LBOZ is a coefficient used in
spectrophotometry
Spectrophotometry is a branch of electromagnetic spectroscopy concerned with the quantitative measurement of the reflection or transmission properties of a material as a function of wavelength. Spectrophotometry uses photometers, known as sp ...
to estimate
selectivity
Selectivity may refer to:
Psychology and behaviour
* Choice, making a selection among options
* Discrimination, the ability to recognize differences
* Socioemotional selectivity theory, in social psychology
Engineering
* Selectivity (radio), a ...
(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 ''k''th component is calculated from the following formula:
:
where
means a
pseudoinverse
In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element ''x'' is an element ''y'' that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inv ...
of the matrix and
means an
euclidean length of a vector.
Properties
The image above show synthetic
gaussian
Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below.
There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymo ...
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
Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable ...
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
*
*
* {{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
Absorption spectroscopy