Weighted momentum transfer DCS jacobian
IRENE
Qianqian Fang
hi Irene,
the DCS replay was my previous attempt of extending the replay-based Jacobian towards momentum transfer and DCT back in 2018 - despite at the time, and still, I don't have experience with DCT.
Frankly, I don't really know if this saved quantity could be used for DCT reconstruction at all, so I am happy that you paid attention to it, perhaps you can let me know if this is in the right direction.
what otDCT output actually saves is w_p*(1-cos(theta)) after every scattering event of the replayed photon, where
w_p is the detected weight of the p-th replayed photon, and
theta is the zenith/pole angle of the scattering; (1-cos(theta)) is the momentum transfer of the scattering event.
this formula attempts to mimic the replay-Jacobian of mua, i.e. Eq. 8 of the replay paper
https://opg.optica.org/boe/fulltext.cfm?uri=boe-9-10-4588
where J_mua = -\bar{L} = -sum(w_p * L_p,v)/sum(w_p); when building J_mua, the replay phase accumulates w_p*L in each voxel - a weighted back-projection of the derivative to absorption at the detector to the volume.
similarly, I imagined that by accumulating w_p*(1-cos(theta)) during the replay, I could also create a "back-projection" like operator to the voxels where scattering event happens. However, I did not do any derivation nor did I specify what quantity was the derivative taken against.
please let me know if this quantity has any potential use for what you want to do, if not, what would be a sensible quantity to output?
Qianqian
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