Time-Resolved Fluorescence Wiki

how_to_measure_the_instrument_response_function_irf

Anonymous (anonymous@undisclosed.example.com) — 2023-09-07T22:55:03+00:00

2023/09/08 00:54		current
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	===== Using samples with ultrafast decay =====		===== Using samples with ultrafast decay =====

-	Some detectors (particularly SPADs) have wavelength dependent timing response. In this case an IRF recorded at the excitation wavelength may not be useful for precise reconvolution. The solution is to acquire the IRF at the fluorescence wavelength, or at least spectrally closer to the fluorescence emission.	+	Some detectors (particularly MPD SPADs) have a wavelength dependent timing response. In this case an IRF recorded at the excitation wavelength may not be useful for precise reconvolution. The solution is to acquire the IRF at the fluorescence wavelength, or at least spectrally closer to the fluorescence emission wavelength.

	==== General recipe ====		==== General recipe ====

how_to_work_with_the_instrument_response_function_irf

Anonymous (anonymous@undisclosed.example.com) — 2023-02-17T12:41:49+00:00

2021/03/23 11:49		current
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-	{{tag>howto IRF tutorial analysis MT LSM_upgrade}}	+	{{tag>howto IRF tutorial analysis MicroTime LSM_upgrade}}

flim_fret_calculation_for_multi_exponential_donors

Anonymous (anonymous@undisclosed.example.com) — 2023-11-21T10:33:47+00:00

2020/05/12 14:44		current
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	~~NOTOC~~		~~NOTOC~~

-	====== FLIM FRET Calculation for Multi Exponential Donors ======	+	====== FLIM-FRET Calculation for Multi Exponential Donors ======

lifetime-fitting_using_the_flim_script

Anonymous (anonymous@undisclosed.example.com) — 2023-08-03T14:16:00+00:00

2023/02/17 13:42		current
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	Note:\\		Note:\\
-	The software offers the possibility to fit the data using a n-exponential tailfit, n-exponential reconvolution or rapid reconvolution fit. A tailfit can be used when the fitted lifetimes are significantly longer than the instrument response function. A reconvolution fit is usually preferable, because the complete decay is fitted, while for a tailfit, the start of the fitting range is usually a bit arbitrary. A rapidReconvolution fit is needed, if the count rates, with which the image was acquired are significantly above the Pile Up limit. It is also needed, if the pulse frequency is too high for the fluorescence decay to decrease to the background level before the end of the decay window (often, this is the case for 2-Photon-Excitation data acquired with a TiSa-laser with 80MHz repetition rate). Check out the rapidFLIM-analysis tutorial for this case.\\	+	The software offers the possibility to fit the data using a n-exponential tailfit, n-exponential reconvolution or rapid reconvolution fit. A tailfit can be used when the fitted lifetimes are significantly longer than the instrument response function. A reconvolution fit is usually preferable, because the complete decay is fitted, while for a tailfit, the start of the fitting range is usually a bit arbitrary. A rapidReconvolution fit is needed, if the count rates, with which the image was acquired are significantly above the Pile Up limit. It is also needed, if the pulse frequency is too high for the fluorescence decay to decrease to the background level before the end of the decay window (often, this is the case for 2-Photon-Excitation data acquired with a TiSa-laser with 80MHz repetition rate). Check out the rapidReconvolution tutorial for this case (https://www.tcspc.com/doku.php/howto:lifetime-fitting_using_the_rapid_reconvolution_algorithm).\\

	For explanations about the fitting model and the used equations, click on the "Help" button next to the selected model. This opens a help window containing the fitting equation and the explanation of the different parameters.\\		For explanations about the fitting model and the used equations, click on the "Help" button next to the selected model. This opens a help window containing the fitting equation and the explanation of the different parameters.\\

lifetime_fitting_using_the_flim_analysis

Anonymous (anonymous@undisclosed.example.com) — 2015-02-25T13:59:23+00:00

2014/06/18 14:19		current
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	~~NOTOC~~		~~NOTOC~~

-	====== Lifetime fitting Using the FLIM-analysis ======	+	====== Lifetime Fitting Using the FLIM Analysis ======

visualizing_dynamics_using_the_multiframe-flim_script

Anonymous (anonymous@undisclosed.example.com) — 2023-02-17T12:41:10+00:00

2021/10/19 21:59		current
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-	{{tag>howto FLIM multi-frame imaging analysis dynamics tutorial LSM_upgrade SPT SymPhoTime}}	+	{{tag>howto FLIM multi-frame imaging analysis dynamics tutorial LSM_upgrade SymPhoTime}}

	====== Visualizing Dynamics Using the Multi Frame FLIM Analysis (updated for SymPhoTime v2.5 and above) ======		====== Visualizing Dynamics Using the Multi Frame FLIM Analysis (updated for SymPhoTime v2.5 and above) ======

novaflim_calculated_irf

Anonymous (anonymous@undisclosed.example.com) — 2025-03-11T08:19:29+00:00

2025/02/18 14:49		current
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	====== NovaFLIM Calculated IRF ======		====== NovaFLIM Calculated IRF ======
		+	{{tag> faq software novaflim IRF}}
		+

	In the Nova Flim the IRF is parameterized as a combination of two Gaussian curves (a total of 5 fit parameters). These parameters are adjusted during Initial Fit.		In the Nova Flim the IRF is parameterized as a combination of two Gaussian curves (a total of 5 fit parameters). These parameters are adjusted during Initial Fit.

