Retrieving true images through fine grid steps for enhancing the resolution beyond the classical limits: theory and simulations.

We developed the theory of, and tested by extended simulations, a novel method for retrieving true images in a grid step much finer than both the acquisition and the optical microscope limits. We believe that the method is promising in view of avoiding the limitations on the resolution improvement in direct imaging mode systems. Two basic concepts are involved: (i) random (up to 3D) relative displacements of objects with respect to the receiving matrix and (ii) the use of a reference object firmly fixed to small signal objects for avoiding the displacement measurements. The retrieved images are created by rearranging a set of true images acquired with a lower resolution equal to the matrix pixel size. We demonstrate the good quality of the retrieved images and the possibility to visualize and detect small (convolved) objects not observed into the captured images. The method provides good opportunities for effective applications of different inverse algorithms for improving the resolution requiring, as a rule, more precisely sampled images, but at arbitrary relations between the pixel size and the optical diffraction limit. We further demonstrated the application of some deconvolution procedures for extracting highly resolved images in the object and image planes in the presence of noise. The possibility to resolve small objects beyond the two classical limits is shown by means of simulations. The estimates for the method's limiting resolution, combined with proper deconvolution processing, show that resolution in the lower nano-dimension scale (below 10 nm) could be achieved. The requirements to the implementation of the novel method are commented as well.