Difference between revisions of "Fiber Test Stand at JLAB"

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= Fiber Test Stand =
 
= Fiber Test Stand =
−
The purpose of the fiber test stand at JLAB is do determine the number of photo electrons produced by a minimum ionizing particle in a scintillating fiber at a distance of 200cm from the fiber end. The photon detector is a standard photo multiplier, in this case an XP2020. In addition the attenuation length of the scintillator can be determined measuring the light output at several positions along the fiber.
+
The purpose of the fiber test stand at JLAB is to determine the number of photo electrons produced by a minimum ionizing particle in a scintillating fiber at a distance of 200cm from the fiber end. The photon detector is a standard photo multiplier, in this case an XP2020. In addition the attenuation length of the scintillator can be determined measuring the light output at several positions along the fiber.
  
 
== Concept ==  
 
== Concept ==  
−
One end of the scintillation fiber is coupled to the photo cathode of a PMT (XP2020). For monitoring purposes a second fiber (light guide) is also coupled to the same PMT providing light from a blue LED. At a given distance from the PMT surface a collimated Strontium (Sr90) source is mounted above the scintillation fiber. Below the fiber and the Sr90 source a small trigger scintillation detector (TSD) is mounted to trigger on electrons from the Sr90 source. The data acquisition is triggered by TSD and the analog signals from both the XP2020 and the TSD are digitized as well as their timing. Simultaneously a trigger is generated for the LED light source to monitor the XP2020 PMT during the measurement.
+
One end of the scintillation fiber is coupled to the photo cathode of a PMT (XP2020). For monitoring purposes a second fiber (light guide) is also coupled to the same PMT providing light from a blue LED. At a given distance from the PMT surface a collimated Strontium (Sr90) source is mounted above the scintillation fiber. Below the fiber and the Sr90 source a small trigger scintillation detector (TSD) is mounted to trigger on electrons from the Sr90 source that pass through the fiber into the trigger scintillator. The data acquisition is triggered by TSD and the analog signals from both the XP2020 and the TSD are digitized as well as their timing. Simultaneously a trigger is generated for the LED light source to monitor the XP2020 PMT during the measurement.
  
 
== Electronic layout ==
 
== Electronic layout ==
−
A basic sketch of the NIM electronics layout is shown [[Media:fiber_test_electronics_setup.pdf|here]]. <br>The signal from the XP2020 PMT is first amplified by a factor of 10 and then connected to a linear FAN In/Out. The DC offset of the linear FAN In/Out is adjusted such that the true pedestal is above the built in pedestal of the V972N VME ADC, which is about 5pC total charge. This corresponds to about 15mV of negative DC offset for the used gate width. The analog signal is then connected to the ADC adjusted for timing. A second output of the linear FAN In/Out is connected to a discriminator the output of which is then connected to F1TDC. The trigger scintillator is also connected to a linear FAN In/Out. Also here the DC offset is adjusted to move the true pedestal of the signal above threshold in the ADC. The analog signal is also discriminated and one output connected to the trigger OR which is linked to the trigger interface TI in VME of the DAQ system. The second trigger of the system is the trigger for the blue LED for monitoring purposes. The rate of this can be adjusted using two Gate/Delay generators and is set to about 10 Hz during measurements. The trigger rate from the TSD caused by the electrons of the Sr90 source is also in the order of 10 Hz.
+
A basic sketch of the NIM electronics layout is shown [[Media:fiber_test_electronics_setup.pdf|here]]. <br>The signal from the XP2020 PMT is first amplified by a factor of 10 and then connected to a linear FAN In/Out. The DC offset of the linear FAN In/Out is adjusted such that the true pedestal is above the built in pedestal of the V792N VME ADC, which is about 5pC total charge. This corresponds to about 15mV of negative DC offset for the used gate width. The analog signal is then connected to the ADC adjusted for timing. A second output of the linear FAN In/Out is connected to a discriminator the output of which is then connected to F1TDC. The trigger scintillator is also connected to a linear FAN In/Out. Also here the DC offset is adjusted to move the true pedestal of the signal above threshold in the ADC. The analog signal is also discriminated and one output connected to the trigger OR which is linked to the trigger interface TI in VME of the DAQ system. The second trigger of the system is the trigger for the blue LED for monitoring purposes. The rate of this can be adjusted using two Gate/Delay generators and is set to about 10 Hz during measurements. The trigger rate from the TSD caused by the electrons of the Sr90 source is also in the order of 10 Hz.
 +
 
 +
ADC V792: 0-400pC range, 0.1pC/channel 4096 channels.
  
