The number of channels that we want our compressed array to have

The number of channels of our raw arrray that will be in each channel of our compressed array

converting channels over to nanoseconds

converting frequency to compressed frequency

creating upper and lower error limits for compressed frequency

converting raw time to compressed time

creating upper and lower error limits for compressed time

A function to weight the points with respect to the error. We do this for six different weights, then examine results to determine which is the proper weight to use.

Creating vectors for the function fitting algorithm.

guess values for the parameters of:

Prof Decowski's parameters

Mathcad's algorithm for determining parameters

Mathcad's values of tfor each of the different weights.

Diagram 3: Weight Error Analysis

This seems to stabilize with an error weight of
, so using this error weight:

Mathcad's parameters

Diagram 4: Polonium-212 Half-life

OOO

Experimental points

___

Mathcad's parameters

___

Prof Decowski's parameters

Calculating the half life of ^{212}Po (see diagram 6).

^{212}Polonium has a half-life of 313 4 ns.

Diagram 5: OGC Delay Dependance on t

But
is just a constant so:

Therefore, the delay supplied by the OGC does not matter when solving for t.

Diagram 6: Extracting the half-life () from t

but, in this case
. Therefore,
and
. Taking the inverse of both sides,
. Solving for
we find that:

Diagram 7: Thorium-232 Decay Chain

From the Argonne National Laboratory at the University of Chicago, July 2002. http://www.ead.anl.gov/pub/doc/NaturalDecaySeries.pdf