Effects of practical aerosol forward scatter of infrared and visible light on atmospheric coherence diameter

Abstract

A correction to the definition of the atmospheric coherence diameter is suggested here, based on the existence of a practical instrumentation-based aerosol modulation transfer function (MTF), which is often the dominant ingredient of the atmospheric MTF. As defined classically by Fried about 25 yr ago, atmospheric MTF and coherence diameter were related to turbulence MTF only. Lutomirski considered diftractive aerosols, too, but did not consider effects of instrumentation on scattering angles actually recorded in the image. These are limited in the real world by instrumentation to milliradians, rather than by the broad angular spread of diffraction to radians. In the case of a Gaussian approximation of the practical aerosol MTF, an analytical expression is derived for the practical aerosol-derived coherence diameter. This parameter is related to the practical aerosol MTF's cutoff frequency, and to its asymptotic value at high spatial frequencies. Thus, a more general concept of atmospheric coherence diameter is proposed here, which is relevant to actual real-world imaging systems, whether they are passive or active. Quantitative validation of the theory is presented, based on both simulations and actually measured atmospheric MTFs in both the visible and thermal infrared spectral ranges. Overall atmospheric coherence diameter is determined generally by the smaller of the turbulence and practical aerosol coherence diameters, depending on optical depth. The results here appear applicable particularly to cost-effective thermal imaging system design, although applications are considered, too, for the visible and near infrared. For example, blur deriving from aerosol scatter should have much less effect in coherent detection laser radar (LIDAR) than in direct detection imaging.