1. FinCMS Dec 19, 2008 V.Karimäki, Sensor shapes 1 1 Tracker calibration for curved sensors (brief overview) V. Karimäki FinnCMS meeting Helsinki 19.12.2008

2. FinCMS Dec 19, 2008 V.Karimäki, Sensor shapes 2 1 Effect of curved sensor shape Q: track impact point at planar sensor P: true impact point at curved sensor near the true hit position Q': point where our flat detector model assumes the hit lies  u = correction in precise coordinate  v = correction in second coordinate (needed for pixels?)  w = a*uu + b*uv + c*vv 2nd order parameterization of curved surface a,b,c = coefficients of curvature

3. FinCMS Dec 19, 2008 V.Karimäki, Sensor shapes 3 1 Curvature coefficients can be fitted  Track direction (t 1,t 2,t 3 )  Track impact coordinate u_t  Corrected u-coordinates: u_c = u - (t 1 /t 3 )*(a*uu + b*uv + c*vv)  Minimize sum of squared residuals (u_c - u_t)^2  and fit (a,b,c)

4. FinCMS Dec 19, 2008 V.Karimäki, Sensor shapes 4 1 Sensor curvature can be studied  model independent sensor shape  by plotting mean residuals weighted with (t 3 /t 1 )  as a function of u,v

5. FinCMS Dec 19, 2008 V.Karimäki, Sensor shapes 5 1 Verification with Monte Carlo Parameterized surface Fitted surface

6. FinCMS Dec 19, 2008 V.Karimäki, Sensor shapes 6 1 Model independent surface shape  By plotting weighted uncorrected mean residuals

7. FinCMS Dec 19, 2008 V.Karimäki, Sensor shapes 7 1 Summary By simple Monte Carlo:  Demonstrated method to fit sensor shape  Method to correct hit positions  Demonstrated model independent way to look for possible sensor curvature Next:  Do analysis with cosmics  first: model independent study