Effects of imaging system blur on measurements of flow scalars and scalar gradients

Planar imaging of flow scalars is widely used in fluid mechanics, but the effects of imaging system blur on the measured scalar and its gradients are often inadequately quantified. Here, we present a 1-D analytical study that uses simplified models of the scalar profiles and imaging system blur to estimate the measurement errors caused by finite resolution. One objective of this paper is to give the experimentalist a methodology for quantitatively assessing the impact of imaging system blur on the accuracy of scalar measurements. The scalar profiles are modeled as either error or Gaussian functions, and the imaging system resolution is cast in terms of the line-spread function (LSF), which is modeled as Gaussian. The analysis gives the errors induced in the scalar structure thickness, gradient, and dissipation, for varying degrees of blur, the latter of which is quantified by sigma, the standard deviation of the Gaussian LSF. The results show that, to keep errors in the peak scalar gradients and dissipation to less than 10%, the 20%-width of the scalar structures should be at least 7.5sigma. Typical flow imaging experiments require fast (i.e., low f/#) optics that may suffer from significant blur and, therefore, this requirement may be difficult to meet in many applications. It is also shown that the resolution requirements for measuring the dissipation are more restrictive than for structure thicknesses. Further simulations were made to assess the effects of having clustered, or closely spaced, dissipation structures. Compared to the single structure results, there is a less severe resolution requirement to obtain scalar structure length scales, but a more severe requirement on the scalar gradient and dissipation.