02-05 Cell-Oriented CGH′s 国内外计算全息课间 PART I MATHEMATICAL PRELIMINARIES.pdfVIP

Part II: Chapter Five Page 1 of 5 COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas. (Friday, January 14, 2005, 6:32 AM) PART II: CHAPTER FIVE CELL-ORIENTED CGHs Introduction We consider two closely related hologram types: the Lohmann Type III, binary CGH and its circular overflow corrected version. We will show how a handy mathematical solution can transform the troublesome linear phase error into the familiar false image decomposition. The Lohmann Type-III Binary CGH We first do the calculation for an ideal Lohmann type III hologram. In the next section we will expand the calculation to include circular overflow correction. The resolution cell structure for ideal type-III CGH is that a single rectangular aperture is placed in the cell. The aperture is centered vertically. Its height is proportional to the desired amplitude transmittance. Its lateral position is shifted proportionally to the phase of the complex amplitude transmittance for that cell. We express the hologram transmittance as a sum of rectangle functions  m φmn   n  ∞ ∞ ξ − −  η−∆y  T ∑∑rect  ∆x 2π∆x rect   CGH 1 A =−∞ =−∞  mn  m n  2∆x   ∆y  On inverse Fourier transforming this array of rectangles assumes an interesting but somewh