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Applied Optics

Applied Optics


  • Vol. 42, Iss. 26 — Sep. 10, 2003
  • pp: 5334–5350

Spatio-temporal operator formalism for holographic recording and diffraction in a photorefractive-based true-time-delay phased-array processor

Andrew Kiruluta, Gour S. Pati, Gregory Kriehn, Paulo E. X. Silveira, Anthony W. Sarto, and Kelvin Wagner  »View Author Affiliations

Applied Optics, Vol. 42, Issue 26, pp. 5334-5350 (2003)

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We present a spatio-temporal operator formalism and beam propagation simulations that describe the broadband efficient adaptive method for a true-time-delay array processing (BEAMTAP) algorithm for an optical beamformer by use of a photorefractive crystal. The optical system consists of a tapped-delay line implemented with an acoustooptic Bragg cell, an accumulating scrolling time-delay detector achieved with a traveling-fringes detector, and a photorefractive crystal to store the adaptive spatio-temporal weights as volume holographic gratings. In this analysis, linear shift-invariant integral operators are used to describe the propagation, interference, grating accumulation, and volume holographic diffraction of the spatio-temporally modulated optical fields in the system to compute the adaptive array processing operation. In addition, it is shown that the random fluctuation in time and phase delays of the optically modulated and transmitted array signals produced by fiber perturbations (temperature fluctuations, vibrations, or bending) are dynamically compensated for through the process of holographic wavefront reconstruction as a byproduct of the adaptive beam-forming and jammer-excision operation. The complexity of the cascaded spatial-temporal integrals describing the holographic formation, and subsequent readout processes, is shown to collapse to a simple imaging condition through standard operator manipulation. We also present spatio-temporal beam propagation simulation results as an illustrative demonstration of our analysis and the operation of a BEAMTAP beamformer.

© 2003 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(070.1060) Fourier optics and signal processing : Acousto-optical signal processing
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(090.0090) Holography : Holography
(280.5110) Remote sensing and sensors : Phased-array radar

Original Manuscript: November 5, 2002
Revised Manuscript: April 16, 2003
Published: September 10, 2003

Andrew Kiruluta, Gour S. Pati, Gregory Kriehn, Paulo E. X. Silveira, Anthony W. Sarto, and Kelvin Wagner, "Spatio-temporal operator formalism for holographic recording and diffraction in a photorefractive-based true-time-delay phased-array processor," Appl. Opt. 42, 5334-5350 (2003)

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