Reconstruction the phase front of a vortex laser beam is conducted by use of a Hartmann-Shack wavefront sensor. The vortex beam in the form of the Laguerre-Gaussian LG(0)(1) mode is generated with the help of a spiral phase plate. The new reconstruction technique based on measured wavefront gradients allows one to restore the singular phase surface with good accuracy, whereas the conventional least-squares approach fails.

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The phase correction of a vortex laser beam is undertaken in the closed-loop adaptive system including a Hartmann-Shack wavefront sensor with singular reconstruction technique and a bimorph piezoceramic mirror. After correction the vortex doughnutlike beam is focused into a beam with bright axial spot that considerably increases the Strehl ratio and optical system resolution. Since the phase break cannot be exactly reproduced on the flexible mirror surface, off-axis vortices appear in the far field at the beam periphery.

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An adaptive optical system is developed to correct the wavefront of laser radiation distorted by a turbulent air flow. The use of a field-programmable gate array as the main control element makes it possible to achieve a system bandwidth of 2 kHz. The results of experiments on dynamic correction of the phase of a laser beam distorted by a flow of heated air are presented and analysed.