When the first material is semitransparent to the laser wavelength (due to a crystalline structure
or to the presence of pigments within their matrix), in establishing the energetic and geometrical
characteristics of the heat source at the interface, a quantification of the laser beam scattering is
necessary. Since the use of classical approximation based on the Beer-Lambert law can lead to
inaccurate results in the case of scattering media, a new approach is used. Its detail description is given
in previous works [8] [9]. Basically, it involves two steps: (a) based on measurements of the
transmitted intensity (in % from the incident one) for three thickness of the same semitransparent
material, the scattering characteristics of the media (particles diameter, the relative refractive index and
the particle concentration) are computed by applying an inverse algorithm. This allows obtaining an
equivalent material which produces the same attenuation and broadening of the laser beam as the real
one. In the second step, the laser beam profile within the semi-transparent material is determined by
using a numerical model based on Mie theory and Monte Carlo method.
For the ABS plates, the measurements of the transmitted intensity (table 2) indicate an
equivalent material having the following scattering characteristics: particle diameter d=0.46μm,
relative refractive index nparticle/nmatrix=1.42 and particle concentration c=0.44%. Using these
characteristics as input data in the numerical model (Mie +Monte Carlo), the transmitted laser beam
profile was obtained. In spite the fact that the incident laser beam has a rectangular shaped profile with
a uniform distribution of the energy (figure 3-a) the transmitted beam has an elliptical spot and a
Gaussian energy distribution (figure 3-b,c), the polymer acting like an optical filter. The characteristic
radii (the radius where the laser beam intensity decreases with 1/e2) for the elliptical spot were rx=2.5
mm and ry=2.69 mm