  Acoustic wave equation seeks to represent wavefield in terms of a radiation
source which possesses finite energy over space and time. The wavefield may be
represented over a surface bounding the source, and calculated by solving an
associated boundary-value problem via imposing conditions on the boundary of a
chosen solution space. This manuscript aims to study approaches for obtaining
unique solution to acoustic wave equation in terms of either a volumetric
radiation source $s$, or surface source. For the latter, the wavefield is
described using a Kirchhoff-Helmholtz or Rayleigh-Sommerfeld integral over the
surface. Using a monopole version of these integral formulae, a singlet surface
source is defined in terms of minus normal pressure derivative
$-(\partial/\partial \boldsymbol{n})p$ or its equivalent $\rho_0 \partial
u^{\boldsymbol{n}}/ \partial t$. Here, $p$ is the pressure, $\rho_0$ is the
ambient density, and $u^{\boldsymbol{n}} = \boldsymbol{u} \cdot \boldsymbol{n}$
is the normal velocity with $\boldsymbol{n}$ a unit vector outwardly normal to
the surface. Using a dipole variant of these surface integral formulae, the
surface source is defined as a doublet source in terms of pressure $p$. It will
be shown that an interior-field dipole variant of these integral formulae
represents the back-projected field from observations of the wavefield over a
surface. The key step for numerically approximating all these derived
analytical formulae is inclusion of source, and will be studied in this
manuscript carefully. It will be shown that a numerical approximation of a
dipole version of these surface integral formulae has a limitation regarding
how to account for obliquity factors or their equivalent solid angles
efficiently, especially for describing a back-projected field from observations
over a measurement surface.
