Wavelength Isolation Sequence Pairs

In the early 1950s, Golay studied binary sequence pairs whose autocorrelation properties are ideal for use in the design of multislit spectrometers. He found examples for some small lengths, but, unable to find more, he suggested that perhaps further examples do not exist and turned his attention to an alternative solution to the design problem (involving what are now called Golay complementary sequence pairs). The original sequence pairs that Golay sought appear to have been overlooked in the sixty years since. We present examples of these pairs, which we call wavelength isolation sequence pairs, for two new lengths. We provide structural constraints on these sequence pairs and describe a method whereby each of the currently known examples can be constructed from a perfect Golomb ruler. 1 History and Motivation A spectrometer is a device that produces a spectrum from a source of electromagnetic radiation (see [3] for background on spectrometers). For example, such a device may be used in the analysis of light emitted from an unknown incandescent material in order to establish its chemical makeup. When the incident radiation comprises more than one wavelength, it is often desirable to distinguish a particular wavelength of interest from background radiation. In 1951, Golay [5] discussed a spectrometer design that isolates radiation of interest (desired radiation) from background radiation by processing incoming radiation in two ‘streams’, each consisting of an entrance mask, an exit mask and a detector. The entrance and exit masks are opaque surfaces with a pattern of narrow, equally spaced rectangular slits through which radiation passes on its way to identical detectors. The principle is that if radiation of a background wavelength is always passed through the two streams in equal quantities, while radiation of the desired wavelength is passed differentially by the two streams, then the difference in total energy as measured by the two detectors is wholly attributable to radiation of the desired wavelength. Fig. 1 shows a schematic representation of such a spectrometer. ? J. Jedwab is supported by an NSERC Discovery Grant. ?? J. Wodlinger was supported by an NSERC Canada Graduate Scholarship.