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Free-space optical interconnects have been identified as the immediate successors to the troubled electrical wiring in most short-distance and high-speed digital applications. We apply the modified mode expansion method to calculate the maximum channel density (the number of channels per unit area) possible in a typical free-space optical interconnect configuration. We proceed to show that the density can be increased by departing from the traditional confocal optical design, by optimal positioning of the laser array relative to the transmitter microlens array. We also show that the interconnect density can be increased by using laser beams of higher frequencies and larger beam waists.