The contradictory requirements are presented to acousto- optic tunable filters (AOF) of spectral image analysis. On the one hand AOF should have high speed. On the other hand it should have good spectral resolution and wide angular aperture. Thus when AOF is fastly tuned with chirp transients, the diffracted wave intensity at different moments of transient process can considerably diverge form its quasistatic level. It means that spread function (SF) depends on the velocity of frequency tuning, i.e., it is described by 2D function with variables - wave length and velocity of frequency tuning. In Cartesian frame this dependence is presented by some surface being dynamic SF (DSF). It characterizes speed and selectivity properties of AOF. In this work DCF mathematical model was constructed and basic properties of spectral image analysis AOF were investigated. It has been established that the greatest distortions of DSF occur if velocity of frequency tuning has exceeded some critical value connected with acousto-optic interaction geometry and aperture sizes of beams. In this case the side lobes of SF will make 'false' maxima which begin to prevail over the basic. In addition under the conditions of phase mismatch DSF loses the symmetry to position of the main maximum. These effects reduce the accuracy of spectral measurements when tuning velocity is high.
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