Cylindrical angular spectrum using Fourier coefficients of point light source and its application to fast hologram calculation.

Abstract

We will introduce a new simple analytic formula of the Fourier coefficient of the 3D field distribution of a point light source to generate a cylindrical angular spectrum which captures the object wave in 360° in the 3D Fourier space. Conceptually, the cylindrical angular spectrum can be understood as a cylindrical version of the omnidirectional spectral approach of Sando et al. Our Fourier coefficient formula is based on an intuitive observation that a point light radiates uniformly in all directions. Our formula is defined over all frequency vectors lying on the entire sphere in the 3D Fourier space and is more natural and computationally more efficient for all around recording of the object wave than that of the previous omnidirectional spectral method. A generalized frequency-based occlusion culling method for an arbitrary complex object is also proposed to enhance the 3D quality of a hologram. As a practical application of the cylindrical angular spectrum, an interactive hologram example is presented together with implementation details.