An exact, linear solution to the problem of imaging through turbulence

We show how, in principle, to solve the ‘blind deconvolution' problem. This is in the context of the problem of imaging through atmospheric turbulence. The approach is digital but not iterative, and requires as input data but two short-exposure intensity images, without the need for reference point sources. By taking the Fourier transform of each image and dividing, a set of linear equations is generated whose unknowns are sampled values of the two random point spread functions that degraded the images. An oversampling by 50% in Fourier space equalizes the number of unknowns and independent equations. With some prior knowledge of spread function support, and in the absence of added noise of image detection, the inverted equations give exact solutions. The two observed images are then inverse filtered to reconstruct the object.