Critical Overlap for Elliptical Arrays

Multi-channel receive RF coils for MRI are usually comprised of an array of loops. These loops come in various shapes – circles, rectangles, hexagons, octagons, etc. Coil designers try to decrease the coupling between the loops through overlapping – partial overlapping of the two closed contours allows reduction of magnetic coupling between the loops to minimum. This configuration is called a critical overlap. While the critical overlap for circular loops is mentioned in multiple papers, a similar recipe is missing for elliptical loops. In this work we calculate the overlap coefficients for isotropic uniform elliptical arrays.