Diffraction-limited imaging with astronomical telescopes

Thesis (Ph.D.)--University of Rochester. College of Engineering and Applied Science. Institute of Optics. This thesis was digitized by the Institute of Optics in 2014 and was determined to have lapsed into the public domain. If you are the author and have questions about the digitization of your work, please contact Kari Brick, Graduate Program Coordinator for the Institute of Optics, at kbrick@ur.rochester.edu. Other contact information for the Institute is available at http://www.optics.rochester.eduThis thesis is a theoretical investigation of a digital processing technique that can be used to obtain diffraction-limited images of stellar objects from large, ground-based astronomical telescopes. The input to this processing scheme consists of a set of short-exposure photographs taken of an object over a short period of time. An averaging process is used which suppresses the atmospheric noise and thereby removes the blurring caused by the atmospheric seeing. A related processing method, developed by Labeyrie, has already been used to recover diffraction-limited information about several double stars on the 200-inch Hale telescope. The output of Labeyrie's technique is in the form of the autocorrelation of the object. This information is quite sufficient for studying an object such as a double star but it is not very useful for viewing an arbitrarily shaped object. The extra knowledge that is needed is the phase of the Fourier transform of the object. The processing method presented in this thesis averages the short-exposure images in a different manner, which retains this phase information. When the phase is combined with the modulus of the object Fourier transform, as determined by Labeyrie's technique, it is then possible to reconstruct a diffraction-limited image of the object. As a result, this method should be particularly useful for the study of extended objects whose surface details are presently masked by the atmospheric turbulence. The properties of the technique are analyzed theoretically using a gaussian phase model to describe the atmospheric seeing. The calculations show that a detailed knowledge of the atmospheric conditions at the time of observation is not necessary for the technique to work. The only condition on the atmosphere, required by the technique, is that the r.m.s. value of the wavefront distortions across the aperture of the telescope be large, i.e. greater than one wavelength of light. The effects of telescope aberrations on the technique are also considered. It is shown that the technique is very insensitive to any aberrations which may be introduced by the optical system. In other words, the resolution of the processed images corresponds to the resolution that would be obtained with a telescope of the same size that had no aberrations. An extensive analysis has also been made on the effects of noise on the quality of the reconstructed images. It is shown that the reconstructions are most sensitive to errors made in determining the phase of the object Fourier transform. In general, the fluctuations in the processed images vary inversely with the square root of the number of photographs used in the averaging procedure. To further investigate the technique, a one-dimensional computer simulation was performed. The parameters of the simulation were chosen to correspond to a 200-inch telescope with 2 arc seconds seeing. The resolution obtained by processing a set of computer generated "blurred" images corresponded to the near diffraction-limited performance of the 200-inch telescope. In all cases, the results showed excellent agreement between the input object functions and the processed output. This was true even when several wavelengths of telescope aberrations were included in the simulation. No astronomical photographs have been processed to demonstrate the proposed technique, but a complete description of how to process actual data is included. The theoretical calculations from the main part of the thesis are used to explain the proper method of choosing the scanning and processing parameters. These parameters, and therefore the processing costs, will vary from night to night because they depend on the quality of the seeing at the time of observation