![]() ![]() (3.87), horizontal steps that are several wavelengths long are often sufficient when the bottom slope is gentle. For the forward field, however, the a m, n part of Eq. (3.87), the stair steps should preferably be shorter than a quarter of a wavelength, at least in the up-sloping case. To compute the backward field accurately, the b m, n part of Eq. With this approach, a sloping bottom must be replaced by a number of stair steps. The task of handling media with a solid bottom appears to remain as a research problem. A gradient half-space at depth is also possible. Undesired reflections from the lower boundary can be reduced by artificially introducing layers at depth with successively increasing absorption. The assumption of a traction-free or rigid lower boundary at z = z b is useful, since no branch-cut integral is needed for the representation of the field. The resulting diagonal matrices are, of course, easy to invert. With appropriate ordering of the modes in the different range segments, all off-diagonal elements in the coupling matrices are ignored in the well-known adiabatic approximation (e.g., Ref. The approximation could obviously be improved by further outward and inward marching steps. (3.91) would be solved for decreasing n temporarily setting a n = 0 all the time but adding the b n from the outward marching step giving b n = D n − 1 At a subsequent inward marching step, Eq. (3.91) would be solved for increasing n setting b n+1 = 0 all the time, giving a n + 1 = ( A n − B n In the notation here, the outward marching step would start with b 1 = 0 and a 1 according to Eq. , the reduction to small dimensions is achieved without additional approximations. Compared with the two-way (outward followed by inward) marching single-scattering solution proposed in Ref. ![]() The reflection-coefficient method proposed in Section 3.3.4.2 is economical, since matrix inversion is only needed for the rather small matrices of dimension N M × N M, where N M is the number of modes, after truncation, in each range segment. Ivansson, in Applied Underwater Acoustics, 2017 3.3.4.3 Final Remarks A 0.3−μm spatial resolution and 5% total accuracy of the refractive index has been obtained by this correction. This effect of the finite beam spot size can be corrected by numerical calculation. Spatial resolution is usually limited to about 1–2 μm by the spot size of the incident beam. For borosilicate fibers, the result changes rapidly with time because of atmospheric exposure of the dopant. A fractured end surface gives better results than does a polished end surface. Accuracy is strongly affected by the flatness of the end surface. The refractive index profile is obtained from the reflection coefficient profile by shifting the reference point. A laser light beam with a small spot size is focused into the end surface of a sample, and the reflection coefficient is measured by comparing the incident and reflected light intensity, as shown in Table III. The refractive index profile of an optical fiber can be measured by utilizing this principle. The reflection coefficient of a dielectric material is related to the refractive index at the incident surface. Some simple reflections can be performed easily in the coordinate plane using the general rules below.Kenichi Iga, in Encyclopedia of Physical Science and Technology (Third Edition), 2003 VI.C Reflection Pattern The fixed line is called the line of reflection. When reflecting a figure in a line or in a point, the image is congruent to the preimage.Ī reflection maps every point of a figure to an image across a fixed line. Figures may be reflected in a point, a line, or a plane. ![]()
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