Time-Resolved Fluorescence Wiki

irf

Anonymous (anonymous@undisclosed.example.com) — 2014-02-21T13:28:43+00:00

2014/02/21 14:28		current
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	IRF stands for Instrument Response Function. The IRF is the best approximation to a temporally infinitely short process possible to measure with a given instrument. A synonyme sometimes used is 'lamp function', which stresses the fact that the temporal profile of the excitation is the most intuitive contribution to the IRF. Of course, the temporal resolution of all components of the instrument contribute to both shape and width of the IRF. The observed decay in a time domain measurement is a [[convolution]] of the 'real' decay with the IRF.		IRF stands for Instrument Response Function. The IRF is the best approximation to a temporally infinitely short process possible to measure with a given instrument. A synonyme sometimes used is 'lamp function', which stresses the fact that the temporal profile of the excitation is the most intuitive contribution to the IRF. Of course, the temporal resolution of all components of the instrument contribute to both shape and width of the IRF. The observed decay in a time domain measurement is a [[convolution]] of the 'real' decay with the IRF.

-	see also [[howto:how_to_measure_the_instrument_response_function_irf\|[[howto:How To Measure the IRF]]]]	+	see also [[howto:how_to_measure_the_instrument_response_function_irf\|How To Measure the IRF]]

differential_count_rate

Anonymous (anonymous@undisclosed.example.com) — 2017-09-26T11:46:03+00:00

2017/09/24 05:34		current
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	Not really. In case of pulsed signals the average count rate is a misleading quantity. An average count rate value does not take into account when and how those photons are emitted and detected. Interpreting a 100 kcps intensity as a constant emission rate (Poisson mean rate, in math terms) is a misconception. The physics of the measurement is completely different. These photons are obviously not emitted evenly, one by one over the whole one second period. They arrive to the detector bunched, as flashes. These are short time intervals with huge photon density (rate), separated by long "dark", quiet periods.		Not really. In case of pulsed signals the average count rate is a misleading quantity. An average count rate value does not take into account when and how those photons are emitted and detected. Interpreting a 100 kcps intensity as a constant emission rate (Poisson mean rate, in math terms) is a misconception. The physics of the measurement is completely different. These photons are obviously not emitted evenly, one by one over the whole one second period. They arrive to the detector bunched, as flashes. These are short time intervals with huge photon density (rate), separated by long "dark", quiet periods.

-	Getting a final count at "1% of SYNC rate" is a result of **low sampling rate of a high rate signal**.	+	In yet another words, achieving a final count rate at "1% of SYNC rate" is a result of **sparse sampling with dead time**. The sampled signal features much higher photon density, but lasts only for a short time.

	In mathematical terms, "average count rate of 1..2% of SYNC rate" means the overall detection probability, integrated over the whole duration of a measurement. The concept of //differential count rate// is related to the //probability density function//. The detected signal in TCSPC has a very inhomogeneous time distribution.		In mathematical terms, "average count rate of 1..2% of SYNC rate" means the overall detection probability, integrated over the whole duration of a measurement. The concept of //differential count rate// is related to the //probability density function//. The detected signal in TCSPC has a very inhomogeneous time distribution.

	Note: for detectors that exhibit count rate dependent shifting of the IRF, extra care has to be taken when measuring the IRF and directly using it for decay analysis. ((Takuhiro Otosu, Kunihiko Ishii and Tahei Tahara, Note: Simple calibration of the counting-rate dependence of the timing shift of single photon avalanche diodes by photon interval analysis, Rev. Sci. Instrum. 84, 036105 (2013); [[http://dx.doi.org/10.1063/1.4794769]]))		Note: for detectors that exhibit count rate dependent shifting of the IRF, extra care has to be taken when measuring the IRF and directly using it for decay analysis. ((Takuhiro Otosu, Kunihiko Ishii and Tahei Tahara, Note: Simple calibration of the counting-rate dependence of the timing shift of single photon avalanche diodes by photon interval analysis, Rev. Sci. Instrum. 84, 036105 (2013); [[http://dx.doi.org/10.1063/1.4794769]]))

deconvolution

Anonymous (anonymous@undisclosed.example.com) — 2013-08-06T14:41:19+00:00

2013/08/06 16:13		current
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	====== Deconvolution ======		====== Deconvolution ======
-
-	===== What is "Deconvolution"? =====

	Deconvolution is used in time domain data analysis for removal of broadening effects due to instrumental resolution. In this context deconvolution is mainly concerned with the [[IRF]] (or lamp function) including the finite light source pulse width and other broadening effects (e.g. electronics). The effects caused by the [[IRF]] are dominant in the onset of a decay curve.		Deconvolution is used in time domain data analysis for removal of broadening effects due to instrumental resolution. In this context deconvolution is mainly concerned with the [[IRF]] (or lamp function) including the finite light source pulse width and other broadening effects (e.g. electronics). The effects caused by the [[IRF]] are dominant in the onset of a decay curve.
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	===== How deconvolution should be done =====		===== How deconvolution should be done =====

