL junk.
But you shook MICH at a certain freq and the signal in each Q signal was calibrated such that the peak has the same height.
So the calibration should give you a correct sensing matrix.

If you tune the demod phases precisely and use less integrations for MICH, you might be able to see the residual MICH lines up on the Q plot.

 The goal of the measurements we made ( my previous 3 elogs) was to characterize the laser frequency thermal actuator that is a part of the FOL- PID loop.

For this we made indirect TF measurements for the thermal actuator by looking at the PZT response by 1)arm cavity( ETM ,ITM) displacement  and 2) temperature offset excitation. The goal was to do something like getting G1=TF3/TF1 and G2=TF3/TF2 and ultimately dividing G2/G1 to get TF2/TF1 with correct calibration. The final TFs obtained are the X and Y arm TFs for Laser frequency response vs temperature offset in(HZ/count). The calculations  in detail are:

Obtained    G1 = PZT response/ Temperature Offset (count/count): (in detail here )

Obtained    G2 = PZT response/  X and Y arm displacement( count/ count) : (in detail here)

Calibrated G2 to count/m ( in detail here)

Divided G2/G1 to get X and Y arm displacement/ Temperature Offset( m/ count) to get G3

Did these calculations:

dL/ L = dF /F

F = c/lambda ;Lambda = 532 nm  ; L = 

X arm length = 37.79 +/- 0.05 m

Y arm length = 37.81 +/- 0.01 m

TF: Laser Freq/ Temperature Offset = G3 *F/L       (HZ/Count)

The calibration coefficients for the ends  are :

X End:  [23.04 +/-  0.23 ]* 10^3  (HZ/Count)

Y End:    [18.71 +/-  0.2 ]* 10^3 (HZ/Count)

For the TFs of the temperature actuator on laser frequency I used ITMs for both the arms. The bode plots for the calibrated( HZ/Temp Count) are attached.

 For the X-Arm Thermal Actuator, I calculated the TFs at two different frequency ranges and combined the results where the coherence is high(>0.7). At 1 Hz the coherence was not as good as the other frequencies(due to the suspension resonance at 0.977 Hz).

The poles and zeroes are estimated after fitting this data using Matlab vectfit tool.The  graphs showing fit and measured values are attached.

Y arm Thermal Actuator:

5th order TF fitted: 

Gain: 9000

Zeroes:

z1 = -0.9799;

z2 = 2.1655; 

z3 = -2.9746- i * 3.7697

z4 = -2.9746+ i * 3.7697

z5 =  95.7703 + 0.0000i 

Poles:

p1 = -0.0985- i* -0.0845

p2 = -0.0985+ i* -0.0845

p3 = -0.6673- i* -0.7084

p4 = -0.6673+ i* -0.7084

p5 = -8.7979.

X-arm Thermal Actuator:

5th order TF fitted: 

Gain = 20

Zeroes:

z1= -305.7766

z2 =   -18.2774

 z3 =  -16.6167

 z4 =   -1.2486

 z5 =   28.1080

Poles:

p1  = -0.1311 - 0.1287i

p2 =  -0.1311 + 0.1287i

 p3  =  -8.3797 + 0.0000i

 p4 =  -4.0588 - 7.5613i

  p5 = -4.0588 + 7.5613i

I will use get the poles and zeroes from these fitted  bode plots and use it to build the PID loop.

To estimate in-loop MICH noise:

(a) Calibrate MICH_ERR:

1. Lock the arms for IR using POX11 and POY11.
2. Misalign the ETMs.
3. Obtain the average peak-to peak (bright to dark fringe) counts from the time series of AS55_Q_ERR. I measured this to be d = 6.358 counts.
4. This gives the calibration factor for AS55_Q_ERR [Calibration factor = 2*pi*d/1064/10^-9 = 3.7546x10^7 counts/m]

(b) In-loop MICH noise:

1. Lock MICH using AS55_Q.
2. Since LSC input matrix sets MICH_IN1 = 1* AS55_Q_ERR, the power spectrum measured using dtt and calibrated using the calibration factor from step 4 in (a) gives us the calibrated in-loop MICH noise.

The plot below shows the in-loop MICH noise and the dark noise (measured by closing the PSL shutter):

Compared with old measurements done by Keiko elog 6385 the noise levels are much better in the low frequency region below 100 Hz.
(No, no, no... this is not an apple-to-apple comparison: KA)

I calibrated noise spectrum of green lock.

