  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.
