  Purpose: Provide a closed-form solution to the sinusoidal coil sensitivity
model proposed by Kern et al. Solution allows for the precise computations of
varied, simulated bias fields which can be directly applied onto raw intensity
datasets.
  Methods: Fourier distribution theory and standard integration techniques were
used to calculate the Fourier transform of measured magnetic field produced
from line segment sources.
  Results: A $L^1_{\rm loc}(\mathbb{R}^3)$ function is derived in full
generality for arbitrary line segment geometries. Sampling criteria and
equivalence to the original sinusoidal model are discussed. Lastly a CUDA
accelerated implementation $\texttt{biasgen}$ is provided for on-demand
sensitivity and bias generation.
  Conclusion: Given the modeling flexibility of the simulated procedure,
practitioners will now have access to a more diverse ecosystem of simulated
datasets which may be used to quantitatively compare prospective debiasing
methods.