1. Measurement of conversion factor of ADC input from V to ct:

As a preparation, first I measured a conversion factor at ADC input of C1;GCX1SLOW_SERVO1.

It was measured while the output of AI ch6 as the output of C1;GCX1SLOW_SERVO2 with 1Hz, 1000ct(2000ct_pp) was directly connected into AA ch7 as the input of C1;GCX1SLOW_SERVO1. Amplitude at the output at AI ch6 was 616mVpp measured by oscilloscope, and C1;GCX1SLOW_SERVO1_IN1 read as 971.9ct_pp. So the conversion factor is calculated as 6.338e-4[V/ct].

2. Injection of a calibration signal:

When Green laser was locked to cavity with fast PZT and slow thermal, I injected 100Hz, 1000ct EXC at ETMX ASL. The signal was measured at C1:GCX1SLOW_SERVO1_IN1 as 5.314ct_rms. It can be converted into 3.368e-3Vrms using above result, and then converted into 3368Hz_rms using PZT efficiency as 1MHz/V. This efficiency was obtained from Koji's knowledge, but he says that it might have 30% or higher error. If somebody get more accurate value, put it into the conversion process from V to Hz here.

3. Conversion;

Frequency of green f=c/532nm=5.635e14[Hz] is fluctuating with above 3368Hz_rms,so the fluctuation ratio is 3368/5.635=5.977e-12, and it corresponds to length fluctuation of 37.5m. So, cavity fluctuation will be 5.977e-12*37.5=2.241e-10m_rms by 100Hz, 1000ct EXC at ETMX ASL.

4. Results;

Finally, we knew 5.314ct corresponds to 3368Hz and 2.241e-10m, so conversion factor from ct to Hz and ct to m are ;

633.8[Hz/ct] @ C1:GCX1SLOW_SERVO1

4.217e-11[m/ct] @ C1:GCX1SLOW_SERVO1

5. Calibration:

You can measure green noise spectrum at C1;GCX1SLOW_SERVO1_IN1 during lock,  and mutiply above result to convert Hz or m.

This calibration is effective above corner frequency of slow and fast servo around 0.5Hz and UGF of fast servo around 4kHz.

I show an example of calibrated green noise.

Each color show different band-width. Of course this results of calibration cactor does not depend on band-width. Noise around 1.2Hz is 6e-8Hz/rHz. It sounds a bit too good by factor ~2. The VCO efficiency might be too small.

Note that there are several assumptions in this calibration;

1. TF from actual PZT voltage to PZT mon is assumed to be 1 in all frequency. Probably this is not a bad assumption because circuit diagram shows monitor point is extracted PZT voltage directly.

2. However above assumption is not correct if the input impedance of AI is low.

3. As I said, PZT efficiency of 1MHz/V might be wrong.

I also measured a TF from C1:SUS-ETMX_ALS_EXC to C1:GCX1SLOW_SERVO1_IN1. It is similar as calibration injection above but for wide frequency. This shows a clear line of f^-2 of suspension.

Files are located in /users/osamu/:20110127_Green_calibration.

Plan to calibrate single arm actuation strength

1. Lock single arm cavity (e.g. YARM)
2. Lock YAUX laser to arm cavity (actuation point is ETMY)
3. With the notch on the YARM loop filter (actually on ETMY),
4. Turn on cal line (e.g. DARM osc) to move ITMY; here the frequency is chosen to be away from 600 Hz (line harmonic) and from violin modes for ITMY (642 Hz). The lower value of 575.17 Hz was chosen to avoid demodulating noise peaks at 455 Hz and 700 Hz.
5. Get raw YALS beatnote (we chose the demod angle of -35 deg to minimize Q).

The analysis is as follows:

1. Get demodulated IQ timeseries for the duration of the locks before lowpass filter (C1:CAL-SENSMAT_DARM_BEATYF_I_DEMOD_I_IN1); we are also storing the raw beatnote if we want to do software demodulation.
2. Look at the allan deviation of I and Q to establish the timescale over which our measurement is dominated by statistical uncertainty -- after this time, the uncertainty is expected to be due to systematic error / drift. In this case as shown by Attachment #1 the time is around 60.6 seconds.
3. At this frequency and with 500 gain the ITMY coils should be actuating 7.32 pm of amplitude displacement.
4. The minimum allan deviation does indeed predict the statistical uncertainty limited rms if we look at the power spectra of the demodulated cal line over different time periods (Attachment #2), notice I lowpassed the raw timeseries.
5. I think the next step is to get the nominal calibration value and repeat the measurment for more than a single cal line.
6. Roughly from the deviation plot, our fractional beatnote deviation is a proxy for the calibration uncertainty. 1.15e-16 of beatnote stability should translate to a fractional displacement stability of ~4.57e-15 at 60 seconds; giving an ultimate statistical calibration uncertainty of 0.06% at this particular frequency when averaging for this long. It might be interesting to see a calibration frequency dependent allan deviation plot.

