We describe a reciprocal-lattice vector method for analysis of the diffractive self-imaging (or Talbot effect) of a two-dimensional periodic object. Using this method we analyze the fractional Talbot effect of a hexagonal array and deduce a simple analytical expression for calculation of the complex amplitude distribution at any fractional Talbot plane. Based on this new formula, we design a hexagonal array illuminator (HTAI) with a high fractional parameter. A computer simulation for demonstration of the HTAI is also given.
© 2007 Optical Society of America
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