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Computed holograms traditionally fall into one of two classes: Fourier holograms, appropriate for far-field Fraunhofer diffraction, and Fresnel holograms, which produce images in the near field. The fundamental difference between these two diffraction models is the range of length scales in which they "operate." In particular, Fraunhofer diffraction requires that the monochromatic light source, the diffracting aperture, and the screen (or viewer) be sufficiently distant from each other that the paraxial approximation applies. The geometry of this requirement is captured by the Fresnel Number, defined by F = a 2 / L d ,where a is the characteristic dimension of the diffracting aperture, L is the distance from the diffracting aperture to the viewer, and 1 is the wavelength of light illuminating the aperture. When F << I , the optical system is said to be in the Fraunhofer zone; when F 2 1, it is said to be in the Fresnel zone. The mathematical framework that describes Fourier optics provides an accessible starting point for computing far-field holograms Comparison Of Fourier ( a ) and F r ~ ~ e and underlies most early computing techniques. But the imagel ( b )playback geometries. producing capability of such far-field holograms is not optimal for display holography; the images produced are flat, self-luminous, and clearly exhibit multiple orders (including the bright zero order) in the output. Further, they offer only modest parallax-in fact, there is very little "3-D" about them. Fresnel holograms, by contrast, offer greater capacity to produce realistic images for visual display; they can offer high angular and spatial resolution, can reconstruct deep, three-dimensional scenes, and can be generated so that only a single diffracted order is visible in the output. A comparison of the play-

Note As with Dreamweaver objects, you don t see the OK, Cancel, and Help buttons that appear when the parameter form is actually used. Dreamweaver displays these buttons to the upper-right part of your interface.

Before having InDesign generate the TOC (described later in this chapter), you can change the alphabetization order by changing the Language option in the Character panel s flyout menu when no text or text frame is selected. The TOC then takes on the chosen language s rules for alphabetizing. n

Event handlers in MXML object declarations expressed as XML attributes The ActionScript addEventListener() method

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Within a set of objects constituting a group, one or more subsets of objects may satisfy the requirements to form a group under the same multiplication operation as defined for the whole group. We then call the subset a subgroup of the larger group. As a rather trivial example, consider the set of real numbers, which obviously forms a group under addition with zero as the identity. The set of all integers, including zero, is a subset of this set and is also a group. Therefore, under addition the real numbers form a group and the integers form a subgroup of this group. As another simple example, the permutation group on three objects S3 has a a subgroup the permutation group on two s objects Sz. It also has a subgroup A3 = (1, (123),(321)}, which is the group of even permutations on three objects (see Exercise 5.3).

FileMaker reads data from disk into memory when a database file is opened. The contents of the cache (data not yet written back to disk) are then maintained as fields and records are updated. Cached data is written back to disk periodically, keeping the cache s size within a defined range.

precise determination of [L] but instead assume that [L] and [L]0 are approximately the same. Obviously they are not, especially at concentrations of [L]0 less than any K d values. Fortunately, we can avoid problems with using this approximation provided that the experimental data set converges to saturation as closely as possible. The best way to verify this is to plot x versus log[L]0 (semi-log plot). If the experimental data plots out in the form of a sigmoid approaching an asymptotic plateau at high values of log[L]0 (see Figure 7.15, where x is equivalent to B), then we can be sure that receptor R binding sites are approaching saturation and that the experimental data set is adequate for the determination of binding constants. Obviously, this semi-log plot diagnostic approach only applies when strong positive

After the B-C-D sort is complete, perform the A sort in the next pass (see Figure 8-24).

face downward. Snap the copies to the roof edge copies made in step 1. The copied face and edges will subdivide the vertical faces of the building.

Hypohalous acids either preformed or prepared in situ readily add to carbon-carbon multiple bonds.142-144 The addition is an electrophilic reaction with the positive halogen attaching itself predominantly to the less substituted carbon. The Markovnikov rule, therefore, is followed in most cases. The addition of the elements of hypohalous acids may be carried out by the use of reagents serving as positive

Here lx and ly are the two components of the small stretching vector ln+1 . Assuming that |lo | = 1, the magnitude of the length stretch is given by

5.7 The adjoint representation for S U ( 2 ) consists of three 3 x 3 matrices T,, since SU(2) has three generators. Fkom (5.14) and (5.31) the elements of these matrices are (T,)ij = - i c i j a , with a, i, j = 1-3. Therefore,

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