  Quark orbital angular momentum (OAM) in the proton can be calculated directly
given a Wigner function encoding the simultaneous distribution of quark
transverse positions and momenta. This distribution can be accessed via proton
matrix elements of a quark bilocal operator (the separation in which is Fourier
conjugate to the quark momentum) featuring a momentum transfer (which is
Fourier conjugate to the quark position). To generate the weighting by quark
transverse position needed to calculate OAM, a derivative with respect to
momentum transfer is consequently required. This derivative is evaluated using
a direct derivative method, i.e., a method in which the momentum derivative of
a correlator is directly sampled in the lattice calculation, as opposed to
extracting it a posteriori from the numerical correlator data. The method
removes the bias stemming from estimating the derivative a posteriori that was
seen to afflict a previous exploratory calculation. Data for Ji OAM generated
on a clover ensemble at pion mass $m_{\pi } = 317\, \mbox{MeV} $ are seen to
agree with the result obtained via the traditional Ji sum rule method. By
varying the gauge connection in the quark bilocal operator, also Jaffe-Manohar
OAM is extracted, and seen to be enhanced significantly compared to Ji OAM.
