Scientech S310 Vector - Manual (Page 36)

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The error, in theory, is only dependent upon the value of ∑dV
i
, that is the cumulative random error of V
i
. This
number should approach zero if data is carefully taken. The accuracy is also increased if the time interval, dt, is
minimized. Numerical integration can yield accurate results, but is a tedious task.
Initial Voltage Interpolation:
A method used to eliminate the tedious numerical integration task is to project the thermal decay envelope on to
the voltage axis, determine the 1/e decay time constant T, and estimate the total energy value (E):
E = (V
o
/S) x T
The change from thermal absorption to thermal transport phenomena near the peak causes difficulty in
accurately projecting the envelope on to the voltage axis introducing an error, dV
o
. Further, the determination of
the time constant T, introduces another error, dT. The total error is the sum of the two errors.
dE = (V
o
/S)dT + (T/S)dV
o
The difficulty in eliminating the potential error makes this method typically less accurate than numerical
integration, but much faster in application.
Peak Voltage Estimate:
The peak voltage method requires using an independent determination of total energy and referencing it back to
the peak voltage value, V
p
.
For a given pulse, use the numerical integration method to obtain E. Note the peak voltage, V
p
. Compute the
value, F
F = E/V
p
For the next pulse compute the total energy: E = F x V
p
The error in using this method yields: dE = FdV
p
+ V
p
dF
The accuracy of this measurement depends upon the error in the original calibration, dF, and the error in the
peak voltage dV
p
. A careful numerical integration yields a value for dF near zero. The value of dV
p
can be
minimized by maintaining the geometry of the system (i.e. beam intensity, beam profile, wavelength and
environment) during operation to be the same as during calibration. Under controlled circumstances, the peak
method accuracy usually falls between the numerical integration and initial voltage interpolation methods.