 
== Dark Box ==
 
== Dark Box ==
 
The detectors, scintillators and Sr90 source are currently located in an improvised dark box to protect the system for ambient light. Picture of the setup can be seen here as well and the fiber coupling to the PMT and the Sr90 source collimation:<br> [[Image:fiber_test_stand_darkbox.jpg|160px]] [[Image:fiber_coupling.jpg|160px]] [[Image:collimation.jpg|160px]] [[Image:sr_source.jpg|160px]]
 
The detectors, scintillators and Sr90 source are currently located in an improvised dark box to protect the system for ambient light. Picture of the setup can be seen here as well and the fiber coupling to the PMT and the Sr90 source collimation:<br> [[Image:fiber_test_stand_darkbox.jpg|160px]] [[Image:fiber_coupling.jpg|160px]] [[Image:collimation.jpg|160px]] [[Image:sr_source.jpg|160px]]
 +
 +
=== Sr90 collimation ===
 +
The Sr90 source is collimated by a piece of copper shown in the above picture. A schematic view is shown below. The scintillation fiber lies in a 1mm x 1mm groove of the copper collimator thereby being fixed in position. At the center of the copper piece a 0.5mm wide and 5mm long slit provides the collimation. The slit is in the center and parallel to the groove where the fiber is located.<br> [[Image:sr90_collimation.gif|160px]]
 +
<br> To illustrate the setup of the trigger scintillator with the collimated Sr90 source some pictures are shown here. First the full assembly with indicators to explain the individual components. The Trigger scintillator is located below the fiber and is readout by a Hamamatsu photo multiplier H3165-10. Above the trigger scintillator is small Aluminum platform for positioning the collimator. The collimator is a 5mm thick
 +
Copper piece with a 1mm groove to hold the fiber. The collimation of the electrons from the Sr90 is done by a 0.5mm wide and 5mm long slit
 +
at the center allowing the passage of electrons through the central part of the fiber.<br>
 +
[[Image:trigger_setup.gif|160px]] [[Image:assembly.gif|160px]] [[Image:platform.gif|160px]] [[Image:collimator.gif|160px]]<br>
 +
The second picture shows the front part of the XP2020 housing. There are two feed-through for the fibers. The left black tapped one is the fiber from the blue LED. The right is the fiber to be tested and has no black tape or other protective clading. The feed through itself is a screw with a whole drilled through its length to hold the fiber in place. THE FIBER IS PUSHED UP AGAINST THE PMT ENTRANCE WINDOW. THE COUPLING IS AIR ONLY. NO OPTICAL GREASE IS USED!
 +
The last two pictures show the collimator assembly and Sr90 source. A detailed description is given below.
  
