Legendre moment

To extract information on molecular orientation distribution from experimental data, the most widely known technique, the Legendre moment expansion approach can be taken. In this section, this approach will be discussed first, followed by methods to elucidate atomic resolution details of the structures of ordered polymers with orientation-dependent NMR interactions, such as those from chemical shielding, dipole-dipole and quadrupolar coupling. Then, solid-state NMR studies of the torsion angles of the peptide backbone of highly ordered silk fibroin fiber, a protein that has been studied extensively as a model for fibrous proteins, will be described. 

The anisotropy of the vector X may exhibit either alignment or orientation. These terms specify whether or not the distribution of X is symmetric with respect to a plane perpendicular to the Z-axis. If reflection in this plane leaves the distribution unchanged, X is aligned but not oriented only even-order Legendre moments will then be non-zero. If reflection does change the distribution, X is oriented odd-order moments then are non-zero and measure the sense and size of the orientation. 

In summary, the weight of the Legendre moments 027 to the fluorescence intensity from any LIF study of an arbitrary anisotropic distribution which... 

Among all the moments that have been reviewed, orthogonal moments are chosen for this study, as they provide no information redundancy and efficient image reconstruction computation. Two orthogonal moments have been chosen for this study, one from the continuous family, called the Legendre moments, another from the discrete family, called the Tchebichef moments. 

If only Legendre moment of order (m + n)finite series of L by using equation... 

Pew-Thian, Y., and Paramesran, R. (2005) An efficient method fa- the computation of Legendre moments. Pattern Analysis and Machine Intelligence, IEEE Transactions on 27, 1996-2002. 

D. G. Truhlar and N. C. Blais, Legendre moment method for calculating differential scattering cross sections from classical trajectories with Monte Carlo initial conditions, J. Chem. Phys. 67 1532 (1977). 

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