An Analog Filter Approach to Frequency Domain Fluorescence Spectroscopy.
Bottom Line:
The rate equations found in frequency domain fluorescence spectroscopy are the same as those found in electronics under analog filter theory.The techniques described here can be used to separate signals from fast and slow fluorophores emitting into the same spectral band, and data collection can be greatly accelerated by means of a frequency comb driver waveform and appropriate signal processing of the response.The simplification of the analysis mathematics, and the ability to model the entire detection chain, make it possible to develop more compact instruments for remote sensing applications.
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PubMed Central - PubMed
Affiliation: Special Technologies Laboratory, National Security Technologies, LLC, 5520 Ekwill Street, Santa Barbara, CA, 93111, USA. trainhcp@nv.doe.gov.
ABSTRACT
The rate equations found in frequency domain fluorescence spectroscopy are the same as those found in electronics under analog filter theory. Laplace transform methods are a natural way to solve the equations, and the methods can provide solutions for arbitrary excitation functions. The fluorescence terms can be modelled as circuit components and cascaded with drive and detection electronics to produce a global transfer function. Electronics design tools such as SPICE can be used to model fluorescence problems. In applications, such as remote sensing, where detection electronics are operated at high gain and limited bandwidth, a global modelling of the entire system is important, since the filter terms of the drive and detection electronics affect the measured response of the fluorescence signals. The techniques described here can be used to separate signals from fast and slow fluorophores emitting into the same spectral band, and data collection can be greatly accelerated by means of a frequency comb driver waveform and appropriate signal processing of the response. The simplification of the analysis mathematics, and the ability to model the entire detection chain, make it possible to develop more compact instruments for remote sensing applications. No MeSH data available. Related in: MedlinePlus |
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Mentions: Fluorescence from a three level system can be represented by the diagram in Fig. 3. The driving term is Γ13, and it excites population from level 1 to level 3. Level 3 quickly relaxes to level 2. Level 2 then relaxes more slowly back to level 1. Some portion of level 3 also relaxes directly back to level 1, but that transition is typically very weak compared to the relaxation from level 3 to level 2. The fluorescence signal is proportional to the population accumulated in level 2. We denote that time dependent population by n2(t), and correspondingly similar notation for the populations of the other levels. The rate equations for the three levels are: 21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{@{}rcl@{}} \frac{dn_{1}}{dt} &=& \Gamma_{31}n_{3} + \Gamma_{21}n_{2} - \Gamma_{13}n_{1} \end{array} $$\end{document}dn1dt=Γ31n3+Γ21n2−Γ13n122\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{@{}rcl@{}} \frac{dn_{2}}{dt} &=& \Gamma_{32}n_{3} - \Gamma_{21}n_{2} \end{array} $$\end{document}dn2dt=Γ32n3−Γ21n223\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{@{}rcl@{}} \frac{dn_{3}}{dt} &=& -\Gamma_{31}n_{3} - \Gamma_{32}n_{3} + \Gamma_{13}n_{1}. \end{array} $$\end{document}dn3dt=−Γ31n3−Γ32n3+Γ13n1.Fig. 3 |
View Article: PubMed Central - PubMed
Affiliation: Special Technologies Laboratory, National Security Technologies, LLC, 5520 Ekwill Street, Santa Barbara, CA, 93111, USA. trainhcp@nv.doe.gov.
No MeSH data available.