  The occultation of the radio galaxy 0141+268 by the asteroid (372) Palma on
2017 May 15 was observed using six antennas of the Very Long Baseline Array
(VLBA). The shadow of Palma crossed the VLBA station at Brewster, Washington.
Owing to the wavelength used, and the size and the distance of the asteroid, a
diffraction pattern in the Fraunhofer regime was observed. The measurement
retrieves both the amplitude and the phase of the diffracted electromagnetic
wave. This is the first astronomical measurement of the phase shift caused by
diffraction. The maximum phase shift is sensitive to the effective diameter of
the asteroid. The bright spot at the shadow's center, the so called
Arago--Poisson spot, is clearly detected in the amplitude time-series, and its
strength is a good indicator of the closest angular distance between the center
of the asteroid and the radio source. A sample of random shapes constructed
using a Markov chain Monte Carlo algorithm suggests that the silhouette of
Palma deviates from a perfect circle by 26+-13%. The best-fitting random shapes
resemble each other, and we suggest their average approximates the shape of the
silhouette at the time of the occultation. The effective diameter obtained for
Palma, 192.1+-4.8 km, is in excellent agreement with recent estimates from
thermal modeling of mid-infrared photometry. Finally, our computations show
that because of the high positional accuracy, a single radio interferometric
occultation measurement can reduce the long-term ephemeris uncertainty by an
order of magnitude.