 
== XP2020 PMT responses to blue LED ==  
 
== XP2020 PMT responses to blue LED ==  
−
The response of the XP2020 on the LED light is shown for two different LED intensities (Low Voltage settings) in the form of the ADC spectra. The fit is a Poisson distribution weighted sum of Gaussian distributions that are convoluted with the pedestal width and an exponential background.<br> [[Image:xp2020_led_response_2200V_A.gif|160px]] [[Image:xp2020_led_response_2200V_B.gif|160px]]<br> The HV of the XP2020 PMT is set at -2200V. The corresponding single photo electron peak position (fit parameter P1) is about 41 ADC channels corresponding to a gain of the PMT of 2.6*10^6. The fit parameter mu is the mean number of photo electrons from the Poisson distribution.
+
The response of the XP2020 on the LED light is shown for two different LED intensities (Low Voltage settings) in the form of the ADC spectra. The voltage divider used here for the XP2020 is a VD124K/T from Photonic (Type C divider). The fit is a Poisson distribution weighted sum of Gaussian distributions that are convoluted with the pedestal width and an exponential background.<br> [[Image:xp2020_led_response_2200V_A.gif|160px]] [[Image:xp2020_led_response_2200V_B.gif|160px]]<br> The HV of the XP2020 PMT is set at -2200V. The corresponding single photo electron peak position (fit parameter P1) is about 41 ADC channels corresponding to a gain of the PMT of 2.6*10^6. The fit parameter mu is the mean number of photo electrons from the Poisson distribution.
  
 
== Trigger Scintillator response ==
 
== Trigger Scintillator response ==
−
The ADC spectrum of the trigger scintillator using a H3165-10 PMT and a 10cm long, 10cm thick and 8mm wide scintillator bar is shown here<br> [[Image:trigger_scintillator_response.gif|160px]]
+
The ADC spectrum of the trigger scintillator using a H3165-10 PMT and a 10cm long, 1cm thick and 8mm wide scintillator bar is shown here<br> [[Image:trigger_scintillator_response.gif|160px]]
  
 
= The Fit Function =
 
= The Fit Function =
 
<math>F(x) = A\cdot\sum_{n=0}^{N}\frac{\mu^ne^-\mu}{n!}\cdot((1-w)G_n(x)+w\theta(x)I_{G_n \otimes E}(x))</math> <br>
 
<math>F(x) = A\cdot\sum_{n=0}^{N}\frac{\mu^ne^-\mu}{n!}\cdot((1-w)G_n(x)+w\theta(x)I_{G_n \otimes E}(x))</math> <br>
−
where <math>A</math> is the number of events, <math>G_n(x)</math> is the nth Gaussian convoluted with the pedestal-Gaussian and <math>I_{G_n \otimes E}(x)</math> is the nth Gaussian convoluted with and exponential background with <math>w</math> the probability of such an exponential background event occuring.
+
where <math>A</math> is the number of events, <math>G_n(x)</math> is the nth Gaussian convoluted with the pedestal-Gaussian and <math>I_{G_n \otimes E}(x)</math> is the nth Gaussian convoluted with and exponential background with <math>w</math> the probability of such an exponential background event occuring. The function <math>\theta(x)</math> is a step function being 0 for <math>x<P_n</math> and 1 for <math>x>P_n</math>.
  
−
<math> G_n(x) = \frac{1}{\sigma_n \sqrt{2\pi)} }e^{\frac{-(x-P_n)^2}{2 \sigma^2}}</math> with <math>P_n=P_0+n \cdot P_1</math> the ADC position of the nth Gaussian with width <math>\sigma_n=\sqrt{\sigma_0^2+n \cdot \sigma_n^2}</math>. The index 0 refers to the pedestal and n=1,2,... is the number of photo-electrons.
+
<math> G_n(x) = \frac{1}{\sigma_n \sqrt{2\pi)} }e^{\frac{-(x-P_n)^2}{2 \sigma^2}}</math> with <math>P_n=P_0+n \cdot P_1</math> the ADC position of the nth Gaussian with width <math>\sigma_n=\sqrt{\sigma_0^2+n \cdot \sigma_1^2}</math>. The index 0 refers to the pedestal and n=1,2,... is the number of photo-electrons.
  
 
<math>I_{G_n \otimes E}(x)=\frac{\alpha}{2}e^{-\alpha(x-P_n-\alpha \sigma_n^2)}\left[erf(\frac{|P_0-P_n-\alpha\sigma_n^2|}{\sigma_n\sqrt{2}}) + sign(x-P_n-\alpha \sigma_n^2)\cdot erf(\frac{|x-P_n-\alpha\sigma_n^2|}{\sigma_n\sqrt{2}})\right]</math> is the convolution of the nth Gaussian with the exponential background leading to a tail for each Gaussian on the right side of the peak.
 
