Ballistic photons

The equation of radiative transfer will not be solved here since solutions to some approximations of the equation are well known. In photon radiation, it has served as the framework for photon radiative transfer. It is well known that in the optically thin or ballistic photon limit, one gets the heat flux as q = g T[ - T ) from this equation for radiation between two black surfaces [13]. For the case of phonons, this is known as the Casimir limit. In the optically thick or diffusive limit, the equation reduces to q = -kpVT where kp is the photon thermal conductivity. The same results can be derived for phonon radiative transfer [14,15]. 

Typical values of p s are around 10 cm Consequently, there are practieally no unscattered or ballistic photons for tissue thicker than 1 cm [149]. Instead, the photons must be considered to diffuse through the tissue. Consequently, the spatial resolution of DOT images is extremely poor and cannot compete with positron emission, X-ray and MRI techniques. 

The situation is quite different for the camera. The camera records the image as it appears from the top of the sample. A sharp image is obtained only from the ballistic (unscattered) fluorescence photons. The effective point-spread function is a sharp peak of the ballistic photons surrounded by a wide halo of scattered pho-... 

Pa —4 3nd the single scattering approximation is used. The arrow indicates the part of the distribution that is due to the ballistic photons, ie, the arrow represents a Dirac distribution. This illustration does not allow for analysis of the ratio of ballistic to scattered photons, but we invite the reader to see Fig. 14. 

This approach significandy simplifies solution of the mesoscopic problem. Thus, we consider only two subsets in the photon population the photons that arrive direcdy from the surface T (did not undergo any scattering events) will be called ballistic photons, and the photons that have undergone only one scattering event will be called the scattered photons. ... 

The incoming intensity is equal to zero because on the one hand, there is no emission at the boundaries for this population (only ballistic photons are emitted at the boundary. F), and on the other hand, reflectivity of T and H. is zero in the present case. 

Fig. 13 presents the angular distribution of L resulting from the singlescattering approximation for the equivalent transport problem a, and Ph 4 as well as the reference solution produced by the Monte Carlo method for and k xt and the phase function of C. reinhardtii. In the reference situation, at the location in question (zq = 3 cm), the ballistic beam is completely attenuated all the photons have undergone at least one scattering event but deviated very htde from their incident direction (see Section 3.2). This situation results in a complex angular distribution centered around the incident direction (see Fig. 13A). In our equivalent transport problem, this complex distribution is replaced by the sum of a Dirac distribution (contribution of the ballistic photons, ie, 75% of the photons in the present case, see Fig. 14) and a relatively broad distribution (contribution of the scattered photons) that is simply modeled as Eqs. (62) and (63) under the single-scattering approximation (see Fig. 13B). The angular distribution of the scattered intensity at different locations is shown in Fig. 15.

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. 

In Section 3.3, Fig. 13, we saw that the equivalent transport problem allows us to separate our radiative study into two simple systems the ballistic photons, for which the exact solution is analytical, and the scattered photons, which correspond to intensity close to isotropy. This relative isotropy of the scattered intensity in the equivalent transport problem suggests that the PI approximation is relevant. Therefore, to formulate the coUimated incidence phenomena, we will address the equivalent transport problem and separate the analysis of ballistic photons from that of scattered photons only scattered photons will be subjected to the PI approximation. In the rest of the chapter, the baUistic population is denoted as (0), whereas the scattered photons wiU be called the diffuse population and denoted as (d). 

Here, the ballistic photons are analyzed separately therefore, = 0 and = 0 in Eqs. (75) and (76) (there is no source at the boundary for the diffuse population). In addition, we ignore reflectivity (ie, p = 0) thus, we have the boundary conditions as follows ... 

This overview shows that optical immersion technology allows one to control effectively optical properties of tissues and blood. Such control leads to essential reduction of scattering and therefore causes much higher transmittance (optical clearing), appearance of a big amount of least scattered (shake) and ballistic photons allowing for successful application of coherent-domain and polarisation imaging techniques. 

The foundation for the development of these techniques is built on investigations into photon migration processes [2, 9]. Subsequent, detailed examination by Everall et al. [10, 11] demonstrated that the inelastically scattered (Raman) component decays substantially more slowly than its elastically scattered counterpart (i.e. the laser light) due to the regeneration of the Raman signal from the laser component. Discrimination between diffusely scattered photons and the ballistic and snake components is achieved by gating the detector in the temporal or spatial domain. 

Use of a metal-semiconductor Schottky diode allowed for the measurement of the steady-state current from the continuous flow of ballistic charge carriers generated by the absorption of photons. Schemes of the photovoltaic device are also described in Fig. 10.9a. To generate electric current through the device, these electrons need enough energy to travel over the Schottky barrier and into the Ti02 conduction band. 

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