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Free-space fourth-moment propagator
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Analysis
Partial differential equation
Helmholtz equation
Phase screen
Parabolic wave equation
Free-space diffraction
2026-09-28
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For
m
x
=
(
i
/
k
)
m
r
1
r
2
, the
free
-
space
fourth-
moment
propagator
multiplies the two-dimensional
Fourier transform
by
e
−
i
x
p
1
p
2
/
k
. In physical coordinates its oscillatory kernel is
K
x
(
r
1
,
r
2
)
=
2
π
x
k
e
ik
r
1
r
2
/
x
.
(1)
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(9)
Free-space diffraction
Parabolic wave equation
Phase screen
Helmholtz equation
Partial differential equation
Analysis
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2023
/
iii
/
Paper 335
/
2
/
iii
/
b
/
Solution
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