Printer identification based on a printed document can provide forensic information to protect copyright and verify authenticity. In addition to intrinsic features (intrinsic signatures) of the printer, modulating the printing process to embed specific signatures (extrinsic signatures) will further extend the encoding capacity and utility. One of the key issues with embedding extrinsic signature is the embedded signature should not be detectable by the human observer but is detectable using a matched sensing device and detection algorithm. In this paper, we will investigate the modeling and experimental characterization of the EP process to obtain the modulation threshold such that the embedding signatures are below human visual threshold. An empirical model is established and a heuristic functional inverse is used to obtain the process modulation threshold.