02-04Point-Oriented CGH′s 国内外计算全息课间 PART I MATHEMATICAL PRELIMINARIES.pdfVIP

Part II: Chapter Four Page 1 of 8 COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Friday, January 14, 2005, 6:32 AM) PART II: CHAPTER FOUR POINT-ORIENTED CGHS Introduction The point oriented hologram is characterized by a resolution cell that has no internal structure. These holograms are generated by calculating the total transmittance of the hologram after the effective interference of the object wave with the reference wave. This total transmittance is then sampled and the sample value is used to determine the transmission of each resolution cell. The most commonly used carriers are the cosine wave and the square-wave. The Perfect CGH The perfect CGH is an idealization that intended to reduce calculations to a bare minimum yet retain some of the properties we will be dealing with throughout the course. This CGH will consist of an array of point apertures. Each aperture has a complex-amplitude transmittance, i.e., it modifies both the amplitude and phase of the light passing through it. Using Comb math, we can write the transmission of an idealized CGH in very compact form. The idealized CGH is one that has a periodic point structure. The points have complex amplitude transmittances and the reconstruction is simply by Fourier transform. Such a hologram transmittance in one dimension is  x  x       T PERFECT_CGH (ξ) = F.T. comb  u(x) ∗comb   = δx