Microscopic analyses of paper printing show some regularly spaced dots whose the shape depends on the technology and the tuning of the printer as well as on the paper properties. The modeling and the identification of paper and ink interactions are required for qualifying the printing quality, for controlling the printing process and also for authentication issues. In this paper, we propose to model the micrometric scan of document printing by a binary response model whose the parameters depend on the location and the shape of dots. A maximum likelihood identification algorithm is provided, its performance is assessed through simulations and true data. Furthermore, we illustrate the benefice of a such model and estimation algorithm in the case of authentication of printer from micro-tag made of four dots.