Stejskal-tanner equation for three asymmetrical gradient pulse shapes used in diffusion NMR

When using pulsed-field gradient nuclear magnetic resonance (NMR) for measurements of translational self-diffusion, the Stejskal-Tanner equation is used to relate the signal attenuation to the experimental parameters and to estimate the diffusion coefficient. However, the conventional form of the equation is valid only if the gradient pulse shapes are perfectly rectangular, which is never the case in practice. In light of three asymmetric gradient pulse shapes having reached the NMR mainstream and been implemented into proprietary software, we present explicit expressions for the corresponding Stejskal-Tanner equations and computer code for easy implementation. We also study the bias introduced by using the common rectangular gradient pulse approximation.