STATUS OF THE ABSORPTION LENGTH MEASUREMENT ANTARES collaboration meeting Clermont-Ferrand (France),...

STATUS OF THE STATUS OF THE ABSORPTION LENGTH ABSORPTION LENGTH

MEASUREMENT MEASUREMENT

STATUS OF THE STATUS OF THE ABSORPTION LENGTH ABSORPTION LENGTH

MEASUREMENT MEASUREMENT

ANTARES collaboration ANTARES collaboration meeting meeting

Clermont-Ferrand (France), Clermont-Ferrand (France), May 17th-20thMay 17th-20th

1H Yepes, JdD Zornoza, J Zuñiga, C Bigongiari, J Ruiz H Yepes, JdD Zornoza, J Zuñiga, C Bigongiari, J Ruiz IFIC (CSIC – Universidad de Valencia)IFIC (CSIC – Universidad de Valencia)

THE EXPERIMENTAL PROCEDURE (REMINDER)

NEW TREATMENT OF ERRORS: DATA FITTING

EXTRACTION OF ABSORPTION LENGTH

CONCLUSIONS AND OUTLOOK

OUTLINEOUTLINEOUTLINEOUTLINE

ANTARES collaboration meeting ANTARES collaboration meeting Clermont-Ferrand, May 17th-Clermont-Ferrand, May 17th-20th20th

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EXPONENTIAL FIT L

Rhitshits

signal eNRN

02

1. THE EXPERIMENTAL SETUP:

One single top LED of the lowest optical beacon in the line flashes to the upper storeys, then the signal hits can be plotted and fitted by means of an exponential function, once quality cuts are applied.

The collected hits are a convolution of:

Physics:

• Absorption length (Labs)

• Scattering (Lsca and = ())

Detector:

• OB – OM relative orientation

• OM efficiency

• ARS token ring dead time

• Charge resolution

To minimize the effects of the detector:

• Only OMs in the same line are considered.

• Consider only the region (Rmin, Rmax) where signal < spe but well above background

THE EXPERIMENTAL PROCEDURETHE EXPERIMENTAL PROCEDURETHE EXPERIMENTAL PROCEDURETHE EXPERIMENTAL PROCEDURE


F2

3

Nnoise

Tmax

Tmin

Nsignal

2. TIME DISTRIBUTION:• Determine the peak Gaussian fit

• Choose a fixed time window [Tmin, Tmax] and select the hits:

Tmin = Tpeak – 3Tmax = Tpeak + 1000 ns

• Calculate their overall charge Qhits and Nhits.

3. NOISE CONTRIBUTION:

• Fit a constant in the [-1000, -50] ns range (B level) and substract the noise contribution (Qnoise, Nnoise):

Nsignal = Nhits(tot)– Nnoise = Ntot – Blevel (Tmin - Tmax)

NOISE LEVEL



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4. CHARGE LOSSES:• Some hits are lost due to the electronic dead time from the readout of the ARSs. Effect related to Rmin.

• Consider only the region where the probability to get more than one photoelectron is negligible (i.e. < 1 %).

5. PMT EFFICIENCY CORRECTION BY NOISE:

• Assume that the Nnoise ~ PMT

• Normalize PMTs signal to their own noise (hits or charge):



PMTsignalnoise

referencenoise

signalsignal NN

NNN *

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6. NOISE FLUCTUATIONS:

• To avoid noise fluctuations at large distances, signal greater than the noise is required Maximum distance to fit Rmax.

7. MEASUREMENT OF ERRORS:

• The estimation of statistical and dispersion errors are being carefully studied for the data:

Each storey provides 3 intensity measurements. These measurements are not treated independently, correlated errors can be obtained. 8. LOW EFFICIENCY OMs CLEANING:

• Low efficiency OMs are removed. Checked from noise plots Compute hits projections, fit a Gaussian and consider only OMs between (+3, -3).

9. THE BACKGROUND “FLATNESS”:

• Efficiency correction by noise is affected by noise fluctuations along the line A “flat” level noise along the line required.



6

22dispstatT

• Then the variable

follows Student’s t distribution:

with ν = n–1 degrees of freedom

• Therefore the error is taken to be: σ = t ∙ s/√n

• In order to have 68.27% errors, the one-side tail of the cumulative Student function must be 84.13% and thus t= 1.32 (for n=3) or t=1.83 (for n=2).

• If only one OM in the storey do not use that storey in the fit.




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• Each storey provides 3 intensity measurements (3 OMs).

• Assume these measurements are independent and gaussian distributed (check this hypothesis later with results).

