One-frame two-dimensional deflectometry for phase retrieval by addition of orthogonal fringe patterns

Deflectometry is a well-known method to characterize pure phase objects by measuring the deformation of fringes. In principle, the retrieved magnitude is the partial derivative of the phase along the coordinate orthogonal to the fringes. In order to recover the phase it is necessary to know the derivatives in two orthogonal directions, which is usually achieved by rotating 90° the original fringes and acquiring a new deformed pattern. This "time-multiplexed" two-dimensional deflectometry is a time-consuming operation if the goal is to characterize phase objects in real time. In the present paper we propose a kind of two-dimensional deflectometry that allows acquisition of fringe patterns in two orthogonal directions in a single frame. The proposed procedure utilizes a two-dimensional ("additive") fringe pattern that allows the application of Takeda's method to each coordinate independently. The advantage of the method (with respect to the traditional one) is that it simplifies the setup and reduces the acquisition time. Validation experiments are presented.