-	Best, not at all ;-). At PQ we use [[reconvolution]] instead, for a variety of good reasons (see [[IRF]]). If one cannot resist applying deconvolution, the best way of doing it (at least for time domain data) would be via Fourier transform. Fourier transform is a slow process (even with [[FFT]]) and it has to be done twice, since the deconvoultion itself is performed on the transformed data set, which has to be retransformed afterwards.	+	Best, not at all ;-). At PicoQuant, for a variety of good reasons (see [[IRF]]) we use [[reconvolution]] instead. If one cannot resist applying deconvolution, the best way of doing it (at least for time domain data) would be via Fourier transform. Fourier transform is a slow process (even with [[FFT]]) and it has to be done twice, since the deconvoultion itself is performed on the transformed data set, which has to be retransformed afterwards.


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	The most prominent application of deconvolution techniques is imaging. Usually one tries to remove blurring by deconvolution (or deconvolution-like) techniques. What holds for time domain data, also holds for imaging: Deconvolution has a disturbingly high potential for producing artefacts - and there is no way of telling apart artefacts and effects. The images may look nicer (which undoubtedly is valuable especially for publication purposes), but the content of information has not necessarily improved.		The most prominent application of deconvolution techniques is imaging. Usually one tries to remove blurring by deconvolution (or deconvolution-like) techniques. What holds for time domain data, also holds for imaging: Deconvolution has a disturbingly high potential for producing artefacts - and there is no way of telling apart artefacts and effects. The images may look nicer (which undoubtedly is valuable especially for publication purposes), but the content of information has not necessarily improved.
-

convolution

Anonymous (anonymous@undisclosed.example.com) — 2013-08-06T14:39:35+00:00

2013/08/06 16:38		current
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	====== Convolution ======		====== Convolution ======

-	The convolution $C$ of a function $F(t)$ with a function $G(t)$ (of a parameter $t$) is defined as	+	The convolution $C$ of a function $F$ with a function $G$ (of a parameter $t$) is defined as

	$C(t)=\int_{-\infty}^t F(t-t')~G(t')~dt'$		$C(t)=\int_{-\infty}^t F(t-t')~G(t')~dt'$

fast_lifetime

Anonymous (anonymous@undisclosed.example.com) — 2013-08-06T14:43:32+00:00

2013/08/06 16:43		current
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	A method for estimating the average lifetime, calculated non-distinctive on different exponentials in a simple single path calculation, compared to a complete fitting operation against a more complex, non-linear model. Often used with [[FLIM]] go get a first idea of the lifetime distribution in the image.		A method for estimating the average lifetime, calculated non-distinctive on different exponentials in a simple single path calculation, compared to a complete fitting operation against a more complex, non-linear model. Often used with [[FLIM]] go get a first idea of the lifetime distribution in the image.

-	In detail, FastLT is calculating the barycentre of the (pseudo–)pixel's decay. The time span from the barycentre of the IRF to the barycentre of the decay equals the average lifetime. This estimate is very fast and does not suffer as much from low statistics. If an [[IRF]] is not available, the "time zero" $t_0_$ has to be estimated differently, for example by using the rising flank of the decay or the entrance of the [[FWHM]] interval. However, this may introduce a systematic shift in the estimated average lifetimes.	+	In detail, FastLT is calculating the barycentre of the (pseudo–)pixel's decay. The time span from the barycentre of the IRF to the barycentre of the decay equals the average lifetime. This estimate is very fast and does not suffer as much from low statistics. If an [[IRF]] is not available, the "time zero" $t_\theta$ has to be estimated differently, for example by using the rising flank of the decay or the entrance of the [[FWHM]] interval. However, this may introduce a systematic shift in the estimated average lifetimes.

reconvolution

Anonymous (anonymous@undisclosed.example.com) — 2015-02-10T16:35:00+00:00

2014/04/09 22:38		current
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	Reconvolution is used in time domain data analysis for removal of broadening effects due to instrumental resolution. In contrast to [[deconvolution]], data processing using reconvolution techniques does not aim at retrieving the raw data as seen by an ideal instrument, but does usually compare artificial decays (simulated on the base of a model) convolved with the measured [[IRF]].		Reconvolution is used in time domain data analysis for removal of broadening effects due to instrumental resolution. In contrast to [[deconvolution]], data processing using reconvolution techniques does not aim at retrieving the raw data as seen by an ideal instrument, but does usually compare artificial decays (simulated on the base of a model) convolved with the measured [[IRF]].