[Paco, Yuta]

Gains in DARM are corrected to make it more calibration friendly.

DARM error signals
 - 0.19 * POX11_I - 0.19 * POY11_I
 - 1 * AS55_Q
 - -0.455 * BHD_DIFF (needs to be checked if LO phase is different)

DARM gain:
 - C1:LSC-DARM_GAIN = 0.04 (it was 0.015 to have UGF of ~150 Hz)

Online calibration:
 - FM2 for C1:CAL-DARM_CINV was turned on, which is a calibration for AS55_Q in FPMI; 1 / (3.64e11 counts/m) = 2.747e-12 m/counts (see sensing matrix below; consistent with 40m/17369).
 - FM2 for C1:CAL-DARM_A was updated to 10.91e-9 (40m/16977).
 - C1:CAL-DARM_W_OUT will be our calibrated FPMI displacement in meters. This is correct with BHD_DIFF locking, if the BHD_DIFF is balanced with AS55_Q before DARM_IN1.

FPMI sensitivity:
 - Attached plot shows the sensitivity of FPMI with AS55_Q and BHD_DIFF, plotted together with their dark noise.
 - The sensisitivty was measured with calibration lines off and notches off, which removed the forest of lines we saw on Jan 11 (40m/17392).

FPMI sensing matrix:
 - Attached is a screenshot of uncalibrated sensing matrix MEDM screen. Audio demodulation phase for DARM was tuned to have stable sign.
 - The following is calibrated sensing matrix measured today with FPMI locked with AS55_Q. BH55 and BHD_DIFF have large uncertainties because LO_PHASE locking is not stable.

Sensing matrix with the following demodulation phases (counts/m)
{'AS55': -168.5, 'REFL55': 92.32, 'BH55': -110.0}
Sensors       DARM @307.88 Hz           CARM @309.21 Hz           MICH @311.1 Hz           LO1 @315.17 Hz           
AS55_I       (-3.28+/-0.90)e+11 [90]    (-0.05+/-2.53)e+11 [0]    (+0.47+/-2.14)e+10 [0]    (-0.06+/-1.76)e+09 [0]    
AS55_Q       (-3.64+/-0.08)e+11 [90]    (-0.09+/-8.30)e+10 [0]    (-0.28+/-2.24)e+09 [0]    (+0.12+/-1.16)e+08 [0]    
REFL55_I       (+0.07+/-1.24)e+12 [90]    (+3.32+/-0.06)e+12 [0]    (-0.01+/-1.39)e+11 [0]    (+0.00+/-1.12)e+09 [0]    
REFL55_Q       (-0.98+/-2.46)e+09 [90]    (-4.68+/-2.04)e+09 [0]    (+0.08+/-1.00)e+09 [0]    (+1.73+/-5.69)e+07 [0]    
BH55_I       (-6.84+/-2.47)e+11 [90]    (+0.43+/-2.32)e+11 [0]    (-0.33+/-6.21)e+10 [0]    (-2.51+/-8.09)e+09 [0]    
BH55_Q       (+5.68+/-1.57)e+11 [90]    (-0.17+/-2.52)e+11 [0]    (-0.46+/-4.39)e+10 [0]    (+0.73+/-5.01)e+09 [0]    
BHDC_DIFF       (-2.48+/-3.47)e+11 [90]    (-0.09+/-1.99)e+11 [0]    (+1.56+/-4.11)e+10 [0]    (-0.49+/-6.78)e+09 [0]    
BHDC_SUM       (-2.12+/-1.84)e+10 [90]    (+0.35+/-1.44)e+10 [0]    (-1.30+/-4.18)e+09 [0]    (-0.03+/-8.17)e+08 [0]    

Current status:
 - After locking FPMI BHD to get the FPMI sensitivity today, we are struggling to re-lock again. LO_PHASE locking is glitchy today for some reason. To be investigated.
 

The ultimate goal of characterizing the temperature actuator turned to be fruitful in obtaining the calibration values for ETMX and ETMY (Calibration of ITMs were done previously  here but not for ETM). In this process, I measured the PZT response by  displacing one of the test masses in the frequency range of 20 Hz and 900 Hz  and measured the transfer functions in counts/counts. 

