
175Measurement and Detection of Laser-Induced Damage
Chapter 6
For a Gaussian beam with the following intensity prole,
Ixy
P
xy
(,)exp=−
+
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
2
2
2
πω
ω
(6.3)
where
P is the power of the beam
ω is the 1/e
2
intensity radius, the portion of laser beam transmitted through the knife-
edge P(a) can be given as
P(aI(x,y)dxdy
P
erfc
a
a
)
⎛
⎝
⎜
⎞
⎠
⎟
∞
−∞
∞
∫∫
2
2
ω
(6.4)
where erfc(x) is the complementary error function,
68
erfc(x) = 1 − erf(x).
Using Equation 6.4, it is possible to obtain theoretical result of unmasked power versus
knife movement distance, shown as the solid line in Figure 6.23. In addition, experimental
data (dotted line) using knife-edge method are a ...