Pseudo-thermal light is a regular source for correlated imaging. Compared to entangled two-photon source of quantum state, it can be easily obtained and used in correlation experiment. Pseudo-thermal light and entangled two-photon have certain similarities, especially in statistic characteristics of light field, which is closely related to the correlated calculation. When the quantum field is a coherent state or classically-random mixture of coherent states, statistic characteristics of the quantum field and classical field are all the same. The zero-mean Gaussian state can be used to describe fully the phase-insensitive coherence propagation of pseudo-thermal light. Based on this model, semi-classical detection theory of pseudo-thermal light is established. The correlation calculation formula of photocurrent in reference path and signal path are derived. The resolution and contrast of ghost imaging and view field of correlated imaging system are analyzed.