Position-varying tip-tilt estimation and region-of-interest PSF derivation by Wiener filter

Recently, we looked at applying our wide field-of-view tip-tilt turbulence visualization method to the visualization of the turbulent wake behind a jet aircraft. We have described successful results previously, in telescopically derived images of the moon’s surface and in horizontal surveillance imaging, in which small regions-of-interest (ROIs) within a turbulence-distorted image are registered to a prototype image. Unfortunately, when applied to a fast jet wake, the method did not produce useful results. This was found to be due to the fact that the background, which forms the reference image when the wake is absent, is heavily blurred when seen through the wake due to higher order wavefront distortions. Instead, the blurring made us wonder whether we could apply a Wiener filter between corresponding ROIs of the turbulence-distorted image and the reference image. This paper describes a new approach to registration that uses a Wiener filter within a scanned ROI to detect a local, space-varying point spread function or PSF. This new approach provides more robust shift information than our previously used cross correlation to describe the random wobble in the image sequence and also provides new information on the shape of the position-dependent blur PSF.