High-precision phase compensation in deflectometry for discrete surfaces

Phase compensation deflectometry enables the rapid assessment of surface figure errors and defects on specular surfaces. This method requires the construction of high-precision compensation fringes, whereas most existing approaches rely on analytical surface models and struggle to handle discrete surfaces. This paper presents a generic geometric modeling and reconstruction method for phase compensation deflectometry on discrete surfaces, overcoming the constraints of conventional height-field models. During ray reconstruction, the method incorporates the Möller-Trumbore algorithm combined with barycentric normal interpolation to accurately compute surface intersection points and normal vectors. Experimental results demonstrate that the Pearson correlation coefficient between the proposed method and interferometer measurements exceeds 0.7. This work provides a versatile and efficient solution for high-precision null testing of discrete surfaces.