Retrieval of angular emission function from whole-city light sources using night-sky brightness measurements

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The radiant-intensity function of a ground-based light source, otherwise called here the city emission function (CEF), is a pivotal modulator of night-sky radiance and is one of the key factors affecting light pollution propagation in a nighttime environment. It is difficult or rather impossible to compute a CEF from databases that are usually incomplete in their description of artificial sources other than public lighting. However, we have developed an indirect remote-sensing method to retrieve the CEF from sky-brightness measurements made at a local meridian that intersects a horizontal circle at the azimuthal position of a city or town. The inversion algorithm is validated for sensitivity and specificity in the reproduction of the initial emission functions, and demonstrates that the solution model succeeds in reconstructing different types of CEFs. The numerical inversion of the integral equation was successful even under extreme conditions, including elevated ground reflectance or zero uplight cases. The good numerical convergence and applicability of the model to experimental data is demonstrated by processing the radiance patterns obtained under natural conditions. The model provides a great opportunity for systematic retrievals of CEF needed by astronomers, physicists, environmental designers, city and suburban planners, as well as biologists and illumination engineers who deal with public lighting systems and must recognize the potentially adverse effects of night-lighting characteristics on the environment.