Photon distribution

In the latter case, the photon distribution peaks at a wave-length (l/co) = 1.7597... times longer than given by Eq. (2), and hence rather far in the infra-red in the solar spectrum. It is a curious coincidence that Eqs. (3), (3 a) and (3 b) can be written on the same form only differing in the coefficient (5,3 and 2, respectively). 

Figure 2. Top Spectral photon distribution of daylight on a sunny day. The distribution remains qualitatively similar on cloudy days with the total photon irradiance (i.e., Ep) in the region 400-800 nm reduced by a factor of up to 10. Bottom The spectral photon distribution under a dense patch of ivy leaves near to the ground surface, measured on the same day as the spectrum on top. Not only is the total photon irradiance (Ep) reduced by a factor of approx. 100 by the leaves, but also the spectral distribution is markedly altered, in particular at around 700 nm and above. (Both spectra from Smith [13].)...

Figure 2 Characterization of the photon distribution in directions and wavelengths.

Fig. 4.26. Photon distribution as a function of the scanning speed. Dependent on the scanning speed the photons are squeezed to the left side of the distribution (fast scan) or weU resolved (slow speed). Prom the dependence of A both number as well as diffusion rate can be determined...

Now let us turn to the photon distribution function (PDF)/(n) = (n pm(t) n), where n) is the multimode Fock state, n = (n, m,...), and pm(t) is the time-dependent density matrix of the mth field mode in the Schrodinger picture. Note that all the calculations in the preceding sections were performed in the... 

In the most compact form the information on the photon distribution f n) in some mode (we suppress here the mode index) is contained in the generating function... 

The first and second derivatives of the generating function (146) at z = 1 yield the first two moments of the photon distribution (hereafter we suppress subscript m)... 

The photon distribution function can be expressed in terms of the Legendre polynomials, according to the general formula (151)... 

Fig. 2. Ozone effect on solar radiation (left) and dependence of ozone concentration on atmospheric altitute (right). In the left part the dotted curve represents the photon distribution of solar energy outside the atmosphere (based on the assumption of black body radiation at T = 5773 K). The full curve gives the photon distribution of solar radiation reaching earth surface (see Ref.8. The ozone effect is shown by shadowed area, the dicline above 800 nm is mainly due to absorption by water vapour. On the right side the full curve represents qualitatively a typical ozone profile, the real ozone distribution significantly depends on the local situation (geography), see Ref.15)...

If photon counting is used, the detection time of the individual photons can be measured with a channel resolution of a few picoseconds, and can be used to build up the photon distribution versus time. Time-correlated single photon counting yields a time channel width of less that 1 ps, or an effective sample rate of more than 1 THz. 

The width of the time ehannels of the recorded photon distribution ean be made as small as 1 ps. The small time-bin width in conjunction with the high number of time ehannels available makes it possible to sample the signal shape adequately aeeording to the Nyquist theorem. Therefore standard deconvolution techniques [389] ean be used to determine fluorescence lifetimes much shorter than the IRF width and to resolve the eomponents of multiexponential decay functions. 

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