1. 28/11/02Guy Dewhirst1 Ultra Light Weights Method Guy Dewhirst Imperial College London

2. 28/11/02Guy Dewhirst2 Weights Weights for pulse height calculation created using method described by Pascal Paganini (CMS IN 2000/3). One set of 12 weights are used –4 Pre-pulse for pedestal subtraction –8 On pulse Function for weights is derived from averaged pulses of an electron run.

3. 28/11/02Guy Dewhirst3 Application of Weights Pedestal is subtracted then only the 8 on pulse weights are applied. A timing correction must be applied to allow for the data being asynchronous.

4. 28/11/02Guy Dewhirst4 Timing Correction Variation in peak height is corrected by: –Taking 1ns TDC bins –Cutting and correcting for position variation to give a more gaussian height distribution –Fitting the 25 distributions –Plotting the 25 means with TDC and fitting with a 3 rd order polynomial

5. 28/11/02Guy Dewhirst5 TDC Correction A 3 rd order polynomial timing correction can be derived for each crystal. Alternatively one correction function can be used with a timing offset to allow for channel to channel jitter.

6. 28/11/02Guy Dewhirst6 Timing with Weights Weights can also be used to determine the timing of the pulses. The weights used are 1, 0, -1 applied to the maximum three points and normalised. A 3 rd order polynomial is used to convert the result back to something similar to the TDC offset. The same function can be used for all channels.

7. 28/11/02Guy Dewhirst7 Timing Resolution Timing resolutions of under 1ns can be achieved for all the channels tested. Channel to channel jitter can be related to the  T observed when the TDC is used.

8. 28/11/02Guy Dewhirst8 Weights Timing Correction Using weights to determine the timing of a pulse and seems to eliminate the  T.

9. 28/11/02Guy Dewhirst9 Resolution Resolution is calculated using a 4  4mm position cut in the centre of the crystal. MethodResolution Weights with f channel (TDC)1.09% Weights with f(TDC+  T) 1.11% Weights with f(T weights )0.86% Method 01.04% Method 10.95% Method 20.91%

10. 28/11/02Guy Dewhirst10 Conclusions The light weights method gives comparable resolutions to the other methods. Using time derived from weights produces good results. Wish to study laser and pedestal runs to understand resolution in terms of single sample noise.