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Differential phase-contrast X-ray imaging using a Talbot-Lau interferometer has recently shown promising results for applications in medical imaging. However, reducing the applied radiation dose remains a major challenge. In this study, we consider the realization of a Talbot-Lau interferometer in a high Talbot order to increase the signal-to-noise ratio for low-dose applications. The quantitative performance of π and π/2 systems at high Talbot orders is analyzed through simulations, and the design energy and X-ray spectrum are optimized for mammography. It is found that operation even at very high Talbot orders is feasible and beneficial for image quality. As long as the X-ray spectrum is matched to the visibility spectrum, the SNR continuously increases with the Talbot order for π-systems. We find that the optimal X-ray spectra and design energies are almost independent of the Talbot order and that the overall …