A New Method for Wavefront Sensing using Optical Masking Interferometry

Wave front sensing of the surface of equal phase for a propagating electromagnetic wave is a vital technology in fields ranging from real time adaptive optics, to high accuracy metrology, to medical optometry. We have developed a new method of wavefront sensing that makes a direct measurement of the electromagnetic phase distribution, or path-length delay, across an optical wavefront. The method is based on techniques developed in radio astronomical interferometric imaging. The method employs optical interferometry using a 2-D aperture mask, a Fourier transform of the interferogram to derive interferometric visibilities, and self-calibration of the complex visibilities to derive the voltage amplitude and phase gains at each hole in the mask, corresponding to corrections for non-uniform illumination and wavefront distortions across the aperture, respectively. The derived self-calibration gain phases are linearly proportional to the electromagnetic path-length distribution to each hole in the aperture mask, relative to the path-length to the reference hole, and hence represent a wavefront sensor with a precision of a small fraction of a wavelength. The method was tested at $λ=400\,$nm at the Xanadu optical bench at the ALBA synchrotron light source using a rotating mirror to insert tip-tilt changes in the wavefront. We reproduce the wavefront tilts to within $0.1''$ ($5\times 10^{-7}$~radians). We also derive the static metrology though the optical system for non-planar wavefront distortions to $\sim \pm1$~nm repeatability. Lastly, we derive frame-to-frame variations of the wavefront tilt due to vibrations of the optical components which range up to $\sim 0.5"$. These variations are relevant to adaptive optics applications. Based on the measured visibility phase noise after self-calibration, we estimate an rms path-length precision per 1~ms exposure of 0.6 nm.