Phase-resolved phasor method for the spectral separation of photoacoustic signal

This work presents a straightforward methodology for the spectral separation of two optical absorption contributions within a photoacoustic spectroscopy spectrum and directly determining the phase separation of their independent responses. By representing the photoacoustic signal as the sum of phasors from two independent absorption centers, we derived analytical expressions that enable the direct isolation of each center's spectrum. As an improvement over the well-known phase-resolved method, this approach does not require calculating scalar projections of the photoacoustic signal across multiple phase directions, nor does it require visual selection of specific projections based on their varying shapes. Furthermore, our methodology allows validation by comparing the measured spectrum to the one from the phasor sum of the isolated absorption centers’ responses. We tested this methodology on experimental data from aquatic lirium leaves and Golden Delicious apple peels using a standard photoacoustic spectroscopy setup. In each case, the methodology clearly identified the two distinct contributions corresponding to the known composition, with their sum closely matching the measured signal. The obtained phase separation in the responses of the absorption centers was attributed to a 7.1 ms time lag caused by the photosynthetic process in aquatic lirium leaves and to a 32.7 μm spatial separation between the two absorption centers in apple peels.