Geodesic
Spiral beams analysis based on astigmatic transform
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 149 (2007) no. 1, pp. 110-114 
P. G. Kharskii; K. N. Afanas'ev. Spiral beams analysis based on astigmatic transform. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 149 (2007) no. 1, pp. 110-114. http://geodesic.mathdoc.fr/item/UZKU_2007_149_1_a16/
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     author = {P. G. Kharskii and K. N. Afanas'ev},
     title = {Spiral beams analysis based on astigmatic transform},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {110--114},
     year = {2007},
     volume = {149},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2007_149_1_a16/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The phase retrieval algorithm for spiral beams with preset intensity distribution is demonstrated. Two-dimensional light field with like-sign phase singularities can be reduced to one-dimensional field under astigmatic transform, performed by ordinary cylindrical and spherical optics. The result field contains complete information about initial one and at the same time is more convenient for observation and registration. The following interference analysis allows to restore the quantity of singularities and their location in the low-intensity areas.

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