In this paper, we present a practical approach for phase analysis of sinusoidally phase shifted interference signals, which are generally used to detect optical path length changes in one arm of the interferometer based on an algorithm introduced by de Groot. We describe the original algorithm from our point of view and try to emphasize the limitations and some details that need to be known for practical implementation. We introduce methods for how to overcome these limitations, and in addition, we provide an extension of the algorithm to a temporal high-resolution mode, which provides a possibility to calculate a phase value for each sampled point of an interference signal and opens new applications for the existing measurement devices without any hardware changes. Simulated and experimental results verify our extensions.