In this paper we are concerned by authentication of printer technologies from microscopic analysis of paper print. At this scale, a print is made of regularly spaced dots whose shape varies from a print to another and also inside the same document. Thus, dot at the microscopic scale can be considered as an intrinsic signature of printer technologies. Modeling and estimating such a signature for the authentication of printer technologies are really challenging. In this paper, we propose an original modeling of the micrometric scan of document printing. It consists in an extension of the binary response model which takes into account the dot shape. The digital image of a dot is therefore modeled as a set of random pixels distributed following to the so called inverse link function which depends on the center, tone of black, its spreading and its shape. A maximum likelihood estimation algorithm is provided in order to estimate the location, the darkness, the scale and shape parameter of the dot. From experimental results on three different printer technologies (inkjet, laser and offset), we show that the shape parameter is relevant for designing an identification scheme of printer technologies.