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A new method allowing an automated, polarization resolved, complete characterization of fiber pigtailed semiconductor optical amplifiers is presented and discussed. The method is applied to a high performance, polarization insensitive 1310 nm strained layer multiple-quantum-well semiconductor optical amplifier. For this amplifier 36 dB fiber to fiber gain, a 3 dB gain saturation output power of 15 dBm and a noise figure of 6.5 dB are demonstrated and the polarization dependence of these key performance figures is clarified. The result is presented in a form which should enable the end-user to derive realistic performance figures which will be obtained for a fluctuating random input signal state of polarization.