For differential microphone arrays, most of the performance evaluation measures that are used in the context of noise reduction are based on the energy of the signal. In this paper, we propose a spectral entropy-based measure, which quantifies the ratio of the spectral information contained in the desired and actual outputs of the microphone array, and can evaluate the performance in terms of the average of lost/gain information. At the same time, the value of the spectral entropy-based measure shows whether a speech signal is noisy or if some information has been lost. The proposed measure provides some advantages over the energy-based measures, such as the array gain. Moreover, the performance of a first-order-differential microphone array designed based on the maximum value of the array gain is evaluated using the proposed spectral entropy-based measure.