Overview: The purpose of this chapter is to introduce the basic features of a Gaussian-beam wave in both the plane of the transmitter and the plane of the receiver. Our main concentration of study involves the lowest-order mode or TEM 00 beam, but we also briefly introduce Hermite-Gaussian and LaguerreGaussian beams as higher-order modes, or additional solutions, of the paraxial wave equation. Each of these higher-order modes produces a pattern of multiple spots in the receiver plane as opposed to a single (circular) spot from a lowest-order beam wave. Consequently, the analysis of such beams is more complex than that of the TEM 00 beam. One advantage in working with the TEM 00 Gaussian-beam wave model is that it also includes the limiting classical cases of an infinite plane wave and a spherical wave.We facilitate the free-space analysis of Gaussian-beam waves by introducing two sets of nondimensional beam parameters-one set that characterizes the beam in the plane of the transmitter and another set that does the same in the plane of the receiver. The beam spot radius and phase front radius of curvature, as well as other beam properties, are readily determined from either set of beam parameters. For example, we use the beam parameters to identify the size and location of the beam waist and the geometric focus. The consistent use of these beam parameters in all the remaining chapters of the text facilitates the analysis of Gaussian-beam waves propagating through random media.When optical elements such as aperture stops and lenses exist at various locations along the propagation path, the method of ABCD ray matrices can be used to characterize these elements (including the free-space propagation between elements). By cascading the matrices in sequence, the entire optical path between the input and output planes can be represented by a single 2Â2 matrix. The use of these ray matrices, which is based on the paraxial approximation, greatly simplifies the treatment of propagation through several such optical elements. In later chapters we will extend this technique to propagation paths that also include atmospheric turbulence along portions of the path.

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We develop a model for the probability density function (pdf) of the irradiance fluctuations of an optical wave propagating through a turbulent medium. The model is a two-parameter distribution that is based on a doubly stochastic theory of scintillation that assumes that small-scale irradiance fluctuations are modulated by large-scale irradiance fluctuations of the propagating wave, both governed by independent gamma distributions. The resulting irradiance pdf takes the form of a generalized K distribution that we term the gamma-gamma distribution. The two parameters of the gamma-gamma pdf are determined using a recently published theory of scintillation, using only values of the refractive-index structure parameter C n 2 (or Rytov variance) and inner scale l 0 provided with the simulation data. This enables us to directly calculate various log-irradiance moments that are necessary in the scaled plots. We make a number of comparisons with published plane wave and spherical wave simulation data over a wide range of turbulence conditions (weak to strong) that includes inner scale effects. The gamma-gamma pdf is found to generally provide a good fit to the simulation data in nearly all cases tested. © 2001 Society of Photo-Optical Instrumentation Engineers.

Central America (1), natural genetic variations in flowering time enabled early Native Americans to select maize adapted to a range of latitudes and lengths of growing seasons, including the very short summer season typical of the eastern Canadian region of Quebec. Under such conditions, early flowering allows seed to mature before the onset of frost. Flowering time is also a key trait of improved drought tolerance. Indeed, it has been shown that a single day of drought during flowering can decrease yield by as much as 8% (2). One way to address such losses is to develop and grow cultivars characterized by a short cycle and able to flower before predictable drought episodes.The genetic variability available for maize breeding is essentially quantitative; i.e., it involves allelic variation at different quantitative trait loci (QTLs), which are influenced by environmental effects. Although a large body of mapping information on QTLs is available for flowering time (3), relatively little is known about the molecular basis of QTLs, with only one gene, Dwarf8, correlated thus far with quantitative effects (4, 5). Furthermore, a few mutants for flowering time have been described (6, 7), two of which, id1 (8) and dlf1 (9), have been cloned. Our results (i) show that the allelic variation responsible for the major flowering-time QTL, Vegetative to generative transition 1 (Vgt1) (10, 11) on chromosome 8, is confined to an Ϸ2-kb intergenic region upstream of an Ap2-like flowering-time gene, (ii) identify maize-sorghum-rice evolutionarily conserved noncoding sequences (CNSs) within Vgt1, and (iii) support a cisacting transcription-regulatory role for Vgt1. ResultsPositional Cloning of Vgt1. Previous work (12) mapped Vgt1 to a 1.3-cM region (Fig. 1A) on bin 8.05, based on a mapping population derived from the cross N28 ϫ C22-4. The strain C22-4 is nearly isogenic to N28 and carries the early Vgt1 allele in an Ϸ7-cM introgression originating from the early maize variety Gaspé Flint. By using standard positional cloning, Vgt1 was confined to an Ϸ2-kb region (Fig. 1 B-D). Sequence annotation of the original BAC clone and the corresponding sequences derived from N28 and Gaspé Flint genetic backgrounds showed that Vgt1 is apparently noncoding and is located Ϸ70 kb (61-76 kb, depending on the genetic background) upstream of an Ap2-like gene identified here as ZmRap2.7. This gene is orthologous to Rap2.7 (also known as TOE1), a transcription factor that regulates flowering time in Arabidopsis (13,14). No other genes were annotated between Vgt1 and ZmRap2.7. Pseudogenes due to transduplication events mediated by nonautonomous helitron elements (15) were observed in N28 and other genetic backgrounds but not in Gaspé Flint (data not shown). Within the Vgt1 region, the contrasting QTL alleles showed 29 SNPs and insertion/deletion-type polymorphisms (Indels) and one 143-bp insertion into the Gaspé Flint allele of a Mite transposon belonging to the Tourist (16) family [ Fig. 4 Lower and supporting information (SI) Fig. 5].Association M...

Plants regenerated from relatively undifferentiated callus cultures possess a vast array of genetic changes.