Traditionally, observation of optical interference in intensity requires the balance of the paths of the two interfering fields within the coherence length of the optical fields. With intensity correlation fourth-order measurement between two detectors, such a requirement can be relaxed. Here, we report the observation of interference in a path-unbalanced Mach-Zehnder interferometer by mixing the output field with a weak coherence reference field before making a fourth-order intensity correlation measurement. Detailed theoretical analysis is made and is consistent with the experimental observation. As a side product of the study, when the coherent reference field is not present, the path-unbalanced interferometer realizes a Hong-Ou-Mandel interference effect that can be used to measure the coherence time of the input field with $g^{\left(2\right)}=1$. Such a technique of recovering interference, which is otherwise absent with the traditional observation method, should find wide applications in optical sensing by extending the applicable range.

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• Optical coherence
• Quantum optics