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3.3. Diffraction
represents an outgoing spherical wave, while the negative exponent
represents an incoming spherical wave. The positive and negative
exponentials represent two linearly independent solutions to the
Helmholtz equation, as required for any second order, ordinary
differential equation.
We assume an opaque, planar screen of infinite extent, with one
or more apertures or openings of arbitrary shape and position in
the screen. This is shown schematically in Figure 3.9. The screen
Figure 3.9: Geometry for Sommerfeld’s solution by Green’s function.
is assumed to be illuminated by an arbitrary collection of sources
(not shown), such that the amplitude at position x 0 in the plane
of the screen is u(x 0 ). This amplitude is assumed to be known.
3.3. Diffraction
represents an outgoing spherical wave, while the negative exponent
represents an incoming spherical wave. The positive and negative
exponentials represent two linearly independent solutions to the
Helmholtz equation, as required for any second order, ordinary
differential equation.
We assume an opaque, planar screen of infinite extent, with one
or more apertures or openings of arbitrary shape and position in
the screen. This is shown schematically in Figure 3.9. The screen
Figure 3.9: Geometry for Sommerfeld’s solution by Green’s function.
is assumed to be illuminated by an arbitrary collection of sources
(not shown), such that the amplitude at position x 0 in the plane
of the screen is u(x 0 ). This amplitude is assumed to be known.