Bipolar gradient
= Bipolar gradient
A <bipolar gradient> is a <magnetic field gradient> waveform with lobes of opposite sign. In <nuclear magnetic resonance>, such waveforms can control sensitivity to position and motion. Opposite signs alone do not guarantee equal signed areas, and an applied waveform must be distinguished from its effective encoding waveform when refocusing pulses change phase evolution.
For an original counterexample, apply $+10\,\mathrm{mT/m}$ for $1\,\mathrm{ms}$ and then $-10\,\mathrm{mT/m}$ for $2\,\mathrm{ms}$. The <gradient zeroth moment> is
$$
m_0=(0.010)(0.001)-(0.010)(0.002)=-10^{-5}\,\mathrm{T\,s/m}.
$$
The waveform is bipolar but unbalanced.
If the two durations are instead equal to $\tau$, and the effective lobes are contiguous, $+G$ from time 0 to $\tau$ and $-G$ from $\tau$ to $2\tau$, then $m_0=0$ but the <gradient first moment> is $m_1=-G\tau^2$. Thus cancellation of stationary-position phase can coexist with sensitivity to constant <velocity>. The sign follows this stated ordering.
Bipolar pulses also appear outside flow imaging. A 1989 <stimulated echo> study addressed background gradients that distort <diffusion> measurements. Alternating pulses could cancel a cross term under specified conditions; tests used proton signals from homogeneous and granular samples.<Pulsed field gradient stimulated echo methods for improved NMR diffusion measurements in heterogeneous systems by R. M. Cotts and others>[Primary abstract: background-gradient reduction, conditional cross-term cancellation and measurements]{ref} This is a sequence-specific result, not a promise that every bipolar pair removes every imaging error.