The interaction between an ultra-intense laser pulse and a relativistic electron beam is the main experimental method of strong-field quantum electrodynamics (QED). However, how to measure the accuracy of laser-electron-beam interaction, and then realize the accurate collision of micron precision, is a crucial reason limiting the development of strong-field QED experiments. Here, the dynamics of electrons and photons emitted during the interaction of an ultra-intense laser pulse and a relativistic electron beam is investigated via Monte Carlo numerical simulations. The correlation between the dynamics of electrons and emitted photons with the collision offset of laser pulse and electron beam is explored. Our simulations show that the spatial distribution information of emitted photons can effectively reflect the collision offset of the laser pulse and the electron beam. Based on the research results, the information of photon spatial distribution detected can be used to adjust the accuracy of laser- electron-beam interactions, which is expected to promote the development of strong field QED experimental technology.