Wigner distribution function retrieval via three-dimensional intensity measurement

Phase space is an artificially structured space jointly represented by the space and spatial frequency variables, and the Wigner distribution function (WDF) is widely used to describe the phase space. Compared with the coherent optical field expressed by two-dimensional (2D) complex amplitude, the four-dimensional WDF (2D space and 2D spatial frequency) can characterize optical field with arbitrary coherent state (coherent, partially coherent and incoherent). It is especially advantageous for the characterization of partially coherent optical fields. The WDF is real and may have negative values, which are the result of phase-space interference. The direct measurement of phase space can only obtain the absolute value of the whole WDF because the camera sensors can only obtain intensity, therefore, the negative values of measured WDF are mixed with positive values. In this paper, an improved phase-space retrieval method is demonstrated. First, capture three-dimensional intensity focal stack by camera sensors. Then, phase space tomography (PST) combined with a non-linear iterative algorithm is conducted to reconstruct the whole WDF.