A general formula for determining the coupling loss between two single-made fiber collimators with the simultaneous existence of separation, lateral offset and angular tilt misalignments, and spot-size mismatch is theoretically derived by use of the Gaussian held approximation. Based on this general formula, the formulas for coupling losses that are due to the misalignment of insert separation, lateral offset, and angular tilt are given. The formula for the coupling loss that is due to Gaussian spot-size mismatch of two single-mode collimators is also given. Good agreement between these formulas and experimental results is demonstrated with gradient-index rod lens-based fiber collimators operating in the 1300 nm band. (C) 1999 Optical Society of America.A general formula for determining the coupling loss between two single-made fiber collimators with the simultaneous existence of separation, lateral offset and angular tilt misalignments, and spot-size mismatch is theoretically derived by use of the Gaussian held approximation. Based on this general formula, the formulas for coupling losses that are due to the misalignment of insert separation, lateral offset, and angular tilt are given. The formula for the coupling loss that is due to Gaussian spot-size mismatch of two single-mode collimators is also given. Good agreement between these formulas and experimental results is demonstrated with gradient-index rod lens-based fiber collimators operating in the 1300 nm band. (C) 1999 Optical Society of America.