To reduce the sampling data and the computational cost of white light interferometry, and improve the measurement speed, fast and stable white light interferometry is proposed. The mathematical model of light interferometry is deduced from the white light interference microscope model, and the relationship between light interference intensity function and envelop function is confirmed. On the basis of these studies, the envelope algorithm of Hilbert transform function extracting interference signal is proposed by increasing the sampling interval of discrete sampling point. And the sampling interval that satisfies the condition of the proposed algorithm is analyzed and determined based on the sampling principle. The algorithm effectiveness is then verified by a simulation test. The white light interference intensity signal of the sample has the direct current (DC) bias noise, which affects the stability of the fast white light interference measurement method. Therefore, median filtering method is used to eliminate background noise. And the quality of the filtered light intensity envelope is analyzed. The white light interference images of the sample are collected by a white light interference microscope, and the three-dimensional surface topographies reconstructed with different sampling intervals are compared. The results show that the envelope algorithm can improve the speed of three-dimensional reconstruction by 20 times compared with the traditional method. Meanwhile, the stability is improved as well.