A superresolution telescope that uses aberration effects suppression, deconvolution by dimensional reduction, optimal convexity and convexity normalization for image size and dark noise

In this dissertation we claim to have found the solution to the problem of resolving beyond the diffraction limit (superresolution). This problem is solved by dimensional reduction, convexity optimization, and convexity normalization for image size and dark noise. By dimensional reduction we mean deconvolution on isophote ridges, which are one dimensional, thus we have reduced the dimensionality of the problem from two to one. By optimizing convexity we mean that we choose points to test for image sources for which the second derivative (convexity) of the intensity along isophote ridges is the highest. By normalization of convexity for dark noise and image size we are making sure that our optimization of convexity is not biased by dark noise at different exposures or different background convexities for images of different sizes. This biasing would create artifacts.; We also invented ways to speed up our computation and overcome inverse matrix errors. For example we found a simple way to solve the illconditioned matrix problem so we could use the inverse matrix technique, and we are allowed here to replace explicit least squares with the more convenient minimum of the sum of amplitudes squared. We use methods to overcome astigmatism and spherical aberration which are not new. With a narrow field of view we don't need to use the usual iterative stochastic methods (such as MAP). This is because smoothing is effective here since the scale of the PSFs (point spread functions) is much larger than the noise scale.; In this superresolution telescope we get a narrow field of view by a microscope-telescope combination. Pointing errors must be minimized to ensure that aberration effects are minimized, and astigmatism produced by air turbulence must be corrected for.; Experiments have produced repeatable 1/10 Rayleigh distance resolution for SNR = 60 (with no prior knowledge of source configuration assumed). Through significant air turbulence over a 400 foot line of sight we get 1/6 Rayleigh resolution for 1.5 inch reflecting and refracting telescopes, about a factor of 12 better than you would expect.