<math>I_{G_n \otimes E}(x)=\frac{\alpha}{2}e^{-\alpha(x-P_n-\alpha \sigma_n^2)}\left[erf(\frac{|P_0-P_n-\alpha\sigma_n^2|}{\sigma_n\sqrt{2}}) + sign(x-P_n-\alpha \sigma_n^2)\cdot erf(\frac{|x-P_n-\alpha\sigma_n^2|}{\sigma_n\sqrt{2}})\right]</math> is the convolution of the nth Gaussian with the exponential background leading to a tail for each Gaussian on the right side of the peak.
 +
 +
<b>The Fit parameters are:</b>
 +
# <math>P_0</math> : pedestal position
 +
# <math>\sigma_0</math> : pedestal width (<b>FIXED</b> from fit to pedestal only)
 +
# <math>P_1</math> : single photo electron peak position
 +
# <math>\sigma_1</math> : single photo electron peak width
 +
# <math>\alpha</math> : exponential background
 +
# <math>w</math> : probability of exponential background
 +
# <math>\mu</math> : <b>MEAN NUMBER OF PHOTO ELECTRONS</b>
  
 
= Fiber types =
 
= Fiber types =
  
 
The following fibers have been tested:
 
The following fibers have been tested:
−
* Kuraray (MC=Multi-Clad)
+
* <b>Kuraray</b> (MC=Multi-Clad)
 
** Blue 81 MC lot:0801/103 <br>[[JLAB Fiber test results|Results]]:<br> The following plots show the PMT response to the Sr90 source positioned at 65cm, 165cm and 194cm from the photo cathode. In the pannels the value labled "mu" is the mean number of photo electrons detected by the PMT.<br> [[Image:kuraray_81MC_sr_65cm.gif|160px]] [[Image:kuraray_81MC_sr_165cm.gif|160px]] [[Image:kuraray_81MC_sr_194cm.gif|160px]]  
 
** Blue 81 MC lot:0801/103 <br>[[JLAB Fiber test results|Results]]:<br> The following plots show the PMT response to the Sr90 source positioned at 65cm, 165cm and 194cm from the photo cathode. In the pannels the value labled "mu" is the mean number of photo electrons detected by the PMT.<br> [[Image:kuraray_81MC_sr_65cm.gif|160px]] [[Image:kuraray_81MC_sr_165cm.gif|160px]] [[Image:kuraray_81MC_sr_194cm.gif|160px]]  
 
** Blue 78 MC lot:0801/104 <br>[[JLAB Fiber test results|Results]]:<br> Similar the following plots show the PMT response to the Sr90 source positioned at 61cm, 94cm and 194cm from the photo cathode. Again as above the value labled "mu" in the pannel is the mean number of photo electrons detected by the PMT.<br> [[Image:kuraray_78MC_sr_61cm.gif|160px]] [[Image:kuraray_78MC_sr_94cm.gif|160px]] [[Image:kuraray_78MC_sr_194cm.gif|160px]]
 
** Blue 78 MC lot:0801/104 <br>[[JLAB Fiber test results|Results]]:<br> Similar the following plots show the PMT response to the Sr90 source positioned at 61cm, 94cm and 194cm from the photo cathode. Again as above the value labled "mu" in the pannel is the mean number of photo electrons detected by the PMT.<br> [[Image:kuraray_78MC_sr_61cm.gif|160px]] [[Image:kuraray_78MC_sr_94cm.gif|160px]] [[Image:kuraray_78MC_sr_194cm.gif|160px]]
−
** Green 3HF MC lot:0801/105 <br>[[JLAB Fiber test results|Results]]
+
** Green 3HF MC lot:0801/105 <br>[[JLAB Fiber test results|Results]]:<br> As above, plots for the green fiber the Sr90 source positioned at 65cm, 165cm. <br> [[Image:kuraray_3HF_MC_sr_65cm.gif|160px]] [[Image:kuraray_3HF_MC_sr_165cm.gif|160px]]
 +
 
