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We applied Fourier space analysis to a comprehensive study of the propagation of pulsed two-dimensional images through single and coupled image resonators.  The Fourier method shows that the image can propagate through the resonator successfully as long as the spatial and temporal Fourier components of the image are within the bandwidth of the amplitude and phase transfer functions. The relevant steep dispersion of the cavity can yield delayed or advanced images. The Fourier method reproduces characteristic aspects of the experimental observations of the image propagation, and also predicts new aspects, such as the spatial image profile dependence on the observation time and the coupling strength. To demonstrate the time evolution of the experiment, space- and time-resolved image propagations were performed using a streak camera

Fourier Analysis of Slow and Fast Image Propagation through Single and Coupled Image Resonators