Reconstruction of structured light beams after random phase distortions

The paper investigates the process of measuring the spatial characteristics of a chaotic speckle pattern. Our approach is based on measuring the amplitudes and phases of the Hermite-Gauss (HG) modes in the speckle pattern formed by the superposition of the HG and LG modes. The speckle pattern was formed on the hologram of the spatial light modulator. This method made it possible to measure a spiral beam of light in the shape of a regular triangle and restore not only the original pattern, but also each of its own HG modes.