Correlations between G-tilt, Z-tilt, centroid motion, and quad-cell measurements

Correlations between Z-tilt, G-tilt, and centroid motion as a function of thresholding are studied through simulations and analyses. The Z-tilt, or Zernike tilt, is the first moment of the phase distribution over the aperture, while the G-tilt, or gradient tilt, is the average phase gradient over the aperture. It is found that raw centroid motion best correlates with G-tilt, but that even a small amount of thresholding makes Z-tilt the stronger correlation. The Zernike decomposition of the G-tilt is also presented. Using this decomposition, a theoretical value for the correlation between Z-tilt and G-tilt is determined. It is further demonstrated that the quad-cell signal best correlates with Z-tilt even though no thresholding is involved.