Phase determination in interference-based superresolving microscopes through critical frequency analysis

Automatic deconvolution in 4Pi-microscopy with variable phase

4Pi-microscopy doubles the aperture of the imaging system by coherent addition of the wavefronts for illumination and/or detection through opposing objective lenses. This improves the axial resolution 3-7 fold, but the raw data usually features ghost images which have to be removed by image reconstruction. This straightforward procedure is sometimes precluded by imperfect alignment of the instrument or a specimen with strong variations of its refractive index, because the image formation process now depends on the space-variant phase difference between the counter-propagating wavefronts. Here we present a computationally fast method of parametric blind deconvolution that allows for automatic and robust simultaneous estimation of both the object and the phase function in such cases. We verify the performance of our approach on both synthetic and real data. Because the method does not require a-priori knowledge of the phase function it is major step towards reliable 4Pi-imaging and automatic image restoration by non-expert users.

Automatic deconvolution of 4Pi-microscopy data with arbitrary phase

We propose a maximum a posteriori-based method that solves an important practical problem in the deconvolution of 4Pi images by simultaneously delivering an estimate of both the object and the unknown phase. The method was tested in simulations and on data from both test samples and biological specimen. It generates object estimates that are free from interference artifacts and reliably recovers arbitrary relative phases. Based on vectorial focusing theory, our theoretical analysis allowed for a simple and efficient implementation of the algorithm. Taking several 4Pi images at different relative phases of the interfering beams is shown to improve the robustness of the approach.

4Pi microscopy deconvolution with a variable point-spread function

To remove the axial sidelobes from 4Pi images, deconvolution forms an integral part of 4Pi microscopy. As a result of its high axial resolution, the 4Pi point spread function (PSF) is particularly susceptible to imperfect optical conditions within the sample. This is typically observed as a shift in the position of the maxima under the PSF envelope. A significantly varying phase shift renders deconvolution procedures based on a spatially invariant PSF essentially useless. We present a technique for computing the forward transformation in the case of a varying phase at a computational expense of the same order of magnitude as that of the shift invariant case, a method for the estimation of PSF phase from an acquired image, and a deconvolution procedure built on these techniques.