Helping Hubble Even though it operates well above the worst of atmospheric interference, the Hubble Space Telescope still benefits enormously from the tools of linear image restoration. These classic tools assume that the blurring operator is constant across the viewing field, when in fact it varies with position a deviation that was particularly acute with Hubble s original defective mirrors. A number of investigators, including Nagy and Dianne O Leary of the University of Maryland, have shown that the resolution of Hubble images can be improved with a spatially varying representation of the blurring operator. Nagy and O Leary use a block interpolation scheme that exhibits good convergence behavior with preconditioned conjugate gradients. In spite of the success of these and similar techniques, Ellerbroek says that for earth-based astronomical observation the method of phase diversity may have bragging rights because it has been tested on real data.
Simulations sometimes omit higher-order terms that appear in real data.
Phase diversity does not rely on knowledge of the blurring operator and, in fact, attempts to estimate the phase errors simultaneously with the pristine image. Phase diversity has been perfected by John Seldin and Richard Paxman of the Environmental Research Institute of Michigan. In its simplest form, phase diversity collects the usual carefully focused image of the object, along with another image that is deliberately out of focus by a known amount. The restoration of these spatial frequencies is a very difficult inverse problem, and the resulting restored images often have severe oscillatory artifacts due to the poor recovery of these spatial frequencies. What is interesting and useful about phase diversity is that by adding a known aberration the phase error associated with defocus to the unknown aberrations, a complementary point-spread function is created in a new channel of data.