complementary medium by a superlens in order to cancel the scattering of object A, and then to shift another object (B) into the position of object A, therefore, when we detect the scattering pattern we will find that object A appears like object B. TO is a strict method to design illusion devices in theory. However, some restrictions should be noted: (I) Complementary media and superlenses are composed of negative index materials, which require the help of evanescent waves to fulfill the functions of illusion devices. Therefore, in order to ensure the performance of the illusion, the external device (superlens) and the object should be as close as possible (in the near field) to receive adequate evanescent waves. (II) The introduction of negative index materials inevitably makes the device loss sensitive, which is a key factor limiting its performance. (III) The material parameters of the device are very complex, including negative index materials, magnetic materials, anisotropic materials, etc. These are a few of the main reasons why these illusion devices are too difficult to put into real applications.In addition to the method of TO, a new way to artificially manipulate electromagnetic waves has been proposed in 2015 by using spatial Kramers-Kronig (KK) media. [26] This method modifies the scattering potentials in the wave vector domain and makes the scattering potentials zero in the backward direction, that is, no reflections. This method has also been employed to design absorbers and invisibility cloaks. [27][28][29][30] Due to the asymmetrical properties of the scattering potentials, these KK media always require complex materials (with loss or gain). A similar method has been proposed recently to design all-dielectric cloaks, [31] which eliminates two symmetrical areas of scattering potentials in the 2D wave vector domain to make the object invisible within a specified frequency band, and the symmetric conditions ensure that the material has no loss or gain. Besides the above method, some other methods [32,33] for cloaking and illusions are also interesting, for example, characteristic mode method, [34] metasurface method. [35] Our method has several advantages compared with the conventional TO method: first, no external devices are needed in our design because we only slightly modify the scattering potential of the object and the nearby surroundings, which is more of a cosmetic operation for an object; second, no negative refractive index materials are introduced, which is a key factor restricting the effect of the illusion; third, all of the materials are isotropic, nonmagnetic, and with relative permittivity above unity, which makes this method more feasible for real applications of illusion. Now we show the designing method by deducing the relation between the scattering amplitude and the Fourier component of the scattering potential. Considering the 2D case (in