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While information is ubiquitously generated, shared, and analyzed in amodern-day life, there is still some controversy around the ways to asses theamount and quality of information inside a noisy optical channel. A number oftheoretical approaches based on, e.g., conditional Shannon entropy and Fisherinformation have been developed, along with some experimental validations. Someof these approaches are limited to a certain alphabet, while others tend tofall short when considering optical beams with non-trivial structure, such asHermite-Gauss, Laguerre-Gauss and other modes with non-trivial structure. Here,we propose a new definition of classical Shannon information via the Wignerdistribution function, while respecting the Heisenberg inequality. Followingthis definition, we calculate the amount of information in a Gaussian,Hermite-Gaussian, and Laguerre-Gaussian laser modes in juxtaposition andexperimentally validate it by reconstruction of the Wigner distributionfunction from the intensity distribution of structured laser beams. Weexperimentally demonstrate the technique that allows to infer field structureof the laser beams in singular optics to assess the amount of containedinformation. Given the generality, this approach of defining information viaanalyzing the beam complexity is applicable to laser modes of any topology thatcan be described by 'well-behaved' functions. Classical Shannon informationdefined in this way is detached from a particular alphabet, i.e. communicationscheme, and scales with the structural complexity of the system. Such a synergybetween the Wigner distribution function encompassing the information in bothreal and reciprocal space, and information being a measure of disorder, cancontribute into future coherent detection algorithms and remote sensing.

Quantifying information via Shannon entropy in spatially structured optical beams