LBOZ

Definition

Let X be a matrix of the spectra (absorbances), where the k rows correspond to the components in mixture and n columns correspond to the sequence of wavelengths. The LBOZ criterion for kth component is calculated from the following formula:

where X + means a pseudoinverse of the matrix and ∥ ⋯ ∥ means an euclidean length of a vector.

Properties

The image above show synthetic gaussian spectra. The LBOZ criteria are: 0.561 for black compound, 0.402 for red compound, 0.899 for green and 0.549 for blue. LBOZ always lie in range <0,1> and has strong mathematical sense - it presents the amount of spectral signal which is not overlapped by the others. Hence, the uncertainty of a compound quantity increases by 1 / ξ in presence of the other compounds. In this case, the highest uncertainty is expected during determination of red compound - theoretically 2.38 times greater than during determination of its compound alone.