A study of the stochastic description of the Talbot effect in the temporal domain under random timing jitter is presented. The relevant statistical quantity is the variance. The variance of a train of pulses, each one affected by random timing jitter, shows peaks in the edges of the pulses. When this train is Talbot-imaged, the variance becomes flattened along the unit interval corresponding to each pulse as a result of the dispersion of the individual pulses of the train. Fractional Talbot devices are also analyzed. In particular, it is shown that this smoothing effect also occurs in Talbot devices leading to N× repetition rates of the original train.
© 2004 Optical Society of America
(030.1670) Coherence and statistical optics : Coherent optical effects
(060.2340) Fiber optics and optical communications : Fiber optics components
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(320.5550) Ultrafast optics : Pulses
Carlos R. Fernández-Pousa, Felipe Mateos, Laura Chantada, María Teresa Flores-Arias, Carmen Bao, María Victoria Pérez, and Carlos Gómez-Reino, "Timing jitter smoothing by Talbot effect. I. Variance," J. Opt. Soc. Am. B 21, 1170-1177 (2004)