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Angular orientation reconstruction of the Hall sensor calibration setup By Zdenko van Kesteren Supervisor: prof. dr. Frank Linde Outline • • • • Hall sensors Calibration set up Determining internal parameters Angular orientation analysis ATLAS muonspectrometer 3D magnetic field sensor • 3D sensor with 10-4 precision • Prototype designed & built by NIKHEF • Need to be calibrated • Felix Bergsma (CERN) Hall effect (semi)conductor in magnetic field Hall effect VH = IB/nqd q = charge carrier n = carrier density Hall sensor calibration • Rotate sensors over two orthogonal axes in accurately known homogeneous magnetic field • Repeat for several field strengths and temperatures • Angular orientation should be measured very precisely, order of 10-5 rad Hall sensor calibration • Calibration set up #1 @ CERN (F. Bergsma) (magnet with B about 3 x 10-5 T) • Calibration set up #2 Jaap Kuijt, Henk Boterenbrood, Fred Schimmel Currently @ NIKHEF Calibration setup Coil measurements Noise levels Angular orientation • Need to know and < 10-4 both • Calibration setup offers several ways to measure and : – Absolute encoder readout – 3 orthogonal coils integrated on probe – Reference Hall board (will not be covered here) Determining internal parameters • Constructing a model to describe coils • Imperfections in set up -> parameters in model – Rotation axes parameters – Coil geometry parameters – Coil electronics parameters • Fitting model to coil data Rotation axes geometry Coil geometry Plus 3 angles to fix coils in space: 1, 2 , 1 Coil electronics • Pedestal voltage • Electronical gain • RC-times Shell internal parameters • Rotation geometry – 1 2 1 2 2 • Coils geometry – 12 13 23 1 2 1 • Coil electronics – Gi Pi i (i = 1, 2, 3) 20 parameters! Coil voltage vs. time Modeled coil data Internal parameters • Values and errors of the parameters are not reliable • Wrong assumption to fix i in fit • Normalized 2 on noise RMS • Parameters are used to analyse the angular orientation Obtaining orientation • Set up offers two ways to obtain angular information: – Direct from the absolute encoders relies on 1 2 1 2 2 – By using the coil measurements relies on all parameters Coil measurement method • Values of C1, C2 and C3 gives rise to a reconstructed trec (found by fitting) • 1 trec and 2 trec give rotation angles x, y • Rotation angles relate to angular orientation , Absolute Encoder method • Encoder readout give AX and AY • AX and AY relate to rotation angels x, y • Rotation angles relate to angular orientation , Angular orientation → Trajectory x Results • , reconstruction • <10-4 rad precision not met • Internal parameters not reliable Conclusions • Data not reliable – ADCs coils do not behave properly • Bergsma reconstructed B; B of 10-3 T • Fit not reliable – The i should be floating parameters in fit – Including i in fit yields correlations between parameters