Beyond Channel Count: Metrological Performance Metrics for Compact Multi-Channel Spectral Sensors

Compact multi-channel spectral sensors based on thin-film interference filters offer a low-cost, integrable alternative to dispersive spectrometers, yet their performance is too often assessed by channel count alone, an indicator blind to inter-channel crosstalk, filter bandwidth, and the underdetermined nature of the spectral measurement. We present a metrological framework that formalises the channel-wise measurement model, identifies the dominant Type B instrumental uncertainty contributions (interference-filter centre-wavelength tolerance, responsivity line-shape deviation, PGA gain tolerance, and ADC quantisation and noise), and propagates them from the digital-count domain to irradiance through the device calibration curve. From the same datasheet parameters, the framework derives two figures of merit: the inter-channel crosstalk matrix C and the effective number of independent measurements Meff, obtained as the participation ratio of the eigenvalues of C. The uncertainty budget is developed in detail for the AS7343, a device with broad and overlapping filters, under three calibration scenarios of increasing effort, while the figures of merit are computed for both the AS7341 and the AS7343. Predictions are cross-validated against the experimental spectral reconstruction errors reported in our previous calibration study on xenon illuminants. Although the AS7343 carries three more nominal channels than the AS7341, the two devices share an almost identical effective channel count (Meff = 7.05 versus 7.07) and reconstruct the xenon test source comparably, demonstrating that channel count is a poor predictor of metrological quality and that the proposed metrics offer a predictive, datasheet-level basis for sensor characterisation and selection.