High-frequency demodulation of wide area optical signals in a snapshot manner remains a technological challenge. If solved, it could open tremendous perspectives in 3D imaging, vibrometry, free-space communications, automated vision, or ballistic photon imaging in scattering media with numerous applications in smart autonomous vehicles and medical diagnosis. We present here a snapshot quadrature demodulation imaging technique, capable of estimating the amplitude and phase from a single acquisition, without synchronization of emitter and receiver, and with the added capability of continuous frequency tuning. This all-optical optimized setup comprises an electro-optic crystal acting as a fast sinusoidal optical transmission gate, and allows four quadrature image channels to be recorded simultaneously with any conventional camera. We report the design, experimental validation and examples of applications of such wide-field quadrature demodulating system that allowed snapshot demodulation of images with good spatial resolution and continuous frequency selectivity up to a few 100s of kilohertz.