A type of scalable self-imaging capable of variable magnification or minification of periodic objects is demonstrated in the focal plane of a lens illuminated by a point source. The theory and the experimental results show that the self-imaging phenomenon can also be realized in the focal plane of a lens regardless of whether the distances satisfy the lens formula or not. The particular property of this scalable self-imaging effect is that the images in the focal plane can be controlled with different scaling factors only when the distances between the point source and the periodic object satisfy a certain condition. This discovery should open a new field of diffraction imaging and new application opportunities in precision measurement.