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]]))

lifetime_fitting_using_the_tcpsc_fitting_script

Anonymous (anonymous@undisclosed.example.com) — 2023-09-07T22:43:32+00:00

2023/09/08 00:37		current
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	{{ lifetime_fitting_using_the_tcpsc_fitting_script_Image_6.png?600 }}		{{ lifetime_fitting_using_the_tcpsc_fitting_script_Image_6.png?600 }}

-	Note: The software offers the possibility to fit the data using a n-exponential tailfit or a n-exponential reconvolution fit. A tailfit can be used when the fitted lifetimes are significantly longer than the instrument response function. Still a reconvolution fit is usually preferable, because the complete decay is fitted, while for a tailfit, the start of the fitting range is usually a bit arbitrary.\\	+	Note: The software offers the possibility to use a n-exponential tailfit or a n-exponential reconvolution model fit. A tailfit can be used when the expected lifetimes are significantly longer than the FWHM of instrument response function. Still a reconvolution fit is usually preferable, because the complete decay, including its rising edge is analyzed, while for a tailfit, the start of the fitting range is usually a bit arbitrary.\\
-	For explanation about the fitting model and the used equations, click on the "Help" button next to the selected model. This opens a help window containing the fitting equation and the explanation of the different parameters.	+	For explanation about the fitting model and the used equations, click on the "Help" button next to the selected model. This opens a help window containing the fitted model l equation and the explanation of the different parameters.

	* Click: "Initial Fit" (marked in orange).		* Click: "Initial Fit" (marked in orange).
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	The χ²-value approaches 1.\\		The χ²-value approaches 1.\\
	The calculated fitting values are reasonable.\\		The calculated fitting values are reasonable.\\
-	Usually the fitting model with least parameters is selected.\\	+
		+	Usually the fitting model using the smallest amount of adjustable parameters is selected.\\
	=> In this example, the fit is already sufficient.		=> In this example, the fit is already sufficient.

roi_fitting_using_the_flim_script

Anonymous (anonymous@undisclosed.example.com) — 2023-02-23T07:08:46+00:00

2020/05/13 11:42		current
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-	This tutorial shows step-by-step, how the [[glossary:flim\|FLIM]] script of [[products:SymPhoTime64\|SymPhoTime 64]] can be used to fit several regions of interest (ROIs), and how to extract and interpret the results. In detail, the FLIM script is started using a daisy pollen image from the "Samples" – workspace, then three regions of interest are defined which are finally fitted.	+	This tutorial shows step-by-step, how the [[glossary:flim\|FLIM]] script of [[products:SymPhoTime64\|SymPhoTime 64]] can be used to fit several regions of interest (ROIs), and how to extract and interpret the results. In details, the FLIM script is started using a daisy pollen image from the "Samples" – workspace, then three regions of interest are defined which are finally fitted.

