J. Kissel, O. Patane

The QOSEM and analog CDS team have been adjusting the analog whitening filter applied to the X, Y, and SUM signals of the QOSEM satamps; Oli has a nice summary in LHO:91998.

I wanted to compare the raw ADC voltage for the QOSEM signals under the most recent whitening configurations; 
    - the current whitening filter parameters ( {z:p} = {0.0144 : 2.89} [Hz], the so-called "1st modification") 
    - the previous filter parameters ( {z:p} = {0.263 : 2.89} [Hz], the so-called "2nd modification")

Here I attach the ASDs of the raw ADC voltage (comes in as ADC counts, and I've converted it in DTT to ADC volts using a gain of 40/2^16 [V/ct]) compared against the expected typical 16-bit ADC noise from T0900450 for the X DOF and the SUM.

Observations/Conclusions
    (1) Even with much less whitening, the X signals are still above the ADC noise floor where the sensor is actually measuring suspension motion. Good!
    (2) In the {z:p} = {0.0144 : 2.89} [Hz] filter configuration, the SUM signals used to sit a factor of 2-3x above the ADC noise floor at all frequencies. Unclear if that's because the SUM was ADC noise or real LED intensity noise (if that's what limits the SUM, or if that's the "signal" of the SUM). There are some differences in shape between 0.1 to 10 Hz from channel to channel, so my guess is that it's LED intensity noise (or, again, whatever's limiting the SUM, or whatever the actual "signal" is in the SUM).
    (3) In the {z:p} = {0.263 : 2.89} [Hz] filter configuration, the SUM signals are all identical in shape, falling as 1/f^(1/2), and -- somehow -- surpassing the ADC noise floor above 30 [Hz]. I don't understand this.
    (4) The F1 QOSEM SUM voltage is saturating the ADC constantly. As such, there's no amplitude spectral density, because the number 2^15 doesn't have noise. That stinks.

What next?

    (A) Without having as much knowledge about the QOSEM system as Tom, I'm trying to understand how to calibrate normalized spot position, s_X or s_Y, in [ct/ct = V/V = radians] into physical beam spot and thus flag displacement, x or y, in [meters] or [microns]. In LLO:81079 and LHO:90154 aLOGs, 4000 [ct/m] (or (1/4000) [m/ct] = 0.00025 [m/ct] = 250 [um/ct]) is tossed around "citing Tom Roocke" -- and these calibration gains are applied to the normalized sum, so the units should be [m / (ct/ct)] or [m/rad] or something like that. 

I want to understand that number so that we can reverse engineer adding the ADC noise floor to any QOSEM noise budgets. If I understand how to calibrate a QPD (like derived in, e.g. LHO:91210), then
 
       x = sqrt(pi/8) * w * s_{x}
            and
       y = sqrt(pi/8) * w * s_{y}

where  
        - sqrt(pi/8) is the "centered beam" approximation to 1/erf(sqrt(2)) from integrating the Gaussian beam, and
        - w is the beam spot radius at the lens surface

So we need to know the spot radius at the lens surface.
        
Then, we can propagate the noises from individual segments (i.e. ADC noise) into a QPD's normalized spot displacement units, if we know the whitened SUM's ASD, S, or the SUM's DC voltage, S_{DC} and the whitening filter frequency response, W, as I expect the conversion from ADC voltage noise is something like 
        
        n_ADC,X = n_ADC,Y = n_ADC * sqrt(pi/8) * w * sqrt(2) / (W * S_{DC})

where 
        - n_ADC is a single segment's ADC voltage, 
        - sqrt(pi/8) is the "centered beam" approximation to 1/erf(sqrt(2)) from integrating the Gaussian beam, 
        - w is the beam spot radius at the lens surface
        - sqrt(2) is the "centered beam" approximation to sqrt(2 + 4*s^2), with s as either the X or Y normalized spot position signal
        - W is the whitening filter (in [V/V]), and
        - S_{DC} is the DC ADC voltage

    We know the whitening filter response, and (except for F1 :-( ) we know S_{DC} in ADC [counts], so easy to convert to ADC [V]. We again, just need to know the beam spot radius.

    Hopefully Tom has this number in his design documentation.

    (B) We're still trying to understand why the QOSEM noise floor is so much worse than expected. Tom's ruled out a lot of noise sources, but I'd yet to see ADC noise on any of his noise budgets. So, if we can understand where the ADC noise floor lies with respect to the signal -- especially as we reduce the amount of whitening, then we can either rule out ADC noise as the issue or put it on the suspicion list. These plots show that the X signal is NOT limited by ADC noise, but there's definitely something confusing about the SUM signal. So this should be understood.