Illustration of our use of a Möbius transform to derive the total power measured by a KID on a simulation. Top-left: black diamonds are individual I,  Q points on a circle (blue curve). Top-right: normalised circle transformation of the points into the reference circle coordinates. The resonance is reached at (1,0). Bottom-left: Complex inverse of the points in the previous complex plane (the Möbius transform). Bottom-right: 1D polynomial fit (blue curve) to the derivative data points corresponding to dI,  dQ normalised, inverted and selected on the imaginary axis.