J. Borgnino

Theoretical spatiotemporal analysis of angle of arrival induced by atmospheric turbulence as observed with the grating scale monitor experiment

Theoretical investigations of the statistical properties of the wave front perturbed by atmospheric turbulence are presented. They are deduced from the calculation of the two-dimensional spatial covariance and the temporal cross spectrum of the angle-of-arrival fluctuations with a finite outer scale over a pair of circular pupils as in the case of the grating scale monitor or any other Shack–Hartmann-type sensor. Both calculations lead to integral expressions that are numerically evaluated and hold for any baseline vector in the mean wave-front plane. It is proposed to retrieve the wave-front outer scale L0 from estimations of this two-dimensional spatial covariance, normalized by the angle-of-arrival structure function. To eliminate instrument vibration errors, the covariance and the structure function are estimated from measurements obtained by mechanically independent and mechanically coupled devices, respectively. The angle-of-arrival temporal cross spectrum is calculated for any mean wind velocity vector. It is shown that the baseline component in the mean wind direction affects the phase of the angle-of-arrival temporal cross spectrum, whereas the component in the perpendicular direction affects the modulus. From simultaneous measurements of the phase of the angle-of-arrival temporal cross spectrum obtained with two nonparallel baselines, one can calculate the mean wind speed and direction, which allows estimation of the coherence time for techniques of optical observation at high angular resolution through the atmosphere.

SPECTRALLY RESOLVED MICHELSON STELLAR INTERFEROMETRY. I. EXACT FORMALISM IN THE MULTISPECKLE MODE

We detail the theoretical description of a modern optical stellar interferometer by studying the addition of spectral capabilities in such instruments. We give what we believe is the first complete formalism to describe such an interferometer operating in the visible where the fringe signal from large telescope apertures is recorded at the output of a spectrograph. The dispersed-fringes mode and the multichromatic modes are detailed analytically in terms of spectral density and visibility analysis. All the theoretical results are validated through numerical simulation.

The solar seeing monitor MISOLFA: presentation and first results

PICARD is a space mission developed to observe the Sun at high angular resolution. One of the main space objectives of PICARD is to measure the solar diameter with few milli arc-seconds accuracy. A replica of the space instrument will be installed at Calern Observatory in order to test our ability to make such measurement from ground with enough accuracy. High angular resolution observations with ground-based instrument are however limited by atmospheric turbulence. The seeing monitor MISOLFA is developed to give all observation conditions at the same moments when solar images will be recorded with the twin PICARD instruments. They will be used to link ground and space measurements. An overview of the PICARD mission and the solar ground-based experiments will be ¯rst given. Optical properties of MISOLFA will be after presented. The basic principles to measure atmospheric parameters and the methods used to obtain them from solar images will be given. Finally, some recent results obtained at Calern Observatory will be presented and discussed.

Polychromatic transfer functions in stellar speckle interferometry

A general expression has been derived for the dichromatic speckle cross spectrum (DCS), using as a unique assumption Korff’s log-normal model for the complex wave amplitude at the telescope pupil. For a given spectral bandwidth, it is shown that the attenuation of the DCS with respect to the monochromatic spectrum is strongly seeing dependent. A high-frequency asymptotic form is derived for the rapid numerical computation of the DCS, thus making it possible to estimate with ease the allowable spectral bandwidth for any given speckle experiment. The performance of the instrumental achromatization technique is analyzed and shown to be useful only with good seeing and narrow bandwidths.

EFFECTS OF ATMOSPHERIC SPECTRAL DECORRELATION ON VISIBILITY MEASUREMENTS IN MICHELSON INTERFEROMETRY

We analyze the degrading effects of spectral decorrelation introduced by atmospheric turbulence on astronomical images obtained from a long-baseline Michelson interferometer. Our approach consists of a theoretical computation of the polychromatic spectrum, based on a numerical model of the atmospheric turbulence. The model uses the von Karman definitions parameterized by the Fried parameter r0 and the outer scale L0. Through the theoretical analysis of fringe visibility estimated from the polychromatic spectrum, we show how the turbulence model can reproduce visibility behavior with respect to the spectral bandwidth and the separation of two spectral bands. This validation is realized by comparing theoretical to measured visibilities of α Cephei. The future use of this work is to calibrate these losses to improve the accuracy of the GI2T interferometers observations.

Optimized spectral bandwidth in high angular resolution imaging effect of a finite spatial-coherence outer scale

In the case of high angular resolution techniques (speckle interferometry, long baseline Michelson interferometry), one has studied how varies the signal-to-noise ratio (SNR) in terms of the spectral bandwidth Δλ. For values of Δλ varying from 0 up to 100 nanometers, it is shown that the SNR, contrary to the predictions, has no maximum value. In addition, in the case of the high frequency approximation, the effects of a finite spatial-coherence outer scale, the influence of the turbulence model used and of the “optical energy” of the turbulence on the optimal spectral bandwidth have been analyzed and discussed.

Experimental characterization of the turbulence inside the dome and in the surface layer

We present the concept of a new instrument dedicated to modeling turbulence inside the dome and in the surface layer. It consists of using parallel laser beams separated by non redundant baselines between 0.1 and 2-3m and measuring Angle-of-Arrival (AA) fluctuations from spots displacements on a CCD. We use weighted least-square method to fit the measured AA longitudinal and transverse covariances with theoretical forms deduced from the usual models of turbulence. Then, the whole parameters characterizing this turbulence are provided from a complete spatio-temporal analysis of AA fluctuations. Thus, the surface layer turbulence energy in terms of C2N constant is provided from the AA structure function as in the DIMM instrument.

Estimation of the spatial-coherence inner scale of the wavefronts perturbed by the atmospheric turbulence from first order angle-of-arrival statistics

The variance of the angle-of-arrival fluctuations is theoretically calculated taking into account the effects of limit scales for the spatial coherence of the wavefronts perturbed by an atmospheric turbulence described by the Von Karman model. A technique is proposed allowing the estimation of the spatial-coherence inner scale from measurements of the angle-of-arrival fluctuations (variance) with and without spatio-angular filterings. In order to support the theoretical study, a numerical simulation is performed. In addition the possibility to use in situ measurements has been evaluated introducing the vertical turbulence profiles, in the theory. A method is presented allowing, by means of spatial filters with linear amplitude transmittance, the observation of the angle-of-arrival fluctuations without spatial filtering, and afterwards an experimental concept is derived. Finally, the influence of the model used to describe atmospheric turbulence is discussed.

Optical turbulence in confined media. Part II:first results using the INTENSE instrument

Optical system performances can be affected by local optical turbulence created by its surrounding environment (telescope dome, clean room, or atmospheric layer). This paper follows a previous one introducing the INdoor TurbulENce SEnsor (INTENSE) instrument for optical turbulence characterization in a local area by exploitation of laser beam angle-of-arrival fluctuations. After a brief summary of the theoretical background, we present in this part results obtained using the INTENSE instrument in various optical integration testing clean rooms and telescope domes, each with specific air behavior conditions.

The INdoor turbulENce SEnsor (INTENSE) instrument

Optical system performances can be affected by local optical turbulence created by its surrounding environment (telescope dome, clean room, atmospheric surface layer). We present our new instrument INTENSE (INdoor TurbulENce SEnsor) dedicated to this local optical turbulence characterization. INTENSE consists of using several parallel laser beams separated by non-redundant baselines between 0.05 and 2.5m and measuring Angle-of-Arrival fluctuations from spots displacements on a CCD. We present detailed characterization of instrumental noise and first results for the characterization of the turbulence inside clean rooms for optical testing and integration.