This paper considers the fault-diagnosis problem for low-degree all-optical networks. Failure-detection schemes which subject to topological constraints are proposed. Optical probe signals are sent in parallel along a set of designed lightpaths. The network health state is derived from the results of this end-to-end test (i.e., probe syndromes). The design objectives are to minimize the diagnosis cost which is represented by the number of probes. We obtain a lower bound of the number of the probes to identify any single link failure and implement this scheme in several networks as well.