Radiometry and Photometry for Autonomous Vehicles and Machines - Fundamental Performance Limits

Abstract

As autonomous vehicles and machines, such as self-driving cars, agricultural drones and industrial robots, become ubiquitous, there is an increasing need to understand the objective performance of cameras to support these functions. Images go beyond aesthetic and subjective roles as they assume increasing aspects of control, safety, and diagnostic capabilities. Radiometry and photometry are fundamental to describing the behavior of light and modeling the signal chain for imaging systems, and as such, are crucial for establishing objective behavior. As an engineer or scientist, having an intuitive feel for the magnitude of units and the physical behavior of components or systems in any field improves development capabilities and guards against rudimentary errors. Back-of-the-envelope estimations provide comparisons against which detailed calculations may be tested and will urge a developer to “try again” if the order of magnitude is off for example. They also provide a quick check for the feasibility of ideas, a “giggle” or “straight-face” test as it is sometimes known. This paper is a response to the observation of the authors that, amongst participants that are newly relying on the imaging field and existing image scientists alike, there is a general deficit of intuition around the units and order of magnitude of signals in typical cameras for autonomous vehicles and the conditions within which they operate. Further, there persists a number of misconceptions regarding general radiometric and photometric behavior. Confusion between the inverse square law as applied to illumination and consistency of image luminance versus distance is a common example. The authors detail radiometric and photometric model for an imaging system, using it to clarify vocabulary, units and behaviors. The model is then used to estimate the number of quanta expected in pixels for typical imaging systems for each of the patches of a MacBeth color checker under a wide variety of illumination conditions. These results form the basis to establish the fundamental limits of performance for passive camera systems based both solely on camera geometry and additionally considering typical quantum efficiencies available presently. Further a mental model is given which will quickly allow user to estimate numbers of photoelectrons in pixel.