Coherence volume

With the coherence length lS.s = c/Aa in the propagation direction of the radiation with the spectral width Aa and the coherence surface the 

A unit surface element of a source with the spectral radiance Lo, [W/(m sr)] emits La fico photons per second within the frequency interval dm = 1 Hz into the unit solid angle 1 sr. 

The mean number n of photons in the spectral range Am within the coherence volume defined by the solid angle Af2 = X /A and the coherence length Asc = cAtc generated by a source with area As is therefore 

For a thermal radiation source, the spectral radiance for linearly polarized light (given by (2.28) divided by a factor 2) is for cos = 1 and L dv = 

The mean number of photons within the coherence volume is then with A = 

The mean number n of photons per mode is often called the degeneracy parameter of the radiation field. This example shows that the coherence volume is related to the modes of the radiation field. This relation can be also illustrated in the following way  

The mean number n of photons in the spectral range Aw within the coher- 

As = cAt generated by a source with area A is therefore n = (Lw/Hw)A AflAwAt  

The mean number of photons within the coherence volume is then with X = c/v n = l/[exp(hv/feT)-l].  

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Consider one resolution cell xm of the spectrum. The number of df, zm, is defined as the number of independent volumes that exist over the volume swept out by photons leaving the entrance slit during one exposure time t (see Fig. 3). An independent volume is the three-dimensional space over which a photon is coherent. Hence, if it has a coherence length c Arm, with c the speed of light and Arm the coherence time, and if it has a coherence area cTm, the coherence volume is simply their product, or c Arm om. On the other hand, the total volume swept out by a wave front of photons all leaving the aperture of area A during exposure time t is ctA. Hence the number of coherence volumes is... 

For the best thermal sources, the mean number of photons in the coherence volume (i.e., the degeneracy parameter ) is less than 10 . ... 

At high (>10 MeV) excitation energies, in several reactions, broad giant resonances were observed for virtually all nuclei. These can be attributed to coherent (volume) oscillations of the protons and neutrons. For a review see Harakeh and Van der Woude (2001). 

If a constant time-independent phase difference A0 = 0(Pi) — 0( 2) exists for the total amplitudes A = Aqc at two different points Pi, P2 the radiation field is spatially coherent. All points P, P that fulfill the condition that for all times r, 0(P, t) — (j) Pn, 01 < tt have nearly the same optical path difference from the source. They form the coherence volume. 

The superposition of coherent waves results in interference phenomena that, however, can be observed directly only within the coherence volume. The dimensions of this coherence volume depend on the size of the radiation source, on the spectral width of the radiation, and on the distance between the source and observation point P. 

Multiplication with the coherence length Ajc = c/ Am yields again the coherence volume Fc = Aoc/Am = r A c/(AmAs) of (2.137). We shall now demonstrate that the coherence volume is identical with the spatial part of the elementary cell in the general phase space. 

Figure 2.34 Coherence volume and phase space cell...

This coherent volume on High Energy Spectroscopy returns to a more focused content as found in the first four volumes of the Handbook. The plans for this volume started in early 1983 as a result of a suggestion from our editorial board who recommended that a thorough discussion of a currently topical aspect of the physics and chemistry of the rare earths should occasionally be assembled as the need arose. This volume is the first of these volumes. Over the next six months the contents of this volume began to take shape, especially with the help of Professor S. Hiifner, who was invited to serve as a special co-editor for this volume. 

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