This paper presents the results of theoretical and experimental investigation into adaptive optical systems (AOSs) based on a wave-front sensor with spatially separated control channels. The main feature of such systems consists in the fact that signals received by each photodetector can be directly used for control of deformable mirror (DM) actuators. For this purpose, light wave phase modulation at the same frequency for the entire wave front (WF) is used. A multi-element photodetector is placed in the plane, optically conjugate with a phase corrector of the optical system. That is why such systems seem analogous, to some extent, to aperture sounding (multidither) systems. Theoretical analysis has shown that two variants of the adaptive optical systems based on wave-front sensor (WFS) with spatially separated control channels are possible. The first one involves phase modulation directly in the corrector plane. The second one involves phase modulation in the focal plane of the WFS objective. In both of these cases, the signal from a photodetector is equal to zero, if the WF local curvature in the corresponding region is also zero. Such WFS are often referred to as curvature sensors. It is shown that stability of adaptive optical systems based on wave-front sensor with spatially separated control channels and phase modulation in the corrector plane strongly depends on the WF tilts. But their sensitivity (for equal focal lengths) is much higher than that of the AOSs with phase modulation in the focal plane of the WFS objective. The laboratory setup used for experimental study of the adaptive optical systems based on wave-front sensor with spatially separated control channels is described. In this setup, we used deformable mirrors with correspondingly 7 and 37 PZT actuators of special type. One of the features of these actuators was the existence of two sections: the control section and the modulation one. To study the operation of AOS with phase modulation in the focal plane of the WFS objective, we used special design of phase modulators.