We have conducted the first systematic study of Herbig Ae/Be stars using the technique of long baseline stellar interferometry in the near-infrared. The principal result of this paper is that the IOTA interferometer resolves the source of infrared excess in 11 of the 15 systems surveyed. The visibility data for all the sources has been interpreted within the context of four simple models which represent a range of plausible representations for the brightness distribution of the source of excess emission: a Gaussian, a narrow uniform ring, a flat blackbody disk with a single temperature power law, and an infrared companion. We find 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 Gaussian intensity). A further major result of this paper is that the sizes measured, when combined with the observed spectral energy distributions, essentially rule out accretion disk models represented by blackbody disks with the canonical radial temperature law with exponent -3/4. We also find that, within the range observed in this study, none of the sources (except the new binary) shows varying visibilities as the orientation of the interferometer baseline changes. Taken as an ensemble, with no clear evidence in favor of axi-symmetric structure, the observations favor the interpretation that the circumstellar dust is distributed in spherical envelopes (the Gaussian model) or thin shells (the ring model).
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