The space-time mutual coherence function for some electric field E ( t ) measured at two points in a plane of observation ( call them 1 and 2 ), is defined to be
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Far away from the sources, however, we should expect the mutual coherence function to be relatively large because the sum of the observed fields will be almost the same at any two points.
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Normalization of the mutual coherence function to the product of the square roots of the intensities of the two electric fields yields the complex degree of second-order coherence ( correlation coefficient function ):
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Given the restrictions noted above ( ergodicity, linearity ) the coherence function estimates the extent to which y ( t ) may be predicted from x ( t ) by an optimum linear least squares function.
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Thus, if we are observing two fully incoherent sources we should expect the mutual coherence function to be relatively small between the two random points in the observation plane, because the sources will interfere destructively as well as constructively.
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While the quantum coherence functions might yield the same results as the classical functions, the underlying mechanism and description of the physical processes are fundamentally different because quantum interference deals with interference of possible histories while classical interference deals with interference of physical waves.
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In this case, when we calculate the mutual coherence function for an extended coherent source, we would not be able to simply integrate over the intensity function of the source; the presence of non-zero cross terms would give the mutual coherence function no simple form.
18.
In this case, when we calculate the mutual coherence function for an extended coherent source, we would not be able to simply integrate over the intensity function of the source; the presence of non-zero cross terms would give the mutual coherence function no simple form.
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Additional practical concerns are how to effectively include effects such as inelastic and diffuse scattering, quantized excitations ( e . g . plasmons, phonons, excitons ), etc . There was one code that took these things into consideration through a coherence function approach called Yet Another Multislice ( YAMS ), but the code is no longer available either for download or purchase.
