  The two-dimensional (2D) offset linear canonical transform (OLCT) in polar
coordinates plays an important role in many fields of optics and signal
processing. This paper studies the 2D OLCT in polar coordinates. Firstly, we
extend the 2D OLCT to the polar coordinate system, and obtain the offset linear
canonical Hankel transform (OLCHT) formula. Secondly, through the angular
periodic function with a period of 2{\pi}, the relationship between the 2D OLCT
and the OLCHT is revealed. Finally, the spatial shift and convolution theorems
for the 2D OLCT are proposed by using this relationship.
