= James Keeler
{c}
<James Keeler> works on high-resolution <nuclear magnetic resonance> methods and explains their physical basis through experiments and mathematical models. His university profile identifies this research focus and his authorship of \i[Understanding NMR Spectroscopy].<James Keeler at the University of Cambridge>[Research and Textbooks sections]{ref} The author-hosted Irvine notes give a particularly concrete account of how receiver electronics turn rotating nuclear <magnetization> into a signed frequency measurement.<Understanding NMR Spectroscopy by James Keeler (Irvine course notes)>[Chapter 9, sections 9.2.1–9.2.3, pages 9-2–9-5]{ref}
A single receiver channel proportional to $\cos(\Omega t)$ cannot distinguish offsets $+\Omega$ and $-\Omega$, because <cosine> is even. Two receiver references separated in <phase> by $\pi/2$ give <quadrature detection>: the two outputs represent $\cos(\Omega t)$ and $\sin(\Omega t)$ and combine into the <complex number> $e^{i\Omega t}$. This determines the sense of rotation in the <rotating frame> as well as its rate.<Understanding NMR Spectroscopy by James Keeler (Irvine course notes)>[Section 9.2.2, page 9-4, two mixers and complex signal]{ref}
For an original numerical illustration, offsets of $+100\,\mathrm{Hz}$ and $-100\,\mathrm{Hz}$ at $t=1.25\,\mathrm{ms}$ have phases $+\pi/4$ and $-\pi/4$. Both give the same real channel $1/\sqrt2$, but the imaginary channels are respectively $+1/\sqrt2$ and $-1/\sqrt2$. This is why retaining both receiver channels preserves information lost by a single real measurement.
\Image[https://www.ch.cam.ac.uk/files/styles/staff_portrait/public/portraits/jhk10.jpg?itok=15c227G7]
{title=James Keeler, portrait linked from his University of Cambridge staff profile}
{height=260}
Back to article page
