The instrumental resolution function of synchrotron radiation powder diffractometers in the presence of focusing optics

The theory developed by Caglioti and co-workers [Caglioti, Paoletti & Ricci (1958). Nucl. Instrum.3, 223-228; Caglioti, Paoletti & Ricci (1960). Nucl. Instrum. Methods, 9, 195-198; Caglioti & Ricci (1962). Nucl. Instrum. Methods, 15, 155-163] and Sabine [(1987). J. Appl. Cryst.20, 23-27, 173-178] that provides an analytical description of the instrumental resolution function of single-crystal and powder diffractometers consisting of sequences of collimators and crystals is extended by including the effect of collimating and refocusing mirrors. A simple analytical expression with only two fitting parameters (the beam divergence after reflection by the collimating and the refocusing mirrors) is determined, this expression being applicable to all mirror settings. The new theory is applied to experimental data collected at the Swiss Light Source Materials Science beamline powder diffractometer for three photon energies under extreme mirror bending conditions using the small-linewidth powder sample Na2Ca3Al2F14.