Extended depth of focus in optical microscopy: Assessment of existing methods and a new proposal

Due to depth of focus constraints, the acquisition of a single 2-D completely in-focus image of 3-D objects characterized by a relevant depth dimension is not possible with a standard light microscope. Since the Seventies numerous methods have been proposed to overcome this problem, mainly through different fusion processing techniques to extend the microscope's depth of focus. However, given a specific application, it is very difficult to know which method yields the best results because there are no validated approaches or tested metrics that are suitable for real world cases typically lacking in a reference ground truth. Although the Universal Quality Index (UQI) is widely used to evaluate output quality in image processing, it requires a reference ground truth. Some UQI extensions have been proposed to evaluate the output of fusion methods without a ground truth, but sufficient analyses have not been carried out to confirm their equivalence to the standard UQI in terms of (evaluation) performance. We propose a new method to extend the microscope's depth of focus and, using synthetic stacks of images with ground truth attached, show that it is superior to state-of-the-art methods. We also demonstrate that the output of metrics proposed as UQI extensions is different from that of the UQI. Finally, we validate a new approach to evaluate extended depth of focus methods using real world stacks of slices, as per the UQI, but without the need for a reference ground truth.