  We design a new absolute optical instrument by composing Luneburg lens and
Lissajous lens, and analyze its imaging mechanism from the perspective of
simple harmonic oscillations. The imaging positions are determined by the
periods of motions in x and y directions. Besides, instruments composed with
multi parts are also devised, which can form imaging or self-imaging as long as
the motion periods of x and y directions are satisfied to similar conditions.
Our work provides a new way to analyze the imaging of different lens by simply
dissociating the equations of motions, and reveal the internal mechanism of
some absolute optical instruments.
