Intensity solid angle

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. 

The intensity of SS /. from an element in the solid angle AD is proportional to the initial beam intensity 7q, the concentration of the scattering element N., the neutralization probability P-, the differential scattering cross section da(0)/dD, the shadowing coefficient. (a, 5j ) and the blocking coefficient(a,5 ) for the th component on the surface ... 

A unifonn monoenergetic beam of test or projectile particles A with nnmber density and velocity is incident on a single field or target particle B of velocity Vg. The direction of the relative velocity m = v -Vg is along the Z-axis of a Cartesian TTZ frame of reference. The incident current (or intensity) is then = A v, which is tire number of test particles crossing unit area nonnal to the beam in unit time. The differential cross section for scattering of the test particles into unit solid angle dO = d(cos vji) d( ) abont the direction ( )) of the final relative motion is... 

As Sherman15 points out, the enhancement components are generated within the sample and radiated with spherical symmetry, so that it is necessary to integrate at every point over the entire solid angle in order to obtain their intensities. In other words, one must deal here with broad, divergent beams,16,17 and this leads to integrands of the form [log (a + bx)]/x, which are more difficult to handle than the simple exponential integrand that underlies Equation 6-5. 

The intensity of the scattered neutrons is given by the double-differential cross section 02er/0Q dE, which is the probability that neutrons are scattered into a solid angle cl l with an energy change 6E = hm. 

Isotropization in the Case of Fiber Symmetry. If methods for the analysis of isotropic data shall be applied to scattering patterns with uniaxial orientation, the corresponding isotropic intensity must be computed. By carrying out this integration (the solid-angle average in reciprocal space) the information content of the fiber pattern is reduced. One should consider to apply an analysis of the longitudinal and the transversal structure (cf. Sect. 8.4.3). 

Problem. Let a polymer fiber contain rod-shaped structural entities in an amorphous matrix with some preferential orientation. Let us assume that the rods are crystalline. Our interest is to study the crystalline structure of the rods. Instead of sharp hkl reflections we observe that each reflection is smeared over a spherical cap in solid angle. Thus the observed intensity is suitably expressed in polar coordinates... 

Consider continuous radiation with specific intensity I incident normally on a uniform slab with a source function 5 = Bv(Tex) unit volume per unit solid angle to the volume absorption coefficient Kp and is equal to the Planck function Bv of an excitation temperature Tcx obtained by force-fitting the ratio of upper to lower state atomic level populations to the Boltzmann formula, Eq. (3.4). For the interstellar medium at optical and UV wavelengths, effectively S = 0. 

Radiant intensity can be described as the amount of power (watt) heading in your direction, i.e., per steradian, from a light source. The total amount of power emitted by the source is the radiant flux (watt). If you integrate the radiant intensity over all solid angles, you get the total radiant flux. If it is weighted by the photopic response, then it is the luminous intensity and the luminous flux. 

Two other definitions are important the power P of radiation is the energy of the beam that reaches a given area per second. The intensity / is the power per unit solid angle in a particular direction. Both are related to the square of the amplitude, and are often used interchangeably, but they are not synonymous. 

The intensities of diffuse reflectance and fluorescence are both distributed over the solid angle according to Lambert s cosine-law. An ultraviolet-visible (UV/VIS)-... 

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. 

A laser is spatially coherent as is a conventional source that is infinitely small. Referring to Figure 8, this may be achieved by moving the observation point P to infinity, at which point a, the angle subtended at P, approaches zero as does the area of emission. We should point out, however, that brightness for a finite source is defined as power per unit area per unit solid angle. Therefore, achieving coherency in this manner reduces the intensity to zero and would require infinite exposure time. Fortunately we do not need perfect coherency, a point that will be treated in more detail later. 

For comparison the output power of a high-pressure mercury lamp (Osram HBO 200) also is listed. The reader has to consider, however, that the mercury lamp radiates this power into the unit solid angle (= 60°) distributed over the spectral range from 2000 to 6000.A, whereas the laser intensity is concentrated at a single wavelength and collimated in a beam with a very small divergence between 10 and 10" sterad. 

With respect to intensity, most of the laser transitions therefore are superior to conventional lamps, especially for experiments which demand a narrow spectral range or a small solid angle of the incoming light. 

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