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Fresnel Diffraction
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Fresnel-Kirchhoff
E
p
=
−
i
k
2
π
E
s
e
−
i
ω
t
∬
O
b
s
t
a
c
l
e
F
(
θ
)
e
i
k
(
r
+
r
′
)
r
r
′
d
A
E_p = \frac{-ik}{2\pi}E_s e^{-i\omega t} \iint_{Obstacle} F(\theta)\frac{e^{ik(r+r')}}{rr'} \,dA
E
p
=
2
π
−
ik
E
s
e
−
iω
t
∬
O
b
s
t
a
c
l
e
F
(
θ
)
r
r
′
e
ik
(
r
+
r
′
)
d
A
Skewness Factor
F
(
θ
)
=
1
+
cos
θ
2
F(\theta) = \frac{1+\cos\theta}{2}
F
(
θ
)
=
2
1
+
cos
θ
Raius of Fresnel Zones
R
n
≈
n
L
λ
where
1
L
=
1
p
+
1
q
R_n \approx \sqrt{nL\lambda} \,\,\,\,\,\,\,\ \textup{where} \,\,\,\,\,\,\,\ \frac{1}{L}=\frac{1}{p}+\frac{1}{q}
R
n
≈
n
L
λ
where
L
1
=
p
1
+
q
1