Inclinations and Position Angles for Disc Galaxies in the SGA sample

We present a data-driven method for determining the inclination and position angle (PA) of disc galaxies using a Fourier-Laguerre basis decomposition of imaging data. We define a dimensionless metric, $\eta$, that characterises the ratio of the quadrupole and monopole coefficients in the Fourier-Laguerre basis function expansion. This metric serves as a robust measure which is related to the inclination of a galaxy. We find an empirical relationship between $\eta$ and inclination which is agnostic to the galaxy morphology. The PA is derived directly from the phase of the quadrupolar Fourier-Laguerre functions. Across a benchmark sample of galaxies, the method reproduces published inclination and PA values to within a median of 10$^\circ$ and 5$^\circ$, respectively, while also demonstrating essentially zero catastrophic failures. Applying this pipeline to galaxies from the Siena Galaxy Atlas (SGA), we report measurements of $\eta$, scale length and PA for three different bands of 133,942 disc galaxies. Our computationally inexpensive technique automates parametrisation analysis and returns reproducible results for large surveys. We release a Python package ready for application to next generation surveys.