| a, Optical setup task encodes the four-dimensional vector field onto a two-dimensional intensity measurement (not to scale). The collimated beam is split, with one part used to measure the spectral phase and the rest passing through a birefringent medium (BM), creating a relative spectral chirp between the polarizations. Next, a microlens array (MLA) encodes the wavefront. The resulting pattern is imaged by a 4f system with a diffraction grating (DG) placed near the Fourier plane, providing the spectral encoding, and a polarization filter array (PFA) is used on the sensor. b, Extraction and processing of the encoding pixels. At each point in space, the spectral and polarization information is recovered, with uncertainty estimates. c, Aggregation of the information from the encoder pixels into the vectorial near field. d, Propagation to focus. |