ImSyn™(1,2) is a commercial opto-electronic processing system that is currently in production. It is a Fourier transform processor designed for applications where the FFT algorithm is difficult to use. These applications involve transforming data on non-rectangular grids. Many real sensor systems produce such data. Examples include: magnetic resonance imaging, computer tomography, ultrasound, radio astronomy, synthetic aperture radar3 and a new modality, the synthetic aperture microscope. ImSyn takes a list of x-frequency, y-frequency and complex valued amplitude and produces a fully complex Fourier transform. ImSyn can accept complex valued data either in amplitude and phase mode or as in-phase and quadrature.