The invariant cross section as a function of transverse momentum for antideuterons produced in 158A GeV͞c per nucleon Pb 1 Pb central collisions has been measured by the NA44 experiment at CERN. This measurement, together with a measurement of antiprotons, allows for the determination of the antideuteron coalescence parameter. The extracted coalescence radius is found to agree with the deuteron coalescence radius and radii determined from two particle correlations. PACS numbers: 25.75.Dw, 14.20.Dh, 25.40.Ve In central collisions of heavy ions, e.g., Pb 1 Pb, at ultrarelativistic energies, a region of highly compressed and heated nuclear matter is formed. This region subsequently expands both along and transverse to the beam direction until the constituent particles cease to interact at freezeout. In order to be able to derive characteristic energy and matter densities, it is important to determine the spatial extent and the density profile of the expanding source at the time of freeze-out. Such information has so far come primarily from Hanbury-Brown and Twiss (HBT) interferometry, where the extent of the source can be estimated from the dependence of the two particle correlation function on the relative momentum of the two particles (e.g., p 2 p [1,2]). Interpretation of HBT data normally relies on assumptions on the density profile of the emitting source.Independent information on source characteristics can be obtained from a different two body correlation, namely, the formation of deuterons and antideuterons. As a consequence of the small binding energy of the deuteron (2.2 MeV) compared to typical kinetic energies of the particles in the fireball, deuterons can survive only when the probability for collisions within the expanding source is very small, i.e., near freeze-out. At the same time, the formation of the bound two nucleon state requires the presence of a third body to conserve energy and momentum. This introduces a delicate dependence of the formation and survival probability of the (anti)deuteron on the size and density profile of the source.It is of particular interest to study the production of antideuterons and the associated freeze-out volume. Antideuterons are all produced in the collision, and the production rate will thus depend on the production and annihilation probabilities of antiparticles in the medium. Additionally, antideuterons have no contribution from spectator fragments, thus guaranteeing a measurement of the participant source volume. This Letter reports on the first systematic measurement of antiproton and antideuteron yields at nonzero transverse momenta from 158A GeV͞c Pb 1 Pb central collisions at the CERN SPS accelerator. Earlier measurements from Si 1 Au at the AGS and for minimum bias and p t 0 Pb 1 Pb (SPS) are reported in Refs. [3][4][5].In a simple coalescence approach [6,7], composite particles are formed only if the constituent particles are close in phase space at freeze-out. The invariant cross section of the cluster is then expressed as the product of the invaria...