  The matter-wave interference picture, which appears within the quantum Talbot
effect, changes qualitatively in response to even a small randomness in the
phases of the sources. The spatial spectrum acquires peaks which are absent in
the case of equal phases. The mathematic model of the effect is presented. The
manifestations of the phase randomness in experiments with atomic and molecular
Bose condensates, is discussed. Thermometry based on observable consequences of
phase randomness is proposed.
