The phase shifting technique is the most widely used approach for detecting the envelope in low coherence interferometry. However, if the phase shifts calibration contains errors, some parasitic fringe structure will propagate into the calculated envelopes and cause imprecision in the envelope peak detection. To tackle these problems, a five-point stencil algorithm is introduced into the phase shifting interference microscopy. Considering the amount of parasitic fringes, envelope peak detection and computational efficiency, the presented approach leads to satisfactory results in performance. In combination with a simple polynomial curve fitting method the proposed algorithm exhibits good performance on envelope peak detection in surface profiling. Both of the simulated results and the experimental results indicated that the presented approach can be taken as an alternative to the currently existing methods used for phase shifting low-coherence interference microscopy.