It is known that image reconstruction (Talbot images) and spectra restoration (Talbot spectra) phenomena can be found for light diffraction of linear periodic structures. In this work the possibility of finding similar effects for a circular symmetric object, especially for one with amplitude transmittance J0(ρ) (zero-order Bessel function of the first kind) is discussed theoretically. The transfer function approach and the spatial-spectral correspondence relationship are used to investigate these effects, and conditions for image reconstruction and spectra restoration in the near field are obtained. The discussion of a more general form of amplitude transmittance is also included, and a comparison between the two types (linear periodic and circular symmetric structures) is made.