Astro890L7 - Astronomical Seeing and Adaptive Optics As a...

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Astronomical Seeing and Adaptive Optics As a plane wavefront passes through the Earth's atmosphere it gets distorted by inhomogeneities in the index of refraction of air due to variations in temperature, pressure, and humidity (precipitable water content) in the different layers of the atmosphere. The sources of these inhomogeneities are convection cells, wind shear, and other hydrodynamics instabilities in the air above the telescope. The net result is that by the time the wavefront reaches the telescope the wavefront will be significantly distorted on the scale of the turbulent field it passed through. This graphic, taken from Roddier's book, shows an illustration of the basic process: Each circle represents a region with a higher (blue) or lower (red) index of refraction than the average air at that layer. The diameter represents the size of the inhomogeneity. As the incoming plane wave propagates downward through this model atmosphere, the wavefront is substantially distorted. We call the overall degradation in image quality due to random phase aberrations of the wavefront "seeing". To a good approximation, the random variations in the atmospheric index of refraction are well- described by stationary Kolmogorov Turbulence . Two size scales are used to describe Kolmogorov turbulence in a fluid: Outer Scale of Turbulence ( L 0 ), which defines the largest eddies in the flow introduced by bulk wind shear. This scale varies widely, but a good astronomical site will have L 0 of order 10s of meters. Nobody knows what sets the outer scale, but the usual explanation is that it is about the vertical thickness of the wind-shear layer at the Tropopause. Inner Scale of Turbulence (l 0 ). Larger scale eddies cascade downward in size in a scale-invariant way until they become so small that viscous dissipation of the turbulent energy halts the cascade. In air, the inner scale l 0 varies from a few millimeters near the ground to a few centimeters at high altitude. The main effect of variations in the index of refraction is to introduce a random phase shift in the wavefront passing through the medium. The phase shift at between two points separated by distance r in the sky plane produced by a fluctuation in the index of refraction n in a layer between heights ( h,h+dh ) above the ground is given by 2 () (,) hd h h rn r z d z π φ λ + =
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In the model of Tatarski (1961, Wave Propagation in a Turbulent Medium ), these phase fluctuations can be described as a Gaussian normal distribution to a good approximation, and the turbulent field can be described statistically in terms of a second-order Structure Function : 2 () ( ) Dr r r r φ φφ =− + For Kolmogorov turbulence, the structure function of variations in the index of refraction, n , is: 22 / 3 nn Dr Cr = where C n is the refractive index structure constant . 2 n C is a function of height (h) above the ground. Shown below is a median 2 n C profile for Mt. Graham between 0 and 20 km altitude: The variation of 2 n Ch with altitude is usually divided into two distinct "layers": 1. Ground Layer
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This note was uploaded on 07/17/2008 for the course ASTRO 890 taught by Professor Martini during the Spring '08 term at Ohio State.

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Astro890L7 - Astronomical Seeing and Adaptive Optics As a...

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