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An extension of Nomarski differential interference contrast microscopy enables isotropic linear phase imaging through the combination of phase shifting, two directions of shear, and Fourier space integration using a modified spiral phase transform. We apply this method to simulated and experimentally acquired images of partially absorptive test objects. A(More)
When a single molecule is detected in a wide-field microscope, the image approximates the point spread function of the system. However, as the distribution of molecules becomes denser and their images begin to overlap, existing solutions to determine the number of molecules present and their precise three-dimensional locations can tolerate little to no(More)
Photo-activation localization microscopy is a far-field superresolution imaging technique based on the localization of single molecules with subdiffraction limit precision. Known under acronyms such as PALM (photo-activated localization microscopy) or STORM (stochastic optical reconstruction microscopy), these techniques achieve superresolution by allowing(More)
Recently, single molecule-based superresolution fluorescence microscopy has surpassed the diffraction limit to improve resolution to the order of 20 nm or better. These methods typically use image fitting that assumes an isotropic emission pattern from the single emitters as well as control of the emitter concentration. However, anisotropic single-molecule(More)
We demonstrate the use of a 30-period dielectric stack structure as a highly dispersive device to spatially separate two beams with a 4-nm wavelength difference by more than their beam width. Unlike previous devices, our structure is simple to fabricate and relatively compact. We discuss possible applications of our device within wavelength-division(More)
General solutions representing rotations of intensity distributions around and along the propagation axis are derived for the paraxial wave equation. The formalism used is a key for understanding and synthesizing such waves as experimentally demonstrated. A necessary and sufficient condition for rigid rotation as well as limitations on the rotation rate are(More)
Propagation invariance is extended in the paraxial regime, leading to a generalized self-imaging effect. These wave fields are characterized by a finite number of transverse self-images that appear, in general, at different orientations and scales. They possess finite energy and thus can be accurately generated. Necessary and sufficient conditions are(More)
Localized nonlinear modes, or solitons, are obtained for the two-dimensional nonlinear Schrödinger equation with various external potentials that possess large variations from periodicity, i.e., vacancy defects, edge dislocations, and quasicrystal structure. The solitons are obtained by employing a spectral fixed-point computational scheme. Investigation of(More)