diffct: Differentiable CT Operators from Circular Orbits to Arbitrary Trajectories

diffct is a CUDA-accelerated computed tomography library that exposes differentiable forward operators and their exact discrete adjoints for 2D parallel beam, 2D fan beam, and 3D cone beam imaging. The main branch provides the stable circular-orbit lineage released on PyPI, including Siddon and separable-footprint (SF) projector families, while the dev branch extends the Siddon-based projector/backprojector interface to arbitrary per-view trajectories through explicit source and detector arrays. This report rewrites the project description directly from the current source code, examples, tests, and the related CT literature. We formalize the geometry parameterization used by the implementation, derive the differentiable Siddon-style projector and its exact discrete adjoint, explain how gradients are transported through torch.autograd.Function wrappers backed by Numba CUDA kernels, document the analytical filtered backprojection and Feldkamp–Davis–Kress pipelines implemented on main and ported into the dev, and record how the circular-orbit SF algorithms from main fit into the broader architecture.