Tip Tilt Research Articles

Science Programs for a 2-m Class Telescope at Dome C, Antarctica: PILOT, the Pathfinder for an International Large Optical Telescope

AbstractThe cold, dry, and stable air above the summits of the Antarctic plateau provides the best ground-based observing conditions from optical to sub-millimetre wavelengths to be found on the Earth. Pathfinder for an International Large Optical Telescope (PILOT) is a proposed 2 m telescope, to be built at Dome C in Antarctica, able to exploit these conditions for conducting astronomy at optical and infrared wavelengths. While PILOT is intended as a pathfinder towards the construction of future grand-design facilities, it will also be able to undertake a range of fundamental science investigations in its own right. This paper provides the performance specifications for PILOT, including its instrumentation. It then describes the kinds of projects that it could best conduct. These range from planetary science to the search for other solar systems, from star formation within the Galaxy to the star formation history of the Universe, and from gravitational lensing caused by exo-planets to that produced by the cosmic web of dark matter. PILOT would be particularly powerful for wide-field imaging at infrared wavelengths, achieving near diffraction-limited performance with simple tip–tilt wavefront correction. PILOT would also be capable of near diffraction-limited performance in the optical wavebands, as well be able to open new wavebands for regular ground-based observation, in the mid-IR from 17 to 40 μm and in the sub-millimetre at 200 μm.

Impacts of probe-tip tilt on scanning probe microscopy

The effects of tip tilt on measurement uncertainty in scanning probe microscopy and tip-shape calibration for inclined tip have been discussed. Uncertainty of the untouchable region is the essential component of measurement uncertainty. Tip tilt is one of the most important parameters to determine the uncertainty of the untouchable region. The presence of tip tilt deteriorates fidelity of images and precision of critical-dimension measurements. It is necessary to use equivalent tip for calibrating the dilation of feature by inclined tip.

A two-axis tip–tilt platform for x-ray interferometry

We describe the design and demonstrate a two-axis tip–tilt platform stacked on atranslation stage for combined x-ray and optical interferometry. The platform iselectronically controlled to compensate for parasitic rotations and straightnesserrors. The key characteristic of the platform is the way in which it carries outtranslations and rotations by sliding. In spite of the potential stop-and-go motion,an x-ray interferometer was successfully operated and guiding errors were kept towithin 1 nrad and 1 nm. The platform made it possible to move the x-rayinterferometer by up to a couple of millimetres. In addition, the combined x-rayand optical interferometer allowed us to investigate the microdynamics of sliding.

Ball tip–stylus tilt correction for a stylus profilometer

Ball tip and stylus tilt are two error sources found in coordinate measurement machines (CMMs). The magnitude of these errors is dependent on the ball tip radius and the degree of misalignment between the stylus motion axis and lateral referencing plane determined by the x and y axes of the CMM used. It is shown that these two errors are actually coupled and that their correction can be accomplished in one process. The overall benefit and versatility of this correction routine on a more general basis are given.

Two-dimensional modelling of opticalHubble Space Telescopeand infrared tip-tilt images of quasar host galaxies

A description is given of the method used to extract quasar host-galaxy parameters from the deep Hubble Space Telescope (HST) quasar images presented by McLure, Dunlop and co-workers. We then give the results of extensive testing of this technique on a wide range of simulated quasar+host combinations spanning the redshift range of our HST study (0.1<z<0.3). These simulations demonstrate that, when applied to our deep HST images, our method of analysis can easily distinguish the morphological type of a given host galaxy, and determine its scalelength, luminosity, axial ratio and position angle to within an accuracy of a few per cent. We also present new infrared tip–tilt images of four of the most luminous quasars in our HST sample, along with the outcome of modelling these data in a similar manner. The results provide further confidence in the accuracy of the derived host-galaxy scalelengths, and allow an accurate determination of R−K colours for this subset of sources. All four of these quasar host galaxies have very similar red colours, R−K=2.9±0.2, indicative of a well-evolved stellar population.

