LHCb Velo - Module-05 Metrology 1 Data Analysis

This version is for final metrology procedure where pinholes are NOT used.

The measured x,y co-ordinates of 5 fiducials are mapped to the nominal positions
by minimising the differences in x,y of measured and nominal points using three
free parameters, x0, y0 and rotation angle Zrot: Fit results Summary available.

Xm - ( Xn*cos(Zrot) - Yn*sin(Zrot) - x0 )
Ym - ( Xn*sin(Zrot) + Yn*cos(Zrot) - y0)

	LHCb y (mm)	LHCb x (mm)	Zrot (mrad)
R si transformation fit	130.033	-275.004	-0.024
P si transformation fit	130.025	-275.010	-0.035
x co-ordinate of post	0.000
Dowel centre offset from post	32.028
Nominal centre relative to dowel	98.000	275.000	0.000

R si centre relative to dowel	98.005	275.004	-0.024
P si centre relative to dowel	97.997	275.010	-0.035

R si offset relative to nominal	0.005	0.004	-0.024
P si offset relative to nominal	-0.003	0.010	-0.035
Mean offset relative to dowel	0.001	0.007

P si offset relative to R si	0.008	-0.006	-0.011

Z envelope for top of module

The envelope for the top of the module in the z co-ordinate (beam direction) is
esentially given by the top edge measurements of the R and Phi silicon.
As a cross check the optical measurements on the silicon and hybrid taken near the
top edge are transformed to match the top edge. (This is necessary as the axis
defined by the temporary pin holes is arbitrary with respect to the base centre line.
Straight lines are fitted to the two most extreme points in the y-z plane for the
R and P silicon measurements and the transformation to match these to the top edge
silicon measurements calculated. This transformation is then applied to all the
measured points near the top edge and the minimum and maximum found for each set
of measurements. The overall minimum and maximum define the envelope for the module.

	Zshift	Xrot
R si offset	0.021	0.000199
P si offset	0.091	-0.000049
Mean offset	0.056	0.000075

	Zmin	Zmax	delZ/Y Twist	delZ/X Toe
R Silicon	-1.116	-1.051	0.065	-0.052
P Silicon	1.035	1.097	0.062	-0.111
R Hybrid	-0.752	-0.658	0.094
P Hybrid	0.676	0.769	0.093
R Si Top	-1.171	-1.127	0.044
P Si Top	0.961	1.027	0.066
Overall	-1.171	1.097	0.064		Mean tilt = -0.037 Max Z range = 2.268

Separation at bottom of silicon = 2.327, Toe-in = -0.059

Fit Planes to Si surface measurements

The measured x,y co-ordinates of 5 fiducials and 5 extra points are fitted to
a plane Z - Vy*X - Vx*Y - Z0 = 0 by minimising deviations in Z

Free parameters are Vx, Vy and z-displacement Z0:

Min dz / Max dz / RMS mean / are about the mean of the Z measurements (μm)

RMS plane is the rms variation in z about the fitted plane (μm)

Liverpool (Fit Summary)

Module	Glued	Type	Min dz	Max dz	RMS mean	Vx (mrad)	Vy (mrad)	Module Z0 (mm)	RMS plane
05	R	R	-61	35	27	-0.514	-1.136	-1.130	14
05	R	Phi	-80	62	42	-0.548	-2.319	1.019	12

Z top R = -1.148, Z top P = 0.992, Separation = 2.140
Zplane R = -1.130, Zplane P = 1.019, Separation = 2.149
WARNING: Top_R measurement height not normal
WARNING: Top_P measurement height not normal