The Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA) instrument measured stratospheric temperatures and trace species concentrations with high precision and spatial resolution during two missions. The measuring technique is infrared limb-sounding of optically thin emissions. In a general approach, we investigate the applicability of the technique to measure gravity waves (GWs) in the retrieved temperature data. It is shown that GWs with wavelengths of the order of 100–200 km horizontally can be detected. The results are applicable to any instrument using the same technique. We discuss additional constraints inherent to the CRISTA instrument. The vertical field of view and the influence of the sampling and retrieval imply that waves with vertical wavelengths ∼3–5 km or larger can be retrieved. Global distributions of GW fluctuations were extracted from temperature data measured by CRISTA using Maximum Entropy Method (MEM) and Harmonic Analysis (HA), yielding height profiles of vertical wavelength and peak amplitude for fluctuations in each scanned profile. The method is discussed and compared to Fourier transform analyses and standard deviations. Analysis of data from the first mission reveals large GW amplitudes in the stratosphere over southernmost South America. These waves obey the dispersion relation for linear two-dimensional mountain waves (MWs). The horizontal structure on 6 November 1994 is compared to temperature fields calculated by the Pennsylvania State University (PSU)/National Center for Atmospheric Research (NCAR) mesoscale model (MM5). It is demonstrated that precise knowledge of the instrument's sensitivity is essential. Particularly good agreement is found at the southern tip of South America where the MM5 accurately reproduces the amplitudes and phases of a large-scale wave with 400 km horizontal wavelength. Targeted ray-tracing simulations allow us to interpret some of the observed wave features. A companion paper will discuss MWs on a global scale and estimates the fraction that MWs contribute to the total GW energy (Preusse et al., in preparation, 2002).