A K-means Cluster-Driven Calibration to Improve the Accuracy of Personal Wearable UV Sensors

In recent years, there has been a surge in the commercialization of wearable "personal" ultraviolet (UV) sensors designed to help consumers stay ahead of overexposure to UV radiation. To be accurate, these sensors must exhibit a spectral sensitivity to sunlight similar the skin’s sensitivity, also called the "erythema spectrum". Sensors, however, never perfectly exhibit this spectral sensitivity and as a result their measurement are erroneous when they are exposed to "unknown" spectra, i.e. spectra against which they were not calibrated. On the other hand, because of the atmosphere, sun exposure at the surface of the earth exhibits an infinity of different spectra. In theory, sensors need to be calibrated for all spectra to measure them accurately outside of the laboratory but, in practice, it is impossible. Here, we use a K-means clustering method on the "UVNet" public database of solar spectra to generate what we call "centroid spectra" designed to be replicated in a laboratory and used for calibrating personal UV sensors. We hypothetize that using these centroid spectra for calibration will greatly improve the accuracy of sensors when they face unknown spectra, which we validated through numerical simulations. To our knowledge, this work brings the first rigorous approach into the selection of calibration spectra in radiometry, with useful applications beyond personal UV dosimetry. 1 The two main issues impeding the accuracy of wearable UV sensors UV exposure, whether from sunlight or tanning beds, has been demonstrated to have on the skin both short-term impacts, e.g. a sunburn, and long-term impacts, e.g. skin cancer. [Matsumura and Ananthaswamy, 2004]. In recent years, there has been a surge in the commercialization of wearable UV sensors as a quantitative tool to better guide sun protection. Essentially, these products are UV dosimeters that alert consumers when they reach a UV dose that would be harmful to them. Because UV can lead to life-threatening skin reactions in some cases, ensuring that these personal wearable UV sensors are accurate is of paramount importance. The accuracy of UV sensors in real-world conditions, that is when they measure UV radiation from sunlight in direct sunlight, indirect sunlight, in the shadow, under a cloud cover, etc., is primarily driven by their spectral sensitivity, i.e. the relative efficiency of detection of light as a function of the wavelength, and the spectral profile of the light source used to calibrate them. 32nd Conference on Neural Information Processing Systems (NeurIPS 2018), Montréal, Canada. 1.1 Personal wearable UV sensors must follow the erythema spectrum To be useful to consumers, UV sensors need to exhibit a spectral sensitivity similar to the skin’s sensitivity. McKinlay and Diffey [1987] found that the sensitivity of the human skin to light follows a very specific pattern, which they called the "erythema spectrum". This spectrum weights higherenergy UVB (280-310 nm) exponentially higher than lower-energy UVA (310-400 nm). It was later adopted by the World Health organization and standardized as ISO 17166. The erythema spectrum definition is given in Equation 1. w(λ) =  1 250 < λ ≤ 298 100.094(298−λ) 298 < λ ≤ 328 100.015(139−λ) 328 < λ ≤ 400 0 400 < λ (1) Where λ is the wavelength in nanometers. The World Health Organization has defined the "UV index" to be 25 mW/m of erythemaly-weighted irradiance. There is no wearable UV sensor, today, whose spectral sensitivity matches perfectly the erythema spectrum. As a result, all wearable UV sensors will be prone to errors when they are used to estimate the UV index of a light spectrum different from the spectrum of the light source used for their calibration. However, the error arising from this spectral mismatch can be compensated by a thorough calibration against all spectra that the sensors are supposed to measure. 1.2 A proper calibration would require the replication of sunlight in the laboratory Historically, UV sensors were commercialized to ensure that the UV lamps used in water treatment are still functioning at the desired level of irradiance. In this situation, the UV spectrum of interest is not changing except in its overall intensity over time. As a result, a calibration of these sensors against a similar UV lamp of known intensity would ensure that the sensors remain accurate when measuring the same UV lamps with declining intensity over time. As opposed to a UV lamp, sunlight is known to exhibit an infinity of different spectra at the surface of the earth, due to the impact of the atmosphere [Iqbal, 1983]. Since wearable UV sensors are used by consumers to measure sun exposure, they will be used to estimate the UV index of an infinite amount of different spectra. The only way to ensure perfect accuracy would be to calibrate UV sensors against all these spectra. Of course, it is impossible to replicate all sunlight spectra in a laboratory. To solve this problem, we use a K-means clustering method on public database of solar UV spectra to generate what we call "centroid spectra" designed to be replicated in a laboratory and used for calibrating personal UV sensors. We hypothesize that using these centroid spectra for calibration will greatly improve the accuracy of sensors when they are used to estimate the UV index of spectra against which they were not calibrated. We validated this hypothesis through numerical simulations. 2 Using the UVNet database of solar spectra to inform sensor calibration To better understand what type of spectra personal UV sensors are supposed to be measuring, we used a public database of solar spectra. From 1998 to 2003, the US Environmental Protection Agency (EPA) used ten ground Brewer spectrophotometers across the United States to collect data on UV exposure. Every 6 minutes, each spectrophotometer measured the irradiance of the sun every 0.5 nm from 286.5 nm to 363 nm, except during night and maintenance times. The two primary goals of this governmental effort were to provide information on the geographical distribution and temporal trends of UV radiation in the United States and provides long-term records of UV irradiance to scientists studying effects of UV on biota and materials. The outcome database of these solar UV spectra is the UVNet dataset [UVN]. Specifically, the UVNet database is composed of 73,557 spectra. Each spectrum is a represented by a vector of dimension 154 with the irradiance in W/nm/nm from 286.5 to 363 nm every 0.5 nm. Header information include GPS coordinates, the date, and the time of the day. Some sample spectra are represented in figure 1.