A CRITICAL ANALYSIS OF THE DETERMINATION OF LOCAL STATISTICS IN LIQUID SPRAYS WITH APPLICATION TO AN OPTICAL IMAGING METHOD

The nature of the indirect relation between optical spray measurements, the spray data needed in various applications, and the underlying statistics of a spray was examined to provide certain guidelines in the use of such data and to highlight important factors in the design of spray analysis systems. The relationship between spray measurements and the data employed in their applications is an indirect one for several reasons. First, the results of any measurement technique will be indicative of but a limited subset of the underlying spray statistics. The inference of statistical moments from the measurements, other than those moments contained in that subset, necessarily involves assumptions regarding the underlying spray statistics. Second, the inference of spray properties from optical measurements requires assertions as to the nature of the light-spray interaction, perhaps in terms of unknown optical properties of the spray. Third, every instrument, to some extent, is subject to stochastic phenomena in the measurement process. The determination of the spray properties thus requires information regarding the convolution of the instrument statistics with the spray statistics. As an illustration of these relations, an automated video imaging system was investigated. Finite depth of field considerations led to ambiguities associated with determining both the positions and sizes of droplets in the spray. To account for this, a special mathematical inversion that utilizes measured information from both in-focus and out-of-focus images was employed. The statistical variance associated with the instrument was determined to be significant. Measurements of stationary targets revealed that up to several thousand samples were required to statistically represent the instrument\u27s response, although the number depended upon the size of the target and its distance out-of-focus. Further, when statistical variances associated with the spray were compounded with those associated with the instrument, an exceedingly large number of samples were required to yield reliable statistical results. Such a situation seriously compromises the capability of the instrument to yield reliable data for sprays in virtually any situation, regardless of how the data may be processed