Optimal aperture sizes and positions for EMCD experiments

The signal-to-noise ratio (SNR) in energy-loss magnetic chiral dichroism (EMCD)--the equivalent of X-ray magnetic circular dichroism (XMCD) in the electron microscope--is optimized with respect to the detector shape, size and position. We show that an important increase in SNR over previous experiments can be obtained when taking much larger detector sizes. We determine the ideal shape of the detector but also show that round apertures are a good compromise if placed in their optimal position. We develop the theory for a simple analytical description of the EMCD experiment and then apply it to dynamical multibeam Bloch wave calculations and to an experimental data set. In all cases it is shown that a significant and welcome improvement of the SNR is possible.