Quantitative analysis of imperfect frequency multiplying in fractional Talbot planes and its effect on high-frequency-grating lithography

Fractional Talbot images of amplitude line gratings, with small opening slits compared to the period, are characterized by an integer multiple of the gratings' spatial frequency. We investigate the formation of fractional Talbot images analytically within a scalar framework and give a comprehensible insight into the paraxial limits involved. Particular attention is paid to nonparaxial effects on the intensity distribution at fractional Talbot planes and their lateral periodicities. We present a comparison between the measured intensity distributions and a numerical implementation of our analytical method. Both ways reveal the paraxial limits of frequency multiplication on fractional Talbot images. The use of fractional Talbot images for lithography results in ghost diffraction orders. We roughly estimate the ghost orders quantitatively with a simple numerical model for monochromatic and polychromatic illumination.