ETMX = [12.27  x 10 ^-9/ f² ] m/count

ETMY = [14.17  x 10 ^-9/ f²] m/count

I calculated these calibration values from the measurements that we have taken( in detail : elog)  and did the following calculations: 

The measurements I made were :PZT count/ Actuator Count separately for all the test masses.

PZT count/ Actuator count = [PZT count/ arm cavity displacement(m) ]*[ displacement of a test mass(m) / Actuator Count]

For a same laser and assuming flat response of the PZT, the term [PZT count/ arm cavity displacement(m) ] remains for all the test masses.

The fitting was done on the gain plots of the PZT Response vs Test mass displacement and a function G * f ^-2 was fitted. The resulting G values were:

ETMX: 8.007* f ^-2 

ITMX: 3.067* f ^-2

ETMY :11.389* f ^-2

ITMY : 3.745* f ^-2

To calculate the calibration of ETMX:

 [PZT count/ Actuator count : ETMX ] / [ displacement of a test mass(m) / Actuator Count :ETMX] =  [PZT count/ Actuator count : ITMX ] / [ displacement of a test mass(m) / Actuator Count :ITMX]

putting the values from the above fitting and Kiwamu's elog,

the calibrated value was calculated to be [12.27 * 10^-9 /f^-2 ]m/count.

A similar calculation was done for ETMY.

The attached are the fitting plots for the measurements taken.

 Now using these and the previously measured calibrations, I will get the complete calibrated TF of the thermal actuator.

[Yuta, Manasa]

Measured actuator response between 50Hz and 200 Hz in (m/counts).

BS     = (20.7 +/- 0.1)    x 10 ^-9 / f²

ITMX = (4.70 +/- 0.02)  x 10 ^-9/ f²

ITMY = (4.66 +/- 0.02) x 10 ^-9/ f²

Actuator response differs by 30% for all the 3 mirrors from the previous measurements made by Kiwamu in 2011.

Calibration of BS, ITMX and ITMY actuators

We calibrated the actuators using the same technique as in Kiwamu's elog.

A) Measure MICH error

1. Locked Y-arm and X-arm looking at TRY and TRX.
2. Misaligned ETMs
3. Measured  MICH error using ASDC and AS55_Q err (MICH_OFFSET = 20 - to compensate for offset in AS_Qerr which exists even after resetting LSC offsets)

B) Open loop transfer function for MICH control

1. Measured the transfer function between C1:LSC-MICH_IN1 and C1:LSC-MICH_IN2 by exciting on  C1:LSC-MICH_EXC.
MICH filter modules used for measurements(0:1 , 2000:1, ELP50). ELP50 used so that actuation signals above 50 Hz are not suppressed.

C) Calibration of BS/ ITMX/ ITMY actuators

1. Measured transfer function between actuation channels on BS/ ITMX/ ITMY and C1:LSC-AS55_Q_ERR.

[ericq, gautam]

While trying to resolve the strange SRCL loop shape seen yesterday (which has been resolved, eric will elog about it later), we got a chance to put in the correct filters to the "CINV" branch in the C1CAL model for MICH, PRCL, and SRCL - so we have some calibrated spectra now (Attachment #1). The procedure followed was as follows:

1. Turn on the LO gain for the relevant channel (we used 50 for MICH and SRCL, 5 for PRCL)
2. Look at the power spectra of the outputs of the "A" and "CINV" filter banks - the former has some calibrated filters in place already (though I believe they have not accounted for everything).
3. Find the peak height at the LO excitation frequency for the two spectra, and calculate their ratio. Use this to install a gain filter in the CINV filter module for that channel. 
4. Look at the spectrum of the output of the "W" filter bank for that channel - the plot attached shows this information.

The final set of gains used were:

MICH: -247 dB

PRCL: -256 dB

SRCL: -212 dB

and the gain-only filters in the CINV filter banks are all called "DRMI1f".

Once we are able to lock the DRFPMI again, we can do the same for CARM and DARM as well...

I have completed the calibration of the demod board efficiencies.  Here is the schematic of the set-up.

The data is given below and the data-file is attached in several different formats.

ADC: 2¹⁶counts = 4V Hence, calibration of ADC is 2¹⁴counts/V.