• Assign one signal intensity per storey computed as the average of the 3 OMs

– OM signal extraction as before: subtract background, correct by efficiency, discard bad OMs

• Compute error by means of Student’s t (this is the usual treatment for the estimation of the mean and standard deviation of a gaussian distribution when none of the two parameters are known):

n

ii

n

ii

xxn

s

xn

x

1

22

1

)(1

1

1

s

xt

2/)1(2 )/1()2/(

)2/)1(()(

ttf

NEW TREATMENT OF ERRORS:




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SOME NEW FIT EXAMPLES (t-STUDENT TEST):

• Some errors give low - high values for .

• ↓, 2 ↑, forces to fit for this point, deforming the tendency.

L2 L2L2

L12




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TRANSMISSION LENGTH RESULTS:

Blue UV

Blue

UV




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TRANSMISSION LENGTH RESULTS:

Blue UV

Blue

UV




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• The mean value of the distribution of the L errors from the fits shows a good agreement with the RMS of the transmission length distribution (Blue: 3.0m vs 2.4m, UV: 2.1 vs. 1.1):

= 470 nm = 400 nm




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Blue = 470 nm) Student’s t error values

Entries 29

L ± RMS[m] 55.1±3.0

Average σfit (RMS) [m] 2.4 (0.9)

Mean Prob (2) (RMS) 0.66

RMS Prob (2) 0.36

Entries with Prob (2) < 1% 1

UV ( = 400 nm) Student’s t error values

Entries 13

L ± RMS[m] 38.1±2.1

Mean σfit (RMS) [m] 1.1 (0.6)

Mean Prob (2) 0.61

RMS Prob (2) 0.31


• Reasonable fit probabilities

• Variability of L ~6% (RMS/L):

RMS of L in agreement with average σfit : 3.0 m vs 2.4 m

Change of L with time not much larger than statistical

• Somewhat high probabilities: cluster close to 1 and

• Mean Prob (2) = 0.66 (should be 0.5)

• RMS Prob (2)=0.36 (should be 1/√12=0.29)

• Good fit probabilities

• Variability of L around 6% (RMS/L):

RMS of L distribution in agreement with average σfit :2.1 m vs. 1.1 m

• Small cluster at high probabilities:

• Mean Prob (2) = 0.6 (should be 0.5)

• RMS Prob (2)=0.31 (should be 1/√12=0.29)

What errors would give a flat Prob (2) (assuming they are the same at all distances) for the blue runs?

Answer: 5% relative errors

FITTING TRANSMISSION LENGTH: RESULTS




EQUAL ERROR ASSIGNMENT FOR ALL THE EXPERIMENTAL POINTS (σ/x = 0.05):

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Blue UV

Blue

UV




EQUAL ERROR ASSIGNMENT FOR ALL THE EXPERIMENTAL POINTS (σ/x = 0.05):

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Blue UV

Blue

UV




• For an equal error assignment (5 %), once again good agreement with the RMS of the transmission length distribution:

= 470 nm = 400 nm

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Blue = 470 nm) Fixed 5% relative errors

Entries 29

L ± RMS[m] 54.5±2.4

Average σfit (RMS) [m] 1.9 (0.3)

Mean Prob (2) (RMS) 0.46

RMS Prob (2) 0.33


UV ( = 400 nm) Fixed 5% relative errors

Entries 14

L ± RMS[m] 37.1±1.2

Mean σfit (RMS) [m] 0.7 (0.1)

Mean Prob (2) 0.37

RMS Prob (2) 0.36


• Not a significant change in L (55.1 vs 54.5)

• Average σfit is slightly lower than RMS of distribution

(1.9 vs 2.4), but not much room for non-statistical variability

• Not a significant change in L (38.1 vs 37.1)

• Average σfit is slightly lower that RMS of distribution

(0.7 vs 1.2), but not much room for non-statistical variability

L(t-5%) < 1m

ΔR can be extracted from time distributions !!!

t

EXTRACTION OF ABSORPTION LENGTHEXTRACTION OF ABSORPTION LENGTH


SCATTERING CONTRIBUTION TO THE TRANSMISSION LENGTH (L) (“R technique”):• The effect of scattering is to increase the photon path length in ΔR on average.• Perform the exponential fit using (mean photon path), R + ΔR instead of R.

R

ΔR

R+ΔR

w direct wR c t t c t

• ΔR should be proportional to the scattering.• Exponential fit with R + ΔR will be more insensitive to scattering since the greater the scattering the greater the delay and viceversa, making the L parameter closer to the real absorption length.

