Fast calculation method for computer-generated cylindrical hologram based on wave propagation in spectral domain

Abstract

A fast calculation method for computer generation of cylindrical holograms is proposed. The calculation method is based on wave propagation in spectral domain and in cylindrical co-ordinates, which is otherwise similar to the angular spectrum of plane waves in cartesian co-ordinates. The calculation requires only two FFT operations and hence is much faster. The theoretical background of the calculation method, sampling conditions and simulation results are presented. The generated cylindrical hologram has been tested for reconstruction in different view angles and also in plane surfaces.

Digital plasmonic holography

“…1d . The following is completely analogous to the angular spectrum method 45 and is applied here to the propagation of plasmons on a surface. In this case, the plasmonic field is given in polar coordinates and is propagated radially inward with using the Fourier series relationship given here: …”

Fast calculation method for computer-generated cylindrical holograms based on the three-dimensional Fourier spectrum

“…The calculation time is about 60 s. If the total calculation time is proportional to the product of the sampling numbers of the object and the observation surface, our method would be approximately 100 times faster than the method proposed in [7], in which FFTs are not used. The other reported methods [8][9][10] use FFTs and have speeds comparable to the proposed method. However, the other methods suffer from a serious drawback in that hidden surface cannot be removed.…”

“…The fast Fourier transform (FFT) is the most common technique for fast calculation and its effect is drastic. Algorithms using FFTs, in which the diffraction integral for a cylindrical surface is calculated through a convolution method [8] and through a spectral propagation method [9], have been proposed by defining a 3D object in the cylindrical coordinate system. Kashiwagi and Sakamoto proposed a new method based on the angular spectrum of a plane wave; in this method, a 3D object is defined in the Cartesian coordinate system [10].…”

Fast calculation method of computer-generated cylindrical hologram using wave-front recording surface

“…The calculation time required in their method is 10,000 times less than that of the direct method, however the object is limited to be a cylinder. Jackin et al [8] proposed a method which uses a helical wave spectrum method in cylindrical coordinates. This method uses only two FFT loops for simulating the wave propagation, but the shape of the object is also limited to be a cylinder.…”

“…A CGCH is obtained to execute the diffraction calculation from the WRS to the CGCH, and propagate the recorded optical field of the WRS to the cylindrical hologram surface using helical wave spectrum algorithm [8] with three FFT operations. From WRS to CGCH, only outward wave propagation surface is considered.…”