Here - PMOD/WRC

in,max
P
mum available input power , and the uncertainty in
the 4n power measurements. For simplicity, we limit our
calculations to the situation where the n power measurements
have P evenly spaced between zero and P .
in
in,max
Furthermore, we assume that all of the 4n power measurements
have identical statistical uncertainty. The calculation
is based on a least squares algorithm. T c is adjusted
within the calculation to the value that minimizes u()/.
The result is approximated by the following expression:
()
u
= V
x P
() x
in,max
NL
() P
22.5 u
n 2.5 P
2
E / L
The dependence on the cavity parameters and available
optical power is described by the empirical function V,
which is plotted in Fig. 2. u(P)/P is the relative statistical
uncertainty in each of the 4n power measurements.
log10 (V(x))
5
4
3
2
1
0
-1
log( V(
x))
= c log( x)
1
-4 -2 0 2 4
Figure 2. The empirical function V(x), which is used in the
approximate result in Eq. 2.
The relative discrepancy between the full numerical calculations
and the empirical expression in Eq. 2 is found from
Monte Carlo simulations to be within ±10% in the pa-
in,max
P
rameter range 0.001