Talbot imaging is a well-known effect that causes sinusoidal patterns to be reimaged by diffraction with characteristic period that varies inversely with both wavelength and the square of the spatial frequency. This effect is treated using the Fresnel diffraction integral for fields with sinusoidal ripples in amplitude or phase. The periodic nature is demonstrated and explained, and a sinusoidal approximation is made for the case where the phase or amplitude ripples are small, which allows direct determination of the field for arbitrary propagation distance. Coupled with a straightforward method for calculating the effect in a diverging or converging beam, the Talbot method provides a useful approximation for a class of diffraction problems.
© 2010 Optical Society of America
Diffraction and Gratings
Original Manuscript: May 19, 2010
Revised Manuscript: August 20, 2010
Manuscript Accepted: August 31, 2010
Published: September 24, 2010
Ping Zhou and James H. Burge, "Analysis of wavefront propagation using the Talbot effect," Appl. Opt. 49, 5351-5359 (2010)