The number of phase levels of a Talbot array illuminator is an important fa
ctor in the estimation of practical fabrication complexity and cost. We sho
w that the number it) of phase levels of a Talbot array illuminator has a s
imple relationship to the prime number. When there is an alternative pi -ph
ase modulation in the output array, the relations are similar. (C) 2001 Opt
ical Society of America OCIS codes: 070.6760, 050.1950, 050.1980.