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Applied Optics

Applied Optics


  • Vol. 40, Iss. 23 — Aug. 10, 2001
  • pp: 3894–3900

Hexagonal binary arrays with perfect correlation

Axel Busboom and Hans Dieter Lüke  »View Author Affiliations

Applied Optics, Vol. 40, Issue 23, pp. 3894-3900 (2001)

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Two-dimensional binary signals (arrays) with good autocorrelation properties are needed for coded-aperture imaging systems. In many astrophysical instruments, circular detectors with hexagonally packed detector elements are used, such that hexagonal coded apertures are often preferable to rectangular ones. A general method for folding a one-dimensional sequence into a hexagonal array is presented, by which the periodic or odd-periodic correlation properties of the original sequence are preserved. This method is applied to a known family of sequences with perfect odd-periodic correlation, yielding a new family of almost-binary and odd-perfect—or binary and almost odd-perfect—hexagonal arrays with optimum properties for coded-aperture imaging. The new odd-perfect arrays have near-uniform side lengths and exist for many more sizes than known families of even-periodic hexagonal arrays with good imaging properties.

© 2001 Optical Society of America

OCIS Codes
(170.1630) Medical optics and biotechnology : Coded aperture imaging
(340.7430) X-ray optics : X-ray coded apertures

Original Manuscript: September 8, 2000
Revised Manuscript: April 26, 2001
Published: August 10, 2001

Axel Busboom and Hans Dieter Lüke, "Hexagonal binary arrays with perfect correlation," Appl. Opt. 40, 3894-3900 (2001)

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