Measurement of modulation transfer function of the atmosphere in the surface layer by moire technique

Abstract

The turbulence of the atmosphere puts an upper limit on the quality of the image of a ground object obtained by long-exposure photography from low or high altitudes in the atmosphere or in the space. By using good optics and high resolution film or CCD and a stable platform, this limit could be approached but not exceeded. A useful quantity for indicating the magnitude of this limit is the integral of the modulation transfer function (MTF) associated with the turbulence. In this work, we introduce a new method for measuring the MTF of the atmosphere in the surface layer, based on moire technique. In this technique, from a low frequency Ronchi grating, installed at a certain distance from a digital camera equipped with a tele lens, successive images are recorded and then transferred to a PC. By rotating each image by θ/2 and -θ/2, say ±3°, and superimposing them, a large number moire patterns are produced. The average transmittance function of the superimposed image gratings is measured in a moire fringe interval. The latter function is measured by scanning the moire pattern by a slit parallel to moire fringes. It is shown theoretically that from the Fourier transform of the latter function the MTF of the atmosphere can be deduced, if the MTFs of the imaging system and the grating are given or their effects are negligible. The atmospheric MTFs have been measured at different turbulence conditions. Also, we have studied the behavior of the atmospheric MTF respect to exposure time.