![]() For example, Irwan & Lane (1999) just considered the size of the CCD and the related truncation problem. On the other hand, many parameters are involved in the estimation of the centroid calculation error as explained below, and therefore there are many ways to approach this problem. Arines & Ares (2002) analysed the thresholding method. Thus, the lowest useful signal is determined by spot detection rather than by centroiding noise.Ĭoncerning the CoG approaches, different types of algorithms have been developed to improve the basic centroid calculation in a SHWFS: mean-square-error estimator ( van Dam & Lane 2000), maximum a posteriori estimator ( Sallberg, Welsh & Roggemann 1997) or Gram–Charlier matched filter ( Ruggiu, Solomon & Loos 1998). When the spot is not detected, the centroid calculation with such methods is completely wrong. This presents a problem to common centroid algorithms like thresholding that rely on the brightest pixel(s) to determine approximate centre of the spot. In case of strong RON and weak signal, the spot can be completely lost in the detector noise, at least occasionally. In this paper, three main classes of algorithms are considered: quad cell (QC) estimator, centre of gravity (CoG) approaches and correlation (Corr) methods.Ĭentroid measurements are usually corrupted by the coarse sampling of the CCD, photon noise from the guide star, readout noise (RON) of the CCD, and speckle noise introduced by the atmosphere. The goal of this study is to compare quantitatively different estimators of spot positions and suggest best suitable methods in cases of low and high photon fluxes. The accuracy of such measurements depends on the strength of the different noise source as well as on a non-negligible number of WFS parameters such as the detector size, the sampling factor, field-of-view (FOV) size, etc. A good estimation of the wavefront distortion is therefore obtained from a good measurement of the spot positions. The wavefront is then analysed by measuring, in real time, the displacements of the centroids of those spots which are directly proportional to the local wavefront slopes averaged over subapertures. 2003), remains a workhorse of astronomical AO systems now and in the near future.Ī SHWFS samples the incident wavefront by mean of a lenslet array the telescope aperture is divided into an array of square subapetures, which produces an array of spots on a detector. Yet, the classical Shack–Hartmann WFS (SHWFS), used for example in NACO the AO installed at the VLT ( Rousset et al. New ideas like pyramid WFS ( Ragazzoni & Farinato 1999 Esposito & Riccardi 2001) are being proposed. These developments, in turn, put new requirements on wavefront sensing devices (WFS) in terms of their sensitivity, precision and linearity. 2005) or extreme AO (ExAO) ( Fusco et al. New varieties of AO, such as multi-object AO (MOAO) ( Gendron et al. Turbulence, instrumentation: adaptive optics 1 INTRODUCTIONĪdaptive optics (AO) is nowadays a mature astronomical technique. Finally, examples of applications are given to illustrate the results obtained in the paper. ![]() It is shown that at high flux, centre of gravity approaches and correlation methods are equivalent (and provide better results than QC estimator) as soon as their parameters are optimized. ![]() At high-flux levels, the dominant errors come from non-linearity of response, from spot truncations and distortions and from detector pixel sampling. Both methods can work with average flux as low as 10 photons per subaperture under a readout noise of three electrons. We find that at very low flux the noise of QC and weighted centroid leads the best result, but the latter method can provide linear and optimal response if the weight follows spot displacements. For each method, optimal parameters are defined in function of photon flux, readout noise and turbulence level. Analytical theory is combined with extensive numerical simulations to compare different flavours of centroiding algorithms: thresholding, weighted centroid, correlation, quad cell (QC).
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