LBOZ

LBOZ is a coefficient used in spectrophotometry to estimate selectivity (amount of overlapping of spectra) in a quantitative manner. It is named after its creators: Lorber, Bergmann, von Oepen, and Zinn.
Definition.
Let formula_1 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 "k"th component is calculated from the following formula:
where formula_3 means a pseudoinverse of the matrix and formula_4 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 formula_5 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.