-	Reconvolution is used in PicoQuant software packages (mainly [[products:FluoFit]] and [[products:SymPhoTime]]) for compensating IRF effects.	+	Reconvolution is used in PicoQuant software packages (mainly [[software:FluoFit]] and [[software:SymPhoTime]]) for compensating IRF effects.

cfd

Anonymous (anonymous@undisclosed.example.com) — 2015-09-23T14:55:11+00:00

2013/08/06 16:37		current
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	[{{ glossary:constantfraction.png?400\|Comparison of threshold activation (left) to CFD activation (right) }}]		[{{ glossary:constantfraction.png?400\|Comparison of threshold activation (left) to CFD activation (right) }}]

-	The CFD is used to extract precise timing information from electrical detector pulses that may vary in amplitude. Thereby the overall system IRF can be narrowed and some of the random background signal can be suppressed. This cannot not be achieved with a simple threshold detector (comparator). Constant fraction discrimination is very important, especially in the case of [[PMTs]], because their pulse amplitudes vary significantly.	+	The CFD is used to extract precise timing information from electrical detector pulses that may vary in amplitude. Thereby the overall system IRF can be narrowed and some of the random background signal can be suppressed. This cannot not be achieved with a simple threshold detector (comparator). Constant fraction discrimination is very important, especially in the case of [[PMT]]s, because their pulse amplitudes vary significantly.

	A CFD compares the original detector signal with an amplified and delayed version of itself. The signal derived from this comparison changes polarity exactly when a constant fraction of the detector pulse height is reached. The zero crossing point of this signal is therefore suitable to derive a timing signal independent from the amplitude of the input pulse. This is done by comparing this signal to a zero cross level. This level should be adjusted to remove events that originate from signal noise. CFDs furthermore permit to set a discriminator threshold for the pulse amplitude.		A CFD compares the original detector signal with an amplified and delayed version of itself. The signal derived from this comparison changes polarity exactly when a constant fraction of the detector pulse height is reached. The zero crossing point of this signal is therefore suitable to derive a timing signal independent from the amplitude of the input pulse. This is done by comparing this signal to a zero cross level. This level should be adjusted to remove events that originate from signal noise. CFDs furthermore permit to set a discriminator threshold for the pulse amplitude.

fwhm

Anonymous (anonymous@undisclosed.example.com) — 2013-08-06T14:45:49+00:00

2013/08/06 16:45		current
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	FWHM stands for Full Width at Half-Maximum: a measure for the broadness of a peak, for example, of the [[IRF]] in an [[TCSPC]] measurement or the focal width(s) in a [[FLIM]] measurement.		FWHM stands for Full Width at Half-Maximum: a measure for the broadness of a peak, for example, of the [[IRF]] in an [[TCSPC]] measurement or the focal width(s) in a [[FLIM]] measurement.

-	see also [[wp:FWHM]]	+	see also [[wp>FWHM]]

poisson_distribution

Anonymous (anonymous@undisclosed.example.com) — 2014-04-09T20:47:01+00:00

2014/04/09 22:46		current
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	$$P_{\nu}(n)={{\nu^n~e^{-\nu}}\over{n!}}$$		$$P_{\nu}(n)={{\nu^n~e^{-\nu}}\over{n!}}$$

-	The Poisson distribution is of interest especially for [[TCSPC]]: The expected number of photons in any TCSPC channel is given by the 'real' decay (including convolution with the IRF etc.), while the stochastic nature of the measurement process (either a photon is detected or it is not) introduces noise, which follows a Poisson distribution. In the limit of large ${\nu}^{}_{}$ the Poisson distribution approaches a [[Gaussian distribution]] with a width of $\sqrt{\nu}$ centred around ${\nu}^{}_{}$.	+	The Poisson distribution is of interest especially for [[TCSPC]]: The expected number of photons in any TCSPC channel is given by the 'real' decay (including convolution with the IRF etc.), while the stochastic nature of the measurement process (either a photon is detected or it is not) introduces noise, which follows a Poisson distribution. In the limit of large ${\nu}^{}_{}$ the Poisson distribution approaches a [[wp>Normal_distribution\|Gaussian distribution]] with a width of $\sqrt{\nu}$ centred around ${\nu}^{}_{}$.

	In the Gaussian limit [[least squares]] [[wp>Regression_analysis\|fitting]] may be applied, otherwise [[MLE]] [[wp>Regression_analysis\|fitting]] is preferable.		In the Gaussian limit [[least squares]] [[wp>Regression_analysis\|fitting]] may be applied, otherwise [[MLE]] [[wp>Regression_analysis\|fitting]] is preferable.