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This study relates to the INFN project SYRMA-3D for in vivo phase-contrast breast computed tomography using the SYRMEP synchrotron radiation beamline at the ELETTRA facility in Trieste, Italy. This peculiar imaging technique uses a novel dosimetric approach with respect to the standard clinical procedure. In this study, optimization of the acquisition procedure was evaluated in terms of dose delivered to the breast. An offline dose monitoring method was also investigated using radiochromic film dosimetry. Various irradiation geometries have been investigated for scanning the prone patient's pendant breast, simulated by a 14 cm-diameter polymethylmethacrylate cylindrical phantom containing pieces of calibrated radiochromic film type XR-QA2. Films were inserted mid-plane in the phantom, as well as wrapped around its external surface, and irradiated at 38 keV, with an air kerma value that would produce an estimated mean glandular dose of 5 mGy for a 14 cm-diameter 50% glandular breast. Axial scans were performed over a full rotation or over 180°. The results point out that a scheme adopting a stepped rotation irradiation represents the best geometry to optimize the dose distribution to the breast. The feasibility of using a piece of calibrated radiochromic film wrapped around a suitable holder around the breast to monitor the scan dose offline is demonstrated.