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Hexagonal sampling in the infrared domain: an introduction to array set addressing

It has been known since the early 1960s that hexagonal sampling is the optimal sampling approach for isotropically band-limited images, providing a 13.4% improvement in sampling efficiency over rectangular sampling. Despite this fact and other significant advantages of hexagonal sampling, rectangular sampling is still used for virtually all modern digital image processing systems. This is arguably due to the lack of an efficient addressing system for hexagonal grids. Array set addressing (ASA) is a recent advance in addressing hexagonal grids that allows image processing techniques to be performed efficiently on hexagonally sampled images. This paper will describe ASA and discuss its advantages. With ASA, a renewed interest in sensors that sample hexagonally is occurring. We will describe a new visible imager that simultaneously samples both hexagonally and rectangularly. This novel research tool has the ability to provide real imagery that can be used to quantitatively compare the performance of an image processing operation on both hexagonally sampled and rectangularly sampled images. We will also describe current efforts and plans for future visible sensors that sample hexagonally. The advantages of hexagonal sampling are not limited to the visible domain and should be equally realizable in the infrared domain. This paper will discuss considerations for developing infrared sensors that sample hexagonally. On-focal plane array (FPA) processing, readout architectures, detector materials, and bump-bonding are among the topics to be discussed.