Encoding complex valued fields using intensity

We present an approach enabling the representation of complex values using intensity only fields. The method can be used for imaging with structured illumination and allows the study of new propagating physical quantities with the classical coherent or incoherent light field playing the role of hidden variable. This approach can further be generalized to encode higher order N-dimensional vectors and ensembles of N orthogonal fields. Different orthogonal, incoherent illumination patterns (Hadamard, sinusoidal, Laguerre-Gauss) have been experimentally tested in a single-pixel detection imaging scheme in order to compare their performances in terms of obtainable resolution. We show experimentally that our encoding technique allows to reduce the required number of illuminations for a given, desired resolution.