The theoretical analysis of a nonlinear holographic watermarking system

This research examines the nonlinearity of a previously proposed digital holographic watermarking system (Cheng et al 2005 Opt. Commun. 248 105–16). This system constructs a digital holographic watermark using modified Mach–Zehnder interferometric architecture and implements authentication watermark detection using an optical VanderLugt 4-f correlator. To analyze the nonlinearity of the system, the power law function is used to model the nonlinear characteristics of the spatial light modulator; the output of the nonlinear spatial light modulator can be obtained by an inverse Laplace transform. The theoretical study shows that the nonlinearity results in a sum of infinite harmonic series, where the mth-order term is phase-modulated m-fold by the original phase of the transformed mark. Importantly, only the first harmonic term preserves the original phase and leads to a correlation signal. Accordingly, a mathematical model for the nonlinear watermarking system is derived. Then, we apply the proposed model to design an optimal threshold for reliable authentication watermark detection.