  The Kikuchi bands arise from Bragg diffraction of incoherent electrons
scattered within a crystalline specimen and can be observed in both the
transmission and reflection modes of scanning electron microscopy (SEM).
Converging, rocking, or grazing incidence beams must be used to generate
divergent electron sources to obtain the Kikuchi pattern. This paper report the
observation of Kikuchi pattern from SEM images of an exceptional rotating
crystal with continuous rotation in the local crystal direction and satisfying
cylindrical symmetry, named a cylindrically symmetric rotating crystal. SEM
images of cylindrically symmetric rotating crystals reflect the interactions
between electrons and the sample in both the real- and momentum-space.
Furthermore, we identify an unexpected mathematical relationship between the
electron backscattered diffraction (EBSD) Kikuchi pattern matrix map and the
SEM image of the present sample which can be rationalized as a concrete example
of the Banach fixed-point theorems in the field of EBSD technique.
