Validation of bubble sizes obtained with incoherent imaging on a sloped viewing window

A sampling-followed-by-imaging technique for sizing bubbles in flotation systems has been developed (Proceedings of the 34th Annual Meeting of the Canadian Mineral Processors, pp. 389–402, Miner. Eng. 17 (2004) 53). The technique directs a sample of bubbles into a viewing chamber where they are exposed and digitally imaged using incoherent backlighting. The images are automatically analyzed by means of a threshold criterion. The chamber is sloped to spread the bubbles over the surface of the viewing (glass) window, a configuration chosen to reduce bubble overlap and facilitate definition of the focal plane. The design also means that the defocus distance (object to focal plane) is small and always negative (the object lies between the focal plane and light source). This simplifies fundamental assessment of factors contributing to image size.Measurements from the images were compared with standard bubble sizes obtained with the displaced-volume method. Thresholding at half the intensity level, sizes were systematically underestimated and the bias was correlated to bubble size, increasing from 0.3% at ca. 0.7 mm to 2% at ca. 4 mm. The evidence is that reflected rays slightly bias towards underestimating size whereas the inclined window causes a small overestimation due to bubble flattening. These two effects are of similar magnitude and tend to cancel. Consequently, the underestimation trend can be attributed to the defocus distance. A semi-empirical correction procedure is suggested which uses the fundamental method of Bongiovanni et al. (Exp. Fluids 23 (1997) 209) to correct the bias due to system optics along with an empirical approach to compensate for bubble flattening.