Target Configuration
Loop 1: He4
Loop 2: He3, LH2
Loop 3: LD2 


Dummy to Al can ratio calculation:

Average cell wall thicknesses for loops 1,2,3.  Use just points A and C
on his diagram.
Meek assigns a measurement uncertainty of 0.0013 mm.  Blow up error
a little since we don't sample exactly one point.

Al 7075: Density = 0.101 lb/in3 * (1 in/2.54 cm)**3 * (1000 g/ 2.205 lb)
                 = 2.7952 g/cm3

Loop 1 = 0.1327 mm +/- 0.002 mm = 0.0371 +/- 0.0005 g/cm2 
Loop 2 = 0.1219 mm +/- 0.002 mm = 0.0341 +/- 0.0005 g/cm2
Loop 3 = 0.1213 mm +/- 0.002 mm = 0.0339 +/- 0.0005 g/cm2

Dummy Target thickness = 0.2626 +/- 0.0003 (foil 1) 
			 + 0.2633 +/- 0.0003 (foil 2)   g/cm2

		       = 0.5259 +/- 0.0004 g/cm2

Dummy/Can ratios:

Loop 1 = 0.5259/(2*0.0371) = 7.088 +/- 0.135
Loop 2 = 0.5259/(2*0.0341) = 7.711 +/- 0.146
Loop 3 = 0.5259/(2*0.0339) = 7.757 +/- 0.147


******UPDATE 7/13/2007*********************************************

The above analysis assumes that the beam goes through the exact points
A and C at which Meekins measured the cryotarget wall. Since we know we ran
with the beam offset ~4.5 mm realtive to the target center (not to mention the
finite width of the beam coming from the raster), this may not be the best
value to use.

On the other hand, taking the average of the 4 points (A,B,C,D) at which the cell
thickness was measured may also not be the best approach. We have decided to split 
the difference, and take the effective window thickness as the average of the above
(A+C) and (A+B+C+D) - this biases our result to the points closest to the 
beam position, but still allows for some effects from cell wall non-uniformity.

Re-doing the above analysis for all 4 meaurements:

Loop 1 = 0.1330 mm +/- 0.006 mm = 0.0372 +/- 0.0017 g/cm2 
Loop 2 = 0.1207 mm +/- 0.003 mm = 0.0337 +/- 0.0008 g/cm2
Loop 3 = 0.1194 mm +/- 0.004 mm = 0.0334 +/- 0.0011 g/cm2

Dummy Target thickness = (as above)

Dummy/Can ratios:

Loop 1 = 0.5259/(2*0.0372) = 7.069 +/- 0.228
Loop 2 = 0.5259/(2*0.0337) = 7.803 +/- 0.168
Loop 3 = 0.5259/(2*0.0334) = 7.873 +/- 0.233

So - now taking the average of "(A+C)/2" vs. "(A+B+C+D)/4":

Loop 1 = 7.079 +/- 0.228 
Loop 2 = 7.757 +/- 0.167
Loop 3 = 7.815 +/- 0.231

(for the uncertainty, I have just taken the larger of the 2 fractional errors
 from the methods above).


ADDITONAL CORRECTION FOR BEAM OFFSET:

So additionally, we need to correct for the fact that since the beam
is offset from the center of the target, it will travel through more
of the (curved) cell wall. This is pretty straightforward to estimate.

First define a coordinate system with the center of the cell at (0,0).
Define the x direction to be in direction of our total beam-target offset
(and with size dx = 4.6 mm). Denote the outer radius of the target can
R, and the cell wall thickness, t. The equation for a circle yields:

R**2 =  dx**2 + y1**2        for the outer edge of the can and
(R-t)**2 = dx**2 + y2**2     for the inner edge of the can.

solving for y1 and y2 and taking the difference:

y1-y2 = sqrt(R**2-dx**2) - sqrt( (R-t)**2-dx**2)

For R=20 mm, t = 0.125 mm, and dx = 4.6 mm

y1-y2 = 0.1283 mm, so the effective wall thickness changes by 
0.1283/0.125 = 1.0264, or 2.64%.

That means, then that the Dummy/wall ratio will be reduced by 1/1.0264.

Since this is a 2.6% effect on a ~20% subtraction (yielding a total 0.52% 
correction on the dummy-subtractedyield), I see no need to determine the 
correction more precisely than this.