L

RR

eIIR)(

02

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Parameterization of R for MC:

Extracting R from the time distributions gives a linear dependence of R+R on R, both for MC and data.

The values of the above slopes are then related to the Rayleigh scattering ().

MC simulations can give an idea about the scattering contribution, from the relationship between R + R and R: R + R = p0+p1*R (p depends on scattering)

Correlation between R and R+R

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Parameterization factor distributions



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Transmission length (L) dependence on scattering parameters, and scat (no corrected by R):

• L depends on scat,eff . Almost constant if scat,eff ↑ (parameterization is needed).

cos1scateff

scat

L-scat,eff (by



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• L is strongly correlated to scat . Low values of scat , gives low values for L. (same color->same ).

• L shows an anti-correlation with . High values of give low values of L (same color -> same scat).

SCATTERING EFFECTS ARE MOST REMARKABLE AND EVIDENT

L-scat (by ) L-(by scat)

Transmission length (L) dependence on scattering parameters, and scat (no corrected by R):



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L → constant if scat,eff ↑ (scat,eff > 150 m)

L-scat,eff (by L-scat,eff (by sca

cos1scateff

scat

cos1scateff

scat

Transmission length (L) dependence on scattering parameters, and scat (corrected by R):



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MC transmission length (L) plots for dependence on and scat (corrected by R):

• When L is corrected by R, there is not much dependence on the tested water parameters, except for extreme models.

• Intermediate values for scat (~50 m) and low values for (0.14), gives the nearest value for L to abs.

L-scat (by ) L-(by scat)



Parameterization constant (p1) as a function of scattering length and effective scattering length ( - scattering length):

• A dedicated study of the correct parameterization of R, is actually ongoing in order to reach the best estimation in MC and then to be implemented the technique for data .

• Parameterization constant “p1” is correlated to scat and then to scat,eff for different considered.

• For different scat, p1 has also a strong dependence to scat,eff .23

p1-scatp1-scat,eff (by scat)



L with R parameterization MCL without R correction MC

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New results of R technique for MC simulations:

• Fitting L to <R+R> seems to “recover” abs, with some small constant shift

• Some cross-overs in the p1 dependence on the input parameters seems to point out the need of more statistics (ongoing !).

• Results for data soon !!!

L(R-R+R) ~ 4 – 5 m

CONCLUSIONS AND OUTLOOKCONCLUSIONS AND OUTLOOKCONCLUSIONS AND OUTLOOKCONCLUSIONS AND OUTLOOK


DATA FITTING:

• New method based on averaging the OM signals of each storey and computing the error using the Student t distribution gives reasonable χ2 values both for blue and UV light.

• The “transmission length” is rather stable in time for both wavelengths and the RMS of its distribution is close to the average σfit , therefore there is not much room for the variation of L due to changes in the medium (at least for the type of runs we use, i.e. low background periods).

• There are a few cases of bad fits (due mostly to one single point with very small error) and a tendency towards too high probabilities (overestimate of errors). If the errors in all the storeys are fixed by hand to 5% we get a flatter Prob(χ2). In any case, the change in the computed transmission length is small (ΔL ≤ 1m).

• The stability in time and reproducibility of the transmission length (with different errors, for different lines, with different LEDs) gives confidence in the analysis. However, we will continue investigating possible systematic effects.

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CONCLUSIONS AND OUTLOOKCONCLUSIONS AND OUTLOOKCONCLUSIONS AND OUTLOOKCONCLUSIONS AND OUTLOOK


EXTRACTION OF ABSORPTION LENGTH:

• Assuming that most of the effect of the scattering length in the transmission length comes from the increased path length (“ΔR”) of photons, this additional path length can be extracted from the time distribution as a function of distance. A corrected transmission length can be computed inputting R+ ΔR in the fits (instead of R).

• The corrected value of scat does not depend strongly on the input water parameters, except for extreme models.

• New runs with other values of the input abs and more statistics are underway to check the stability of the method.

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BACKUP BACKUP SLIDESSLIDESBACKUP BACKUP SLIDESSLIDES

BACKUP SLIDESBACKUP SLIDESBACKUP SLIDESBACKUP SLIDES


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STUDENTS t DISTRIBUTION:

A

BACKUP SLIDESBACKUP SLIDESBACKUP SLIDESBACKUP SLIDES


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2 DISTRIBUTION:

A

STATUS OF THE ABSORPTION LENGTH MEASUREMENT ANTARES collaboration meeting Clermont-Ferrand (France),...

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