Determination of actual object size distribution from direct imaging

Direct imaging is a technique commonly used in the study of particle, bubble, and droplet size distribution in a dynamic system. Objects such as particles, bubbles, and droplets can be present at various distances from the imaging device when images are captured. Hence, the location of the object will need to be known in order to determine the actual size of an individual object. However, the location of the object cannot be determined from a single image. A single calibration scale defined at the focusing plane is normally used for the determination of all the object sizes from images. When the focus is close to the imaging device, the change in magnification with location is large. The size distribution obtained from the use of a single calibration scale would thus give a considerable deviation from the actual size distribution. In this study, a statistical method is proposed to reconstruct the actual object size distribution from the experimental object size distribution obtained from images using a single calibration scale defined at the focusing plane. Experiments are performed to validate the accuracy of the proposed method on the particle size distribution determination in a settling system. The stability of the proposed method is also analyzed theoretically for imaging devices with different depth-of-field (DOF), focusing location, and change in magnification with distance.