  We propose a differentiable imaging framework to address uncertainty in
measurement coordinates such as sensor locations and projection angles. We
formulate the problem as measurement interpolation at unknown nodes supervised
through the forward operator. To solve it we apply implicit neural networks,
also known as neural fields, which are naturally differentiable with respect to
the input coordinates. We also develop differentiable spline interpolators
which perform as well as neural networks, require less time to optimize and
have well-understood properties. Differentiability is key as it allows us to
jointly fit a measurement representation, optimize over the uncertain
measurement coordinates, and perform image reconstruction which in turn ensures
consistent calibration. We apply our approach to 2D and 3D computed tomography,
and show that it produces improved reconstructions compared to baselines that
do not account for the lack of calibration. The flexibility of the proposed
framework makes it easy to extend to almost arbitrary imaging problems.
