Wavelength-dependent characteristics of modulo N(lambda)0 optical wavefront control

A Fourier analysis treatment of the wavelength dependences associated with modulo (lambda)r optical path control, treating the general case of a modulo (lambda)r optical path difference function OPD (x, y) mod (lambda)r in which the reset wavelength (lambda)r, is allowed to be an integer multiple of a nominal wavelength (lambda)0, (lambda)r=N(lambda)0, 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.