Recurrence formulas for fast creation of synthetic three-dimensional holograms

A method for accelerating the synthesis of computer-generated three-dimensional (3-D) holograms, based on conventional ray tracing, is proposed. In ray tracing, computers expend almost all of their resources in calculating the 3-D distances between each one of the point sources composing an object and a sampling point on the hologram. We present recurrence formulas that precisely compute the distances and reduce the computation time for synthesizing holograms to one half to one quarter, depending on the processor type. We demonstrate that a full-parallax hologram with an area of 4800 x 4800 pixels, synthesized for a 3-D object containing 966 point sources of light, is computed within 17 min and is optically reconstructed.