Passive Imaging Through Media with Distributed Inhomogeneities Using an Extension of the Phase Closure Technique

  • K. A. Marsh
  • J. M. Richardson
Part of the Acoustical Imaging book series (ACIM, volume 15)


We have investigated the application of the phase closure technique to the problem of passive imaging of a spatially uncorrelated noise source through an inhomogeneous medium whose properties are known only statistically. The measurement system consists of an array of transducers whose signals are processed in a manner similar to that used in radio interferometry of celestial sources. Although the standard phase closure technique is not directly suited to a medium with distributed inhomogeneities, a simple pre-processing step can be used to overcome this limitation in many cases. This procedure, to which we refer as “cross-correlated subarrays” involves processing the transducer signals in groups, corresponding to operating the array as a series of smaller subarrays. The beamwidth of a subarray is chosen to restrict the response of the system to the angular field over which the assumptions of phase closure are valid. If we let Δxc be the coherence scale of the field (a function of the parameters of the medium, together with range R and wavelength λ) then for phase closure to be valid (with or without cross-correlated subarrays) we require Δxc > (λR)1/2. Cross-correlated subarrays are required explicitly if the maximum source separation, s, is such that s > Δxc. These expectations have been tested by means of a series of numerical experiments, and the results will be presented.


Phase Error Beam Pattern Phase Distortion Phase Closure Coherence Scale 
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Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • K. A. Marsh
    • 1
  • J. M. Richardson
    • 1
  1. 1.Rockwell International Science CenterThousand OaksUSA

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