Effects of phase-shifting error upon the self-referencing interferometer wavefront sensor

A few years ago the Air Force Research Laboratory developed a Self-Referencing Interferometer (SRI) wavefront sensor (WFS) that is able to accurately detect the magnitude and phase of propagating electromagnetic waves in a strong scintillation environment. This proved to be very useful in applications of adaptive optics when detecting light or transmitting laser beams through moderate to high turbulence. The SRI operates by interfering a beacon beam, which has been aberrated by atmospheric turbulence, with a reference beam having a known phase and detecting the intensity of the interference pattern. The phase of the beacon is then determined from those interference patterns. At least three different phases of a reference beam are needed to accurately determine the phase on the beacon beam, but four are preferable. These phases shift the reference beam by 0, π/2, π, and 3π/2. In this paper we examine the effects of phase shift errors. Our method can be extrapolated to any WFS utilizing the Carre algorithm with π/2 phase steps. These results show that the SRI is amazingly tolerable to phase shifting errors, specifically that an adaptive optic loop still closes even with a phase error 'epsilon' of nearly ±π/2. Even more unexpected, it is possible to increase Strehl over the nominally aligned system by as much as 11% in closed loop operation when phase errors are purposefully induced.