Disclosed are methods and apparatus for detecting defects in a semiconductor sample. An inspection tool is used to collect intensity data sets at a plurality of focus settings from each of a plurality of xy positions of the sample. A polynomial equation having a plurality of coefficients is extracted for each of the xy position's collected intensity data sets as a function of focus setting. Each of the coefficients' set of values for the plurality of xy positions is represented with a corresponding coefficient image plane. A target set of coefficient image planes and a reference set of coefficient image planes are then analyzed to detect defects on the sample.