LI Gain Curves

1. LI Gain Curves • The Idea: Fit all the information for one strip together->gives constraints on the model and parameters. • Each end of the strip is flashed by a different led and read out by; • The near end pmt • The far end pmt • A high gain pin • A low gain pin • Eight sets of measurements at 20 different led intensities Oxford Meeting, January 06 Peter Litchfield

2. The model • The raw LI data is corrected; • For missing pulses below threshold at low light levels • For saturation of the electronics according to Giles’s LiLinearity correction • Each pmt and pin is then assumed to saturate according to Giles’s function (a pole term) pt= corrected, true, pulse height p= measured pulse height c1, c2 are constants • Any pmt or pin which seems not to be fully represented by the pole is multiplied by a polynomial in the pulse height, gn are constants

3. The model • Each true value is assumed to be associated with the others by a constant • The superscripts n and f refer to the near and far readout of the led side A or B. Thus • We have 12 equations at each of 20 light levels, 240 measurements and 40 parameters for a fit up to quadratic on all Pmts and Pins. • Fit for parameters using MINUIT/ROOT

4. Results PB12 • I selected at random Pulser Box 12 and looked, again at random, at some of the Leds. Pulser Box 13 is at the far side. I only look at strips which have the same leds flashed on the two sides. • I run for 100 strips attached to each Led, the plots look the same for all 640 strips but the plots are too big for Powerpoint! • The Pmt’s are fitted up to adc’s of 12000, before they should completely saturate and the Pins are fitted over their whole range • I plot • the residuals etc for individual strips • pt versus p superimposed on one plot for all the strips • I show first details of Led 12 which had significant non-linearity

5. PB12 Led12 Linear fit For each side B side A side Note • No pole term or polynomial • Near Pmt – Far Pmt non-linear, saturation • Low Gain – High Gain Pin non-linear, non-linearity in the Pins • Lots of structure

6. PB12 Led 12 Pole+Quadratic B side A side • Note • Most of the structure has gone, still possibly some on the B side

7. PB12 Led 12 Pole + Quadratic • For each of 100 strips plot 100 equally spaced point of p (x-axis) v pt (y-axis) • Red line is p=pt Note • Generally consistent behavior of the pins for different strips (as expected) • Pin B High Gain has a wriggle • Pmt’s show signs of saturation with pt>p at high adcs • Pmt saturation starts around 6000-8000 adcs

8. PB12 Led12 • From the linear fit it looks like the B high gain pin and A low gain pins could be non-linear • After some investigation try pin Bhigh with two extra terms (up to p4) and pin Alow with quadratic. • Pins Blow and Ahigh are constrained to be linear • Good fit • The extra terms in Alow improve the 2 but the biggest effect is in Bhigh

9. PB12 Led12 • My best bet as to what is happening • The Led of course should be the same for all strips. • It looks like there are two bands in Pin B high. I will investigate. They may be just displaced from each other • I will try finding the average parameters for each and fixing them for all strips.

10. PB12 Led 2 • Fit with a pole + quadratic term • This time it is side A high gain pin which is strongly non-linear, side B pins look OK. • Side A pmt looks mostly linear up to 12000 adc

11. PB12 Led 2 • Still some structure in side A • Pin probably needs more than a quadratic term

12. PB12 Led 13 • Pole + quadratic term • Led 13 looks OK • All pins quite linear • Side B pmts seem to saturate more than side A

13. PB12 Led 13 • No significant structure after a quadratic fit

14. PB12 Led 15 • Pole + quadratic fit • This one’s a disaster, everything is all over the place • I haven’t had time to investigate it further

15. PB 12 Led 15 • Lots of structure even after a quadratic fit • Clearly more than one pin has structure • PmtA v PMT B quite flat • High gain v low gain pins have wiggles • Probably just a pin problem • May (or may not) be able to sort it out with higher order fits

16. Conclusions • It is possible to make reasonable fits to all the data but it requires high order polynomials in some cases • The problem seems to be in the pins, I have not seen any cases where the pmts require more than a pole term. • Not all the pins are affected. The amount of non-linearity varies, maybe there is some in all of them but in some cases it is too small to notice. • I have only looked at one pulser box, I do not know that it is true for others • I have only looked at one month’s data, it will be interesting to see if there is any time variation

17. How do we do a Pmt Calibration? • We (I?) could examine each pin in turn, make fits and try to determine a parameterisation for every element in the detector. • A lot of work • Hard to automate since only a fraction of pins seem to need fixing • Fits are somewhat sensitive, just throwing MINUIT at them doesn’t work • It may be possible to make a minimal pin correction (pole term?) and get a reasonable parameterisation of the pmt saturation. • This could probably be automated, the fits are less sensitive • Need to check against some fully parameterised channels that the pmt corrections are conserved • We can forget the pins and assume the far pmt is linear and calibrate the near pmt against it • We can check at least a few cases that the pmt parameters are consistent with those from a full fit.

18. What about the hardware? • Do we care if we don’t understand why the pins don’t work? • Can we be sure that the pmts are working if the pins aren’t? • Is anybody going to work on understanding the pin hardware? • As a first step we could have another attempt at a swap of a pin readout board?