Dynamical properties of speckled speckles

Steen Grüner Hanson, Theis Faber Quist Iversen, Rene Skov Hansen

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We consider the dynamical properties of speckles observed through a second static diffuser arising from a linear or angularly displaced first diffuser. Analytical expressions are obtained for general situations where both the space between the displaced and the static diffuser and the space between the static diffuser and the plane of observation consist of an optical system that can be characterized by a complex-valued ABCD-matrix (e.g. simple and complex imaging systems, free space propagation in both the near-and far-field, and Fourier transform systems). The use of the complex ABCD-method means that diffraction due to inherent apertures is included. One of the diffusers is assumed to give rise to fully developed speckle, i.e. the scattered phase is assumed to be delta-correlated, whereas the second and dynamic diffuser has a finite lateral scale. The illumination of the displaced diffuser is assumed to be Gaussian but the derived expressions are not restricted to a plane incident beam. The results are applicable for speckle-based systems for determining mechanical displacements, especially for long-range systems, and for analyzing systems for measuring biological activity beyond a diffuse layer, e.g. blood flow measurements through human skin.
Original languageEnglish
Pages (from-to)738716
Publication statusPublished - 2010
EventSpeckle 2010: Optical Metrology - Florianapolis, Brazil
Duration: 13 Sep 201015 Sep 2010


ConferenceSpeckle 2010: Optical Metrology
OtherSPIE volume 7387

Bibliographical note

Copyright 2010 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic 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.


  • Bio speckles
  • Speckled speckles
  • Velocity measurement
  • Tissue optics
  • Speckle dynamics


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