Measurement of two-dimensional small rotation angles by using orthogonal parallel interference patterns

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 Δθ and Δφ 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 × 1.5 mm(2) are achieved in the measurement. Theoretical analysis and experimental results show that error ε(1) in the measurement of Δφ is almost equal to -0.01Δθ and error ε(2) in the measurement of Δθ is almost equal to -0.01Δφ. For small rotation angles of less than a few tens of arcseconds, the random errors whose standard deviations are 0.6 arcsec are dominant.