Wigner Distribution Moments Measured as Intensity Moments in Separable First-Order Optical Systems

After the introduction of the Wigner distribution (WD) [1] for the description of coherent and partially coherent optical fields [2], it became an important tool for optical signal/image analysis and beam characterization [3, 4, 5]. The WD completely describes the complex amplitude of a coherent optical field (up to a constant phase factor) or the mutual coherence function of a partially coherent field. As the WD of a two-dimensional optical field is a function of four variables, it is difficult to analyze. Therefore, the optical field is often represented not by the WD itself, but by its global moments. Beam characterization based on the second-order moments of the WD thus became the basis of an International Organization for Standardization standard [6]. Some of the WD moments can directly be determined from measurements of the intensity distributions in the image plane or the Fourier plane, but most of the moments cannot be determined in such an easy way. In order to calculate such moments, additional information is required. Since first-order optical systems [7]—also called ABCD systems— produce affine transformations of theWD in phase space, the intensity distributions measured at the output of such systems can provide such additional information. The application of ABCD systems for the measurements of the second-