Weighted Center Of Gravity Research Articles

Analysis of the wavefront reconstruction error of the spot location algorithms for the Shack–Hartmann wavefront sensor

Spot location algorithms greatly influence the wavefront measurement error of the Shack–Hartmann wavefront sensor. Based on numerical simulations and experiments, we compare the wavefront reconstruction error of several spot location algorithms under different signal-to-noise ratio (SNR) conditions. We solve the problem of how to select the most suitable spot location algorithm and optimal parameters under different SNR conditions, which mimic the realistic working environment of the adaptive optics system changes. We find the optimal threshold and optimal window setting rules of the center of gravity (COG), intensity weighted centroiding, and weighted center of gravity (WCOG) algorithms. The correctness of our recommendation of spot location algorithms under different SNR conditions is supported by numerical simulations and experiments. We find that when the SNR is extremely low, that is the SNR is lower than 2, the cross-correlation algorithm and the thresholding WCOG algorithm are the best choices. When the SNR is moderately low, that is the SNR ranges from 2 to 10, the best choice is the thresholding WCOG algorithm. When the SNR is high, that is, the SNR is higher than 10, the simple algorithm of thresholding COG is the best choice.

Method of reducing photon noise and turbulence for laser guide-star detection on large-aperture telescopes

Adaptive optics systems (AOSs) rely on good estimation of a distorted wavefront. Two problems make centroid detection difficult, namely, the problem of a relatively large subaperture that brings high-order aberrations and that of a large laser guide-star spot that brings in a large photon noise. To solve these problems, we proposed an estimation method based on Poisson statistics to reduce the photon noise, and the high-order aberrations are partly separated from a spot image to well estimate the slope in the subaperture. Simulation results indicate that our method performs better than the weighted center-of-gravity (WCOG) method and correlation method (CM). Under the condition of SNR =20 and r0=13cm The root-mean-square values of the residual wavefront using the proposed method are approximately 10%, 50%, and 35% lower than those of the COG, WCOG, and CM, respectively. The proposed method would be highly beneficial for ground-based astronomical AO systems intended to provide moderate to high Strehl ratios at near infrared wavelengths on larger than 10m-aperture telescopes.

The Cournot game under a fuzzy decision environment

The conventional precision-based decision analysis methodology is invalid for business decision analysis when precise assessment data seldom exist. This paper considers the Cournot game with fuzzy demand and fuzzy costs that are assumed to be triangular fuzzy numbers. Our model utilizes the weighted center of gravity (WCoG) method to defuzzify the fuzzy profit function into a crisp value. We derive the equilibrium Cournot quantity of each firm by simultaneously solving the first-order condition of each firm. Our model explicitly derives the necessary condition to avoid an unreasonable outcome of negative equilibrium quantities and lack of flexibility for modification of the ranking method. In addition, we examine the standard deviation of the fuzzy profit resulting from the fuzziness of each firm’s cost and market demand functions. We conduct sensitivity analysis to investigate the effect of parameter perturbations on firms’ outcomes. The results indicate that the center of parameter plays an important role in sensitivity analysis and dominates over variations in equilibrium quantity due to a perturbation of fuzzy parameters.