Oblique ray

An extension of these metliods to 3D is the Feldkamp algorithm [7], a standard in 3D-tomographic reeonstruction today. In this case off-midplane voxels are taken into eonsideration through weighted filtered 3D-baekprojection. llie weighting compensates for the longer way an oblique ray has to travel. 

The information-gathering power of an objective lens depends on its ability to collect the oblique rays leaving the object, a factor that depends on the angular aperture [u in Figure 3) subtended by the lens at the object. Because of the effect of refraction at the... 

Figure 4 The effect on numerical aperture of the refractive index, n, of the medium between the object and the objective lens. In the examples shown, in (A), where the medium is air, the most oblique rays accepted by the objective leave the object at 39° with oil-immersion (B), rays leaving at up to 60° are collected.

Figure 4. Apparatus for measuring reflectance of oblique rays by a liquid crystal film.

In Figure 4.12a, the optical path of a collimated beam oblique to the optical axis is illustrated. This ray, simply called an oblique ray, comes from the upper edge of the circular entrance aperture and makes an angle a to the optical axis after passing through the collimator. The oblique ray is supposed to reach the moving mirror Mj when it is displaced by x/2 from the position of zero OPD. 

To avoid a large decrease in wavenumber resolution arising from oblique rays, a circular aperture, called the Jacquinot stop (J-stop), is placed in the focal plane of the collimator as shown in Figure 4.12a. The optimal diameter of the J-stop is determined in order to make the wavenumber shift due to oblique rays smaller than the wavenumber resolution 8v determined by the OPD for the beam parallel to the optical axis. 

Refraction the change of direction of a ray of light in passing obliquely from one medium into another in which the speed of propagation differs. 

The parallelization of crystallites, occurring as a result of fiber drawing, which consists in assuming by crystallite axes-positions more or less mutually parallel, leads to the development of texture within the fiber. In the case of PET fibers, this is a specific texture, different from that of other kinds of chemical fibers. It is called axial-tilted texture. The occurrence of such a texture is proved by the displacement of x-ray reflexes of paratropic lattice planes in relation to the equator of the texture dif-fractogram and by the deviation from the rectilinear arrangement of oblique diffraction planes. With the preservation of the principle of rotational symmetry, the inclination of all the crystallites axes in relation to the fiber axis is a characteristic of such a type of texture. The angle formed by the axes of particular crystallites (the translation direction of space lattice [c]) and the... 

It should be noted that equatorial or diequatorial conformers of substituted cyclohexanes could be accommodated in the thiourea canals by the stacking of guests at an oblique angle or parallel to the canal axis. X-ray structural data is so far unavailable... 

Obviously, it is possible to use X-ray diffraction for structure refinement of tabular shaped microcrystals. However, oblique texture electron diffraction patterns have the following advantages firstly, they can provide data from the full 3D diffraction pattern in a single exposure, secondly, there is a possibility of obtaining almost perfectly oriented samples, which, owing to the minimization of their overlapping, produce diffraction patterns with good resolution of reflections. Extremely small crystals can and should be used - thinner than what is needed for X-ray powder diffraction. 

Examine each external weld visually to ensure there are no surface defects, and record. Examine each interior weld and adjacent areas, both visually and by the use of a horoscope. Welds not accessible with the horoscope must be examined by y-ray with photo. 3 shot by weld two perpendicular to the tube axis (moved at 90°) and one oblique compared to the tube axis. 

Fig. 7.3. Ray model of an acoustic lens with negative defocus aa is an arbitrary ray, which is reflected at such an angle that is misses the transducer (or else hits the transducer obliquely and therefore contributes little to the signal because of phase cancellation across the wavefront) bb is the axial ray, which goes straight down and returns along the same path cc is the symmetrical Rayleigh propagated wave, which returns to the transducer normally and so also contributes to the signal. The wavy arrow indicates the Rayleigh wave.

In radiographic investigations the image of an object is distorted if the X-rays strike the photographic plate at an oblique angle. In order to calibrate the distortion a spherical ball is investigated. The image is an ellipse with centre (p j 2) and further parameters P3 p and P5 as described by the equation... 

When diffracted X-ray beams fall on a photographic film at different angles, as the different layer lines in a cylindrical-film rotation photograph do, it is necessary to correct for the absorption of X-rays in different thicknesses of film. (Since double-coated films are normally used, the effect on the back layer depends on the absorption in the film.) This was first considered by Cox and Shaw (1930) Whittaker (1953) gives a formula which is more accurate and deals with greater obliquity and a thicker film Grenville-Wells (1955) gives the corrections when the multiple film method is used. 

The region prohibited by the experiment, cosmology and 7-ray background radiation from the supernovae are also shown in Fig. 1 by the dotted region, the vertically hatched region, and obliquely hatched region, respectively. 

X-ray lithography also takes advantage of the increased resist sensitivity due to the thinner imaging films of multilayer systems. Thinner imaging films further improve X-ray resolution by minimizing the penumbra effect, a problem associated with an uncollimated X-ray beam. Consequently, the oblique exposure of features near pattern edges are minimized by multilevel resist processes, thereby restoring the desired profile. 

Fig. 6 In the case of the oblique unit cell the intensity of the (—11) signal in the XRD pattern is usually higher than the intensity of the (11) signal (left). This indicates that the layer fragments in the crystallographic unit cell are inclined toward the shorter diagonal [the crystallographic plane (—11)] of the primitive unit cell (right). The electron density map was reconstructed from the X-ray data (see Sect. 3) bright regions are filled by the aromatic parts of molecules while the dark regions are filled by the alkyl chains. Dotted lines show midplanes of the blocks...

Refractive index (RI) is a measure of the refraction of light rays as they pass obliquely from one solution to another of different density. Refractive index is commonly used to measure the solids level of sweeteners. The refractive index of a sweetener is a function of the carbohydrate profiles, ash level, solids level and temperature of the solution. 

---