A means for losslessly implementing arbitrarily space-variant optical interconnections in free space without sacrificing optical space-bandwidth product or power is described. The technique uses space-variant mirrors and polarization beam splitters to separate and combine sets of device output spots, where a different interconnection operation is performed on each spatially separable set. These space-variant mirrors are inexpensive and easily fabricated. Example applications for Banyan interconnections and laser array combination are presented. Current experimental limits are discussed.