 +
*<b>Saint Gobain (aka Bicron)</b>
 +
** GREEN BCF20 #5 Set2 1/8<br> [[JLAB Fiber test results|Results]]:<br> This green fiber is about 200cm long and has been received in the latest batch in May 2008. The Sr90 source is put at 192cm and 100cm from the photo cathode of the PMT. The adc spectra are shown below. <br> [[Image:bcf20_number5_2007_sr_at_100cm.gif|160px]]  [[Image:bcf20_number5_2007_sr_at_192cm.gif|160px]]
 +
** GREEN BCF20 #7 Set2 3/8<br> [[JLAB Fiber test results|Results]]:<br> This green fiber is also about 200cm long and was received in May 2008. The fiber is not trait and actually rather wobbly after about 100cm till the end. The Sr source was positioned at 56cm, 100cm and 193cm from the end of the fiber touching the photo cathode of the XP2020 tube. <br> [[Image:bcf20_number7_2008_sr_at_56cm.gif|160px]] [[Image:bcf20_number7_2008_sr_at_100cm.gif|160px]] [[Image:bcf20_number7_2008_sr_at_193cm.gif|160px]]
 +
** GREEN BCF20 #620-MC-37 101796/18580 12/07/07<<br> [[JLAB Fiber test results|Results]]:<br> This green fiber is also about 200cm long and was received in Dec. 2007 batch of green and blue fibers. The Sr source was positioned at 59cm, 100cm and 193cm from the end of the fiber touching the photo cathode of the XP2020 tube. <br> [[Image:bcf20_620mc_37_2007_sr_at_59cm.gif|160px]] [[Image:bcf20_620mc_37_2007_sr_at_100cm.gif|160px]] [[Image:bcf20_620mc_37_2007_sr_at_193cm.gif|160px]]
 +
** BLUE BCF12 #612-MC-5 20535 12/07/07<br> [[JLAB Fiber test results|Results]]:<br> This is a blue fiber about 180 cm long and was received in December 2007. The Sr source was positioned at 56cm, 101.5cm and 176cm away from the PMT photo cathode.<br> [[Image:bcf12_sr_at_56cm.gif|160px]] [[Image:bcf12_sr_at_101cm.gif|160px]]  [[Image:bcf12_sr_at_176cm.gif|160px]]
 +
** GREEN BCF60 #660-MC-16 10854 12/07/07 line30<br> [[JLAB Fiber test results|Results]]:<br> This is a green fiber of about 180cm length. It was received from Saint Gobain in December 2007. The Sr90 source was positioned at 56cm, 96cm and 196cm from the photo cathode.<br> [[Image:bcf60_sr_at_56cm.gif|160px]]  [[Image:bcf60_sr_at_96cm.gif|160px]]  [[Image:bcf60_sr_at_196cm.gif|160px]]
 +
 
 +
= Long term stability =
 +
Run 46 3.1 million event were taken over a period of 2 days. The data are analyzed and fitted in junks of 500000 events. The spectra are shown below with a list of the obtained value for <math>\mu</math>. <br> [[Image:r46_0.gif|160px]] [[Image:r46_1.gif|160px]] [[Image:r46_2.gif|160px]] [[Image:r46_3.gif|160px]] [[Image:r46_4.gif|160px]] [[Image:r46_5.gif|160px]]
 +
During the same period the response to the LED was measured and the mean number of photo electrons extracted. The bias voltage on the LED was constant at -7.91 Volt. The trigger rate for the LED was about 10 Hz.
 +
 
 +
<pre>
 +
  Data Set        Sr90 <math>\mu</math>                LED <math>\mu</math>
 +
  --------------------------------------------------
 +
      1        2.62  +/- 0.02        1.89 +/- 0.02
 +
      2        2.63  +/- 0.02        1.87 +/- 0.01
 +
      3        2.62  +/- 0.03        1.86 +/- 0.02
 +
      4        2.57  +/- 0.03        1.88 +/- 0.04
 +
      5        2.60  +/- 0.02        1.88 +/- 0.01
 +
      6        2.65  +/- 0.03        1.82 +/- 0.01
 +
</pre>
 +
 
 +
This demonstrates that the data taking and resulting fit values are very stable with time.

