Projection Description: The earth’s atmosphere is a swirling ball of gas. The cause of the swirling, especially near the surface, is due to different temperatures of the air. These different air temperatures change the index of refraction for the air in the atmosphere. Thus when light travels through this turbulent/random medium the light ends up getting speckled. It is these speckles, caused by the turbulent atmosphere that limited the resolution of earth-bound astronomical observations until the invention of adaptive optics. You have observed this phenomenon any time you’ve looked at a star. It is the motion of these speckles over our eyes that causes the stars to twinkle. The graphic below illustrates how light from a source ends up distorted by the atmosphere resulting in a specular image. Our problem focuses on a particular aspect of imaging through turbulence. In the early 1970’s it was shown by Lawrence, Clifford and Oochs and Lee and Harp that the primary source of the variation of the intensity of light on a pair of photo detector was from the wind. This observation can be used to create a poorly posed inverse problem that if one can solve, permits one to compute the cross wind profile along the path of the light beam. The specific relationship relating time-lagged cross covariance and wind speed is given by: where: τ – is the time lag between adjacent pixels L – is the length of the flight path. k – is wave number of the light used (the light is assumed to be monochromatic.) K – has units of 1 / length, is the reciprocal of the size of a turbulent eddy ball. ρ – spacing between detectors v(z) – wind speed parallel to the line connecting the detectors Cn2 (z) – scintillation coefficient Several different authors since then have advertised an ability to measure the gross average wind over long periods of time. (10 minute intervals is a common metric.) Here are several questions that I currently have on this phenomenology. The team will answer any questions that I don’t answer between now and this summer. What is the impact of assuming Cn2 (z) is constant? Most practitioners make this assumption. How is the inverse problem affected if it is not constant? Is it possible to distinguish between affects caused by variable Cn2 (z) and varying wind? The environment is constantly changing, thus measuring the time lagged cross covariance is a very noisy measurement, and difficult to do. In particular, given the underlying noise assumptions of the inputs to this integral equation, what kind of noise does one observe when measuring CχN (ρ,τ)? Question 2 above can be attacked in two ways. The first is an analytic approach the second is a simulation based approach. Can we create a simulation to permit us to assess question 2? A standard technique is based on phase screens. This would require examining the literature, possibly grabbing code off the net, and implementing a simulation in Matlab or similar system. Related to question 2, how long a period of time can one measure CχN (ρ,τ)? Most authors use 10 minutes, can it be done in 10 seconds? 1 second? 0.1 seconds? Key References: (a much longer list will be provided this summer): Laser Beam Propagation through Random Media, Second Edition Larry C. Andrews and Ronald L. Phillips, SPIE Press, 2005. Imaging Through Turbulence, Michael C. Roggemann, Byron M. Welsh, CRC Press, 1996. Lawrence, Ochs, and Clifford, “Use of Scintillations to Measure Average Wind Across a Light Beam”, Applied Optics, 1972, Volume 11, #2, Page 239-243. Barakat, and Buder, “Remote Sensing of Crosswind profiles using the correlation slope method”, Journal of the Optical Society of America, 1979, volume 69, #11, Pages 1604-1608. Lee, Harp, “Weak Scattering in Random Media, with Applications to Remote Probing”, Proceedings of the IEEE, 1969, Volume 57, #4. Pages 375+ Image copied and cropped from: http://www.aanda.org/articles/aa/full/2003/47/aa3613/img193.gif