We have built an infrared beam combiner for the GI2T/REGAIN interferometer of the Observatoire de la Cote dAzur. The beam combiner allows us to record spectrally dispersed Michelson interference fringes in the near-infrared J-, H- or K-bands. The beam combiner has the advantage that Michelson interferograms can simultaneously be recorded in about 128 different spectral channels. The tilt of the spectrally dispersed fringes is a measure of the instantaneous optical path difference. We present the optical design of the beam combiner and GI2T/REGAIN observations of the Mira star R Cas with this beam combiner in the spectral range of 2.00 micron - 2.18 micron (observations on 22 and 25 August 1999; variability phase 0.08; V-magnitude approx. 6; seven baselines between 12m and 24m; reference stars Vega and Beta Peg). The spectrograph of the beam combiner consists of an anamorphotic cylindrical lens system, an image plane slit, and a grism. A system of digital signal processors calculates the ensemble average power spectrum of the spectrally dispersed Michelson interferograms and the instantaneous optical path difference error in real time. From the observed R Cas visibilities at baselines 12.0m, 13.8m and 13.9m, a 2.1 micron uniform-disk diameter of 25.3mas +/-3.3mas was derived. The unusually high visibility values at baselines >16m show that the stellar surface of R Cas is more complex than previously assumed. The visibility values at baselines >16m can be explained by high-contrast surface structure on the stellar surface of R Cas or other types of unexpected center-to-limb variations. The R Cas observations were compared with theoretical Mira star models yielding a linear Rosseland radius of 276Rsun +/-66Rsun and an effective temperature of 2685K+/-238K for R Cas at phase 0.08.
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