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 a principle is built and applied in the indoor segmented mirror experiment system in the lab. According to the co-focus requirement of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, 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.