The selfimaging phenomenon of twodimensional periodic object is studied based on the scalar diffraction theory, and the selfimaging conditions are extended. It is pointed out that if the square ratio of the two period lengths can be expressed as a quotient of two integers, there exist period angles between the two period directions that can achieve selfimaging. On the other hand, if the square of cosine of the period angle between the two period directions is a rational number, it is possible to find a proper proportion of the two period lengths to satisfy selfimaging. Furthermore, the numerical relation between equivalent combinations of period lengths and angles, which describe the same twodimensional periodic object, is analyzed. The analysis can be utilized to determine whether two combinations of period lengths and angles are equivalent. The simulation result agrees well with the discussion.