A new approach to inhomogeneous layer synthesis is proposed that diffe
rs from the classical Fourier transform methods. This approach, based
on the wave-number discretization of the continuous Q function, is des
cribed together with the relationship between the smoothness of the in
homogeneous layer's refractive-index profile, the complexity of the ta
rget reflectance specification, and the total optical thickness of the
layer. An iterative procedure is introduced to overcome the inaccurac
y connected with the approximate Q-function representation. Some contr
ol features of the Q-function phase are studied, and numerical example
s are given.