LBOZ explained
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
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
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
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.
References
- Lorber . Avraham. . Error propagation and figures of merit for quantification by solving matrix equations . Analytical Chemistry . American Chemical Society (ACS) . 58 . 6 . 1986 . 0003-2700 . 10.1021/ac00297a042 . 1167–1172.
- Lorber . Avraham. . Harel . Alon. . Goldbart . Zvi. . Brenner . I. B. . Curve resolution and figures of merit estimation for determination of trace elements in geological materials by inductively coupled plasma atomic emission spectrometry . Analytical Chemistry . American Chemical Society (ACS) . 59 . 9 . 1987 . 0003-2700 . 10.1021/ac00136a004 . 1260–1266.
- Bergmann . Gerhard. . Von Oepen . Birgit. . Zinn . Peter. . Improvement in the definitions of sensitivity and selectivity . Analytical Chemistry . American Chemical Society (ACS) . 59 . 20 . 15 October 1987 . 0003-2700 . 10.1021/ac00147a017 . 2522–2526.