Gain of the AA board, g1 = 0.1

GURALP

Sensitivity = 800 V/ms^-1

2¹⁴ counts/V x 800  V/ms^-1 = 13107200 counts/ms^-1 -----> 7.6294e-08 ms^-1/count

Gain, g2 = 10

Calibration = 7.6294e-08 ms^-1/count x g1 x g2 = 7.6294e-08 ms^-1/count

 STS

Sensitivity = 1500 V/ms^-1

2¹⁴ counts/V x 1500  V/ms^-1 = 24576000 counts/ms^-1 -----> 4.069e-08 ms^-1/count

Gain of the STS electronic breakout box, g3 = 10

Calibration = 4.069e-08 ms^-1/count x g1 x g3 = 4.069e-08 ms^-1/count

I'm pretty sure that don't have any ADC's with this gain. It should be +/- 10V for 16 bits. 

Jenne told us that the ADC was +/- 2V for 16 bits so our calibration is wrong. Since, the ADC is +/- 10V for 16 bits we need to change our calibration and now we can also use the purple STS breakout box.

 New calibration for Guralp:

ADC: 2¹⁶counts = 20V Hence, calibration of ADC is (2¹⁵x0.1) counts/V.

GURALP

Sensitivity = 800 V/ms^-1

(2¹⁵ x 0.1) counts/V x 800  V/ms^-1 = 2621440 counts/ms^-1 ----->  3.8147e-07 ms^-1/count

Calibration = 3.8147e-07 ms^-1/count

Using the above calibration we obtain the following plot:

When we compare this plot with the old plot (see here) we see that in our calibration, we have got a factor of 10 less than the old plot. We do not know the gain of the Guralp. If we assume this missing 10 factor to be the gain of Guralp then we can get the same calibration as the old plot. But is it correct to do so?

 We just checked with a function generator the calibration of the ADC. We set a square wave with amplitude 1V. We measured the voltage with the oscilloscope and we found on the data viewer that one volt is 3208 counts. That's what we expected (+/- 10V for 16bits) but now we are more sure.

Finally, we have found the correct calibration of Guralp and STS2 seismometers.

ADC: 2¹⁶counts = 20V Hence, calibration of ADC is 3.2768e+03 counts/V.

GURALP

Sensitivity of seismometer = 800 V/ms^-1

Gain of the guralp breakout box (reference elog entry) = 20

Calibration = 3.2768e+03 counts/V x 800  V/ms^-1 x 20 = 52428800 counts/ms^-1 -----> 1.9073e-08 ms^-1/count

STS

Sensitivity = 1500 V/ms^-1

Gain of the STS electronic breakout box = 10

Calibration = 3.2768e+03 counts/V x 1500  V/ms^-1 x 10 = 49152000 counts/ms^-1 -----> 2.0345e-08 ms^-1/count

I wanted to check that the calibration of the MC ASS lockins was sensible, before trusting them forevermore.

To measure the calibration, I took a 30sec average of C1:IOO-MC_ASS_LOCKIN(1-6)_I_OUT with no misalignment. 

Then step MC1 pitch by 10% (add 0.1 to the coil output gains).  Remeasure the lockin outputs.

2.63 / (Lockin1noStep - Lockin1withStep) = calibration.

Repeat, with Lockin2 = MC2 pit, lockin3 = MC3 pit, and lockins 4-6 are MC1-3 yaw.

The number 2.63 comes from: half the side of the square between all 4 magnets.  Since our offsets are in pitch and yaw, we want the distance between the line connecting the lower magnets and the center line of the optic, and similar for yaw.  Presumably if all of the magnets are in the correct place, this number is the same for all magnets.  The optics are 3 inches in diameter.  I assume that the center of each magnet is 0.9mm from the edge of the optic, since the magnets and dumbbells are 1.9mm in diameter. Actually, I should probably assume that they're farther than that from the edge of the optic, since the edge of the dumbbell ~touches the edge of the flat surface, but there's the bevel which is ~1mm wide, looking normal to the surface of the optic.  Anyhow, what I haven't done yet (planned for tomorrow...) is to figure out how well we need to know all of these numbers.

We shouldn't care more than ~100um, since the spots on the optics move by about that much anyway.