Combined optical and X–ray interferometry for high–precision dimensional metrology

The requirement for calibrating transducers having subnanometre displacement sensitivities stimulated the development of an instrument in which the displacement is measured by a combination of optical and X–ray interferometry. The need to combine both types of interferometry arises from the fact that optical interferometry enables displacements corresponding to whole numbers of optical fringes to be measured very precisely, but subdivision of an optical fringe may give rise to errors that are significant at the subnanometre level. The X–ray interferometer is used to subdivide the optical fringes. Traceability to the meter is achieved via traceable calibrations of the lattice parameter of silicon and of the laser frequency. Polarization encoding and phase modulation allow the optical interferometer to be precisely set on a specific position of the interference fringe—the null point setting. The null point settings in the interference fringe field correspond to dark or bright fringes. Null measurement ensures maximum possible noise rejection. However, polarization encoding makes the interferometer nonlinear, but all nonlinearity effects are effectively zero at the fringe set point. The X–ray interferometer provides the means for linear subdivision of optical fringes. Each X–ray fringe corresponds to a displacement that is equal to the lattice parameter of silicon, which is ca .0.19 nm for the (220) lattice planes. For displacements up to 1 m the measurement uncertainties at 95% confidence level are ± 30 pm, and for displacements up to 100 m and 1 mm the uncertainties are ± 35 and ± 170 pm, respectively. Important features of the instrument, which is located at the National Physical Laboratory, are the silicon monolith interferometer that both diffracts X–rays and forms part of the optical interferometer, a totally reflecting parabolic collimator for enhancing the usable X–ray flux and the servo–control for the interferometers.

Absolute Tilt from a Laser Guide Star: A First Experiment

Absolute tip–tilt recovery using a tilt signal measured on a Laser Guide Star is a central problem in the framework of the development of Adaptive Optics Systems reaching full sky coverage down to visible wavelengths. In the past few years, various techniques aimed at solving this problemhave been proposed. However only a couple of these has been recentlytested in practice.We report about an experiment aimed at evaluating the performance of one of these techniques called the ‘Elongation Perspective’ technique. Our experiment has been performed using the ALFA system inCalar-Alto (Spain) and involves the simultaneous operation of the 3.6 m and the 2.2 m telescopes at the Observatory.This article describes the telescope configuration used, as well as the datareduction process carried out in order to estimate the scientific objecttilt. The technique performances are discussed in terms of the residualtilt error variance and related correlation coefficient. The analysisshows that, despite the low SNR of our measurements, the atmospheric tiltvariance is reduced to 80% of its initial value corresponding to acorrelation coefficient of about 0.6. To get a betterestimate of the performance achievable using this technique,the tilt error variance due to photon noise in the laser measurementis estimated and removed from the obtained tilt error variance.When this correction is done, thisvariance is reduced to about 50% of its initial value, showingthat the use of this technique can give rise to a significant reduction of the scientific object image motion.

Experimental validation of a technique to measure tilt from a laser guide star

We have experimentally demonstrated for what is believed to be the first time a method for sensing wave-front tilt with a laser guide star (LGS). The tilt components of wave fronts were measured synchronously from the LGS by use of a telescope with a 0.75-m effective aperture and from the star Polaris by use of a 1.5-m telescope. The Rayleigh guide star was formed at an altitude of 6 km and at a corresponding range of 10.5 km by projection of a focused beam at Polaris from the full aperture at the 1.5-m telescope. Both telescope mounts were unpowered and bolted in place, allowing us to reduce substantially the telescope vibration. The maximum value of the measured cross-correlation coefficient between the tilt for Polaris and the LGS is 0.71. The variations of the measured cross-correlation coefficient in the range from 0.22 to 0.71 are caused by turbulence at altitudes above 6 km, which was not sampled by the laser beacon but affected tilt for Polaris, the cone effect for turbulence below 6 km, residual mount jitter of the telescopes, and variations of the signal/noise ratio. The results support our concept of sensing atmospheric tilt by observing a LGS with an auxiliary telescope and indicate that this method is a possible solution for the tip-tilt problem.

Membrane mirror and bias electronics

We have designed and built an electrostatically deformable membrane mirror with simple bias and driver electronics to evaluate its suitability for a curvature-sensing adaptive optics system. It has a 100-mm-diameter aluminized nitrocellulose membrane, with 31 actuators arranged concentrically. The unit operates at atmospheric pressure with a high bias voltage applied to the membrane. The high-voltage electronics are contained within the mirror housing for safety reasons. An entrance window reduces the effects of air-coupled vibration. Details of the device and design rationale are presented. With a proper bias, the unit can provide low-order (including tip-tilt) wave-front correction.

