Baseline Study

From previous study, I found the largest uncertain in estimated NPE for each DOMs is from uncertainty in baseline estimation.

Tried in this page is that more systematic study of baseline using standard candle sample. Standard candle events includes both DOMs with large pulses and small pulses, it is good place to study for finding reasonable baseline estimation from realdata which may be different from MC as MC does not include baseline fluctuation.

Note that ATWD and FADC are however read out full which is different from EHE 9 string analysis sample. The effect from reduced bin especially for FADC will be considered later using BinReducer module applied on the real data.
Then obtained estimated NPE with reduced bin with REDUCED bins will be our scaler for event energy.
Another note is that we make use of the point that if ATWD baseline is incorrectly estimated by 1mV, this corresponds to the NPE values of
NPE_error = 1(mV)*3.3(ns)*128(bin)/43(ohm)/1.6(pC) = 6.1 pe
and for FADC
NPE_error = 1(mV)*25(ns)*256(bin)/43(ohm)/1.6(pC)=93 pe with full readout and
NPE_error = 1(mV)*25(ns)*50(bin)/43(ohm)/1.6(pC)=18 pe with current realdata default readout.

For a large pulse, the larger npe, the smaller the relative error from this mis-estimation.
As for the event-wise npe sum, ehe-event npe sum is mainly determined by those large pulse DOMs.

• A) zero
• B) Iteration
• C) Average of the lowest quarter bins
• D) Average of first or last 3 bins whichever gives smaller value

We know that selecting one of these options doesn't work good enough for SC events as it includes large and small pulses.
Also, ATWD and FADC expect different behavior because of the differences in time range, gain, and baseline shift properties.
Reason for option D) is that we know first 3 bin average for ATWD already contains a part of pulse. Thus a baseline tends to appear a little large. The last 3 bins we don't know if there is a pulse or not, sometime there are but sometime not. Comparing these two values reduce probability to have baseline which obtained from averaged of first or last bins including large entries.
But as we'll see later, for FADC, we don't have problem for this pre-pulse region. Thus for FADC we study only the average of the FIRST 3 bins.
This page studies what's the best combination.

Then as I will introduce later in this page, I compare the results with option E) the first 2 bin average.

• Skip to observation summary
• Skip to conclusion for ATWD baseline

At first let me show the plot of which x-axis is start time of the event and the y-axis is Nch. This plot show which run is 100% run. In the plots below 100% run defined as startUTCDaqTime_ larger than 26.95045*1e16 && startUTCDaqTime_ smaller than 26.95125*1e16 && Nch>160

ATWD - string inclusive

Obtained baselines from different options for different strings.
From the top, the closest to SC string (the same string) and the lower, the away from the string, thus the expected pulses or NPEs are decreased.

ATWD - DOM-wise for each strings

The same as above but as functions of DOM number

Typical Waveforms

Now I'd like to come back to typical waveforms for each string-doms to check what should be the baseline.

string-40, scaled to FADC time range From Left 1) DOM 18, 2)DOM 17, 3) DOM 25	string-40, scaled to ATWD time range From Left 1) DOM 18, 2)DOM 17, 3) DOM 25
string-39, scaled to FADC time range From Left 1) DOM 21, 2)DOM 20, 3) DOM 25	string-39, scaled to ATWD time range From Left 1) DOM 21, 2)DOM 20, 3) DOM 25
string-39-GDOMs, scaled to FADC time range From Left 1) DOM 10, 2)DOM 11, 3) DOM 16	string-39 GDOMs, the same as left different x-axis scale From Left 1) DOM 10, 2)DOM 11, 3) DOM 16
string-29, scaled to FADC time range From Left 1) DOM 22, 2)DOM 21, 3) DOM 16	string-29, scaled to ATWD time range From Left 1) DOM 22, 2)DOM 21, 3) DOM 16
string-21, scaled to FADC time range From Left 1) DOM 22, 2)DOM 21, 3) DOM 16	string-21, scaled to ATWD time range From Left 1) DOM 22, 2)DOM 21, 3) DOM 16, the same as left different x-axis scale

Finally estimated NPE from each baseline option

This can be compared by-eye with the waveforms.

String-40 From Left, baseline option A), B), C) and D)

String-39 From Left, baseline option A), B), C) and D)

String-29 From Left, baseline option A), B), C) and D)

String-21 From Left, baseline option A), B), C) and D)

First-or-Last option or just first option

However when I took a close look at each waveforms, now I don't see advantage on the option D) over the option E) which is just average of a first few bins, with existnace of undershoot.
Also generally there is not much pre-pulse flat region for ATWD. Here I compare First 2 bin average and either first or last 3 bin.

String-40 From Left, first 2bin ave. E) and D)

String-39 From Left, first 2bin ave. E) and D)

String-29 From Left, first 2bin ave. E) and D)

String-21 From Left, first 2bin ave. E) and D)

Difficult Waveforms

Waveforms with first or last 3 bin average gives less than negative 5mV to check the value obtained by the option is consistent with waveforms.
Turns out it may be real, generally it seems to be due to ATWD undershoot. However those waveforms shown below, 4 out of 9 plots, there is no pre-pulse flat region for FADC.
This is different from what we see in the other plots...
It seems this suggests that DOMLaunch time is late and what we see as baselines are under effect of undershoot. This gives a large negative baseline value.

Waveforms with first or last 3 bin average gives less than negative 5mV. to check the value obtained by the option is consistent with waveforms.

The same but scaled to FADC time range

Observation so far

For ATWD,

• For the small pulses, all the 3 options B), C) and D) gives similar values.
  
• However the option B) iteration, gives slightly larger baseline, this is reasonable because the option C) the average of the lower quarter bins, gives smaller value as it should be, and we consider the iteration procedure gives the best baseline for small pulses as studied in hardware calibration.
• There is a double peak structure in the ATWD baseline distribution at -0.4 ~ -0.2mV and at 0.8 ~ 1.0 mV. This may come from ATWD ping-pong channel selection.
• The most stable baseline estimator for from the largest pulse to the smallest pulses is option E) the first 2 bin average, with the assumption that ATWD baseline can be approximated as NPE independent.
  
• The other stable baseline option D) has some denger as it is more sensitive to undershoot.
  
• The option A), use of zerobaseline for ATWD, would result in error of about +6 ~ -3 pe.
  

Conclusion for ATWD

For ATWD,

1. Take option E) first 2 bin average.
2. if the value is smaller than -1mV, larger than 2mV, take option A) i.e., consider the baseline as 0mV
3. Then calculate NPE.
4. If the obtained baseline non-zero and NPE value is less than 20, use the option 2) the iteration method.

send your comments to: aya at hepburn.s.chiba-u.ac.jp