Phase Cycling in Electron Spin Echo Envelope Modulation

. We present a general way to devise efficient phase cycles for arbitrary electron spin echo envelope modulation (ESEEM) experiments. The method determines all coherence transfer pathways contributing to the measured signal, selects those of interest and then examines all possible nested phase cycles in order to find those that achieve the required selection. The procedure is used to find efficient nested phase cycles for ESEEM sequences containing up to nine pulses: two-pulse, three-pulse and five-pulse ESEEM, standard and six-pulse hyperfine sublevel correlation (HYSCORE) as well as their extensions including remote echo detection. In addition, it is shown that by shifting the last pulse by 90° three-pulse ESEEM and HYSCORE do not need phase cycling in the case of a symmetrically excited line.