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Wavelength Isolation Sequence Design

A recent paper by Jedwab and Wodlinger renewed interest in a problem of multislit spectrometer design first proposed by Golay in 1951 but subsequently forgotten. It is shown that Golay's formulation of the problem in terms of 0/1 binary sequences is unduly restrictive. By relaxing the restrictions, infinitely many spectrometer designs satisfying all the original physical criteria can be found. Three constructions for such spectrometer designs are presented, involving Golomb rulers and variants. These constructions explain all nontrivial examples involving at most 26 slits.