The relation between a three-dimensional (3D) object and its diffracted wavefront in the 3D Fourier space is discussed at first and then a rigorous diffraction formula onto cylindrical surfaces is derived. The azimuthal direction and the spatial frequency direction corresponding to height can be expressed with a one-dimensional (1D) convolution integral and a 1D inverse Fourier transform in the 3D Fourier space, respectively, and fast Fourier transforms are available for fast calculation. A numerical simulation of a diffracted wavefront on cylindrical surfaces is presented. An alternative optical experiment equivalent of the optical reconstruction from cylindrical holograms is also demonstrated.
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