Optical EngineeringLimiting aspect ratios of Sagnac interferometers
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Any two-beam interferometer may be employed as a Fourier transform spectrometer. The two most commonly used for Fourier transform spectrometry are the Michelson interferometer and the Sagnac interferometer, the relative merits of which have been discussed in the literature. Typically, it is the interferometer that limits the acceptable range of angles for the input beam, and this maximum acceptance angle in turn limits the etendue, and hence limits the responsivity of the instrument when viewing an extended source. In designs where the interferometer is in a diverging or converging beam, the allowable range of input angles limits the focal ratio of the instrument, while in designs where the beam is collimated through the interferometer, this effect limits the field-of-view of the instrument. In a Michelson, it is a loss of fringe contrast that limits the range of acceptance angles; a limitation that is discussed in many general texts on optics. A Sagnac, however, suffers no such loss of contrast as the range of acceptance angles is increased. The maximum acceptance angle for a Sagnac is instead limited by vignetting, caused by the geometry of the interferometer. The limitation for a Sagnac has an origin and behavior entirely different from that found for a Michelson, and has not been previously discussed in the literature. It is therefore important to understand this limitation when designing a Sagnac interferometer for Fourier transform spectrometry. This vignetting limitation may be quantified by an aspect ratio, which we define as the ratio of the separation of the entrance and exit apertures to the width of these apertures in the plane of the interferometer. To facilitate the design of Sagnac interferometers for Fourier transform spectrometry, we discuss the limitations on the aspect ratio and derive equations for the limiting aspect ratios for nine variations of the Sagnac interferometer.