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Inverse diffraction involves recovery of the image of an object whose diffraction pattern is measured, for example, on a plane. In the case of the Fresnel and Fraunhofer approximations, the inversion is straightforward. In the very near eld, the angular spectrum representation can be used, but then there are some technical issues that need to be addressed. The geometry to be used in the following sections is shown in Figure 6.1. The observation plane and the measurement plane are assumed to be at z z0 and z zr , respectively. Previously, zr was chosen equal to 0. The distance between the two planes is denoted by z0r. The medium is assumed to be homogeneous. The problem is to determine the eld at z z0 , assuming it is known at z zr . Like all inverse problems, the inverse diffraction problem is actually dif cult if evanescent waves are to be incorporated into the solution [Vesperinas, 1991]. Then, the inverse diffraction problem involves a singular kernel [Shewell, Wolf, 1968]. When the evanescent waves are avoided as discussed in the succeeding sections, the problem is well behaved. This chapter consists of four sections. Section 2 is on inversion of the Fresnel and Fraunhofer approximations. Section 6.3 describes the inversion of the angular spectrum representation. Section 6.4 discusses further analysis of the results of Section 6.3. 6.2 INVERSION OF THE FRESNEL AND FRAUNHOFER REPRESENTATIONS The Fresnel diffraction is governed by Eq. (5.2-13). As the integral is a Fourier transform, its inversion is given by je jkz0r j2zk x2 y2 U x; y; zr e 0r lz

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of conventional quantitative nancial risk management His main contention is that things have got way out of hand when it comes to using mathematical and statistical techniques in the markets Very precise measurements are assigned to risks about which we may truly know very little through the use of complex computations that purport to understand the probability distributions governing the human-driven markets But, most interesting, Rebonato also touches upon how quanty types inside banks, consulting rms, and software companies prefer more complexity to less complexity when it comes to dealing with risk The more dif cult risk taming is made to look, the more indispensable the inputs of those with PhDs in physics, math, and computer science appear.

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Too many people simply have too many vested (and very material) interests in convincing the rest of us that nancial risk management is exclusively about extremely sophisticated quantitative techniques, which they just happen to uniquely master In other words, the intimidating peddling would go, if you want to control your risks you better hire quants, grant contracts to specialist consultants, and buy the software packages incorporating the latest statistical gizmos As Rebonato says, whether quantitative risk management is a pure or an applied science has ceased to be the relevant debate What it truly has become is big business, with tasty monetary and professional gains for all those purported as experts It seems only logical that the quant lobby would work very hard at trying to perpetuate the notion (now almost conventional wisdom) that nancial risk is about equations and highpowered computational models.

Figure 19.10. The case of large number of channels (M 200; L 128; l 0:2 nm).

In other words, about measurement rst and foremost The problem with all this is that it is expected that many peddlers of the quantitative snake oil would be perfectly aware of the unworldliness of some of the solutions Of their meaninglessness Perhaps even of the danger that they pose (nothing could be more dangerous than operating in the markets under faulty radars, and VaR has already caused more than its share of trouble, essentially helping increase, not tame, risk) By continuing to sell their wares, they would be incurring an intellectual fraud For people endowed with prestigious doctorates from the world s leading universities, and who might have previously dreamed of academic glory and yearned for the pure discovery of knowledge, the moral dilemma may prove taxing They would be corrupting their beloved and sacred scienti c methodologies in the pursuit of material comfort They would be.

fail to detect deceit and what they can do to become better lie detectors. Such chapters were not included in the 2000 edition. The result, I believe, is a book about deception that is better structured and more comprehensive than the 2000 edition. I also realise that this book contains considerably more text than the 2000 edition, and so perhaps readers will prefer to dip into individual chapters rather than read the book from beginning to end. To facilitate this, I have ensured that the chapters can be read independently from each other.

Some information from the DirecTV site showing the current state of affairs (http://www.hackhu.com/) [15]:

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12/02 Portfolio managers Research analysts Economists Trading Compliance Marketing Administration Client service Other (specify) Total* *The total number of professional staff must match with the actual number of investment staff employed by the rm. 12/01 12/00 12/99

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