Simple forward model of noncontact diffuse reflectance spectroscopy in a center-illuminated-area-detection geometry for measuring myoglobin forms in retail beef

Diffuse reflectance spectroscopy (DRS) relies on a forward model linking the spectral properties of medium with the spectral reflectance to resolve spectrally significant chromophores. Direct analytical inversion of a forward model makes it convenient to obtain the spectral absorption, from which spectral decomposition can be implemented using extinction characteristics of chromophores. To attain such convenience requires a forward model that is simple enough to be analytically invertible and is also robust. We have developed a non-contact DRS in a center-illuminated-areadetection (CIAD) geometry to assess myoglobin forms in beef. We present a simple forward model for this CIAD geometry of our preference that meets the basic needs of analytical inversion. The performance of this simple forward model of the CIAD geometry applying to a homogeneous medium has been examined against Monte Carlo simulations, over a significantly great range of dimension and medium properties. That includes the radius of collection ranging from 1.5 mm to 10 mm, the absorption coefficient varying 5-orders of magnitude as in [0.001, 0.01, 0.1, 1, 10, 100] mm-1, and the reduced scattering coefficient varying 2-orders of magnitude as in [0.1, 1, 10] mm-1 while limited to single scattering phase-function. Compared to a previous cumbersome model of CIAD geometry, this simple model may underperform at low absorption but significantly outperform at absorption coefficient>1 mm-1, showing promises in assessing highly absorbing medium that is challenging to DRS. The model applicable to experimental testing on controlled properties enables analytical inversion to obtain spectral absorption given a priori knowledge of the scattering.