Fraunhofer diffraction at the two-dimensional quadratically distorted (QD) grating.

A two-dimensional (2D) mathematical model of quadratically distorted (QD) grating is established with the principles of Fraunhofer diffraction and Fourier optics. A discrete sampling method is applied for finding a numerical solution of the diffraction pattern of QD grating. An optimized working phase term, which determines the balanced energies and high efficiency of multi-plane images, can be obtained by the bisection algorithm.

Shack-Hartmann versus reverse Hartmann wavefront sensors: experimental results.

With respect to the classical Shack-Hartmann (SH) wavefront sensor (WFS), the recently proposed reverse Hartmann (RH) sensor inverts the locations of the filtering and observation planes and forms a direct image of the pupil on a detector array. The slopes of the wavefront error (WFE) are then reconstructed by using a double Fourier transform algorithm. It turns out that the same algorithm can also be applied to the raw data acquired by SH sensors.

Fresnel diffraction analysis of Ronchi and reverse Hartmann tests.

This paper presents a Fresnel diffraction analysis of classical Ronchi and reverse Hartmann tests. Simplified analytical expressions of the intensity patterns observed by the camera are established, allowing quantitative measurements of the wavefront slopes of the tested optical system. The wavefronts are then reconstructed from their slopes using a double Fourier transform algorithm.

Backward-gazing method for measuring solar concentrators shape errors.

This paper describes a backward-gazing method for measuring the optomechanical errors of solar concentrating surfaces. It makes use of four cameras placed near the solar receiver and simultaneously recording images of the sun reflected by the optical surfaces. Simple data processing then allows reconstructing the slope and shape errors of the surfaces.

Strehl ratio: a tool for optimizing optical nulls and singularities.

In this paper a set of radial and azimuthal phase functions are reviewed that have a null Strehl ratio, which is equivalent to generating a central extinction in the image plane of an optical system. The study is conducted in the framework of Fraunhofer scalar diffraction, and is oriented toward practical cases where optical nulls or singularities are produced by deformable mirrors or phase plates. The identified solutions reveal unexpected links with the zeros of type-J Bessel functions of integer order.

Phase-shifting technique for improving the imaging capacity of sparse-aperture optical interferometers.

We describe the principle of a multiaperture interferometer that uses a phase-shifting technique and is suitable for quick snapshot imaging of astrophysical objects at extreme angular resolution through Fourier inversion. A few advantages of the proposed design are highlighted, among which are radiometric efficiency, field of view equivalent to those of Fizeau interferometers, and a preliminary calibration procedure allowing characterization of instrumental errors. For large telescope numbers, the proposed design also results in considerable simplification of the optical and mechanical design.

Simple Fourier optics formalism for high-angular-resolution systems and nulling interferometry.

Reviewed are various designs of advanced, multiaperture optical systems dedicated to high-angular-resolution imaging or to the detection of exoplanets by nulling interferometry. A simple Fourier optics formalism applicable to both imaging arrays and nulling interferometers is presented, allowing their basic theoretical relationships to be derived as convolution or cross-correlation products suitable for fast and accurate computation. Several unusual designs, such as a "superresolving telescope" utilizing a mosaicking observation procedure or a free-flying, axially recombined interferometer are examined, and their performance in terms of imaging and nulling capacity are assessed.

Fibered nulling telescope for extra-solar coronagraphy.

A family of fibered nulling telescopes is described, based on the joint use of several recent suggested or demonstrated techniques, namely, pupil densification, multiaxial recombination and single-mode fiber modal filtering, and the use of a fully symmetric beam splitter arrangement. The concept seems appropriate for the realization of a spaceborne nulling telescope, searching for Jupiter-like extra-solar planets and a precursor of future missions, such as Darwin or terrestrial planet finder interferometer (TPF-I). However, it is generally not possible to satisfy at the same time two major requirements, being the depth and size of the central nulling area, and the global throughput for the observed planet.

Computing extinction maps of star nulling interferometers.

Herein is discussed the performance of spaceborne nulling interferometers searching for extra-solar planets, in terms of their extinction maps projected on-sky. In particular, it is shown that the designs of Spatial Filtering (SF) and Achromatic Phase Shifter (APS) subsystems, both required to achieve planet detection and characterization, can sensibly affect the nulling maps produced by a simple Bracewell interferometer. Analytical relationships involving cross correlation products are provided and numerical simulations are performed, demonstrating marked differences in the aspect of extinction maps and the values of attained fringes contrasts.

Signal-to-noise ratio of phase sensing telescope interferometers.

The paper described is the third part of a trilogy dealing with the principles, performance, and limitations of what the author named "telescope-interferometers" (TIs). The basic idea consists in transforming one telescope into a wavefront error (WFE) sensing device. This can be achieved in two different ways, namely, off-axis and phase-shifting TIs.

Design of achromatic phase shifters for spaceborne nulling interferometry.

The designs of various achromatic phase shifters (APSs) envisaged for nulling interferometry and the search for extrasolar planets or systems from space are discussed in this Letter. It is shown that APS designs can sensibly influence the performance achieved by a simple Bracewell interferometer if they introduce a field of view (FoV) reversal and a pupil flip along one interferometer arm. Analytical and numerical simulations are presented, showing severe signal-to-noise ratio loss and a weak capacity for serendipitous discoveries.

Analysis of stellar interferometers as wave-front sensors.

The basic principle and theoretical relationships of an original method are presented that allow the wave-front errors of a ground or spaceborne telescope to be retrieved when its main pupil is combined with a second, decentered reference optical arm. The measurement accuracy of such a telescope-interferometer is then estimated by means of various numerical simulations, and good performance is demonstrated, except in limited areas near the telescope pupil's rim. In particular, it permits direct phase evaluation (thus avoiding the use of first- or second-order derivatives), which will be of special interest for the cophasing of segmented mirrors in future giant-telescope projects.