Phase modulation schemes are attracting much interest for use in ultra-fast optical communication systems because they are much less sensitive to fibre nonlinearities compared to conventional intensity modulation formats. Semiconductor optical amplifiers (SOAs) can be used to amplify and process phase modulated signals, but with a consequent addition of nonlinear phase noise (NLPN). Existing SOA NLPN models are simplistic. In this paper we show that a more accurate model can be used, which results in simple expressions for SOA nonlinear noise, in particular when used to amplify differential phase shift keyed (DPSK) modulated data. The model is used to calculate the optical signal to noise ratio introduced by a power booster SOA and the first inline amplifier of a 40 Gb/s NRZ-DQPSK single channel link. © 2011 IEEE.