Wavelength-dependent characteristics of modulo Nlambda0 optical wavefront control

A Fourier analysis treatment of the wavelength dependences associated with modulo lambdar optical path control, treating the general case of a modulo lambdar optical path difference function OPD (x, y) mod lambdar in which the reset wavelength lambdar, is allowed to be an integer multiple of a nominal wavelength lambda0, lambdar=Nlambda0, is presented. Equations are derived describing the wavelength-dependent characteristics of the diffraction efficiency and the wavefront errors associated with all diffracted orders. The results are applied to the cases of diffraction of a planar wavefront and compensation of large aberrations and show that over an extended spectral bandwidth the output field consists of multiple diffracted orders with a range of fractional wavefront errors that diminishes with increasing reset multiple N, but does not reach the diffraction limit associated with conventional optics.