Optical convolutional spectrometer

Optical spectrometers are fundamental across numerous disciplines. However, miniaturized versions, while essential for in situ measurements, are often restricted to coarse identification of signature peaks and are inadequate for metrological purposes. Here we introduce a new class of spectrometer, which uses the convolution theorem as its unique mathematical foundation. Our 'convolutional spectrometer' offers unmatched performance for miniaturized systems and distinct structural and computational simplicity, featuring a centimetre-scale footprint for the fully packaged unit, low cost (~US$10) and a 2,400 cm^-1 (approximately 500 nm) bandwidth in the near-infrared region. We achieve excellent precision in resolving complex spectra with subsecond sampling and processing time, demonstrating wide near-infrared spectroscopic applications from industrial and agricultural analysis to healthcare monitoring. Specifically, our spectrometer system classifies diverse solid samples, including plastics, pharmaceuticals, coffee, flour and tea, with 100% success rate, and quantifies concentrations of aqueous and organic solutions with detection accuracy surpassing commercial benchtop spectrometers. We also realize the non-invasive sensing of human biomarkers, such as skin moisture (mean absolute error = 2.49%), blood alcohol (1.70 mg dl^-1), blood lactate (0.81 mmol l^-1) and blood glucose (0.36 mmol l^-1), highlighting the potential of this new class of spectrometers for low-cost, high-precision, portable and/or wearable spectral metrology.