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: A positively biased sine wave can be written as g(t)=A(1−cos(ωt))/2. Its transform into s-space is 18\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ G(s) = \frac{A}{2} \left( \frac{1}{s} + \frac{s}{s^{2} + \omega^{2}}\right) $$\end{document}G(s)=A21s+ss2+ω2and the s-space response function is 19\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ N(s) = \frac{A}{2} \left( \frac{1}{s} + \frac{s}{s^{2} + \omega^{2}}\right)\left( \frac{1}{s+\Gamma}\right) $$\end{document}N(s)=A21s+ss2+ω21s+ΓSolving the Bromwich integral via the Residue theorem to transform back to the time domain yields 20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ n(t) = \frac{A}{2\Gamma} \left( 1 - \frac{\left( \frac{\omega}{\Gamma}\right)^{2} e^{-\Gamma t} - cos(\omega t) + \left( \frac{\omega}{\Gamma} \right) sin(\omega t)} {1 + \left( \frac{\omega}{\Gamma}\right)^{2}} \right). $$\end{document}n(t)=A2Γ1−ωΓ2e−Γt−cos(ωt)+ωΓsin(ωt)1+ωΓ2.Modeled wave forms of the driver and response functions for several frequencies are shown in Fig. 2. In the figure the time axis for each plot is scaled by the fluorescence lifetime 1/Γ. Multiplying the normalized frequency by Γ/2π (or equivalently, by 1/(2πτ)) converts the frequency scale to Hz. One sees that at low frequency the response is in phase with the driver, and increasing frequency the response lags in phase and begins to demodulate to a DC level.Fig. 2 |
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.