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An improvement in the information transfer rate (the amount of information communicated per unit area) in VCSEL-based free-space optical interconnects can be achieved by reducing the spacing between the microchannels. However, reducing the physical size of optical components results in an increase in diffractive spreading of laser beams and a decrease in the signal-to-noise ratio. The traditional methods used for describing diffraction phenomena tend to be rather cumbersome in most practical situations. However, the mode expansion method of Tanaka et al. (K. Tanaka, M. Shibukawa, O. Fukumitsu, IEEE Trans. Microwave Theory Tech. MTT-20, p749), applied in an improved form derived by the authors, is shown to be accurate and well suited for analysing the FSOI performance. It is also shown to consistently outperform the other approximate methods frequently used in the literature.