  Estimating the sound absorption in situ relies on accurately describing the
measured sound field. Evidence suggests that modeling the reflection of
impinging spherical waves is important, especially for compact measurement
systems. This article proposes a method for estimating the sound absorption
coefficient of a material sample by mapping the sound pressure, measured by a
microphone array, to a distribution of monopoles along a line in the complex
plane. The proposed method is compared to modeling the sound field as a
superposition of two sources (a monopole and an image source). The obtained
inverse problems are solved with Tikhonov regularization, with automatic choice
of the regularization parameter by the L-curve criterion. The sound absorption
measurement is tested with simulations of the sound field above infinite and
finite porous absorbers. The approaches are compared to the plane-wave
absorption coefficient and the one obtained by spherical wave incidence.
Experimental analysis of two porous samples and one resonant absorber is also
carried out in situ. Four arrays were tested with an increasing aperture and
number of sensors. It was demonstrated that measurements are feasible even with
an array with only a few microphones. The discretization of the integral
equation led to a more accurate reconstruction of the sound pressure and
particle velocity at the sample's surface. The resulting absorption coefficient
agrees with the one obtained for spherical wave incidence, indicating that
including more monopoles along the complex line is an essential feature of the
sound field.
