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This letter explores the Gram-Schmidt orthogonalization procedure (GSOP) for compensation of quadrature imbalance in an optical 90 ^deg hybrid. We present computer simulations for an optical QPSK communication system using a digital coherent receiver and investigate the impact of quadrature imbalance on the required optical signal-to-noise ratio for the receiver and the frequency estimation algorithm. We then demonstrate the improvement which can be achieved using the GSOP, including the impact of quantization in the digital coherent receiver. Finally, we show that the GSOP can equally be applied to polarization-division multiplexed systems, applying the GSOP in conjunction with the constant modulus algorithm to demultiplex a PDM-QPSK signal.