We present guidelines for the performance of multilayer mirrors and filters for imaging the earth's inner magnetosphere by isolating the 304-Å He+ emission. Our analysis shows that the combination of filters and multilayer mirrors for an inner magnetosphere imager must attenuate the 1216-Å Lyman α emission by six orders of magnitude and the 584-, 834-, and 1026-Å background emissions by three orders of magnitude relative to the 304-Å signal. Multilayer mirrors with the highest possible reflectance at 304 Å are needed to preserve as much of the low-intensity 304-Å signal as possible. The design of multilayer mirrors is discussed, and the results of an exhaustive computer search for the best multilayer mirror design for 304-Å radiation are presented and analyzed. The theoretical performance of these new multilayer mirror designs is significantly better than that of designs currently used for imaging the solar 304-Å emission. Promising materials for normal-incidence multilayer mirrors for 304-Å radiation are B4C, Be, Si, or SiC used with Al, Mg, or Mg2Si. Promising materials for a filter for this application are Te passivated with Si, or a combination of Al or Si with B or C.