High-frequency demodulation of wide area optical signals in a snapshot manner is a technological challenge that, if solved, could open tremendous perspectives in 3D imaging, free-space communications, or even ballistic photon imaging in highly scattering media. We present here a novel snapshot quadrature demodulation imaging technique, capable of estimating the amplitude and phase of light modulated from a single frame acquisition, without synchronization of emitter and receiver, and with the added capability of continuous frequency tuning. This all-optical setup relies on an electro-optic crystal that acts as a fast sinusoidal optical transmission gate and which, when inserted in an optimized optical architecture, allows for four quadrature image channels to be recorded simultaneously with any conventional camera. We report the design, experimental validation and examples of potential applications of such a wide-field quadrature demodulating system that allowed snapshot demodulation of images with good spatial resolution and continuous frequency selectivity, at modulation frequencies up to 500 kHz; no fundamental impediment in modulating/demodulating in the range 100-1000 MHz range is foreseen.