If I’m understanding your setup correctly, I think you might need something more than the camera calibration and related functions.
Camera calibration is about modeling the mapping from 3D (world) to 2D (image), and has been developed to work for typical cameras and lenses. The model consists of the theoretical pinhole model (image center, focal length) and a distortion model to account for distortions due to physical factors (sensor tilt, lens distortion). The lens distortion part is your only hope, but it’s probably not a good fit.
The distortions you get from the concave surface aren’t necessarily something the camera calibration functions can model. For example, the distortion model is based on an assumption that the distortion is radially symmetric about the image center, so a distortion that behaves differently in the X axis vs the Y won’t be modelled correctly.
I’m not sure how I’d approach this - it would depend on other factors and exactly what you are trying to do.
Can you describe the “image on a cylinder” part a little better? Is it light being projected onto a screen for viewing? What is the end goal? To be able to process the camera image so it appears rectangular as if the cylinder were unrolled?