Latest revision as of 14:32, 15 March 2009

References

  1. E.H. Ballamy et al, Nucl. Inst. and Meth. A 339 (1994)468-476

Fiber Test Stand

The purpose of the fiber test stand at JLAB is to determine the number of photo electrons produced by a minimum ionizing particle in a scintillating fiber at a distance of 200cm from the fiber end. The photon detector is a standard photo multiplier, in this case an XP2020. In addition the attenuation length of the scintillator can be determined measuring the light output at several positions along the fiber.

Concept

One end of the scintillation fiber is coupled to the photo cathode of a PMT (XP2020). For monitoring purposes a second fiber (light guide) is also coupled to the same PMT providing light from a blue LED. At a given distance from the PMT surface a collimated Strontium (Sr90) source is mounted above the scintillation fiber. Below the fiber and the Sr90 source a small trigger scintillation detector (TSD) is mounted to trigger on electrons from the Sr90 source that pass through the fiber into the trigger scintillator. The data acquisition is triggered by TSD and the analog signals from both the XP2020 and the TSD are digitized as well as their timing. Simultaneously a trigger is generated for the LED light source to monitor the XP2020 PMT during the measurement.

Electronic layout

A basic sketch of the NIM electronics layout is shown here.
The signal from the XP2020 PMT is first amplified by a factor of 10 and then connected to a linear FAN In/Out. The DC offset of the linear FAN In/Out is adjusted such that the true pedestal is above the built in pedestal of the V792N VME ADC, which is about 5pC total charge. This corresponds to about 15mV of negative DC offset for the used gate width. The analog signal is then connected to the ADC adjusted for timing. A second output of the linear FAN In/Out is connected to a discriminator the output of which is then connected to F1TDC. The trigger scintillator is also connected to a linear FAN In/Out. Also here the DC offset is adjusted to move the true pedestal of the signal above threshold in the ADC. The analog signal is also discriminated and one output connected to the trigger OR which is linked to the trigger interface TI in VME of the DAQ system. The second trigger of the system is the trigger for the blue LED for monitoring purposes. The rate of this can be adjusted using two Gate/Delay generators and is set to about 10 Hz during measurements. The trigger rate from the TSD caused by the electrons of the Sr90 source is also in the order of 10 Hz.

ADC V792: 0-400pC range, 0.1pC/channel 4096 channels.

Dark Box

The detectors, scintillators and Sr90 source are currently located in an improvised dark box to protect the system for ambient light. Picture of the setup can be seen here as well and the fiber coupling to the PMT and the Sr90 source collimation:
Fiber test stand darkbox.jpg Fiber coupling.jpg Collimation.jpg Sr source.jpg

Sr90 collimation

The Sr90 source is collimated by a piece of copper shown in the above picture. A schematic view is shown below. The scintillation fiber lies in a 1mm x 1mm groove of the copper collimator thereby being fixed in position. At the center of the copper piece a 0.5mm wide and 5mm long slit provides the collimation. The slit is in the center and parallel to the groove where the fiber is located.
Sr90 collimation.gif
To illustrate the setup of the trigger scintillator with the collimated Sr90 source some pictures are shown here. First the full assembly with indicators to explain the individual components. The Trigger scintillator is located below the fiber and is readout by a Hamamatsu photo multiplier H3165-10. Above the trigger scintillator is small Aluminum platform for positioning the collimator. The collimator is a 5mm thick Copper piece with a 1mm groove to hold the fiber. The collimation of the electrons from the Sr90 is done by a 0.5mm wide and 5mm long slit at the center allowing the passage of electrons through the central part of the fiber.
Trigger setup.gif Assembly.gif Platform.gif Collimator.gif
The second picture shows the front part of the XP2020 housing. There are two feed-through for the fibers. The left black tapped one is the fiber from the blue LED. The right is the fiber to be tested and has no black tape or other protective clading. The feed through itself is a screw with a whole drilled through its length to hold the fiber in place. THE FIBER IS PUSHED UP AGAINST THE PMT ENTRANCE WINDOW. THE COUPLING IS AIR ONLY. NO OPTICAL GREASE IS USED! The last two pictures show the collimator assembly and Sr90 source. A detailed description is given below.

