Generalization and Research of the Keitz Equation Inaccuracy when Radiation Flux of Linear Low Pressure UV Lamps is Measuring

Abstract

In 2020, the first edition of the international standard ISO 15727 was issued for measuring the radiation flux of linear low pressure UV germicidal lamps. The document is based on a methodology developed by members of the IUVA Association of Ultraviolet Equipment Manufacturers. This technique measures the irradiance generated by the lamp under near-field conditions, the photometric distance and the length of the lamp. Then, using the so-called Keitz equation, the radiation flux is calculated. This implies the following. First, the lamp-length element has the properties of a uniformly diffuse cylinder. Secondly, the photometry axis connecting the receiver and the lamp divides it in half. Third, the angular response of the receiver corresponds to the cosine. The subject of this article is the study of the Keitz equation under conditions that deviate from these assumptions. In this work, a general formula is derived that connects the irradiance generated by a linear emitter and its energy flow. This formula does not impose restrictions on the light distribution of the lamp, the offset of the receiver relative to its center, the angular response of the receiver. The paper considers special cases, including those leading to the Keitz equation. Errors of the Keitz equation are estimated, due to the difference between the indicatrices of the radiation force of UV lamps and the uniformly diffuse cylinder, as well as the displacement of the receiver. The results of the study can be useful for developers of standards and measurement procedures. In addition, a special case derived for a receiver measuring spherical irradiance is of scientific interest. Despite the fact that at present the design of radiometric heads is mainly intended for measuring the irradiance of a flat area, for assessing the effectiveness of the effect of UV radiation on microorganisms and chemical compounds, it is more suitable for spherical irradiance.