A novel vortex-transform is proposed.This transform allows for generating complex-valued functions from modulated intensity patterns, including high frequency components from modulation, without the generation of unstable phase singularities.From these complex-valued functions it is possible to obtain intensity and pseudo-phase maps to analyze the intensity recordings without the necessity of phase retrieval techniques.The intensity and pseudo-phase maps obtained by using this transform preserve the modulation structure onto the intensity and phase modulo 2π maps, including stable phase singularities.