XP2020 PMT responses to blue LED

The response of the XP2020 on the LED light is shown for two different LED intensities (Low Voltage settings) in the form of the ADC spectra. The voltage divider used here for the XP2020 is a VD124K/T from Photonic (Type C divider). The fit is a Poisson distribution weighted sum of Gaussian distributions that are convoluted with the pedestal width and an exponential background.
Xp2020 led response 2200V A.gif Xp2020 led response 2200V B.gif
The HV of the XP2020 PMT is set at -2200V. The corresponding single photo electron peak position (fit parameter P1) is about 41 ADC channels corresponding to a gain of the PMT of 2.6*10^6. The fit parameter mu is the mean number of photo electrons from the Poisson distribution.

Trigger Scintillator response

The ADC spectrum of the trigger scintillator using a H3165-10 PMT and a 10cm long, 1cm thick and 8mm wide scintillator bar is shown here
Trigger scintillator response.gif

The Fit Function

F(x)=A\cdot \sum _{{n=0}}^{{N}}{\frac {\mu ^{n}e^{-}\mu }{n!}}\cdot ((1-w)G_{n}(x)+w\theta (x)I_{{G_{n}\otimes E}}(x))
where A is the number of events, G_{n}(x) is the nth Gaussian convoluted with the pedestal-Gaussian and I_{{G_{n}\otimes E}}(x) is the nth Gaussian convoluted with and exponential background with w the probability of such an exponential background event occuring. The function \theta (x) is a step function being 0 for x<P_{n} and 1 for x>P_{n}.

G_{n}(x)={\frac {1}{\sigma _{n}{\sqrt {2\pi )}}}}e^{{{\frac {-(x-P_{n})^{2}}{2\sigma ^{2}}}}} with P_{n}=P_{0}+n\cdot P_{1} the ADC position of the nth Gaussian with width \sigma _{n}={\sqrt {\sigma _{0}^{2}+n\cdot \sigma _{1}^{2}}}. The index 0 refers to the pedestal and n=1,2,... is the number of photo-electrons.

I_{{G_{n}\otimes E}}(x)={\frac {\alpha }{2}}e^{{-\alpha (x-P_{n}-\alpha \sigma _{n}^{2})}}\left[erf({\frac {|P_{0}-P_{n}-\alpha \sigma _{n}^{2}|}{\sigma _{n}{\sqrt {2}}}})+sign(x-P_{n}-\alpha \sigma _{n}^{2})\cdot erf({\frac {|x-P_{n}-\alpha \sigma _{n}^{2}|}{\sigma _{n}{\sqrt {2}}}})\right] is the convolution of the nth Gaussian with the exponential background leading to a tail for each Gaussian on the right side of the peak.

The Fit parameters are:

  1. P_{0} : pedestal position
  2. \sigma _{0} : pedestal width (FIXED from fit to pedestal only)
  3. P_{1} : single photo electron peak position
  4. \sigma _{1} : single photo electron peak width
  5. \alpha  : exponential background
  6. w : probability of exponential background
  7. \mu  : MEAN NUMBER OF PHOTO ELECTRONS

Fiber types

The following fibers have been tested:

