Co-phase and co-focus detection is one of the key technologies for large-aperture segmented mirror telescopes. In this paper, a new edge sensor based on fringes of equal thickness is developed, which can detect each segment's relative piston, tilt, and tip errors from the interferograms. Based on the co-focus demand for many ground-based seeing limited segmented mirror telescopes, an edge sensor prototype based on such principle is built and applied in the indoor segmented mirror experiment system in the lab. According to the co-focus requirement of Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST), many simulations and experiments are carried out for co-focus error detection of the segmented mirror system. Experiment results show that the co-focus accuracy is better than 0.02" RMS, which can meet the co-focus requirements of most large or extremely large segmented mirror astronomical telescopes.