Ellerbroek, Brent (Retired), Veran, Jean-Pierre (NRC Herzberg Institute of Astrophysics), Wang, Lianqi (TMT International Observatory)
We generalize the standard Fourier optics measurement equations for the roof- and pyramid wavefront sensor (RWFS and PWFS) concepts to the case of extended (non-point) sources. Samples of such sources include (i) extended astronomical objects such as moons, (ii) point sources with modulation (i.e., tip/tilt nutation), and (iii) elongated laser guide stars. For simple source profiles, for example top-hat or Gaussian functions, the effect of the extended source on the measurement can be represented analytically as a filter function for each of these sample cases. For the RWFS, we use this representation to evaluate the impact of extended source on the wavefront reconstruction error due to noise, as a function of the number of Zernike modes estimated. A limited set of sample results are also presented for more computationally intensive case of the PWFS. The trends are qualitatively similar to the RWFS, but with a modestly larger sensitivity to noise when reconstructing 50 or more Zernike modes. Finally, the measurement equations developed for extended sources indicated that the RWFS and PWFS wavefront measurements may be biased (i.e., nonzero measurements for a null wavefront) when the source is asymmetrical, but the magnitude of this effect has not been studied yet either analytically or via simulation.
10.26698/AO4ELT5.0130- Proceeding PDF