  Advances in multimaterial 3D printing have the potential to reproduce various
visual appearance attributes of an object in addition to its shape. Since many
existing 3D file formats encode color and translucency by RGBA textures mapped
to 3D shapes, RGBA information is particularly important for practical
applications. In contrast to color (encoded by RGB), which is specified by the
object's reflectance, selected viewing conditions and a standard observer,
translucency (encoded by A) is neither linked to any measurable physical nor
perceptual quantity. Thus, reproducing translucency encoded by A is open for
interpretation.
  In this paper, we propose a rigorous definition for A suitable for use in
graphical 3D printing, which is independent of the 3D printing hardware and
software, and which links both optical material properties and perceptual
uniformity for human observers. By deriving our definition from the absorption
and scattering coefficients of virtual homogeneous reference materials with an
isotropic phase function, we achieve two important properties. First, a simple
adjustment of A is possible, which preserves the translucency appearance if an
object is re-scaled for printing. Second, determining the value of A for a real
(potentially non-homogeneous) material, can be achieved by minimizing a
distance function between light transport measurements of this material and
simulated measurements of the reference materials. Such measurements can be
conducted by commercial spectrophotometers used in graphic arts.
  Finally, we conduct visual experiments employing the method of constant
stimuli, and derive from them an embedding of A into a nearly perceptually
uniform scale of translucency for the reference materials.
