  We study the optical appearance of a thin accretion disk around the strongly
naked static Janis-Newman-Winicour singularity. The solution does not possess a
photon sphere, which results in the formation of a complex structure of bright
rings in the central region of the disk image. Such structure is absent in the
case of the Schwarzschild black hole with a thin accretion disk, where instead
of the image we observe the black hole shadow. Some of the rings emit with the
maximal observable radiation flux from the accretion disk, and should be
experimentally detectable. Thus, this qualitatively new feature can be used to
distinguish observationally black holes from naked singularities. We elucidate
the appearance of the ring structure by revealing the physical mechanism of its
formation, and explaining the nature of each of the ring images. We make the
conjecture that a similar structure would also appear for other solutions
without a photon sphere and it can serve as a general observational signature
for distinguishing compact objects possessing no photon sphere from black
holes.
