NumCosmoGalaxyWLObsEllipConv

Method used to compute the ellipticity from the quadrupole moment matrix. The quadrupole matrix can be normalized either by its trace or by a combination of trace and determinant. In both cases, the shape can be described by an ellipse parameterized as $$ \left(\frac{x\cos\theta + y\sin\theta}{a}\right)^2 + \left(\frac{y\cos\theta - x\sin\theta}{b}\right)^2 = 1, $$ where $a$ and $b$ are the semi-major and semi-minor axes, and $\theta$ is the orientation angle.

For the trace normalization (NC_GALAXY_WL_OBS_ELLIP_CONV_TRACE), the ellipticity is commonly defined as $$ \chi = \frac{a^2 - b^2}{a^2 + b^2} e^{2i\theta}, $$ sometimes referred to as the distortion.

For the normalization involving both trace and determinant (NC_GALAXY_WL_OBS_ELLIP_CONV_TRACE_DET), the ellipticity is typically defined as $$ \epsilon = \frac{a - b}{a + b} e^{2i\theta}, $$ which corresponds to the complex ellipticity based on axis ratio.