Beam phase measuring deflectometry featuring physics-compliant object-image mapping

Phase measuring deflectometry has been proven as a competitive technique for measuring complex optical surfaces. However, the commonly used imaging model simply treats the light beam associated with each camera pixel as a single ray, which in turn leads to significant measurement errors for complex surfaces with high curvedness, low reflectivity, or nonideal specularity. To broaden the measurable scope of deflectometry, beam phase measuring deflectometry is proposed. A beam imaging model is developed by defining a discrete light field function and assigning a beam composed of a set of rays to each camera pixel. The conventional framework of the one-to-one mapping between the points on the screen, camera, and surface under test is broken through for the first time, enabling a direct physics-compliant description of the imaging process in deflectometric measurement. The flexibility of the imaging model is guaranteed by a set of tunable parameters, and the difficulty of intensity quantification of images is bypassed through phase rendering. The proposed method shows superior accuracy over traditional approaches for complex surfaces, which reduces the measurement errors from an order of micrometers to hundreds of nanometers, while maintaining numerical reliability and measurement efficiency.