Reconstruction of a wavefront of a light beam containing optical vortices

A method for reconstructing the wavefront of a light beam by analyzing wavefront-gradient data of said light beam, the light beam containing at least one optical vortex (V), considering the contribution of the optical vortices (V) to the wavefront, the method comprising:

• a) providing a phase-gradient map g of the wavefront of the light beam,
• b) generating a Laplacian of a vector potential based on the phase gradient map g, the resulting Laplacian of the vector potential map (−ΔAz), called “Laplacian map”, exhibiting peaks (P), the Laplacian map being obtained by applying a curl operator to the phase-gradient map g,
• the location of each peak (P) corresponding to the location (u) of an optical vortex (V) and the integral of the peak being proportional to a topological charge n of said optical vortex (V),
• c) applying an image processing method to the Laplacian map to extract the location (u) and the charge n of optical vortices, the image processing method comprising a segmentation of the Laplacian map into a plurality of segments (Ω) to obtain a segmented Laplacian map, segments (Ω) being determined so that different peaks of the Laplacian map belong to different segments;
• d) for these different segments (Ω) of the segmented Laplacian map (−ΔAz):
• i) determining the location (u) of the corresponding peak (P) in the segment (Ω) of the Laplacian map (−ΔAz) to locate the corresponding optical vortex (V),
• ii) computing an approximate value of the integral of the corresponding peak (P) over the segment (Ω), and determining the topological charge n of the corresponding vortex (V) based on said approximate value of the integral of said peak (P);
• e) computing a singular phase map φs based on the topological charge n and location (u) of each optical vortex (V) computed in steps i) and ii),
• the singular phase φs map being representative of the contribution of the optical vortex and being computed by:
• iii) generating a vortex-location map, where map values are equal to the corresponding topological charges n of optical vortices at optical vortices locations (u), and
• iv) convoluting said vortex-location map with a single +1 spiral phase profile;
• f) reconstructing the wavefront of the light beam with:
• computing a regular phase φR map of the light beam, the regular phase corresponding to a vortex-free phase computed from the irrotational component,
• adding the regular phase φR to the singular phase φs to obtain the said reconstructed wavefront of the light beam.