By tilting the reference mirror of Twynman-Green interferometer having a reference mirror and a moving mirror, firinge pattern composed of bright and dark parallel lines can be obtained and the fringe pattern is shifted according to the displacement of the mowing mirror. Several studies are executed for displacement measurement by detecting the intensity of the fringe with photo-diodes having small detecting area. In this study, to improve the sensitivity and robustness, the intensity of fringe is detected by using a large-area quadratic photo-diode masked with a grating panel having four kinds of binary grating having phase-difference of 0, {pi}$/4, {pi}$/2, 3 {pi}$/4. The phase of the fringe is calculated with a simple 4-buckets algorithm. A experimental result shows that standard deviation of 5.653 nm is obtained comparing with a capacitive type gap sensor having nearly 1 nm accuracy.