We present a new, to the best of our knowledge, concept of using quadrant Fourier transforms (QFTs) formed by microlens arrays (MLAs) to decode complex optical signals based on the optical intensity collected per quadrant area after the MLAs. From a computational optics viewpoint, we show the most promising use of the QFT in low-cost and passive decoding of laser signals carrying optical angular momenta (OAM) that are prevalent in research frontiers of optical communications, computation, and imaging. There are numerous ways of creating, adding, and combining OAM states in optical waves, while decoding or demultiplexing approaches often turn out to be complicated or expensive. The simple OAM decoder formed by a pair of identical MLAs, which are concatenated in the focal plane and transversely offset by half-pitch length, can accomplish the imaging task with four pixels per cell. By sorting the gradient curls of the optical wave into local quadrant cells, the decoder analyzes the intensity reallocation that is proportional to the gradients and computes the gradient curls accordingly. The low-cost, compactness, and simplicity of the proposed OAM sensor will further promote OAM-based applications, as well as many other applications that exploit the spatial complexity of optical signals.