# Intorduction to light sources, pinhole cameras, and lenses

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1 Intorduction to light sources, pinhole cameras, and lenses Erik G. Learned-Miller Department of Computer Science University of Massachusetts, Amherst Amherst, MA October 26, 2011 Abstract 1

4 light source. However, if the video camera is aimed at a passive non-emitting surface, like a table, then we are measuring the reflected light or scattered light from the surface. However, this reflected light can still be conceptualized as a light source. 2.1 A note about foreshortening Foreshortening is the phonomenon in which a flat surface appears smaller because it is being viewed at an angle, rather than straight on. For example, a white sheet of paper which subtends (or takes up ) 0.2 steradians of solid angle when viewed perpendicularly (or 0 degrees) relative to the viewer would subtend only 0.1 steradians when viewed at an angle of 60 degrees. This computation, A = A cos(θ), where θ is the angle at which the surface is being viewed (relative to perpendicular), A is the solid angle subtended at 0 degrees, and A is the solid angle subtended at an angle of θ, is a consequence of basic trigonometry. To simplify the examples in this document, we have assumed that both the extended light sources and the light detectors are perpendicular to the line connecting them. When this is true, there is no foreshortening, and hence we can ignore this additional mathematical step. However, in real applications, it is important to consider the significant effect that foreshortening can have in many applications. As a real-world example, a solar panel that is always pointed directly at the sun will collect the maximum possible power from the sun. A solar panel that is oriented at 45 degrees relative to the direction of the sun will collect only % of this power. 3 Lenses and cameras Recall the theoretical pinhole camera model discussed in class. The pinhole camera has an infinitely small hole which lets light through, forming an inverted image of the environment on the image plane at the back of the camera. Let s calculate how much light, in watts, from an extended source falls onto a particular element E of a sensor mounted at the image plane of our pinhole camera. Let s assume our camera is pointed at a flat fluorescent lamp which is 10mm wide and 1000mm long, and so has an emitting area of 10, 000mm 2 as viewed from our camera. Furthermore, let s assume that the fluorescent lamp outputs watts per steradian per mm 2. Without going into the details of exactly how large the imaging elements of our sensor are, or how far away the lamp is, let s assume that an area A of the lamp which is 10mm by 10mm, or 100mm 2, is imaged by the single element E of our sensor array. That is, for each point in the small area A of the fluorescent lamp, each ray traced from A, through the camera s pinhole, lands on sensor element E. 4

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