Radiative decays of B hadrons are flavour changing neutral currents (FCNC) proceeding at quark level through a b→qγ transition (q=s,d). Alike semileptonic decays (b→ql+l- where l=e,μ,τ), they are only allowed at loop-level in the Standard Model (SM) which originally made them an excellent probe for tree-level new physics contributions. FCNCs were observed at Tevatron and B-factories with properties compatible with SM values. From then on, they are serving precision tests at LHC experiments, and notably at LHCb. Another side of the physics reach of radiative decays is the determination of the quark mixing parameters, encoded in the Cabbibo-Kobayashi-Maskawa (CKM) matrix. Together with other experimental observables, radiative data can improve the constraints on the small set of independent matrix parameters, in particular through a determination of the |Vtd/Vts| ratio. CKM metrology therefore performs powerful consistency tests of the quark sector of the SM. A key observable in radiative decays is the polarisation of the emitted photon. Indeed, the chirality of the weak interaction dictates that the rate of b→qγ transitions is dominated by a left-handed amplitude while the right-handed amplitude is suppressed by the ratio of quark masses mq/mb. Departure from this prediction would be a clear signal for new physics. Several methods to indirectly measure the photon polarisation were proposed, each posing specific experimental and theoretical challenges. The method of AGS oscillations [1] exploits the time-dependent asymmetry in B and B radiative decays. Thanks to a cancellation of QCD uncertainties, the SM prediction for the asymmetry is quite precise. Furthermore, the method applies to several exclusive Bd and Bs decay modes provided their final state is an eigenstate of CP symmetry, allowing for independent tests and a powerful combination of the results. This project aims to maximise the sensitivity of the current and future LHCb datasets to new physics effects through AGS oscillations. This should be achieved by first considering the full inclusive mass spectrum of final-state hadrons (rather than the mass region where only one resonance dominates) thanks to a better control of the increased backgrounds and a time-dependent amplitude analysis of the Dalitz plot; and secondly by considering several experimentally accessible Bd and Bs decay modes and combining the CP measurements in each of them. A second side of the project is the determination of the |Vtd/Vts| CKM ratio using Cabibbo-favoured b→sγ and Cabibbo-suppressed b→dγ transitions. While this was done at B-factories with Bd decays only, LHCb should be able to also propose a measurement in Bs decays (for which no sensitivity is reported in the Belle2 physics book). Given the backgrounds, the mass resolution in that last case is crucial and this measurement necessarily relies on samples of photons reconstructed as e+e- pairs rather than standalone calorimeter clusters. The low reconstruction efficiency for such photons (converting into the detector material) makes the measurement of the Bs suppressed decay very challenging, even when the Run3 dataset will be made available. It is thus proposed to improve the algorithm itself and deploy it as soon as possible during Run3. [1] D. Atwood, M. Gronau and A. Soni, arXiv:hep-ph/9704272