Abstract

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 λ_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.

© 2006 Optical Society of America

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