
193Statistics of Laser Damage Threshold Measurements
Chapter 7
Substitution of Equation 7.18 into Equation 7.6 gives the PoD curve as
Pr ex
max
max
max
D
if T
wifT T
if T
Ti
i
()
=
≤
()
≥
⎧
⎨
⎪
⎩
⎪
0
1
1
2
φ
−−
φ
D
(7.19)
In Equation 7.19, the value of Pr(D) is zero until the threshold T is reached and, at higher
uences, Pr(D) is xed at a value depending on the πw
2
D
T
product. When the intrinsic
coating threshold, T
i
is exceeded damage is certain. Equation 7.19 is plotted in Figure7.4
for various values of D
T
.
7.3.4.2 Degenerate Case Gaussian Beam
For the case of a Gaussian beam, the 〈n〉 is found by substitution of Equations 7.10 and
7.16 into Equation 7.15, which ...