02-06The Third Dimension 国内外计算全息课间 PART I MATHEMATICAL PRELIMINARIES.pdfVIP

Part II: Chapter Six Page 1 of 32 COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, August 23, 2004, 12:36 PM) PART II: CHAPTER SIX THE THIRD DIMENSION Introduction Until this point, we have restricted our attention to two-dimensional objects and wave propagation in the Fraunhofer regime. We have fabricated holograms and found that the theory and experiment are in reasonable agreement. Holograms are, however, more interesting for their ability to display three- dimensional objects. In this chapter we will shift our attention to the theoretical elements necessary to produce such holograms. These elements focus on illumination, transmission, reflection and propagation. Our more general approach will also describe diffractive optical elements or DOEs. We will see that exactly the same tools that we apply to describing production and defect analysis of display holograms will be directly applicable to DOEs. Our 2-D calculations have concentrated on the illumination being a plane wave, transmission being diffused scattering, and propagation being a Fourier transform. We will continue considering propagation between parallel planes which is one of way of decomposing the most general case. The advantage to this choice is that we will continue to find the Fourier transform a most useful tool. Illumination The reconstruction produced by hologram is, of course, dependent on the illumination. Most often the illumination we assume is a plane wave. For diffractive optical elements we also consider spherical waves and pinhole waves. We consider the computer-generated hologram to be a thin planar element thoug