We experimentally and numerically tested the separability of two independent equally luminous monochromatic and white light sources at the diffraction limit, using optical vortices (OV). The diffraction pattern of one of the two sources crosses a fork hologram on its center generating the Laguerre-Gaussian (LG) transform of an Airy disk. The second source, crossing the fork hologram in positions different from the optical center, generates nonsymmetric LG patterns. We formulated a criterion, based on the asymmetric intensity distribution of the superposed LG patterns so created, to resolve the two sources at angular distances much below the Rayleigh criterion. Analogous experiments in white light allow angular resolutions which are still one order of magnitude below the Rayleigh criterion. The use of OVs might offer new applications for stellar separation in future space experiments.

We study the properties of the Fraunhofer diffraction patterns produced by Gaussian beams crossing spiral phase plates. We show, both analytically and numerically, that off-axis displacements of the input beam produce asymmetric diffraction patterns. The intensity profile along the direction of maximum asymmetry shows two different peaks. We find that the intensity ratio between these two peaks decreases exponentially with the off-axis displacement of the incident beam, the decay being steeper for higher strengths of the optical singularity of the spiral phase plate. We analyze how this intensity ratio can be used to measure small misalignments of the input beam with a very high precision.

Solar-type cycles in late-type secondary components of cataclysmic variables can produce cyclical variations of the quiescent luminosity, the time intervals between consecutive outbursts of dwarf-nova systems, and the orbital period. Analysis of the long-term light curves of several types of close binary systems suggests cyclical variations of the mass-transfer rate which can be ascribed to fractional changes of the radii of the late-type secondaries by Delta R/R in the range 0.00006-0.0003, as expected for a typical solar cycle. The probability density function of the periods of the cycles discovered in both CVs and single main-sequence stars are peaked around 6 yr. The periods of the cycles do not seem to be affected by the rotation regime of the star. A possible correlation between these cycles and the recurrence times of recurrent novae is suggested.