  Ultra-cold atomic gases provide new chance to study the universal critical
behavior of phase transition. We study theoretically the matter wave
interference for ultra-cold Bose gases in the critical regime. We demonstrate
that the interference in the momentum distribution can be used to extract the
correlation in the Bose gas. A simple relation between the interference
visibility and the correlation length is found and used to interpret the
pioneering experiment about the critical behavior of dilute Bose gases [Science
{\bf 315}, 1556 (2007)]. Our theory paves the way to experimentally study
various types of ultra-cold atomic gases with the means of matter wave
interference.
