We have conducted the first systematic study of Herbig Ae/Be stars using th
e technique of long baseline stellar interferometry in the near-infrared, w
ith the objective of characterizing the distribution and properties of the
circumstellar dust responsible for the excess near-infrared fluxes from the
se systems. The observations for this work have been conducted at the Infra
red Optical Telescope Array (IOTA). The principal result of this paper is t
hat the interferometer resolves the source of infrared excess in 11 of the
15 systems surveyed. A new binary, MWC 361-A, has been detected interferome
trically for the first time. The visibility data for all the sources has be
en interpreted within the context of four simple models which represent a r
ange of plausible representations for the brightness distribution of the so
urce of excess emission: a Gaussian, a narrow uniform ring, a flat blackbod
y disk with a single temperature power law, and an infrared companion. We f
ind that the characteristic sizes of the near-infrared emitting regions are
larger than previously thought (0.5-5.9 AU, as given by the FWHM of the Ga
ussian intensity). A further major result of this paper is that the sizes m
easured, when combined with the observed spectral energy distributions, ess
entially rule out accretion disk models represented by black-body disks wit
h the canonical T (r) proportional to r(-3/4) law. We also find that, withi
n the range observed in this study, none of the sources (except the new bin
ary) shows varying visibilities as the orientation of the interferometer ba
seline changes. This is the expected behavior for sources which appear circ
ularly symmetric on the sky, and for the sources with the largest baseline
position angle coverage (AB Aur, MWC 1080-A) asymmetric brightness distribu
tions (such as inclined disks or binaries) become highly unlikely. Taken as
an ensemble, with no clear evidence in favor of axisymmetric structure, th
e observations favor the interpretation that the circumstellar dust is dist
ributed in spherical envelopes (the Gaussian model) or thin shells (the rin
g model). This interpretation is also supported by the result that the meas
ured sizes, combined with the excess near-infrared fluxes, imply emission o
f finite optical depth, as required by the fact that the central stars are
optically visible. The measured sizes and brightnesses do not correlate str
ongly with the luminosity of the central star. Moreover, in two cases, the
same excess is observed from circumstellar structures that differ in size b
y more than a factor of 2 and surround essentially identical stars. Therefo
re, different physical mechanisms for the near-infrared emission may be at
work in different cases, or alternatively, a single underlying mechanism wi
th the property that the same infrared excess is produced on very different
physical scales.