3D polarization speckle as a demonstration of tensor version of the van Cittert-Zernike theorem for stochastic electromagnetic beams

Ning Ma, Juan Zhao, Steen Grüner Hanson, Mitsuo Takeda, Wei Wang

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Laser speckle has received extensive studies of its basic properties and associated applications. In the majority of research on speckle phenomena, the random optical field has been treated as a scalar optical field, and the main interest has been concentrated on their statistical properties and applications of its intensity distribution. Recently, statistical properties of random electric vector fields referred to as Polarization Speckle have come to attract new interest because of their importance in a variety of areas with practical applications such as biomedical optics and optical metrology. Statistical phenomena of random electric vector fields have close relevance to the theories of speckles, polarization and coherence theory. In this paper, we investigate the correlation tensor for stochastic electromagnetic fields modulated by a depolarizer consisting of a rough-surfaced retardation plate. Under the assumption that the microstructure of the scattering surface on the depolarizer is as fine as to be unresolvable in our observation region, we have derived a relationship between the polarization matrix/coherency matrix for the modulated electric fields behind the rough-surfaced retardation plate and the coherence matrix under the free space geometry. This relation is regarded as entirely analogous to the van Cittert-Zernike theorem of classical coherence theory. Within the paraxial approximation as represented by the ABCD-matrix formalism, the three-dimensional structure of the generated polarization speckle is investigated based on the correlation tensor, indicating a typical carrot structure with a much longer axial dimension than the extent in its transverse dimension.
Original languageEnglish
Title of host publicationProceedings of SPIE
Number of pages9
PublisherSPIE - International Society for Optical Engineering
Publication date2016
Article number100222F
Publication statusPublished - 2016
EventHolography, Diffractive Optics, and Applications: SPIE conference 10022 - Beijing International Convention Center, Beijing, China
Duration: 12 Oct 201614 Oct 2016


ConferenceHolography, Diffractive Optics, and Applications
LocationBeijing International Convention Center
SeriesProceedings of SPIE, the International Society for Optical Engineering

Bibliographical note

Copyright 2016 Society of Photo Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic electronic or print reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.


  • Coherence
  • Polarization
  • Polarization speckle
  • Coherence tensor


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