José E. Oti

Design of superresolving continuous phase filters.

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.

Transverse or axial superresolution in a 4Pi-confocal microscope by phase-only filters

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.

Analysis of the signal-to-noise ratio in the optical differentiation wavefront sensor

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.

Visual axial PSF of diffractive trifocal lenses

The ophthalmic applications of a diffractive trifocal lens design with adjustable add powers and light distribution in the foci are investigated. Axial PSFs of the trifocal lenses are calculated and analyzed as a function of the design parameters and the eye pupil size. The optical performance in actual eyes is also simulated by including the measured ocular wave aberration functions of human eyes in the calculation of transverse and axial PSFs, and Strehl ratio axial variation. The effect of the polychromatic character of natural light has also been considered. The calculus and simulation method of this paper can be applied for the design and analysis of any other kind of diffractive or refractive multifocal contact or intraocular lens.

Design of Continuous Superresolving Masks for Ground‐based Telescopes

A number of astronomical applications require resolutions that are moderately beyond the diffraction limit of current telescopes. Fortunately, these telescopes can yield the desired performance through the use of superresolution techniques. In terms of Strehl ratios, the most advantageous superresolution techniques are based on pupil phase masks. Most of these phase masks are composed of discontinuous annuli. However, a continuous design is more useful in a ground-based telescope, because it can be implemented using the deformable mirror of the adaptive optics system. We present a method for obtaining a continuous profile with a desired performance from an annular mask with the same performance. This method for designing continuous masks allows ground-based astronomy to benefit from the great body of information, analysis techniques, etc., developed for annular designs. Finally, we check our designing method using simulated data, and we analyze the resolution improvement and the adaptive optics system requirements.

Pupil apodization for increasing data storage density

We introduce a technique for increasing density in optical data storage systems. This technique is based on the use of a superresolving filter at the pupil of a confocal readout system. The main characteristic of this confocal readout system is that the light beam traverses twice through the pupil filter. We describe how to analyze the system performance for general filters, but we focus the study on filters with no focus displacement. Although the storage density attainable depends on the filter characteristics, we show that the storage density can be easily duplicated.

THE OPTICAL DIFFERENTIATION CORONAGRAPH

We describe a new stellar coronagraph based on the standard coronagraph scheme but transformed to perform the optical differentiation of the incoming field. It offers a new method to detect exoplanets providing both deep starlight extinction and high angular resolution. To perform optical differentiation, the coronagraph occulting disk is replaced by a differentiation mask. Although the theoretical rejection rate of our coronagraph is infinite, numerical simulations of the perfect case, with no phase errors and perfect telescope pointing, are carried out showing that on-axis starlight is reduced to very low intensity levels corresponding to a gain of at least 37 mag (10-15 light intensity reduction). To take full advantage of this design, the distortions of the atmosphere must be reduced either by the use of extreme adaptive optics or space telescopes, although the latter solution is preferred. The deep starlight extinction is mandatory to achieve direct detection of Earth-like exoplanets and, what is more important, to perform spectroscopy of their atmosphere and look for habitable conditions or signs of life.

Reduction of the diffraction pattern in segmented apertures

New discoveries in astronomy require the use of ever larger telescopes. These telescopes require segmented apertures, since cur- rent technology does not provide for the fabrication of monolithic mirrors with diameters much larger than 8 m. As a result, the point spread func- tion PSF of the system presents a diffraction pattern characteristic of the segmentation geometry, and this complicates the task of detecting faint structures with high spatial resolution. In this work, we investigate the use of amplitude filters at the pupil plane to decrease the intensity of this diffraction pattern. It is sufficient if this diffraction pattern is reduced below the residual halo that remains after adaptive optics compensation, so that the intensity distribution that surrounds the PSF core is limited by scattering rather than diffraction. We show different kinds of filters that allow us to achieve this goal. We analyze their performance, taking into account some unavoidable errors in the telescope operation such as imperfect phasing of the telescope segments and gaps between them. Finally, we discuss the application of the technique considering errors in the adaptive optics correction.

PURE AMPLITUDE MASKS FOR EXOPLANET DETECTION WITH THE OPTICAL DIFFERENTIATION CORONAGRAPH

The optical differentiation coronagraph relies on the optical differentiation technique implemented on a standard coronagraph. The use of a coronagraphic mask to estimate the first derivative of the incoming field shows high starlight suppression (theoretically infinite), but it is highly sensitive to pointing errors and suffers from monochromaticity drawbacks. In order to overcome these limitations, we generalize the optical differentiation concept to higher order derivatives. Here we describe a novel set of coronagraphic masks that estimate the second derivative of the incoming field. A mathematical description of the optical differentiation coronagraph is presented. These new masks also achieve a theoretical perfect suppression of the on-axis light, and furthermore, they are less sensitive to pointing errors (fourth-order sensitivity to tip/tilt error leakage). Moreover, they are pure amplitude masks, and hence they do not require a complementary phase mask, which represents an additional advantage. The use of a Gaussian roll-off helps to concentrate the diffracted starlight near the pupil borders, where it could be removed more efficiently by a Lyot stop, and transforms the coronagraph into a nearly band-limited coronagraph.

Coronagraphic mask design using Hermite functions.

We introduce a stellar coronagraph that uses a coronagraphic mask described by a Hermite function or a combination of them. It allows the detection of exoplanets providing both deep starlight extinction and high angular resolution. This angular resolution depends on the order of the Hermite function used. An analysis of the coronagraph performance is carried out for different even order masks. Numerical simulations of the ideal case, with no phase errors and perfect telescope pointing, show that on-axis starlight is reduced to very low intensity levels corresponding to a gain of at least 25 magnitudes (10(-10) light intensity reduction). The coronagraphic throughput depends on the Hermite function or combination selected. The proposed mask series presents the same advantages of band limited masks along with the benefit of reducing the light diffracted by the mask border thanks to its particular shape. Nevertheless, for direct detection of Earth-like exoplanets it requires the use of adaptive optics facilities for compensating the perturbations introduced by the atmosphere and by the optical system.