Astronomical seeing

in this case) as seen through atmospheric seeing. Each star should appear as a single Airy pattern, but the atmosphere causes the images of the two stars to break up into two patterns of speckles (one pattern above left, the other below right). The speckles are a little difficult to make out in this image due to the coarse pixel size on the camera used (see the simulated images below for a clearer example). The speckles move around rapidly, so that each star appears as a single fuzzy blob in long exposure images (called a seeing disc). The telescope used had a diameter of about 7r0 (see definition of r0 below, and example simulated image through a 7r0 telescope). (apparent magnitude = -1,1) in the evening shortly before culmination on the southern meridian at a height of 20 degrees above the horizon. During 29 seconds Sirius moves on an arc of 7.5 minutes from the left to the right. Astronomical seeing has several effects: • It causes the images of point sources (such as stars), which in the absence of atmospheric turbulence would be steady Airy patterns produced by diffraction, to break up into speckle patterns, which change very rapidly with time (the resulting speckled images can be processed using speckle imaging) • Long exposure images of these changing speckle patterns result in a blurred image of the point source, called a seeing disc • The brightness of stars appears to fluctuate in a process known as scintillation or twinkling • Atmospheric seeing causes the fringes in an astronomical interferometer to move rapidly • The distribution of atmospheric seeing through the atmosphere (the CN2 profile described below) causes the image quality in adaptive optics systems to degrade the further you look from the location of reference star The effects of atmospheric seeing were indirectly responsible for the belief that there were canals on Mars. In viewing a bright object such as Mars, occasionally a still patch of air will come in front of the planet, resulting in a brief moment of clarity. Before the use of charge-coupled devices, there was no way of recording the image of the planet in the brief moment other than having the observer remember the image and draw it later. This had the effect of having the image of the planet be dependent on the observer's memory and preconceptions which led the belief that Mars had linear features. The effects of atmospheric seeing are qualitatively similar throughout the visible and near infrared wavebands. At large telescopes the long exposure image resolution is generally slightly higher at longer wavelengths, and the timescale (t0 - see below) for the changes in the dancing speckle patterns is substantially lower. == Measures ==

