Lambertian emission

FIGURE 2.5. Normalised electroluminescence radiation patterns of die 2-D patterned device measured in die x-(filled circles) and y-directions (filled squares) are shown along with die average of die two (black line, no symbols). The radiation pattern of an unpattemed device is also shown (filled triangles) along with radiation pattern obtained from the lambertian emission (dashed line, no symbols). 

Commonly, the Lambertian emission pattern is assumed, and Eq. (310) often approximated by... 

In optoelectronic applications, photometric quantities are often used to express the degree of the current conversion into light. The luminous efficiency with the Lambertian emission pattern is... 

Initially, we will focus on the mesoscopic description associated with the radiative transfer equation. Then, we will introduce the single-scattering approximation and two macroscopic approximations the PI approximation and two-flux approximation. AH of these discussions are based on the configuration shown in Fig. 6. Collimated emission and Lambertian emission wiU also be considered in the discussion later they correspond to the direct component and the diffuse component of solar radiation, respectively. Throughout our study, the biomass concentration Cx is homogeneous in the reaction volume V (assumption of perfect mixing), and the emission phenomena in V are negligible. The concentration Cx is selected close to the optimum for the operation of the photobioreactor the local photon absorption rate. 4 at the rear of the photobioreactor is close to the compensation point A.C (see Section 5 and chapter Industrial Photobioreactors and Scale-up Concepts by Pruvost et al.). 

Contrary to Section 3.3, where we addressed the equivalent transport problem, ballistic photons here are in the minority, except close to = 0, for 0 G [0, r/2]. It is possible to take into account all the ballistic photons in our calculations (Eqs. (75) and (76)) because the mesoscopic solution for is obtained easily, even in the present case, with Lambertian emission and reflection 2Lt z = E. Nonetheless, except for the term that we used in Eq. (84), their contribution to the boundary conditions is negligible for most photobioreactor configurations during operation close to the optimum biomass growth rate. 

Figure 18 The irradiance field G within the photobioreactor shown in Fig. 6, with the same parameters as in Fig. 16, but the Lambertian emission is replaced by collimated emission at 6, — 0. Comparison between the PI approximation (Eq. (88)) and the reference solution (Monte Carlo method, MCM). For collimated incidence, only the boundary condition atz = 0 is modified, in comparison with the solution used in Fig. 16. We still have g(°)(z = 0) =qn/ but the ballistic irradiance becomes G ° z 0) —qn/ni- Therefore, the same solution as in Fig. 16 can be used, but with replacement of 4gn with 2+ /fl )qn in Eq. (88).

Thus, no sharp emission pattern can be expected with the overall emission spectrum. Nevertheless, assuming the Lambertian shape of the emission from microcavity structures may lead to an overestimate as large as 30% [571]. An attempt to compare the measured full spectrum external emission as a function of the emitter thickness (Alq3) with theoretical description of microcavity modes has shown substantial disagreement, the theoretical estimates lead to the emission output much below the experimental data, differing by a factor of 2 for a 40nm-thick emitter [567]. The reason for... 

To better quantify influences of resonant wavelengths on emission characteristics, four parameters are defined the outcoupling efficiency, which is the ratio of the outcoupled emission to internally generated emission the forward enhancement ratio, which is the ratio between the normal-direction luminance of a cavity device to that of an optimized conventional bottom-emitting OLED the color shift, which is defined as [variance of w (0) + variance of w (0)j and measures variation of colors over angles and the Lambertian offset, which is defined as E 1(9)/1(0°) - cos 01 and measures the difference between the emission pattern of a device and the ideal Lambertian distribution (where J(0) is spectrally integrated I(Q,X)). Values of these parameters are obtained using both the simulated data and the measured EL characteristics. 

The derivation of the output from an integrating sphere is similar to that for a cavity blackbody We need to account for multiple reflections, and to do that we need consider the geometry and reflective characteristics of the internal surface (reflectivity, and the extent to which it is Lambertian). For the integrating sphere, however, we also need to know the irradiance at the input port and the nature of the reflectivity of the input and output port assemblies. That part of a port assembly that is truly open has zero reflectivity, but part of the port assembly has some reflectance that may differ from that of the sphere itself. A reasonable approximation would be to assume that reflectivity from the port assemblies is either zero (the open portion) or equal to that of the sphere itself. Another difference is that a blackbody has a high effective emissivity (low reflectivity), while for an integrating sphere we want a high reflectivity. 

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