Abstract

Computer-generated holograms offer the flexibility of storing and displaying images from data which represent 3-D objects. Calculation of the complex amplitude, however, requires long computing times and large storage capacities. These can be reduced by concepts which take the boundary conditions of the reconstruction process into account. A modification of the Fresnel transformation is suggested. The 3-D object is specified digitally in several planes in depth. The middle of the object is placed in the Fourier plane of the hologram. Each plane is Fresnel transformed, and the variation of the quadratic phase term in the vertical direction is suppressed. This modification has two consequences: (1) A slight astigmatism is introduced which vanishes in the Fourier plane, i.e., in the middle of the image. For a human observer, this effect can be kept below the limit of resolution for moderate image extensions. (2) The calculated hologram portion is a narrow stripe in the horizontal direction, which is repeated vertically to achieve a rectangular format. The computing time is reduced by some orders of magnitude compared to Fresnel holograms. Optical reconstructions and demonstrations show the feasibility of this process.

© 1988 Optical Society of America