For now, I get the following #'s for the calibration:

Lockin1 = 7.83

Lockin2 = 9.29

Lockin3 = 8.06

Lockin4 = 8.21

Lockin5 = 10.15

Lockin6 = 6.39

The old values were:

C1:IOO-MC_ASS_LOCKIN1_SIG_GAIN = 7
C1:IOO-MC_ASS_LOCKIN2_SIG_GAIN = 9.6
C1:IOO-MC_ASS_LOCKIN3_SIG_GAIN = 8.3
C1:IOO-MC_ASS_LOCKIN4_SIG_GAIN = 7.8
C1:IOO-MC_ASS_LOCKIN5_SIG_GAIN = 9.5
C1:IOO-MC_ASS_LOCKIN6_SIG_GAIN = 8.5

The new values measured tonight are pretty far from the old values, so perhaps it is in fact useful to re-calibrate the lockins every time we try to measure the spot positions?

The AC response of the actuators on BS, ITMX and ITMY were re-measured by another technique.

Last time I estimated them by measuring the open-loop transfer functions, but this time the responses were measured in a more direct way.

The measured AC responses (60 Hz - 200 Hz) are :

      BS   = 1.643e-98 / f2  [m/counts] (corrected based on the plot below - Manasa)


     ITMX = 3.568e-9 / f2 [m/counts]

     ITMY = 3.542e-9 / f2 [m/counts]

Next : measurement of the PRM actuator response

(The technique) 

 This time a technique that Rana told me a week ago was used.

This technique allows us to directly measure the response of an actuator at high frequency without any loop corrections.

First of all, MICH has to be locked to keep MICH within the linear range of the error signal. So now MICH is a linear sensor to the mirror motions.

In the MICH control a steep low pass filter should be inserted in order to avoid unwanted effects from the control loop at the high frequencies.

For example I put a low pass filter composed of an elliptical filter whose cut-off frequency is at 50 Hz such that the control loop doesn't push the mirrors above the cut-off frequency.

Hence the error signal of MICH above 50 Hz directly corresponds to the motion of the mirrors including BS, ITMX and ITMY.

Taking a transfer function from an actuator to the MICH error signal directly gives the actuator response.

In my measurements MICH was locked by feeding the signal back to BS. The plot below is the expected open-loop transfer function for the MICH control.

You can see that the open loop TF suddenly drops above 50 Hz. The UGF was at about 20 Hz, confirmed by looking at the loop oscillation on DTT.

(Measurement)

 In the technique the error signal has to be calibrated to [m]. This time AS55_Q was used and calibrated based on a peak-to-peak measurement.

The peak to peak value in the MICH error signal was 8 counts, which corresponds to the sensor efficiency of 4.72e+07 [counts/m].

Then I took transfer functions from each suspension (i.e. C1:SUS-XXX_LSC_EXC) to the error signal at AS55_Q over a frequency range from 60 Hz to 200Hz.

For the transfer function measurements I ran the swept sine on DTT to get the data. Note that the PD whitening filters were on.

The plot below is the results of the measurements together with the fitting lines.

In the fitting I excluded the data pints at 60 Hz, because their coherence was low due to the power line noise.

 To calibrate the measured TFs and characterize the thermal actuator for the FOL loop, we [ Me, Eric Q, Koji ] made the TF measurements of PZT response by giving a  disturbance to the position of  each of X and Y arm ETM  and ITM.

In order to make reasonable conclusions, the measurements were done at frequencies greater than 20 Hz (assuming the PZT response to be flat till a few KHz), which is out of the  bandwidth of the control loops operating for other noises at low frequencies, so that we can get the response only( mainly) due to the disturbance of the masses. 

 For this measurement , a Sine sweep excitation was given as an input to one of the test mass and PZT actuation signal was monitored. The channels used for the measurement are: 

Input( Mirror displacement):

ITMX- C1:SUS-ITMX_LSC_EXC

ETMX- C1:SUS-ETMX_LSC_EXC

ITMY- C1:SUS-ITMY_LSC_EXC

ETMY- C1:SUS-ITMX_LSC_EXC

Output ( PZT Response):

C1:ALS-Y_SLOW_SERV_IN1

The units of the TF of these measurements are not calibrated  and are in count/count. For this I will use the ITMX and ITMY calibration values from Izumi's Elog. I will also make some calculations and post in the calibrations of ETMX and ETMY in a separate elog.

I am now estimating the calibrated Thermal Actuator TF and will estimate the location of poles and zeroes to build the PID loop. I will elog the final calibrated TFs in my next elog.

The attached are the Bode Plots  for ETM and ITM for X and Y arms.

With the same method as reported in elog 11785, I calibrated oplevs for ITMX/ETMX.

