Diagram 1: Calibration          Diagram 2: Data Analysis        The channel where we start to get measurements The channel of our last accurate measurement 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 values of t for each of the different weights.
Diagram 3: Weight Error Analysis   This seems to stabilize with an error weight of , so using this error weight: Diagram 4: Polonium-212 Half-life OOO
Experimental points
___
Mathcad's parameters ___
Prof Decowski's parameters   Calculating the half life of 212Po (see diagram 6). 212Polonium 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