  • Kuraray (MC=Multi-Clad)
    • Blue 81 MC lot:0801/103
      Results:
      The following plots show the PMT response to the Sr90 source positioned at 65cm, 165cm and 194cm from the photo cathode. In the pannels the value labled "mu" is the mean number of photo electrons detected by the PMT.
      Kuraray 81MC sr 65cm.gif Kuraray 81MC sr 165cm.gif Kuraray 81MC sr 194cm.gif
    • Blue 78 MC lot:0801/104
      Results:
      Similar the following plots show the PMT response to the Sr90 source positioned at 61cm, 94cm and 194cm from the photo cathode. Again as above the value labled "mu" in the pannel is the mean number of photo electrons detected by the PMT.
      Kuraray 78MC sr 61cm.gif Kuraray 78MC sr 94cm.gif Kuraray 78MC sr 194cm.gif
    • Green 3HF MC lot:0801/105
      Results:
      As above, plots for the green fiber the Sr90 source positioned at 65cm, 165cm.
      Kuraray 3HF MC sr 65cm.gif Kuraray 3HF MC sr 165cm.gif
  • Saint Gobain (aka Bicron)
    • GREEN BCF20 #5 Set2 1/8
      Results:
      This green fiber is about 200cm long and has been received in the latest batch in May 2008. The Sr90 source is put at 192cm and 100cm from the photo cathode of the PMT. The adc spectra are shown below.
      Bcf20 number5 2007 sr at 100cm.gif Bcf20 number5 2007 sr at 192cm.gif
    • GREEN BCF20 #7 Set2 3/8
      Results:
      This green fiber is also about 200cm long and was received in May 2008. The fiber is not trait and actually rather wobbly after about 100cm till the end. The Sr source was positioned at 56cm, 100cm and 193cm from the end of the fiber touching the photo cathode of the XP2020 tube.
      Bcf20 number7 2008 sr at 56cm.gif Bcf20 number7 2008 sr at 100cm.gif Bcf20 number7 2008 sr at 193cm.gif
    • GREEN BCF20 #620-MC-37 101796/18580 12/07/07<
      Results:
      This green fiber is also about 200cm long and was received in Dec. 2007 batch of green and blue fibers. The Sr source was positioned at 59cm, 100cm and 193cm from the end of the fiber touching the photo cathode of the XP2020 tube.
      Bcf20 620mc 37 2007 sr at 59cm.gif Bcf20 620mc 37 2007 sr at 100cm.gif Bcf20 620mc 37 2007 sr at 193cm.gif
    • BLUE BCF12 #612-MC-5 20535 12/07/07
      Results:
      This is a blue fiber about 180 cm long and was received in December 2007. The Sr source was positioned at 56cm, 101.5cm and 176cm away from the PMT photo cathode.
      Bcf12 sr at 56cm.gif Bcf12 sr at 101cm.gif Bcf12 sr at 176cm.gif
    • GREEN BCF60 #660-MC-16 10854 12/07/07 line30
      Results:
      This is a green fiber of about 180cm length. It was received from Saint Gobain in December 2007. The Sr90 source was positioned at 56cm, 96cm and 196cm from the photo cathode.
      Bcf60 sr at 56cm.gif Bcf60 sr at 96cm.gif Bcf60 sr at 196cm.gif

Long term stability

Run 46 3.1 million event were taken over a period of 2 days. The data are analyzed and fitted in junks of 500000 events. The spectra are shown below with a list of the obtained value for \mu .
R46 0.gif R46 1.gif R46 2.gif R46 3.gif R46 4.gif R46 5.gif During the same period the response to the LED was measured and the mean number of photo electrons extracted. The bias voltage on the LED was constant at -7.91 Volt. The trigger rate for the LED was about 10 Hz. 

   Data Set         Sr90 <math>\mu</math>                LED <math>\mu</math> 
   --------------------------------------------------
      1         2.62  +/- 0.02        1.89 +/- 0.02
      2         2.63  +/- 0.02        1.87 +/- 0.01
      3         2.62  +/- 0.03        1.86 +/- 0.02
      4         2.57  +/- 0.03        1.88 +/- 0.04
      5         2.60  +/- 0.02        1.88 +/- 0.01
      6         2.65  +/- 0.03        1.82 +/- 0.01

This demonstrates that the data taking and resulting fit values are very stable with time.

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