Solving inverse radiometric problems arising from infrared recordings

Abstract

The work presented in this thesis arose from the requirement in the military environment to obtain infrared radiation source/signature values of target objects usually of interest to infrared missiles under development. In situ measurements made of such objects are typically over a range of 100–3000 m and are influenced by the environment and by the instrument itself; the need therefore exists for measurement methods and data reduction techniques that incorporate corrections of these unwanted influences on the observed radiation. In this thesis, a measurement equation describing the infrared measurement of solid and gaseous type objects and the influence of the environment and the measuring instrument itself on these measurements is formulated. The measurement equation then forms the starting point of the formulation of a data reduction equation, which represents an inverse radiometric problem to be solved in order to obtain the radiation source values of the object being measured. An aircraft engine plume, for which a radiometric inverse problem is formulated and solved, is the target object of main interest in this work. In situ recordings of a turbine jet engine aircraft were used, but it is also shown that recordings of a micro turbine engine can be used in concept studies of plume emission. An inversion technique is presented for obtaining the three-dimensional inner radiance structure of a plume after the plume source values have been obtained from measurements. The inversion technique makes use of a discretized version of the formal solution to the equation of radiative transfer, which leads to a matrix equation from which the radiances of the volume elements inside the plume are obtained. The plume emission model based on this inner radiance structure is able to predict the observed plume emission at any arbitrary position outside the plume. The intensity predictions of the plume model are verified at the aspect angles for which measurements are available. It is also shown that under controlled laboratory conditions, the influence of the instrument on its own measurements by means of its spectral response can be resolved. The specific measurement set-up, involving only the instrument and a blackbody radiator, is described and the results are used as input to a novel inversion technique. The measurement equation for this instance is a Fredholm Integral Equation of the First Kind (IFK), which is manipulated in such a way that the resulting data reduction equation can be used to obtain the instrument spectral response. The IFK is, however, extremely ill-conditioned and the regularization method of Tikhonov is used in order to obtain a stable answer. The significance of the measurement methods and data reduction techniques presented lies in the improved capability of obtaining accurate radiation source parameters of objects of interest – especially for gaseous type objects such as an aircraft plume, for which the inner radiance structure can also be obtained. With improved source parameter values, the accuracy in the modelling of these objects also improves, leading to the resultant improvement of any electro-optical product being manufactured for the detection, identification and tracking of such objects whenever simulations form part of the product development.