Analysis of modern methods of information protection based on printed documents. It is shown that methods of protection from moiré effect provide reliable and effective protection by gaining new protection technology that is displayed in the optical acceleration motion layers and causes moire in fraud. Latent images can securely protect paper documents. Introduce a system of equations to calculate curvilinear patterns, where the optical formula of acceleration and periods moire stored in its simplest form. There is a need to create new types of protection of printed documents as the means and methods of fraud are becoming more common