Limits for reduction of effective focal volume in multiple-beam light microscopy

Employing interference patterns for illumination has been shown to reduce the focal volume in fluorescence microscopy. For example, the 4Pi technique employs two interfering laser beams and significantly decreases the focal volume, as compared to conventional microscopy. We study theoretically the effect of using multiple interfering laser beams on the focal volume. In realistic setups with three or four beams, the focal volume is about half of that from the 4Pi case. This improvement reaches a limit quickly as more beams are added, and for the idealized case of an infinite number of beams the focal volume is rather close to the three- or four-beam cases. Thus, our study suggests a limit for the possible reduction of the focal volume in a purely optical far-field setup.