Exploring the bronzing effect at the surface of ink layers

We i nvestigate the optical phenomenon responsible for the colored shine that sometimes a ppears at the surface of ink layers i n t he s pecular direction, o ften ca lled bronzing or gloss di fferential. I t seems to co me from the w avelengthdependent refractive index of t he ink, which induces a wavelength-dependent reflectance of t he i nk-air interface. Our experiments o n c yan and magenta i nkjet i nks confirm this t heory. C omplex refractive i ndices ca n b e ob tained from measurements of t he spectral reflectance a nd transmittance of a t ransparency film coated with the ink. We pr opose a correction o f t he cl assical C lapper-Yule model in order to in clude th e colored gloss in the pr ediction of th e spectral reflectance of an inked paper. We also explored effects of scattering by the micrometric or nanometric roughness of the ink surface. The micrometric roughness, easy to model with a geometrical optics model, can predict the spreading of the colored gloss over a large cone. Electromagnetic models a ccounting for the effect of t he nanometric roughness of t he surface also predict the attenuation of short wavelengths observed under collimated illumination.