Total solid angle

For themial light, the iiumber of transitions per second induced by stimulated emission integrated over solid angles, is equal to The total emission, which is the sum of the stimulated and spontaneous emission, may be obtained by letting A A + 1 in the expression for stimulated emission, giving... 

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 use of RBS concurrendy with ERS is necessary for the complete derivation of a hydrogen profile, and it offers some simplifications of analysis. For example, for thin-layer spectra that have been normalized for a common ion fluence Qand solid angle SI, the total yields Y (the areas under the spectral peaks) may be compared in order to derive the layer composition. For... 

The total absorption / at a particular magnetic field is the product of the function f(Ht — H, AH) and the element of solid angle AQ summed over all solid angles, or... 

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. 

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. 

The total fluorescence power collected from the fluorophore distribution by a microscope objective centered in the normal line at a distance r is an integral of f over the objective s aperture which subtends a solid angle fl ... 

The photoelectric cross-section o is defined as the one-electron transition probability per unit-time, with a unit incident photon flux per area and time unit from the state to the state T en of Eq. (2). If the direction of electron emission relative to the direction of photon propagation and polarization are specified, then the differential cross-section do/dQ can be defined, given the emission probability within a solid angle element dQ into which the electron emission occurs. Emission is dependent on the angular properties of T in and Wfin therefore, in photoelectron spectrometers for which an experimental set-up exists by which the angular distribution of emission can be scanned (ARPES, see Fig. 2), important information may be collected on the angular properties of the two states. In this case, recorded emission spectra show intensities which are determined by the differential cross-section do/dQ. The total cross-section a (which is important when most of the emission in all direction is collected), is... 

The actinic flux F( A) is the total incident light intensity integrated over all solid angles, given by... 

The phase function p(0,4>) = S(0, < >) 2/4x2R, which is the fraction of the total scattered light that is scattered into a unit solid angle about a given... 

Of a special interest here is a charge in aperiodic motion, as in a collisional encounter. In that case, the theory of Fourier transforms is used to describe the continuous spectra that result. Specifically, starting from Eq. 2.60 and making use of Parseval s theorem, Eq. 2.52, the total energy radiated in the aperiodic event per unit solid angle and per unit frequency interval is obtained as... 

To interpret the low-frequency loss spectrum, we have to consider the influence of the well depth on the mean localization a, which is defined as a mean solid angle, occupied by the dipoles. As is seen in Fig. 7, for librators this angle is equal 4(3, while rotators occupy the total sphere. Here we shall give the definition... 

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