The MGZ Technique of Elliptical Coordinates

Transferred to the observation that the reflections in moderately anisotropic scattering images are found on ellipses, it appears reasonable to parameterize such images in elliptical coordinates ( , v). The transformation relations are [266] 

Here A is the distance of the foci, which are found on the 512-axis. For = 0 we have plane polar coordinates. Varying v e [0,2n ] at constant u describes an elliptical orbit with a = and b = uits semimajor and semiminor axis, respectively. 

If the elliptical parameterization shall be used for automatic alignment of scattering patterns, control of ellipse rotation and displacement are important. Rotation is controlled by subtraction of a constant from v. A displaced center is readily considered by subtraction on the left side of Eqs. (10.6) and (10.7). 

Transferring Ruland s relation between the ellipticity and the microscopical draw ratio, to the parameterization of Murthy, Grubb and Zero, we receive 

Parameterization of Reflections in Elliptical Coordinates. The authors of the technique define the intensity 

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