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.
© 2013 Optical Society of America
Original Manuscript: September 23, 2013
Revised Manuscript: October 22, 2013
Manuscript Accepted: October 30, 2013
Published: November 27, 2013
Yusuke Sando, Daisuke Barada, Boaz Jessie Jackin, and Toyohiko Yatagai, "Fast calculation method for computer-generated cylindrical holograms based on the three-dimensional Fourier spectrum," Opt. Lett. 38, 5172-5175 (2013)