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Overview: Apodization is an effective way to relieve the influence of sidelobes in the point spread function of an imaging system, and has found many significant applications in imaging and optical communication, such as the coronagraphs in astronomical field and spectral tailoring in silicon integrated Bragg grating devices. Traditional apodization methods are based on the phase or amplitude modulation. By introducing mask with specially designed transmittance or diffractive optical element to the pupil plane of an imaging system, the sidelobes in the diffraction pattern are well suppressed so that weak details can be distinguished. However, these methods suffer from either narrow working bandwidth or reduced spatial resolution. Recently, as one kind of artificially structured materials, the metasurfaces have drawn much attention because they can manipulate light field at the subwavelength scale. Among them, the metasurface based on the geometric phase principle has been applied in achromatic imaging, broadband hologram, orbit angular momentum beam, and so on, which provides a new approach to modulate the electromagnetic field flexibly in a broadband spectrum. Benefiting from the broadband dispersionless phase modulation, the metasurface also brings another access for apodization imaging. In this paper, a metasurface apodization filter is proposed to realize broadband achromatic apodization imaging. With this filter, the nearly dispersionless phase modulation in the entire visible waveband can be achieved. The simulated results indicate that, compared to phase apodization filter, the working bandwidth can be improved from 10 nm to 300 nm with metasurface apodization filter. Moreover, the focusing efficiency of metasurface apodization filter is twice larger than that of the phase apodization filter. The sidelobes in the point spread function can be efficiently suppressed to the scale of 10-5 with our design, which helps to resolving point-objects with large intensity contrast. Additionally, the resolution of diffraction limit or even sub-diffraction can be achieved with increased imaging contrast by using this method compared to traditional Gaussian apodization filter. The metasurface apodization filter offers a promising alternative for apodization imaging and potentially promotes further developments in the field like astronomical observation, spectrum detection, and optical communication.