Double reflections

For cells with a small thickness, the interference pattern method is used. This method consists of measuring the transmittance of the empty cell between two wavenumbers v and v2. It can be seen in Fig. 10.23 that beam S2 has gone through a double reflection on the internal wall of the cell. Thus, if the angle of incidence is normal to the cell wall and if 2d = kX, the addition of both intensities is observed (the two beams Si and S2 are in phase). A modulation of the main beam Si will be observed as a function of wavelength. This modulation is in the order of a few percent. 

To pursue the subject of the stereoscope through all its details, as exhibited in the tubular reflecting, the single and double reflecting stereoscopes, the opera-glass, reading stereoscopes, el cetera, is incompatible with tho limits of this work the student who may desire further acquaintance with the subject is referred to Brewster- on the Stereoscope, or any of tlie works on optical science which are to bo found in libraries, The following remarks will not be out of place — ... 

By applying Sn twice we do two rotation Cn and two reflection <7h since the double reflection is equivalent to the identical operation E and result is a simple rotation through the angle 2 (2n/ n). We may, therefore write... 

Double reflection X rays diffracted by one set of crystal lattice planes may have sufficient intensity to be diffracted again by a second set of planes that are, by chance or design, in exactly the correct orientation. The twice-diffracted beam emerges in a direction that corresponds to a third set of planes with Miller indices equal to the sum of the indices of the two planes causing the double reflection. This double reflection, travelling in the same direction as a singly diffracted beam, will enhance or weaken the intensity of the latter. 

Azimuthal scan A scan of diffraction data measured as the crystal rotates about the diffraction vector. This is used to make an empirical absorption correction and to remove possible errors due to double reflections. 

Tablets were stored in a hydra tor for 168 hr, with tablets withdrawn at regular intervals. Samples were weighed and spectra collected prior to HPLC analysis. Near-IR spectra of the tablets were collected in the 1100 to 2500 nm region, using the double-reflecting sample apparatus described by Lodder and Hieftje [89]. The spectra were processed by PC A...

In one form of comparison reflactometer, a similar double-reflectance geometry is used but the reference is translated while the intensity is monitored (19). when the film thicknesses are equal, two of the four optical paths that result when all possible combinations of front- and back-surface reflections are taken into account are identical and therefore add in phase. This gives rise to an intensity maximum. Accuracies are comparable to those attainable with comparison ellipsometers. 

The exact measurement of the optical path in cells of low thickness is made by interferometry (interference pattern method). The transmittance of the empty cell is measured for an interval between two wavenumbers rq and (in cm ). Figure 10.22 shows that the beam S2 has undergone a double reflection from the internal walls of the cell, thus for a normal incidence, there would be, if 21 = kX, addition of both light intensities (the two beams Sj and S2 are in phase). As a function of the wavelength a modulation of the main beam Sj of a few percent is observed. After calculation, if N represents the number of interference fringes counted between rq and PJ (in cm ), then ... 

The Du Mond diagram for the double reflected beam in each case is given in figures 5.4(b) and 5.5(b). The doubly reflected beam is described by the intersection area of the X-6 curves for each crystal. In the (+, —) case for identical crystals the two curves are coincident and Ad (the... 

When a beam of radiation is directed into the face of a cell, most of the radiation will pass straight through the cell (beam A in Figure 5.3b), Some of the radiation will undergo a double reflection (beam B) and will therefore have travelled an extra distance 2L when compared to beam A, If this extra distance is equal to a whole number of wavelengths then beams A and B will be in-phase and the intensity of the transmitted beam (A+B) will be at a maximum. The intensity will be at a minimum when the two component beams are half a wavelength out-of-phase. 

It should be noted that the experimental spectra are not corrected for double passage of light through the sample. Losses of light to double reflection and absorption of dye film must be considered in order to obtain the true value of the optical density in our optical setup. For this, the reflectance spectrum of J-aggregated PIC 2-18 film was measured (Fig. 25). The corrected optical density of J-aggregated film D(Xcor)=log [Io/(fo--A-R)] was calculated by solving the quadratic equation for the absorption coefficient obtained from the formula for the measured optical density D(A) ... 

Part of the incident beam is reflected at each optical boundary (air-sample boundary in the case of a free-standing thin sample or air-window/window-sample boundaries in the case of a liquid cell), even at normal incidence. Of particular importance is that part of the radiation which undergoes multiple reflections at the two opposite surfaces of a plane-parallel sample. The double-reflected beam can interfere with the original beam, which results in sinusoidal type periodical features in the background of the spectrum (Fig. 6.5). Such features usually cause difficulties during evaluation of spectra. On the other hand, the interference provides access to the effective thickness of the sample as well as the optical quality of its boundaries (deviations from plane-parallelity cause reduced amplitudes of the interference fringes). The effective sample thickness can be calculated according to ... 

The baseline design that was studied is shown in Figure 1. A 1.3 by 1.3 m aperture, optimally filled with a multiplicity of focusing units is assumed. Each unit is either a double reflection conical approximation to a Wolter I telescope or a single reflection conical approximation to a parabolic concentrator. The focal length is FL and the focal plane is an array of hard X-ray detectors that, for the present study, is assumed to have a quantum efficiency of 1 in the whole energy band. Calculations of effective area etc. for the 4 focal lengths listed in Table 1... 

Birefringence (double reflection) is observed mainly in oriented polymers. 

In the review [1978Tho] the TEM micrograph and electron diffraction picture of a Co-Fe-Ni alloy (eompo-sition not specified) are given to discuss appearance of double reflections. 

In early 1948 I thought that there was an experimental solution of the phase problem of X-ray crystallography. The idea was to use a double reflection hj followed by I12 which diffracts in the direction of I13 = hi + I12. If hi is set on the sphere of reflection so that it diffracts for any orientation of the crystal about a suitably chosen rotation axis, then hi and I12 should show an interference effect. This idea, beautiful in principle, was defeated by the mosaic character of crystals and possibly also crystal boimdary effects. Our experiment in which hi is 040 of a glycine crystal failed, although some reflections which were forbidden as single diffractions were observed. Shortly thereafter (1951) Bijvoet published his experimental solution to the phase problem by multiple isomorphous replacement methods, and I thought then that his discovery opened the way to solve protein structures. However, I did not start work in this direction until about 1958, and pursued it seriously beginning in 1961. 

The reflected amplitudes can be calculated from Fresnel s formulas. The total reflected intensity is obtained by summation over all reflected amplitudes taking into account the correct phase. The refractive indices are now selected such that Ai becomes a maximum. The calculation is still feasible for our example of a two-layer coating and yields for the three reflected amplitudes (double reflections are neglected)... 

To further examine the utility of the double-reflecting cone, a hole was drilled in the side of a tablet and packed with 10 mg KCN. When scanned using a single reflecting cone, the sample fell into... 

Floor sweepings 33 conical accessory Reflection with a double reflecting [114]... 

The Space Group determination is occasionally complicated by a phenomenon known as double reflection. If the beam reflected from a set of planes h k l suffers another reflection at appropriate angle from another set of planes /i2fc2 2i then this doubly reflected beam appears to arise from another set of planes... 

Though the intensity of the double reflected beam is usually very weak, sometimes both hikili and /i2 2 2 are very strong giving rise to spurious reflections. However, as this case is not very frequent in the diffraction pattern, the presence of one weak reflection violating the norm of systematic absences may be considered as spurious and can be safely ignored. 

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