Improved mathematical models of structured-light modulation analysis technique for contaminant and defect detection

Surface quality inspection of optical components is critical in optical and electronic industries. Structured-Light Modulation Analysis Technique (SMAT) is a novel method recently proposed for the contaminant and defect detection of specular surfaces and transparent objects, and this approach was verified to be effective in eliminating ambient light. The mechanisms and mathematical models of SMAT were analyzed and established based on the theory of photometry and the optical characteristics of contaminants and defects. However, there are still some phenomena exist as conundrums in actual detection process, which cannot be well explained. In order to better analyze the phenomena in practical circumstances, improved mathematical models of SMAT are constructed based on the surface topography of contaminants and defects in this paper. These mathematical models can be used as tools for analyzing various contaminants and defects in different systems, and provide effective instruction for subsequent work. Simulations and experiments on the modulation and the luminous flux of fringe patterns have been implemented to verify the validity of these mathematical models. In adddition, by using the fringe patterns with mutually perpendicular sinusoidal directions, two obtained modulation images can be merged to solve the incomplete information acquisition issue caused by the differentiated response of modulation