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. Fig. 1. Image formation for a simple lens. We can call the solid collection angle subtended by a pixel the collection cone for the pixel. If a dust particle absorbs or scatters light away from the collection cone (Fig. 2), the light reaching the pixel will be decreased by a factor equal to the fraction of the collection cone blocked by the particle. We call this a dark dust artifact. Fig. 2. Dust blocking a pixel’s FOV. If, on the other hand, a light shining on the lens window is scattered into the collection cone by a dust particle (Fig. 3), then the light reaching the pixel will increase by an additive amount that depends on the intensity of the window illumination. We call this a bright dust artifact. Fig. 3. Dust scattering sunlight into a pixel’s FOV. Bright dust artifacts occur when dust on a lens window is illuminated with an intense light source such as the sun. To help mitigate this lenses are sometimes fitted with sun shades to reduce the range of angles the front lens surface can be illuminated from. Since absorbing or scattering light away from a pixel’s collection cone is much easier to do than scattering light into the collection cone, this paper focuses on dark dust artifacts. We note that this is a purely geometric model. For visible light and the 10 micron and larger particle sizes we are concerned with scattering follows the laws of geometric optics.