Direct, object brightness estimation from atmospheric turbulence degraded images using a new, high-speed, modified phase diversity method

The well known phase diversity technique has long been used as a premier passive imaging method to mitigate the degrading effects of atmospheric turbulence on incoherent optical imagery. Typically, an iterative, slow method is applied that uses the Zernike basis set and 2-D Fourier transforms in the reconstruction process. In this paper, we demonstrate a direct method for estimating the un-aberrated object brightness from phase or phase difference estimates that 1) does not require the use of the Zernike basis set or the intermediate determination of the generalized pupil function, 2) directly determines the optical transfer function without the requirement for an iterative sequence of 2-D Fourier Transforms, 3) provides a more accurate result than the Zernike-based approaches since there are no Zernike series truncation errors, 4) lends itself to fast and parallel implementation, and 5) can use stochastic search methods to rapidly determine simultaneous phases or phase differences required to determine the correct optical transfer function estimate. As such, this new implementation of phase diversity provides potentially faster, more accurate results than previous approaches yet still retains inherent compatibility with the traditional Zernike-based methods. The theoretical underpinnings of this new method along with demonstrative computer simulation results are presented.