Number of phase levels in a two-dimensional separable Talbot array illuminator

The number of phase levels in a Talbot array illuminator (TAIL) is an important factor for estimation of practical fabrication complexity and cost. We show that the number of phase levels in a two-dimensional TAIL (2D-TAIL) has a simple relation to the prime number. When the output array is alternatively pi phase modulated, there are similar simple relations. These simple relations should be highly interesting for practical use. An experiment with the 2D-TAIL based on the joint-Talbot effect is given as well.