An interpretation of the Talbot effect in a tapered gradient-index medium by number theory as the output/input relationship between the integer and the noninteger difference of position and the slope of rays is presented. Unit cell and transverse magnification for Talbot images are evaluated, and two criteria for angular magnification are defined. The study is particularized to a finite set of diffracted rays.
© 2001 Optical Society of America
Original Manuscript: February 20, 2001
Revised Manuscript: April 26, 2001
Manuscript Accepted: April 30, 2001
Published: November 1, 2001
Marı́a Teresa Flores-Arias, Marı́a Victoria Pérez, Carlos Gómez-Reino, Carmen Bao, and Carlos R. Fernández-Pousa, "Talbot effect interpreted by number theory," J. Opt. Soc. Am. A 18, 2707-2716 (2001)