A coupled wave analysis is given of the Bragg diffraction of light by thick hologram gratings, which is analogous to Phariseau's treatment of acoustic gratings and to the “dynamical” theory of X-ray diffraction. The theory remains valid for large diffraction efficiencies where the incident wave is strongly depleted. It is applied to transmission holograms and to reflection holograms. Spatial modulations of both the refractive index and the absorption constant are allowed for. The effects of loss in the grating and of slanted fringes are also considered. Algebraic formulas and their numerical evaluations are given for the diffraction efficiencies and the angular and wavelength sensitivities of the various hologram types.

Coupled wave theory for thick hologram gratings

Iterative algorithms for phase retrieval from intensity data are compared to gradient search methods. Both the problem of phase retrieval from two intensity measurements (in electron microscopy or wave front sensing) and the problem of phase retrieval from a single intensity measurement plus a non-negativity constraint (in astronomy) are considered, with emphasis on the latter. It is shown that both the error-reduction algorithm for the problem of a single intensity measurement and the Gerchberg-Saxton algorithm for the problem of two intensity measurements converge. The error-reduction algorithm is also shown to be closely related to the steepest-descent method. Other algorithms, including the input-output algorithm and the conjugate-gradient method, are shown to converge in practice much faster than the error-reduction algorithm. Examples are shown.

Phase retrieval algorithms: a comparison.

Monthly Notices is one of the three largest general primary astronomical research publications. It is an international journal, published by the Royal Astronomical Society. This article 1 describes its publication policy and practice.

Monthly Notices of the Royal Astronomical Society

We present the results of a comprehensive assessment of companions to solar-type stars. A sample of 454 stars, including the Sun, was selected from the Hipparcos catalog with {pi}>40 mas, {sigma}{sub {pi}/{pi}} < 0.05, 0.5 {<=} B - V {<=} 1.0 ({approx}F6-K3), and constrained by absolute magnitude and color to exclude evolved stars. These criteria are equivalent to selecting all dwarf and subdwarf stars within 25 pc with V-band flux between 0.1 and 10 times that of the Sun, giving us a physical basis for the term 'solar-type'. New observational aspects of this work include surveys for (1) very close companions with long-baseline interferometry at the Center for High Angular Resolution Astronomy Array, (2) close companions with speckle interferometry, and (3) wide proper-motion companions identified by blinking multi-epoch archival images. In addition, we include the results from extensive radial-velocity monitoring programs and evaluate companion information from various catalogs covering many different techniques. The results presented here include four new common proper-motion companions discovered by blinking archival images. Additionally, the spectroscopic data searched reveal five new stellar companions. Our synthesis of results from many methods and sources results in a thorough evaluation of stellar and brown dwarf companions to nearby Sun-likemore » stars. The overall observed fractions of single, double, triple, and higher-order systems are 56% {+-} 2%, 33% {+-} 2%, 8% {+-} 1%, and 3% {+-} 1%, respectively, counting all confirmed stellar and brown dwarf companions. If all candidate, i.e., unconfirmed, companions identified are found to be real, the percentages would change to 54% {+-} 2%, 34% {+-} 2%, 9% {+-} 2%, and 3% {+-} 1%, respectively. Our completeness analysis indicates that only a few undiscovered companions remain in this well-studied sample, implying that the majority (54% {+-} 2%) of solar-type stars are single, in contrast to the results of prior multiplicity studies. Our sample is large enough to enable a check of the multiplicity dependence on various physical parameters by analyzing appropriate subsamples. Bluer, more massive stars are seen as more likely to have companions than redder, less massive ones, consistent with the trend seen over the entire spectral range. Systems with larger interaction cross sections, i.e., those with more than two components or long orbital periods, are preferentially younger, suggesting that companions may be stripped over time by dynamical interactions. We confirm the planet-metallicity correlation (i.e., higher metallicity stars are more likely to host planets), but are unable to check it for brown dwarfs due to the paucity of such companions, implying that the brown dwarf desert extends over all separation regimes. We find no correlation between stellar companions and metallicity for B - V < 0.625, but among the redder subset, metal-poor stars ([Fe/H] <-0.3) are more likely to have companions with a 2.4{sigma} significance. The orbital-period distribution of companions is unimodal and roughly log normal with a peak and median of about 300 years. The period-eccentricity relation shows the expected circularization for periods below 12 days, caused by tidal forces over the age of the Galaxy, followed by a roughly flat distribution. The mass-ratio distribution shows a preference for like-mass pairs, which occur more frequently in relatively close pairs. The fraction of planet hosts among single, binary, and multiple systems are statistically indistinguishable, suggesting that planets are as likely to form around single stars as they are around components of binary or multiple systems with sufficiently wide separations. This, along with the preference of long orbital periods among stellar systems, increases the space around stars conducive for planet formation, and perhaps life.« less

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A survey of stellar families: multiplicity of solar-type stars

We present a digital method for solving the phase-retrieval problem of optical-coherence theory: the reconstruction of a general object from the modulus of its Fourier transform. This technique should be useful for obtaining high-resolution imagery from interferometer data.

Reconstruction of an object from the modulus of its Fourier transform.

Attainment of Diffraction Limited Resolution in Large Telescopes by Fourier Analysing Speckle Patterns in Star Images

Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images

We describe a new type of coronagraph, based on the principle of a phase mask as proposed by Roddier and Roddier a few years ago but using an original mask design found by one of us (D. R.), a four-quadrant binary phase mask (0, n) covering the full Ðeld of view at the focal plane. The mutually destructive interferences of the coherent light from the main source produce a very efficient nulling. The computed rejection rate of this coronagraph appears to be very high since, when perfectly aligned and phase-error free, it could in principle reduce the total amount of light from the bright source by a factor of 108, corresponding to a gain of 20 mag in brightness at the location of the Ðrst Airy ring, relative to the Airy peak. In the real world the gain is of course reduced by a strong factor, but nulling is still performing quite well, provided that the perturbation of the phase, for instance, due to the EarthIs atmosphere, is efficiently corrected by adaptive optics. We show from simulations that a detection at a contrast of 10 mag between a star and a faint companion is achievable in excellent conditions, while 8 mag appears routinely feasible. This coronagraph appears less sensitive to atmospheric turbulence and has a larger dynamic range than other recently proposed nulling techniques : the phase-mask coronagraph (by Roddier and Roddier) or the Achro- matic Interfero-Coronagraph (by Gay and Rabbia). We present the principle of the four-quadrant corona- graph and results of a Ðrst series of simulations. We compare those results with theoretical performances of other devices. We brieNy analyze the di†erent limitations in space or ground-based observations, as well as the issue of manufacturing the device. We also discuss several ways to improve the detection of a faint companion around a bright object. We conclude that, with respect to previous techniques, an instrument equipped with this coronagraph should have better performance and even enable the imaging of extrasolar giant planets at a young stage, when coupled with additional cleaning techniques.

https://www.jstor.org/stable/10.1086/317707

Antoine Labeyrie

Papers

Attainment of Diffraction Limited Resolution in Large Telescopes by Fourier Analysing Speckle Patterns in Star Images

Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images

The Four-Quadrant Phase-Mask Coronagraph. I. Principle

Feasibility of adaptive telescope with laser probe

Interference fringes obtained on Vega with two optical telescopes.