We have made two VLBI images of the nucleus of the quasar 3C 345 from observations in 1989 and 1990 with 1 mas (4 pc) resolution. These 5 GHz images have a dynamic range greater than 1000:1 and show the well-known compact core and superluminal jet, whose subcomponents move away from the core at almost-equal-to 0.3 mas yr-1. Within 5 mas of the nucleus the jet expands with an apparent opening angle of almost-equal-to 25-degrees; between 5 and 11 mas the boundary is approximately cylindrical. In this latter region, the jet appears to be edge-brightened and is suggestive of tangled or perhaps helically wound filaments, consistent with models in which the emission is confined to a boundary layer between the jet and the confining medium. A prominent gap in the jet is found between approximately 11 and 15 mas radius from the nucleus, perhaps resulting from a change in the angle theta which the jet axis makes with the line of sight, but more likely from a sudden reduction in emissivity. Jet emission resumes abruptly at a radius of 15 mas, where an extended component "C1" is found with a surprising morphology, namely a sharp "edge" (representing a flat surface edge-on) facing the core. The apparent opening angle of the jet flares at this point, enlarging to almost-equal-to 35-degrees, perhaps the result of a shock. We show that this component is also superluminal, at a deprojected distance of more than 600 pc from the nucleus. This jet morphology has many similarities with the shock (knot "A") seen in the jet of the radio galaxy M87. Relativistic aberration affects the appearance of the jet: photons received at Earth from the " edge " of C1 were emitted (in the component's rest frame) almost perpendicular to the jet direction. A standard relativistic twin-jet model is consistent with our observations and with imaging at other frequencies at many epochs. Using this model and some simplifying assumptions, we derive jet fluid Lorentz factor gamma and orientation theta from four measured quantities: (a) superluminal motion; (b) a lower limit to the Doppler factor from measured inverse-Compton X-ray emission; (c) limits to the jet to counterjet ratio-no counter-jet detection has been made on parsec scales; (d) the effect of relativistic aberration on jet viewing angle. The derived values (gamma = 7.2 +/- 1.1; theta = 6.8-degrees +/- 1.5-degrees) are the most tightly constrained of any known relativistic jet in an extragalactic object.
