Phase objects can be characterized using well-known methods such as shear interferometry and deflectometry, which provide information on the partial derivatives of the phase. It is often believed that for phase retrieval it is strictly necessary to have knowledge of two partial derivatives in orthogonal directions. In the praxis, this implies that the measurements have to be performed along two dimensions, which often requires a rotation of the object or rotation of the shear direction. This is time consuming and errors can be easily generated from the process of rotation, especially for image registration in the axial direction. In the present Letter, we will demonstrate that only one partial derivative often suffices to recover the phase, and we will discuss under which conditions that is possible. Simulations and validation experiments are presented.
© 2013 Optical Society of America
Original Manuscript: August 12, 2013
Revised Manuscript: October 9, 2013
Manuscript Accepted: October 9, 2013
Published: November 13, 2013
J. Matías Di Martino, Jorge L. Flores, Franz Pfeiffer, Kai Scherer, Gastón A. Ayubi, and José A. Ferrari, "Phase retrieval from one partial derivative," Opt. Lett. 38, 4813-4816 (2013)