Non-contact diffuse reflectance spectroscopy using center-illuminated-area-detection modeled by a simple formulae for assessing myoglobin

A process of convenience that is highly desirable in diffuse reflectance spectroscopy (DRS) is to recover the spectral absorption by direct model-inversion to facilitate decomposition of spectrally significant chromophores. Attaining such convenience that requires a simple forward model has been challenging in non-contact DRS, for assessing myoglobin forms in discoloring meat. This work demonstrates that non-contact DRS configured in a center-illuminated-area-detection (CIAD) geometry [Sun & Piao, 2022] may be modeled by a formula of exceptional simplicity. This simple forward model for DRS in the CIAD geometry on a homogeneous medium has been examined by using Monte Carlo simulations, over a radius of the area of CIAD ranging from 1.5 mm to 10 mm, for the absorption coefficient to vary 5-orders of magnitude over [0.001, 100] 〖mm〗^(-1), and the reduced scattering coefficient to vary 2-orders of magnitude over [0.1, 10] 〖mm〗^(-1) while limited to one scattering phase function. When compared to a previous cumbersome model for the same geometry, the simple model markedly outperforms at high absorption, e.g., >1.0 〖mm〗^(-1). The simplicity of this model facilitates that, with a priori knowledge of the spectral scattering, analytical operation could directly recover the spectral absorption to subsequently use linear inversion to resolve the chromophore proportions. Non-contact DRS in the CIAD geometry of ~4mm in diameter using this simple forward model has been applied to seven longissimus lumborum steaks over 6 days of retail display. The progressive changes of myoglobin, including the decrease of oxymyoglobin and increase of metmyoglobin over 6 days estimated by the simple model of non-contact DRS in CIAD are consistent with those assessed concurrently by a contact DRS using 3mm source-detector-separation [Piao et al, 2022].