Figure 2
From: Pulse sequence design for high field NMR with NV centers in dipolarly coupled samples
(a) Illustration of a CPMG pulse block (upper panel) and its geometric interpretation (lower panel). This panel shows a projection of the sphere in Fig. 1 (b) viewed in a direction parallel to axis \(A\), as represented with the eye symbol. This view facilitates the representation of the projections onto the plane perpendicular to A of (i) The magnetization vector, denoted as \(\vec {M}_k^\perp\), and (ii) The \(\hat{z}\) axis, referred to as \(\hat{z}^{\perp }\). In addition, it shows the trajectory followed by a magnetization vector during a rotation around A (purple circle) and after successive LG4 blocks (yellow ellipse). (b) Upper panel, pulse block of our tailored sequence where the initial \(\pi\) pulse is delivered at a time \(t_1\). With this control, the phase accumulation of the NV is proportional to the projection of \(\vec {M}_k^\perp\) onto \(\hat{l}\) (shown in red), an axis tilted away from \(\hat{z}^\perp\) and aligned with the major axis of the yellow ellipse for optimal contrast. (c) Evolution of the projection of \(\vec {M}_k^\perp\) onto axis \(\hat{z}^\perp\) (red) and onto axis \(\hat{l}\) (blue). The amplitude of the projection onto \(\hat{l}\), resulting from the sequence in panel (b), reaches the maximum value of 1. As the phase accumulated by the NV is directly proportional to this projection, the timing of the pulses in (b) ensures the maximum phase accumulation amplitude.
