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
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)