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25 years after the top quark's discovery, the Large Hadron Collider at CERNproduces proton-proton collision data on unprecedented scales at unprecedentedenergies - and has heralded an era of top-quark precision measurements. Theproduction of a top-quark pair in association with a photon ($t\bar{t}\gamma$)gives access to the electromagnetic top-photon coupling, one of the fundamentalproperties of the top quark. Various extensions of the Standard Model predictmodifications of the coupling strength or structure, and deviations from theStandard Model prediction of the $t\bar{t}\gamma$ production cross-sectionwould indicate new physics. With enough statistics available from the LargeHadron Collider, the electron-muon channel has gained particular interest dueto its high signal purity and precise available theory predictions.  This thesis presents results with the full Run 2 dataset collected with theATLAS detector in proton-proton collisions at the Large Hadron Collider between2015 and 2018 at 13 TeV centre-of-mass energy, corresponding to an integratedluminosity of 139 fb$^{-1}$. In order to compare the results to fixed-ordercalculations that include non-doubly-resonant diagrams, a combined measurementof $t\bar{t}\gamma + tW\gamma$ is performed. The focus is placed on ameasurement of the fiducial inclusive cross-section in the electron-muonchannel. Furthermore, the ATLAS data is unfolded to parton level andmeasurements of differential cross-sections as functions of several observablesare presented. Both fiducial inclusive and differential results are compared tostate-of-the-art fixed-order calculations at next-to-leading order in QCD. Anadditional focus of the thesis is placed on studies to use machine-learningtechniques, in particular deep neural networks, for the identification ofprompt photons.

Cross-section measurements of top-quark pair production in association with a hard photon at 13 TeV with the ATLAS detector