My first question is regarding the arrangement of the crystal indices generated by the function get_view_crystal_indices in sinogram.py. As written in your code, the range of indices for i_tr_start goes from 224 to -224, and for i_tr_end from -1 to -450, without trimming. Could you please clarify what the negative sign represents in these crystal indices? May I interpret it as follows: if the positive indices represent the crystals arranged clockwise starting from 0, then do the negative indices signify a counterclockwise arrangement, with the possibility of a crystal being represented by both a positive and a negative index (for example, crystal 1 = -447)?

My second question pertains to the arrangement of tof-bins in the sinogram generated by joseph3d_fwd_tof_sino in projectors.py. Theoretically, the shape of the projected sinogram should be (nradial, nviews, nplanes, ntofbins). However, as I understand it, the length of the LOR, especially those at the edges of the detector ring, should be less than the diameter of the detector ring. Using the subdivision of each LOR into 29 TOF-bins with a TOF bin width of 169 ps, as mentioned in your article, it appears that the LORs at the ring edges might not be sufficiently long to be divided into 29 TOF-bins. In such cases, do you assign a value of 0 in the sinogram, or is my understanding of the TOF-bins subdivision incorrect? Additionally, how are the TOF-bin indices arranged along an LOR that has been subdivided? Is the bin adjacent to the starting crystal labeled as 0 and the one next to the ending crystal as 28, or is there another arrangement? When generating listmode simulation data using the pyparallelproj framework, I found that some coincidence events with LORs located at the edges have TOF-bin numbers at the ends of the range. My understanding is that the TOF-bin position for a coincidence event should be closer to the starting crystal, but the data generated does not always reflect this.