  This is one of two papers in which we report the detection of structure in
the cosmic infrared background (CIB) between 1.25 - 2.2 micron through the use
of data from the Two Micron Sky Survey (2MASS). This paper concentrates on data
assembly, analysis and the estimate of the various foreground contributions;
the companion paper (Kashlinsky, Odenwald, Mather, Skrutskie, Cutri 2002,
hereafter KOMSC) presents the cosmological results for the CIB fluctuations and
their implications. By using repeated observations of a specific calibration
star field, we were able to achieve integration times in excess of 3900 seconds
compared to the 7.8 seconds in the standard 2MASS data product. This yielded a
point source detection limit (3 \sigma) of +18.5^m in K_s band. The resulting
co-added images were processed to remove point sources to a limiting surface
brightness of +20^m/arcsec$^2 or 40 nW/m^2/sr. The remaining maps contained
over 90% of the pixels and were Fourier transformed to study the spatial
structure of the diffuse background light. After removing resolved sources and
other artifacts, we find that the power spectrum of the final images has a
power-law distribution consistent with clustering by distant galaxies. We
estimate here the contributions to this signal from Galactic foregrounds,
atmospheric OH-glow, zodiacal light and instrument noise, all of which are
small and of different slopes. Hence, this supports the KOMSC identification of
the signal as coming from the CIB fluctuations produced by distant clustered
galaxies.
