“…Roll angular displacement is difficult to measure in the geometric error detection of numerical control (NC) machine tools due to the low resolutions of the conventional methods, whose sensitive directions are orthogonal to the plane of angular displacement [1]. To overcome that problem, many methods have previously been proposed, such as diffraction gratingsbased methods [1,2], polarization intensity variation methods [3][4][5], geometric relation transformation methods [6][7][8][9], collimator methods [10][11][12], polarization phase detection methods [13][14][15][16][17][18][19] and so on [20][21][22][23][24]. The polarization phase detection methods have been adopted by many researchers because of their advantages of having a simple structure and high resolution.…”