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: The Laplace transform of Eq. 4 is 5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sum\limits_{i} N_{i}(s)(s + \Gamma_{i}) - n_{i_{0}} = G(s), $$\end{document}∑iNi(s)(s+Γi)−ni0=G(s),where s is the complex frequency variable, and represent the initial state populations, which are usually zero. The transfer function for Eq. 5 is 6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ F_{i}(s) = N_{i}(s)/G(s) = \frac{1}{s + \Gamma_{i}} $$\end{document}Fi(s)=Ni(s)/G(s)=1s+ΓiFrom this we can determine the phase shift and modulation amplitude of the filter response to a periodic driver function g(t). This is accomplished by restricting s to the imaginary axis, and computing the Mod of the transfer function for the modulation amplitude, and the ratio of the imaginary and real parts for the tangent of the phase shift. Figure 1 shows the theoretical response assuming a single lifetime emission as a function of the drive frequency ω. The phase shift and modulation amplitude evolve on a frequency scale determined by the reciprocal lifetime. The range of frequencies is typically two orders of magnitude centered at the angular frequency of the reciprocal lifetime ω = 2π/τ.Fig. 1 |
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.