Sodium beacon tip-tilt determination with Rayleigh-aided auxiliary telescope technique

The usefulness of tracking the Rayleigh portion of a mesospheric sodium laser guide star as reference for absolute tip–tilt recovery in the frame of the auxiliary telescopes technique is shown. This approach leads to the reduction of the ground occupation needed to attain a given sky coverage by more than one order of magnitude. Speed, tracking precision, and the number of auxiliary telescopes are also reduced, making this new approach a more attractive one. The use of a low-altitude Rayleigh spot reinforces the fundamental limitations affecting this and other techniques, thus degrading significantly the quality of the recovered tip–tilt. However, it is shown that, provided adequate care is taken in the collection and treatment of data, an interesting tilt signal can still be retrieved.

Focus anisoplanatism effects on tip–tilt compensation for adaptive optics with use of a sodium laser beacon as a tracking reference

A Zernike decomposition of the pupil phase variance that is due to focus anisoplanatism for a sodium laser guide star is calculated, including the angular error variance associated with overall tilt. This quantity, or tilt focus anisoplanatism σFA,tt2, is necessary in evaluating the usefulness of new techniques developed to measure the wave-front tilt from a sodium laser guide star. The analytical expression of σFA,tt2 in the case of refractive-index fluctuation with a Kolmogorov power spectral density is given together with numerical results for two different Cn′2(z) profiles. Numerical calculations show that tilt focus anisoplanatism may be a limitation when a sodium laser guide star is used to sense the overall wave-front tilt at visible wavelengths, especially for 8-m-class telescopes.

Auxiliary telescopes for the absolute tip–tilt determination of a laser guide star

A pair of small auxiliary telescopes in the neighbourhood of a telescope that utilizes a sodium-laser-guide star are able to provide information about the absolute tip–tilt of the sodium star. The technology involved is the same as differential seeing monitor techniques, and the coverage obtained by the technique described is of almost the whole sky.

Speckle spectroscopy with tip–tilt operation

A stellar speckle spectrometer with tip-tilt operation is proposed for high-spatial-resolution spectroscopy under atmospheric turbulence. A specklegram is used to drive a tip-tilt mirror for real-time shift-and-add operation to its dispersed specklegram. The proposed speckle spectroscopy attains a long exposure for the spectrum and a slit spectrometer. Several simulation experiments confirm the effectiveness of our method.

Improved performance of adaptive optics in the visible

A simple tip–tilt adaptive optics system can improve the peak intensity of the corrected image in the infrared by a factor of 2 to 3 compared with that of the uncorrected image. With conventional methods this performance cannot be achieved in the visible unless flexible mirrors are used. A method of improving the peak intensity in the visible by a factor of 8 to 10 compared with that of the uncorrected image by use of a simple tip–tilt mirror is presented. To achieve this improvement, the effective wave aberration, that is, the aberration modulo 2π, is used to obtain tilt and defocus of the turbulent wave front. It is shown that correcting the effective aberration is the equivalent in Fourier space of shift-and-add in image space, that is, moving the brightest speckle to the image center. Christou [ Pub. Astron. Soc. Pac.103, 1040 ( 1991)] has demonstrated the potential of a tip–tilt system when using shift-and-add. Operating in Fourier space rather than in image space offers the advantage of being independent of the type of object to be used for the correction. Additionally, this method is applied to the correction of defocus by determination of the brightest speckle in the three-dimensional image space. Thus the full potential of a rigid-mirror adaptive optics system is demonstrated.

Tip–tilt compensation for astronomical imaging

We present a performance analysis of tip–tilt-compensation systems that use natural stars as tilt references. Taking into account properties of the atmosphere and of the galactic stellar populations, we optimize the system operating parameters to determine performance limits for several varieties of tip–tilt-compensation system operating on a 10-m telescope on Mauna Kea, Hawaii. We find that, for systems that use a single tilt reference star, if the image of the star is uncorrected, a one-axis root-mean-square tilt residual of less than 190 nrad can be obtained for at least 99% of all astronomical objects, whereas if the image of the tilt reference star is fully corrected this limit drops to 90 nrad. For systems that use two tilt reference stars the limits drop to 160 nrad if the images of the stars are uncorrected and to 60 nrad if the images of the stars are fully corrected. These residual tilt levels would permit V-band images with long-exposure resolution of 8.5, 4.2, 7.3, and 2.9 times the diffraction limit, respectively, where the diffraction-limited resolution in the V band is 0.011 arcsec. These results may be compared with the typical seeing of 0.75 arcsec.