Based on measuring one-dimensional small rotation angles by using a parallel interference pattern (PIP), a method for measuring two-dimensional (2D) small rotation angles by using two different PIP's that are orthogonal to each other is proposed. We simultaneously measure the 2D small rotation angles Delta theta and Delta phi by detecting the phases of the orthogonal PIP's reflected by an object at two detection points. A sensitivity of 4.9 mrad/arcsec and a spatial resolution of 1.5 x 1.5 mm(2) are achieved in the measurement. Theoretical analysis and experimental results show that error epsilon(1) in the measurement of Delta phi is almost equal to -0.01 Delta theta and error epsilon(2) in the measurement of Delta theta is almost equal to -0.01 Delta phi. For small rotation angles of less than a few tens of arcseconds, the random errors whose standard deviations are 0.6 arcsec are dominant. (C) 1996 Optical Society of America