Wavefront measurement

Complex light fields, such as speckle patterns, contain many phase vortices. One way of determining a vortex-carrying beam's vortex charge includes interference with another beam. On the other hand, we present a single-beam method for analyzing vortices' wavefronts using surface plasmon polaritons. We use a subwavelength slit in a film to slice up a vortex beam, and measure the diffraction of the generated plasmons by scattering off a second slit. By moving the slits across the beam, we create a tomogram, from which we determine the beam's vortex charge visually. The method can easily be extended to more complex light fields; it is foreseen that it may result in a miniature device.

We present a method for analyzing the wavefront of optical vortices that does not involve interferometry but rather uses surface plasmon polaritons (SPPs). We employ a subwavelength slit in a gold film to cut slices from an optical vortex beam and measure the diffraction of the generated SPPs by scattering them off a second slit. By moving the slits across the vortex beam, we create a tomogram, from which we can determine the vortex charge of the incident beam at a glance. We present results for vortex beams of integer- and half-integer-vortex charge.

Shack-Hartmann wavefront sensing relies on accurate spot centre measurement. Several algorithms were developed with this aim, mostly focused on precision, i.e. minimizing random errors. In the solar and extended scene community, the importance of the accuracy (bias error due to peak-locking, quantisation or sampling) of the centroid determination was identified and solutions proposed. But these solutions only allow partial bias corrections. To date, no systematic study of the bias error was conducted. This article bridges the gap by quantifying the bias error for different correlation peak-finding algorithms and types of sub-aperture images and by proposing a practical solution to minimize its effects. Four classes of sub-aperture images (point source, elongated laser guide star, crowded field and solar extended scene) together with five types of peak-finding algorithms (1D parabola, the centre of gravity, Gaussian, 2D quadratic polynomial and pyramid) are considered, in a variety of signal-to-noise conditions. The best performing peak-finding algorithm depends on the sub-aperture image type, but none is satisfactory to both bias and random errors. A practical solution is proposed that relies on the anti-symmetric response of the bias to the sub-pixel position of the true centre. The solution decreases the bias by a factor of ∼ 7 to values of 0.02 pix. The computational cost is typically twice of current cross-correlation algorithms.