We present a procedure for designing to control the three-dimensional light-intensity distribution near focus. Our method is based on the use of a series of figures of merit that are properly defined to describe the effect of general complex pupil functions. As a practical implementation, we have applied our method to obtain super resolving continuous smoothly varying phase-only filters. The advantages of these kinds of filters are that they do not produce energy absorption and they are easy to build with a phase-controlling device such as a deformable mirror. Results of comparisons between the performance of our method and that of other phase-filter designs are provided.

Atmospheric turbulence imposes the resolution limit attainable by large ground-based telescopes. This limit is lambda/r(0), where r(0) is the Fried parameter or seeing cell size. Working in the visible, adaptive optics systems can partially compensate for turbulence-induced distortions. By analogy with the Fried parameter, r(0), we have introduced a generalized Fried parameter, rho(0), that plays the same role as r(0) but in partial compensation. Using this parameter and the residual phase variance, we have described the phase structure function, estimated the point-spread function halo size, and derived an expression for the Strehl ratio as a function of the degree of compensation. Finally, it is shown that rho(0) represents the diameter of the coherent cells in the pupil domain.

High resolution wavefront sensors are devices with a great practical interest since they are becoming a key part in an increasing number of applications like extreme Adaptive Optics. We describe the optical differentiation wavefront sensor, consisting of an amplitude mask placed at the intermediate focal plane of a 4-f setup. This sensor offers the advantages of high resolution and adjustable dynamic range. Furthermore, it can work with polychromatic light sources. In this paper we show that, even in adverse low-light-level conditions, its SNR compares quite well to that corresponding to the Hartmann-Shack sensor.

We report the discovery of K2-98b (EPIC 211391664b), a transiting Neptune-size planet monitored by the K2 mission during its Campaign 5. We combine the K2 time-series data with ground-based photometric and spectroscopic follow-up observations to confirm the planetary nature of the object and derive its mass, radius, and orbital parameters. K2-98b is a warm Neptune-like planet in a 10 day orbit around a V=12.2mag F-type star with M å =1.074±0.042 M e , R å = . We derive a planetary mass and radius of M p =32.2±8.1 M ⊕ and R p = -+ 4.3 0.2 0.3 R ⊕ . K2-98b joins the relatively small group of Neptune-size planets whose mass and radius have been derived with a precision better than 25%. We estimate that the planet will be engulfed by its host star in ∼3 Gyr, due to the evolution of the latter toward the red giant branch.

A novel procedure to design axial and transverse superresolving pupil filters for the 4Pi-confocal microscope is presented. The method is based on the use of a series of figures of merit developed to describe the effect of inserting two identical filters in the two arms of the illumination path of the microscope. As a practical implementation, we have applied our method to obtain superresolving continuous phase-only filters. Different resolution-improving phase functions are shown for the transverse and the axial direction. These filters provided axial gain up to 1.3 and transverse gain up to 1.4 without an increase in sidelobes.