In this paper, we discuss the behaviour of small cylindrical microlens
es, arranged in one-dimensional arrays and as single elements. For thi
s purpose, we apply a standard rigorous diffraction theory, commonly u
sed for diffraction gratings. We investigate the coupling effect betwe
en the elements. It turns out that single elements behave like periodi
c elements if the spacing is chosen correctly. Furthermore, we compute
the complex transmission function by rigorous diffraction theory and
compare them with classical theories (combined ray tracing and the thi
n-element approach). Finally, we discuss the focal properties of micro
lenses in the rigorous regime.