  The generalized hyper-Ramsey resonance formula originally published in Phys.
Rev. A vol 92, 023416 (2015) is derived using a Cayley-Klein spinor
parametrization. The shape of the interferometric resonance and the associated
composite phase-shift are reformulated including all individual laser pulse
parameters. Potential robustness of signal contrast and phase-shift of the
wave-function fringe pattern can now be arbitrarily explored tracking any shape
distortion due to systematic effects from the probe laser. An exact and simple
analytical expression describing a Ramsey's method of separated composite
oscillating laser fields with quantum state control allows us to accurately
simulate all recent clock interrogation protocols under various pulse defects.
