Among the latest developments in Adaptive Optics (AO) systems, Multi Object Adaptive Optics (MOAO) systems span a large sensing field of view in the order of arcminutes, and correct only the small portions of the sensed field of view where the scientific objects of interest are situated, in the order of arcseconds each. Thus, they operate in open loop correction mode, and their wavefront sensors need to deal with the large dynamic range of the uncorrected atmospheric turbulence. This means that they need to be sensitive in low light level scenarios as well as operate in larger fields of view as compared to the traditional closed loop correction mode operation. Besides, Shack-Hartmann wavefront sensors (SHWFS) continue to be the most widely employed and to have the most matured technology amongst wavefront sensors to be found in astronomy applications.
The objective of the present work is to explore the performance of an innovative centroiding algorithm at the subpupil image of a SHWFS, for point-like guiding sources. It has been named Weighted Fourier Phase Slope, because it estimates the image’s displacement in the Fourier domain by directly computing the phase slope at several spatial frequencies, without the intermediate step of computing the phase; it then applies optimized weights to the phase slopes at each spatial frequency obtained by a Bayesian estimation method. The idea has been inspired by cepstrum deconvolution techniques, and this relationship is explained.
This algorithm’s tilt estimation performance is characterized and contrasted with other known centroiding algorithms, such as Thresholded Centre of Gravity (TCoG) and Cross Correlation (CC), through numerical simulations in Matlab™, first at a subpupil level. Figures of merit such as computational cost, sensitivity in low light level conditions, linearity and preferred field of view of operation, and robustness against atmospheric turbulence high order aberrations of the spots, are all taken into account in open loop operation simulations. Some effort has also been made to extend this comparison to a closed loop operation situation. Results show a similar sensitivity to that of the CC algorithm, which is superior to the one of the TCoG algorithm when big fields of view are necessary, i.e., in the open loop correction case. On the other side, its advantage over the CC algorithm is an approximately one order of magnitude lower computational cost. Also, as there is no threshold application over the image, it is useful when the complete spot, including its low light level portion, is to be considered for the centroid computation.
Numerical simulations are then extended to the complete sensor’s pupil with the aid of the Object Oriented Matlab™ for Adaptive Optics (OOMAO) toolbox, thus including the sensor’s fitting error in the simulations. Results are shown as Strehl Ratio (SR) or Encircled Energy (EE) as a function of Natural Guide Star (NGS) magnitude, and are in good coincidence with the subpupil level simulations.
Finally, the laboratory optical setup of the EDiFiSE (Equalized and Diffraction limited Field Spectrograph Experiment) project has been employed to corroborate the results obtained by numerical simulations, and as a means to exemplify the algorithm’s tuning in a real case, which is done by simulating the real system’s geometry. In this regard, the EDiFiSE’s EMCCD (Electron Multiplying Charge Coupled Device) detector at the SHWFS has been characterized and its gain and noise parameters have been measured and introduced in the simulated model.
Pointing the way to the future, the necessary steps to test the algorithm at a telescope’s adaptive optics system are devised. Also, the means to extend the applicability of the algorithm to extended observed sources, such as with a Laser Guide Star (LGS) or in solar AO, is proposed.