RESULTS 

According to this measurement, ratio of the calibration factor derived with this measurement (NEW) and the calibration factor for now (OLD), i.e. NEW/OLD was:   

ETMX_PIT: 4.470

ETMX_YAW: 2.5970

ITMX_PIT: (-)1.1102

ITMX_YAW: 1.8173

NOTE

The calibration factors of the oplevs for ETMY/ITMY are   NOT UPDATED YET. I updated on Dec 11, 2015

http://blogs.mathworks.com/loren/2007/12/11/making-pretty-graphs/

Let Loren help you make your Oplev data readable to humans.

I updated the figures. I think it's easier to read now.

Based on calibration measurement I have done (elog 11785, 11831), I updated calibration factors of oplevs on medm screen as follows. Not to change loop gain oplev servo, I also changed oplev servo gain.

C1:SUS-ETMX_OL_PIT_CALIB, C1:SUS-ETMX_OL_PIT_GAIN

(45.1,16) => (200,3.5)

C1:SUS-ETMX_OL_YAW_CALIB, C1:SUS-ETMX_OL_YAW_GAIN

(85.6,8) => (222,3.0) 

C1:SUS-ETMY_OL_PIT_CALIB, C1:SUS-ETMY_OL_PIT_GAIN

(26,-16) => (140,-3.0) 

C1:SUS-ETMY_OL_YAW_CALIB, C1:SUS-ETMY_OL_YAW_GAIN

(31,-21) => (143,-4.5) 

C1:SUS-ITMX_OL_PIT_CALIB, C1:SUS-ITMX_OL_PIT_GAIN

(110,8) => (122,7.2) 

C1:SUS-ITMX_OL_YAW_CALIB, C1:SUS-ITMX_OL_YAW_GAIN

(81,-11) => (147,-6) 

C1:SUS-ITMY_OL_PIT_CALIB, C1:SUS-ITMY_OL_PIT_GAIN

(159,15) => (239,10) 

C1:SUS-ITMY_OL_YAW_CALIB, C1:SUS-ITMY_OL_YAW_GAIN

(174,-21) => (226,-16) 

After making sure that the upper UGFs were properly in place, I saved these settings to the SDF files. Thanks Yutaro!

Based on elog 1403, I calibrated the oplevs for ITMY/ETMY.

Summary of this method is following:

We lock an arm, and slightly misalign one mirror of the arm. Then, the transmission of the arm starts to decrease quadratically as the misalign angle of the mirror changes. Here, how much the transmission decreases in terms of the misalign angle is determined by geometry of optics, so we can see how much the angle really changes from this quadratic curve.

RESULTS  

These are the relationship between misalign angles measured by oplev (the units are based on the calibration for now) and transmission power.

(I updated following figures on Nov 19 2015. You can find the figures I attached once here in the zipped folder attached.) 

According to this measurement, ratio of the calibration factor derived with this measurement (NEW) and the calibration factor for now (OLD), i.e. NEW/OLD was:  

ETMY_PIT: 5.0265  --->> 5.3922 (without an outlier; the outlier I removed is shown in the figure in zipped folder attached.)

ETMY_YAW: 4.6205

ITMY_PIT: 1.5010

ITMY_YAW: 1.2970

This results show that calibration of oplevs for ITMY is kind of OK, but that for ETMY is so BAD and the calibration factors should be updated.

NOTE

The calibration factors of the oplevs for ETMY/ITMY are   NOT UPDATED YET.  I updated on Dec 11, 2015

If these results are reliable, I will update them tomorrow.   

OMG. Please try to use larger fonts and PDF so that we can read the plots.

I'm not sure that these calibration measurements are reliable. I would feel better if Steve can confirm them using our low accuracy method of moving the QPD by 1 mm and doing trigonometry.

I'm sorry. I will be careful about that. And I updated the plots in elog 11785.

 In this morning, Steve and I looked at the ETMY table and we found that the measurement you suggested might interfere with other optics or detectors because of space constraint. So, before doing this measurement, I roughly estimated the calibration factors for ETMY oplev by using the rough value of the arm length of the optical lever and the beam width of the light just before the QPD.

How I got the arm length and the beam width:

I measured the length of the optical path between ETMY and the QPD. Then I measured the beam width with an iris to screen the beam. To get the beam width from the decrease of the power of the beam detected by QPD, I used this formula: .

Then I got:   (arm length) = 1.8 +/-0.2 m,    w= 0.56 +/- 0.5 mm.

