We have obtained high angular resolution (0.'' 13 FWHM) near-infrared
images of the central similar to 40 '' x 40 '' of the Trapezium cluste
r, using a speckle holography technique that we describe in detail. A
search for close binary systems was made in K-s (2.16 mu m) and H (1.6
5 mu m) mosaic images, in which 45 and 35 stars were detected, respect
ively. The sensitivity limits for stellar detections are K-s similar o
r equal to 14.8 and H similar or equal to 14.9 over the whole mosaics
and K-s similar or equal to 16.0 and H similar or equal to 15.9 for th
ose regions of the mosaics where most data were accumulated, thus pote
ntially including objects with substellar masses down to similar to 0.
04 M.. In total, four binary systems were identified with projected li
near separations in the range of 0.'' 14-0.'' 5 (63-225 AU). The resul
ting binary fraction for low-mass pre-main-sequence stars is 5.9% +/-
4.0%. This fraction agrees well with the binary frequency observed for
main-sequence field stars, but is lower by a factor of similar to 3 t
han the fraction found from observations of young stars in Taurus-Auri
ga over the same range of separations. The difference in binary freque
ncy between the core of the Trapezium cluster and the low-mass, low st
ellar density dark cloud Taurus-Auriga is established at a statistical
significance level of 96% and suggests that binary frequencies are af
fected by the local star-forming environment. We show that the massive
Trapezium star theta(1) Ori A has a nearby companion separated by sim
ilar to 0.'' 2 (similar to 90 AU). The location of this companion is c
oincident, within the positional uncertainties, with a nonthermal and
variable VLA radio source, which was previously associated with theta(
1) Ori A itself. We give H photometry for 32 stars, K-s photometry for
43 stars, and present a color-magnitude diagram for the Trapezium cor
e.