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Phase-measuring deflectometry (PMD)-based methods have been widely used in the measurement of the three-dimensional (3D) shape of specular objects, and the existing PMD methods utilize visible light. However, specular surfaces are sensitive to ambient light. As a result, the reconstructed 3D shape is affected by the external environment in actual measurements. To overcome this problem, an infrared PMD (IR-PMD) method is proposed to measure specular objects by directly establishing the relationship between absolute phase and depth data for the first time. Moreover, the proposed method can measure discontinuous surfaces. In addition, a new geometric calibration method is proposed by combining fringe projection and fringe reflection. The proposed IR-PMD method uses a projector to project IR sinusoidal fringe patterns onto a ground glass, which can be regarded as an IR digital screen. The IR fringe patterns are reflected by the measured specular surfaces, and the deformed fringe patterns are captured by an IR camera. A multiple-step phase-shifting algorithm and the optimum three-fringe number selection method are applied to the deformed fringe patterns to obtain wrapped and unwrapped phase data, respectively. Then, 3D shape data can be directly calculated by the unwrapped phase data on the screen located in two positions. The results here presented validate the effectiveness and accuracy of the proposed method. It can be used to measure specular components in the application fields of advanced manufacturing, automobile industry, and aerospace industry. [ABSTRACT FROM AUTHOR]