Measurement solid angle

Figure 7 Difference between a cone angle and a solid angle. Cone angles completely envelop the ligand and include some unused space in the measure. Solid angles include only the space occupied by the ligand in the measure. (From Ref. 48.)...

There is no bias inherent in BRDF. BRDF is a number derived from the ratio of physical parameters that can be specified in absolute units. However, individual laboratories may have measurement errors that lead to systematic offsets, such as an inaccurately measured solid angle. Other possible mechanisms are discussed in Ref. (8). It is not possible at this time to separate these systematic errors from bias however, intralaboratory measurements on the same instrument typically repeat within 5% (10). 

Measurement of the total Raman cross-section is an experimental challenge. More connnon are reports of the differential Raman cross-section, doj /dQ, which is proportional to the intensity of the scattered radiation that falls within the element of solid angle dQ when viewing along a direction that is to be specified [H]. Its value depends on the design of the Raman scattering experiment. 

In TOF-SARS [9], a low-keV, monoenergetic, mass-selected, pulsed noble gas ion beam is focused onto a sample surface. The velocity distributions of scattered and recoiled particles are measured by standard TOF methods. A chaimel electron multiplier is used to detect fast (>800 eV) neutrals and ions. This type of detector has a small acceptance solid angle. A fixed angle is used between the pulsed ion beam and detector directions with respect to the sample as shown in figure Bl.23.4. The sample has to be rotated to measure ion scattering... 

Experimentally, dvz is directly proportional to the laser bandwidth and is a constant dvx is determined by the slit width and is inversely proportional to the ion arrival time (i.e. a ID solid angle factor) and dvy/dt denotes the time-to-speed transformation in the ion TOF measurement, which can readily be derived from the equation of motion. It was found... 

The conventional differential cross-section1,2 refers to the cross-section per solid angle in the center-of-mass polar coordinate. The desired doubly differential cross-section is then related to the measured quantity by the simple equation... 

The candela (cd) is equal to a lumen per steradian. A steradian is the measure of solid angle. A sphere has 4-7T sr on its surface area. This stems from the fact that the surface area of a sphere, SA = 4-nr2. The surface area divided by r2 gives the total solid angle of the sphere. Similarly, to calculate the solid angle of a piece of a sphere s surface, one takes the area of interest, and divides by the radius squared. This gives the solid angle in steradians. A steradian is dimensionless because it is the ratio of two areas. 

The factor (q/a ) may be obtained from independent optical and geometrical measurements, since q is the transmittance of the attenuator used for the incident beam, a is the solid angle of detection of scattered light and is the thickness of sample. 

The specific optical rotation of a solid substance is usually determined by measuring the angle of rotation at the wavelength of the sodium D-line at a temperature of 20°C, and calculating the result with reference to a layer 1 dm thick of a solution containing 1 g of the substance per ml. It is pertinent to mention here that the specific optical rotation of a solid is always expressed to a given solvent and concentration. 

A rapid method of assessing the behaviour of a particulate mass is to measure its angle of repose. If solid is poured from a nozzle on to a plane surface, it will form an approximately... 

One of the most common ways to characterize the hydrophobicity (or hydrophilicity) of a material is through measurement of the contact angle, which is the angle between the liquid-gas interface and the solid surface measured at the triple point at which all three phases interconnect. The two most popular techniques to measure contact angles for diffusion layers are the sessile drop method and the capillary rise method (or Wihelmy method) [9,192]. 

The experimental configuration for fluorescence measurements is shown in Figure 7. As in the case of transmission measurements, the intensity of the X-rays before the sample is measured using an ionization chamber. The sample is set at 45° to the path of the incident X-rays, so that the maximum solid angle of the fluorescence may be collected at the solid-state detector. 

Luminance is the luminous flux emitted per unit solid angle or per unit projected area of a surface in a light source it is a measure of brightness. 

The problem of first-principles calculations of the electronic structure of solid surface is usually formatted as a problem of slabs, that is, consisting of a few layers of atoms. The translational and two-dimensional point group symmetry further reduce the degrees of freedom. Using modern supercomputers, such first-principles calculations for the electronic structure of solid surfaces have produced remarkably reproducible and accurate results as compared with many experimental measurements, especially angle-resolved photoemission and inverse photoemission. 

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