We propose a concept of multiplexing lobster-eye (MuLE) optics to achieve significant reductions in the number of focal plane imagers in lobster-eye (LE) wide-field X-ray monitors. In the MuLE configuration, an LE mirror is divided into several segments and the X-rays reflected on each of these segments are focused on a single image sensor in a multiplexed configuration. If each LE segment assumes a different rotation angle, the azimuthal rotation angle of a cross-like image reconstructed from a point source by the LE optics identifies the specific segment that focuses the X-rays on the imager. With a focal length of 30 cm and LE segments with areas of 10 x 10 cm^2, ~1 sr of the sky can be covered with 36 LE segments and only four imagers (with total areas of 10 x 10 cm^2). A ray tracing simulation was performed to evaluate the nine-segment MuLE configuration. The simulation showed that the flux (0.5 to 2 keV) associated with the 5-sigma detection limit was ~2 x 10^-10 erg cm^-2 s^-1 (10 mCrab) for a transient with a duration of 100 s. The simulation also showed that the direction of the transient for flux in the range of 14 to 17 mCrab at 0.6 keV was determined correctly with 99.7% confidence limit. We conclude that the MuLE configuration can become an effective on-board device for small satellites for future X-ray wide-field transient monitoring.
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