Moments of the Wigner distribution of rotationally symmetric partially coherent light | Zendy

Martin J. Bastiaans | Zendy; Tatiana Alieva | Zendy

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Moments of the Wigner distribution of rotationally symmetric partially coherent light

Author(s) -

Martin J. Bastiaans,

Tatiana Alieva

Publication year - 2003

Publication title -

optics letters

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.524

H-Index - 272

eISSN - 1071-2763

pISSN - 0146-9592

DOI - 10.1364/ol.28.002443

Subject(s) - physics , wigner distribution function , distribution (mathematics) , fourier transform , symmetry (geometry) , order (exchange) , measure (data warehouse) , velocity moments , method of moments (probability theory) , moment (physics) , optics , rotational symmetry , mathematical analysis , quantum mechanics , mathematics , geometry , quantum , zernike polynomials , statistics , finance , database , wavefront , estimator , computer science , mechanics , economics

The Wigner distribution of rotationally symmetric partially coherent light is considered, and the constraints for its moments are derived. Although all odd-order moments vanish, these constraints lead to a drastic reduction in the number of parameters that we need to describe all even-order moments: whereas in general we have (N + 1)(N + 2)(N + 3)/6 different moments of order N, this number reduces to (1 + N/2)2 in the case of rotational symmetry. A way to measure the moments as intensity moments in the output planes of (generally anamorphic) fractional Fourier-transform systems is presented.

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