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Diffractive optics involves creation of holograms by computation in a digital computer, followed by actual implementation by a recording system such as a laser lm writer, scanning electron beam writer, high resolution printer, usually followed by photoreduction, and the like. Diffractive optics is very versatile since any type of wave can be considered for computation within the computer. Digital holograms created with such technology are more commonly called diffractive optical element (DOE). Another name for DOE is computer-generated hologram (CGH). Because of these equivalent terminologies, the words hologram, DOE, and CGH will be used equivalently in this chapter. In communication engineering, it is well known that a complex signal must be coded in some fashion before it can be transmitted over a single channel. This can be done by modulating the amplitude of a carrier by the modulus of the complex signal and/or by modulating the phase of the carrier by the phase of the complex signal. The real part of this modulated carrier then can be transmitted, and through proper demodulation procedures, the complex signal can be recovered at the receiver. Both holography and diffractive optics are based on such modulation and demodulation principles. DOEs have found applications in many areas such as wave shaping, laser machining, 3-D displays [Yatagai, 1975], optical pattern recognition, optical interconnects, security devices [Dittman, et al., 2001], optical communications/networking, and spectroscopy. Some important advantages of DOEs are as follows: A DOE can perform more than one function, for example, have multiple focal points, corresponding to multiple lenses on a single element. It can also be designed for use with multiple wavelengths. DOEs are generally much lighter and occupy less volume than refractive and re ective optical elements. With mass manufacturing, they can be manufactured less expensively for a given task.

L2 a; b denotes the vector space of continuous functions over C[a,b] (complex values in the interval from a to b) with the inner product u; v u t v t dt

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With electrons and photons in the picture, Feynman s diagrams became a little more complicated. To understand what was happening, he returned to world lines, those graphs with time running up the page and space across. By drawing diagrams for each possible interaction of electrons and photons and combining this with his probability work, it was possible to predict successfully practically everything that happens (except anything involving gravity and the nucleus of an atom, where entirely different types of force are involved). By bringing in the electron, we can understand the strange way that QED says light re ects from a mirror. It s only crazy if we think of re ected light bouncing off a mirror, just as a ball bounces off the oor. But thanks to QED, we know that each photon is absorbed by an electron in the mirror, then a new photon is emitted in a different direction (different because the probability arrow rotates during

The network is at the heart of any enterprise solution, large or small J2EE is no exception; all J2EE solutions are built around the network This means that J2EE developers will take on new problems and complexities as they move from the single application to the J2EE solution world As developers move from building small enterprise solutions to building large ones, they take on further architectural choices, complexities, and consequences, as well as solve new problems that didn t exist in the smaller world In order to succeed in a distributed-networked world of J2EE, the first step is for the developers to understand the new environment in which they are working, and the differences between that environment and the smaller, non-networked one of which they are used to The best summary of the common misconceptions of distributed computing, and therefore J2EE programming, is the eight fallacies of distributed computing.

Multiplication by 2u gives the previous normal vector. 18. A representation is r(u, v) [2 cosh u, 3 sinh u, v]. A normal vector is N [3 cosh u, 2 sinh u, 0]. Note that N is parallel to the xy-plane. Another normal vector is grad (9x 2 4y 2) [18x, 8y, 0] [36 cosh u, 24 sinh u, 0].