Photons coherence length

Adaptive optics requires a reference source to measure the phase error distribution over the whole telescope pupil, in order to properly control DMs. The sampling of phase measurements depends on the coherence length tq of the wavefront and of its coherence time tq. Both vary with the wavelength A as A / (see Ch. 1). Of course the residual error in the correction of the incoming wavefront depends on the signal to noise ratio of the phase measurements, and in particular of the photon noise, i.e. of the flux from the reference. This residual error in the phase results in the Strehl ratio following S = exp —a ). 

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... 

Taking the square modulus of this result to evaluate the overall rate from Eq. (5.6) again introduces a factor of K, which can be evaluated from Eq. (6.5) subject to replacement of by (which is independent of coherence length), the subscripts in the latter case denoting the fact that both laser photons are absorbed by the same molecule. The final result for the rate is then given by ... 

What then is the structural feature most characteristic of a proton conductor system It is generally believed that a proton is transferred through a solid in one of two distinct ways by a vehicular mechanism, whereby the proton rides on a carrier molecule of type NH4 or HjO ion, or by a Grotthuss mechanism, in which the proton jumps from a donor to a suitably placed acceptor molecule (typically, from H30 to H2O, or from H2O to OH ). How then is such a process sensed in a conventional diffraction experiment The nature of the diffraction method is such that we obtain a time- and space-average of the unit-cell content within the characteristic coherence length of the diffraction process (typically, hundreds of Angstroms), and over the duration of the experiment (days to weeks). This follows from the extremely short photon-electron and neutron-nucleus interaction times ( 10 s), which are significantly shorter than the characteristic time of the fastest of the dynamical processes in the structure ( 10 s for the vibration of a covalently bonded atom). It follows then that some type of structural... 

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... 

The frequency profile of the laser beam is usually characterized by its full-width at half-maximum (FWHM), Av. The single parameter that most effectively characterizes the degree of monochromaticity is then the quality factor Q, defined as the ratio of the laser emission frequency to its line width. It is also expressible as the coherence length 1 (the distance over which photons remain effectively in phase) divided by the wavelength ... 

The introduction and diversification of genetically encoded fluorescent proteins (FPs) [1] and the expansion of available biological fluorophores have propelled biomedical fluorescent imaging forward into new era of development [2], Particular excitement surrounds the advances in microscopy, for example, inexpensive time-correlated single photon counting (TCSPC) cards for desktop computers that do away with the need for expensive and complex racks of equipment and compact infrared femtosecond pulse length semiconductor lasers, like the Mai Tai, mode locked titanium sapphire laser from Spectra physics, or the similar Chameleon manufactured by Coherent, Inc., that enable multiphoton excitation. 

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