m-EDI Measurement Using Low-Cost Spectrometric Sensors Based on Photodiode Arrays with Narrowband Color Filters: An Exploration of Alternative Calibration Methods

Recent studies have highlighted the key role of lighting in regulating circadian rhythms and its impact on human health. Exposure to blue light, especially at specific times of day, is now quantified using the melanopic Equivalent Daylight Illuminance (m-EDI) parameter, defined in the CIE S 026 standard. This parameter is proportional to the integral, in the visible range, of the spectral power distribution and the melanopic sensitivity function, which peaks near 490 nm, and is similar to a Gaussian distribution. Low-cost spectrometric sensors using photodiode arrays and narrowband filters offer a cost-effective way to estimate m-EDI through a weighted sum of channel responses. However, due to inherent sensor variability, individual calibration is recommended. The standard approach involves multiple linear regression to fit the sensor's output to reference values using a set of test light sources. This method is easy to implement but depends heavily on the selection of calibration illuminants, which must outnumber the channels. This paper analyzes the sensitivity of this method to the sensor's spectral response and the choice of calibration sources. A revised calibration approach is proposed, selectively discarding channels to reduce deviations from the target response. Applied to several sensors, this method significantly improves calibration accuracy and robustness, reducing the RMS error for several test LEDs from 17.6 to 1.36 lux.