Interferometric coupling of the Keck telescopes with single-mode fibers.

Here we report successful interferometric coupling of two large telescopes with single-mode fibers. Interference fringes were obtained in the 2- to 2.3-micrometer wavelength range on the star 107 Herculis by using the two Keck 10-meter telescopes, each feeding their common interferometric focus with 300 meters of single-mode fibers. This experiment demonstrates the potential of fibers for future kilometric arrays of telescopes and is the first step toward the 'OHANA (Optical Hawaiian Array for Nanoradian Astronomy) interferometer at the Mauna Kea observatory in Hawaii. It opens the way to sensitive optical imagers with resolutions below 1 milli-arc second. Our experimental setup can be directly extended to large telescopes separated by many hundreds of meters.

Millisecond phase acquisition at video rates.

We can measure the phase of a static wave front with great accuracy and resolution by using standard phase-shifting interferometry techniques. Since wave-front changes during or between the acquisition of the individual interferograms cause measurement error, the measurement of transient phenomena still requires an essentially static wave front during acquisition. The 2 + 1 phase-shifting algorithm, originally developed to freeze out vibration when testing large optics, permits fast acquisition by requiring only two time-critical interferograms. The third interferogram provides a dc level or null and is only required once. The current 2 + 1 implementation is a low-cost interferometric system that is capable of phase acquisition in <2 ms at video rates. The repetition rate is limited by the readout time of the detector. The 2 + 1 has produced map movies of turbulent air acquired at the 30-Hz frame rate of a CCD camera.

Adaptive optics for array telescopes using piston-and-tilt wave-front sensing.

A near-infrared adaptive optics system operating at approximately 50 Hz has been used to control phase errors adaptively between two mirrors of the Multiple Mirror Telescope by stabilizing the position of the interference fringe in the combined unresolved far-field image. The resultant integrated images have angular resolutions of better than 0.1 arcsec and fringe contrasts of >0.6. Measurements of wave-front tilt have confirmed the wavelength independence of image motion. These results show that interferometric sensing of phase errors, when combined with a system for sensing the wave-front tilt of the individual telescopes, will provide a means of achieving a stable diffraction-limited focus with segmented telescopes or arrays of telescopes.

Phase shifting interferometry in the presence of vibration: a new algorithm and system.

A modification to the usual phase shifting interferometry algorithm permits measurements to be taken fast enough to essentially freeze out vibrations. Only two interferograms are time critical in this 2 + 1 algorithm; the third is null. The implemented system acquires the two time critical interferograms with a 1-millisecond separation on either side of the interline transfer of a standard CCD video camera, resulting in a reduction in sensitivity to vibration of 1-2 orders of magnitude. The required phase shift is achieved via frequency shifting. Laboratory tests comparing this system with a commercial phase shifting package reveal comparable rms errors when vibrations are low; as expected from an analysis of potential phase errors. However, the 2 + 1 system also succeeded when vibrations were large enough to wash out video rate fringes.

Probability distribution of turbulent irradiance in a saturation regime.

Application of the central limit theorem to the stochastic equation of propagation suggests that the probability distribution of the complex wave amplitude defined on the geometrical phase front is approximately normal. The resulting irradiance probability density function, valid in the strong scintillation regime, is an exponential multiplied by the modified Bessel function I(0) both of argument proportional to the irradiance; it is not the Rice-Nakagami density function. Quantitative tests show that this exponential-Bessel function constitutes as good a fit as the log-normal to the irradiance probability data reported in this paper. Since the normal distribution hypothesis is consistent with the stochastic wave equation, the model proposed here should be a simple substitute to the often used but theoretically incorrect log-normal irradiance probability distribution model.