Based on the standard angular momentum theory, we create an experiment on preparing maximally path-entangled (|N,0 +|0,N )2 (NOON) states of triphotons. In order to explain the error between the theoretical and experimental data, we consider the background events during the experiment, and observe their effect on the uncertainty in S^1. Afterwards, we calculate the quantum Fisher information (QFI) of the states to evaluate their potential applications in quantum metrology. Our results show that by adding the appropriate background terms, the theoretical data of the produced states matches well with the experimental data. In this case, the QFI of the states is lower than maximally entangled NOON states, but still higher than a classical state.