There are three common descriptions of the astronomical seeing conditions at an observatory: • The full width at half maximum (FWHM) of the seeing disc • r0 (the size of a typical "lump" of uniform air within the turbulent atmosphere and is widely used in simulations of astronomical imaging. The model assumes that the wavefront perturbations are brought about by variations in the refractive index of the atmosphere. These refractive index variations lead directly to phase fluctuations described by \phi_{a} \left(\mathbf{r}\right), but any amplitude fluctuations are only brought about as a second-order effect while the perturbed wavefronts propagate from the perturbing atmospheric layer to the telescope. For all reasonable models of the Earth's atmosphere at optical and infrared wavelengths the instantaneous imaging performance is dominated by the phase fluctuations \phi_{a} \left(\mathbf{r}\right). The amplitude fluctuations described by \chi_{a} \left(\mathbf{r}\right) have negligible effect on the structure of the images seen in the focus of a large telescope. For simplicity, the phase fluctuations in Tatarski's model are often assumed to have a Gaussian random distribution with the following second-order structure function: D_{\phi_{a}}\left(\mathbf{\rho} \right) = \left \langle \left | \phi_{a} \left ( \mathbf{r} \right ) - \phi_{a} \left ( \mathbf{r} + \mathbf{\rho} \right ) \right | ^{2} \right \rangle _{\mathbf{r}} where D_{\phi_{a}} \left ({\mathbf{\rho}} \right ) is the atmospherically induced variance between the phase at two parts of the wavefront separated by a distance \boldsymbol{\rho} in the aperture plane, and \langle\cdot\rangle represents the ensemble average. For the Gaussian random approximation, the structure function of Tatarski (1961) can be described in terms of a single parameter r_{0}: D_{\phi_{a}} \left ({\mathbf{\rho}} \right ) = 6.88 \left ( \frac{\left | \mathbf{\rho} \right |}{r_{0}} \right ) ^{5/3} r_{0} indicates the strength of the phase fluctuations as it corresponds to the diameter of a circular telescope aperture at which atmospheric phase perturbations begin to seriously limit the image resolution. Typical r_{0} values for I band (900 nm wavelength) observations at good sites are 20–40 cm. r_{0} also corresponds to the aperture diameter for which the variance \sigma ^{2} of the wavefront phase averaged over the aperture comes approximately to unity: \sigma ^{2}=1.0299 \left ( \frac{d}{r_{0}} \right )^{5/3} This equation represents a commonly used definition for r_{0}, a parameter frequently used to describe the atmospheric conditions at astronomical observatories. r_{0} can be determined from a measured CN2 profile (described below) as follows: r_{0}=\left ( 16.7\lambda^{-2}( \cos \gamma )^{-1}\int_{0}^{\infty} C_{N}^{2}(h) dh \right )^{-3/5} where the turbulence strength C_{N}^{2}(h) varies as a function of height h above the telescope, and \gamma is the angular distance of the astronomical source from the zenith (from directly overhead). If turbulent evolution is assumed to occur on slow timescales, then the timescale t0 is simply proportional to r0 divided by the mean wind speed. The refractive index fluctuations caused by Gaussian random turbulence can be simulated using the following algorithm: \phi_a (\mathbf{r})=\mbox{Re}[\mbox{FT}[R(\mathbf{k})K(\mathbf{k}) where \phi_a(\mathbf{r}) is the optical phase error introduced by atmospheric turbulence, R (k) is a two-dimensional square array of independent random complex numbers which have a Gaussian distribution about zero and white noise spectrum, K (k) is the (real) Fourier amplitude expected from the Kolmogorov (or Von Karman) spectrum, Re[] represents taking the real part, and FT[] represents a discrete Fourier transform of the resulting two-dimensional square array (typically an FFT). ). Turbulent intermittency The assumption that the phase fluctuations in Tatarski's model have a Gaussian random distribution is usually unrealistic. In reality, turbulence exhibits intermittency. These fluctuations in the turbulence strength can be straightforwardly simulated as follows: • RADAR mapping of turbulence • Balloon-borne thermometers to measure how quickly the air temperature is fluctuating with time due to turbulence • V2 Precision Data Collection Hub (PDCH) with differential temperature sensors use to measure atmospheric turbulence There are also mathematical functions describing the C_n^2 profile. Some are empirical fits from measured data and others attempt to incorporate elements of theory. One common model for continental land masses is known as Hufnagel-Valley after two workers in this subject. == Mitigation ==

's surface showing the effects of Earth's atmosphere on the view The first answer to this problem was speckle imaging, which allowed bright objects with simple morphology to be observed with diffraction-limited angular resolution. Later came space telescopes, such as NASA's Hubble Space Telescope, working outside the atmosphere and thus not having any seeing problems and allowing observations of faint targets for the first time (although with poorer resolution than speckle observations of bright sources from ground-based telescopes because of Hubble's smaller telescope diameter). The highest resolution visible and infrared images currently come from imaging optical interferometers such as the Navy Prototype Optical Interferometer or Cambridge Optical Aperture Synthesis Telescope, but those can only be used on very bright stars. Starting in the 1990s, many telescopes have developed adaptive optics systems that partially solve the seeing problem. The best systems so far built, such as SPHERE on the ESO VLT and GPI on the Gemini telescope, achieve a Strehl ratio of 90% at a wavelength of 2.2 micrometers, but only within a very small region of the sky at a time. A wider field of view can be obtained by using multiple deformable mirrors conjugated to several atmospheric heights and measuring the vertical structure of the turbulence, in a technique known as Multiconjugate Adaptive Optics. Another cheaper technique, lucky imaging, has had good results on smaller telescopes. This idea dates back to pre-war naked-eye observations of moments of good seeing, which were followed by observations of the planets on cine film after World War II. The technique relies on the fact that every so often the effects of the atmosphere will be negligible, and hence by recording large numbers of images in real-time, a 'lucky' excellent image can be picked out. This happens more often when the number of r0-size patches over the telescope pupil is not too large, and the technique consequently breaks down for very large telescopes. It can nonetheless outperform adaptive optics in some cases and is accessible to amateurs. It does require very much longer observation times than adaptive optics for imaging faint targets, and is limited in its maximum resolution. ==See also==