Decomposing rule of two-dimensional separable Talbot array illuminator

摘要

Talbot array illuminator (TAIL) based on fractional Talbot effect is useful for illuminating very large array, the number of phase levels of TAIL is a very important factor for estimation of practical fabrication complexity and cost. Based on the symmetry of the phase distribution, we can obtain the maximum phase level number for a given fractional Talbot distance. But because of the redundant equal phase, the exact phase level number is still unpredictable for an arbitrary opening ratio (1/M) of the illumination array. In this paper, we'll show that there is a simple decomposing rule to predict the number of phase levels of two-dimensional Talbot array illuminator (2D-TAIL) with the opening ratios (1/M_x), (1/M_y) in two dimensions, respectively. In the condition that the output array is alternatively π-phase-modulated, there are similar simple relations. These results are generally applicable and should be interesting for practical use. Based on the joint-Talbot effect, we realized a separable 2D-TAIL by using two crossly placed 1D-TAIL. The 1D-TAIL is fabricated with the usual binary-optics technique and the number of phase levels in this experiment can be well explained by our theoretical results.