ScienTECH Vector Series - Initial Voltage Interpolation; Peak Voltage Estimate

PN 10795T 41
i=1
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