Fundamentals of Electromagnetic Wave Scattering

The correlation function g r) is the average of the product of the density fluctuation of the two points with distance r and has the following relationship with dynamic radius distribution function (Fourier transform of the scattering intensity) p r)  

That is, if the measured scattering intensity is inverse Fourier transformed with respect to the magnitude q of the scattering vector, a dynamic radius distribution function can be obtained. This distribution expresses spatial correlation of electron density of two points with relative distance r in the statistically isotropic scattering media. When r = 0, Eq. (3) gives invariance Q that is independent of the structure of the scattering media  

As can be seen ftom Eq. (4), the invariance Q is proportional to the square average of the electron density fluctuation of the scattering media. When the electron density difference Ap is constant, it is proportional to the volume of the scattering media. In this case, the correlation function can be rewritten using the function yo(0 that depends on the shape of the scattering media  

Beyond the maximum distance D of the scattering media, yo(0 diminishes. 

As is obvious from Eq. (3), if the scattering intensity that is observed from the gel is inverse Fourier transformed, the dynamic radius distribution function can be obtained. The fluctuation of the density within the gel, that is, information concerning the gel structure, can be gained to some extent. However, Eqs. (3) and (4) should be applied with caution for various reasons that is, because the actual measurement range of the scattering vector is limited, the measured scattering intensity caimot be extrapolated from 0 and q oo. 

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