An optical model for image artifacts produced by dust particles on lenses

Machine vision systems often have to work with cameras that become dusty during use. Dust particles produce image artifacts that can affect the performance of a machine vision algorithm. Modeling these artifacts allows us to add them to test images to characterize an algorithm's sensitivity to dust and help develop counter measures. This paper presents an optics-based model that simulates the size and optical density of image artifacts produced by dust particles. For dust particles smaller than the aperture area the image artifact size is determined by the size of the lens aperture and not the size of the particle, while the artifact’s optical density is determined by the ratio of the particle and aperture areas. We show how the model has been used to evaluate the effect of dust on two machine vision algorithms used on the 2003 Mars Exploration Rovers. 1. DUST ARTIFACTS IN IMAGES In the pinhole camera models used in machine vision exactly one ray of light from a point in object space will pass through the camera's pinhole to strike the image plane. With a real lens however, light from a point in object space is collected from a solid angle of rays and projected through the lens onto the image plane, as illustrated in Fig 1. The extent of this solid angle of rays is limited by the lens elements and by the diameter of any diaphragms along the optical path. The limiting diaphragm is called the aperture stop of the lens. The entrance pupil of the lens is the image of the aperture stop as it would be seen if viewed from an axial position in front of the lens. To model the effect of dust on an image we follow the path of light collected by the lens for a single pixel and consider how dust particles on the lens affect the light reaching the pixel