How I estimated the calibration factors from these:

The calibration factors (such as C1:SUS-ETMY_OL_PIT_CALIB; (real angle) / (normalized output of QPDXorY)) can be calculated with: . Then, I got

,

though the calibration factors, C1:SUS-ETMY_OL_PIT_CALIB C1:SUS-ETMY_OL_YAW_CALIB, right now are 26.0 and 31.0, respectively. (If I express this in the same way as elog 11785, 5.0 and 4.2 for ETMY_PIT and ETMY_YAW, respectively. they are consistent with yesterday's results.) 

I believe that the calibration factors I estimated today are not different from the true values by a factor of 2 or something, so this estimation indicates that the oplev calibration measurements I did yesterday are reliable, at least for the oplev for ETMY. 

Kiwamu and Koji

Summary

We have visited GariLynn's lab to make a calibration of the metrology interferometer. 

The newly calibrated value is

RoC(SRMU01) = 153.3+/- 1.6 [m]

This is to be compared with the specification of 142m +/- 5m

Although the calibration deviation from the previous value was found to be 1.3%, it is far from explaining the curvature difference between the spec (142m) and the measured value.

Motivation

The previous measurements of the SRM curvatures showed larger RoCs by ~10% compared with the spec.

It can be caused by the mis-calibration of the pixel size of the CCD in the metrology interferometer.
In order to confirm the calibration value, an object with known dimension should be measured by the instrument.

Method

We've got a flat blank optic from "Advanced Thin Film" together with a metalic ring.
The ring has been attached on the blank optic with 3 fragments of a double sided tape.
The RoC of SRMU1 was also measured in order to obtain "the radius of curvature of the day".

The calibration process is as follows:

1. Measure the diameters of the ring by a caliper in advance to its attachment to the blank.
2. Determine the inner and outer diameter of the ring in the obtained image.
   Note that the obtained image is pre-calibrated by the default value given by the measurement program
     (i.e. 0.270194mm/pixel for horizontal)
3. Check the ratio of the diameters with the measured value by the caliper. Correct a systematic effect.
4. Compare the image measurement and the caliper measurement.

Results

1. The outer and inner diameters of 2.000" and 1.660" (measured by a caliper, error 0.005"). The ratio is 0.830+/-0.003.
2. The center and radius for the inner circle were estimated to be (79.7924, 91.6372) and 21.4025 [mm].
   The center and radius for the outer circle were estimated to be (79.6532, 91.6816) and 25.6925 [mm].
   The error would be ~0.01mm considering they sweep 500 pixels by the circle and the pixel size is 0.27mm. i.e. 0.27/Sqrt(500) ~ 0.01mm
3. Ratio of the inner and outer diameter is 0.8330 +/- 0.0005.
   The systematic error of x is given by solving (21.4025+x)/(25.6925-x)=0.83 ==> x = -0.042 +/- 0.043 [mm]. This is just a 0.2% correction.
   By correcting the above effect, we get (Rin, Rout) = (21.36 +/- 0.046, 25.74 +/- 0.047).
4. By comparing the result with the caliper measurement, we get calibration factor of 1.013 +/- 0.005.
   This means we measured "1mm" as "1.013mm". The scale was too small.
   We have got the calibration of 0.2737+/-0.0014 [mm/pixel].

Discussion

Because of the calibration error, we measured too long RoC. The same day, we measured the curvature of SRMU01 as 155.26 m.
The newly calibrated value is

RoC(SRMU01) = 153.3+/- 1.6 [m]

This is the value to be compared with the specification of 142m +/- 5m

 In order to estimate the amount of noise that the oplevs are injecting into the GW channel, we first need to calibrate oplev signals in terms of angular change in the optic. I said in my previous post that there wasn't a calibration factor for OSEM values to radians, but I found that Kakeru had estimated this in 2009 - see entry 1413. However, Kakeru found that this was quite a rough estimate, and that it didn't agree with his calibrated oplev values well. He does quote the 2V/mm calibration factor for the OSEM readings though - does anyone know the provenance of this factor? I searched for OSEM calibration and found nothing.

We don't need a high quality calibration for the optical levers. ~50% accuracy is fine.

For that you can use the OSEM calibration of ~1.7 V/mm (its less than 2 since the OSEMs have been degrading) or you can use the cavity power method that Kakeru used; it worked just fine. There's no benefit in trying for a 1% number for optical levers.

We should be able to connect to this station

Tested the Nikon batteries for the camera. they are supposed to be 7V batteries but they don't hold a charge. I confirmed this with multi-meter after charging for days. Ordered new ones Nikon EN-EL9