Wavefront reconstruction of discontinuous phase objects from optical deflectometry

One of the challenges of phase measuring deflectometry is to retrieve the wavefront from objects that present discontinuities or non-differentiable gradient fields. Here, we propose the integration of such gradient fields based on an L ^p-norm minimization problem. The solution of this problem results in a nonlinear partial differential equation, which can be solved with a fast and well-known numerical method and does not depend on external parameters. Numerical reconstructions on both synthetic and experimental data are presented that demonstrate the capability of the proposed method.