A method was developed to reconstruct the image of an X-ray focal spot distribution from the radiography of a simple circular object. The details of the method are described in the work:

Di Domenico, G., Cardarelli, P., Contillo, A., Taibi, A., & Gambaccini, M. (2016). X‐ray focal spot reconstruction by circular penumbra analysis—Application to digital radiography systems. Medical Physics, 43(1), 294-302.

An ImageJ plug-in for the implementation of the method can be downloaded here.