Leon wrote:
"I guess that the black cylinder is just a waveguide."

Not exactly. At the frequencies used with grid dishes, the feedline is
usually coax. Waveguide would be too big.

The cylinder is a shield which allows a little dipole to illuminate the
dish but does not allow direct radiation in the same direction as that
reflected from the dish.

The rays reflected from the dish are parallel to each other and
perpendicular to the circumference of the dish. Parallel rays reflected
by the dish pass through its focal point where the dipole is located.

The transit time within the dish is long near its center and short near
its edges. Phase between direct feed radiation and reflected radiation
would be a mess were the direct radiation allowed, so the black cylinder
is used to clean up the dish pattern.

Best regards, Richard Harrison, KB5WZI