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

Image:lboz-spectra.png

Let $\mathbf{X}$ 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:

: $\xi_k = \frac{1}{\|\mathbf{X}_{k-row}\| \|\mathbf{X}^{+}_{k-col}\|}$

where $\mathbf{X}^{+}$ means a pseudoinverse of the matrix and $\| \cdots \|$ 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 $1/\xi$ 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

{{cite journal | last=Lorber | first=Avraham. | title=Error propagation and figures of merit for quantification by solving matrix equations | journal=Analytical Chemistry | publisher=American Chemical Society (ACS) | volume=58 | issue=6 | year=1986 | issn=0003-2700 | doi=10.1021/ac00297a042 | pages=1167–1172}}
{{cite journal | last=Lorber | first=Avraham. | last2=Harel | first2=Alon. | last3=Goldbart | first3=Zvi. | last4=Brenner | first4=I. B. | title=Curve resolution and figures of merit estimation for determination of trace elements in geological materials by inductively coupled plasma atomic emission spectrometry | journal=Analytical Chemistry | publisher=American Chemical Society (ACS) | volume=59 | issue=9 | year=1987 | issn=0003-2700 | doi=10.1021/ac00136a004 | pages=1260–1266}}
{{cite journal | last=Bergmann | first=Gerhard. | last2=Von Oepen | first2=Birgit. | last3=Zinn | first3=Peter. | title=Improvement in the definitions of sensitivity and selectivity | journal=Analytical Chemistry | publisher=American Chemical Society (ACS) | volume=59 | issue=20 | date=15 October 1987 | issn=0003-2700 | doi=10.1021/ac00147a017 | pages=2522–2526}}

Category:Absorption spectroscopy