	{{ youtube>g6uyvLQW4nY?large }}		{{ youtube>g6uyvLQW4nY?large }}

update

Anonymous (anonymous@undisclosed.example.com) — 2023-02-23T06:37:29+00:00

2023/02/23 07:24		current
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	===== Introduction =====		===== Introduction =====
	This tutorial shows step-by-step, how the FLIM script of SymPhoTime 64 can be used to fit several regions of interest (ROIs), and how to extract and interpret the results. In detail, the FLIM script is started using an image of mouse kidney tissue in the “Tutorials” workspace, [[https://figshare.com/s/4957fcfa684daef86c23]], a suited fitting model is chosen and a pixel-by-pixel fit is performed.\\		This tutorial shows step-by-step, how the FLIM script of SymPhoTime 64 can be used to fit several regions of interest (ROIs), and how to extract and interpret the results. In detail, the FLIM script is started using an image of mouse kidney tissue in the “Tutorials” workspace, [[https://figshare.com/s/4957fcfa684daef86c23]], a suited fitting model is chosen and a pixel-by-pixel fit is performed.\\
		+
		+
		+	===== Step-by-step Tutorial =====
		+
		+	==== Select a file and start the analysis ====
		+
		+	* Start SymPhoTime 64 software (this tutorial uses version 2.5, there might be differences when working with other versions).
		+	* Open the “Tutorials” workspace via File -> Open Workspace from the main menu.\\
		+
		+	Response:\\
		+	The files of the sample workspace are displayed in the workspace panel on the left side of the main window.
		+	* Highlight the file ''Kidney_Cells_FLIM.ptu'' by a single mouse click.
		+	* Select the "Analysis" tab and in there, open the "Imaging" drop-down menu.\\
		+	* Start the FLIM script by clicking on "Start".\\
		+
		+	{{ howto:startflim.png?200 \|}}
		+
		+
		+	Response:\\
		+	The FLIM analysis is applied to the file ''Kidney_Cells_FLIM.ptu''. Thereby, a new Window opens:
		+
		+	{{ howto:kidneyfullscreen3.png \|}}
		+
		+
		+	Note:\\
		+	The window contains five different sections:\\
		+	1: Setting panel\\
		+	Imaging analysis options can be defined in this section.\\
		+	2: [[glossary:Fast FLIM]] image\\
		+	The FLIM preview image displayed in a false color scale. The brightness encodes the intensity, while the color encodes the average "Fast FLIM" lifetime, i.e. the mean arrival times of the photons after the laser pulse. When not defined otherwise, intensity and color scale stretch from minimum to maximum. As the mean arrival time of the background photons in the areas where no fluorescence is detected, is randomly spread over the TCSPC window, the mean photon arrival time of the dark background is usually very long (with an average up to 1/2 of the TCSPC window), which makes the color scale loaded by default sometimes unsuited for displaying the lifetime contrast in the actual sample. In this case, the scale can be adapted.\\
		+	3: Fluorescence Lifetime Histogram\\
		+	Here the frequency of photon counts corresponding to the individual mean lifetimes is plotted. The settings of the plot can be adapted using the controls on the right of the plot. The histogram is photon weighted.\\
		+	4: Decay Fitting Parameters\\
		+	Here the lifetime fitting model can be selected. Fitting is then applied to the lifetime graph(s) on the lower center ([[glossary:TCSPC]] histogram).\\
		+	5: [[glossary:TCSPC]] Decay window\\
		+	By default, this set shows the [[glossary:TCSPC]] histogram of all photons in the image in green (= dataset 0) and the [[glossary:TCSPC]] histogram of a single pixel in grey (= dataset 1). In red an estimation of the instrument response function (=IRF) is shown. The IRF reconstruction is deducted from the rising edge of the [[glossary:TCSPC]] histogram.\\
		+
		+
		+	* To enhance the lifetime contrast, adapt the color scale by typing the limit values for the "Fast Lifetime [ns]" and "Events[cnts]". Additionally set the "Lifetime Histogram" range on the right hand.
		+	* Tick the checkbox of the detection "Data Channel" (i.e. detector), you want to use - in this case detector channel 4 - and press "Calculate FastFLIM".\\
		+
		+	{{ howto:detectionchannel.png?400 \|}}
		+
		+	Response:\\
		+	The FLIM Preview image will get updated. Optimize contrast by adapting "Min" and "Max" values.
		+
		+	==== Select a file and start the analysis ====
		+
		+	* In the FLIM preview image, ROIs can be selected using the context menu (Right Click).\\
		+
		+	{{ howto:selectmagicwand_w.png?300 \|}}
		+
		+	Note:\\
		+
		+	- The following ROI-selection tools are available: Rectangle ROI, Ellipse ROI for simple drawing and Paint ROI for marking the pixels the mouse passed over. The faster the mouse pointer moves, the broader the marked lines will get. Free ROI draws a free shape. The pixels within the drawn shape will be selected. Finally Magic Wand marks area with similar fast lifetime.
		+	- Using keyboard shortcuts ''<CTRL>+<Z>'' you can undo a selection. Redo also with ''<CTRL>+<Shift>+<Z>'' is possible.\\
		+	- You can add several areas to an existing ROI with the same or different selection tool by keeping the ''<Shift>'' key pressed while drawing the additional regions.\\
		+	- If you want to remove some of the pixels from the selected ROI, just keep the ''<CTRL>'' key pressed when using a ROI selection tool to exclude the unwanted parts.\\
		+	- Additionally you can zoom, move or Invert the ROI. Please see the shortcuts provided for each option in the context menu.\\
		+	- If you want to start again from scratch select "Select all as ROI".\\
		+
		+	* In this step, as an example, we mark an ROI with similar lifetime range using the "Magic Wand" tool. The sensitivity of the tool to lifetime differences can be adjusted in a box below the intensity and color scale options.\\
		+
		+	{{ howto:magicwand_w_thresh.png?300 \|}}
		+
		+	* Increase the threshold to 25.\\
		+
		+	{{ howto:inner_magicwand25_3.png \|}}
		+
		+	Response:\\
		+	The parts of the image with a similar fast lifetime range will be selected and the lifetime histogram will get updated accordingly. If you want to combine several spatially separated regions with a similar lifetime into one single ROI, as it's done here, you have to press "Shift" when selecting the spatial separated areas with the Magic wand tool.
		+
		+	Note:\\
		+	Since this function is based on the displayed image, the sensitivity of the selection is dependent on the scaling of the color-encoded component. Changing the color scale (in general the lifetime) can change the sensitivity of this tool.\\
		+
		+
		+	Response:\\
		+	An extra gray decay corresponding to ''ROI 0'' will appear under decay fit in "Decay Fitting" panel.\\
		+
		+
		+	Note:\\
		+	For fine adjustment, you can use any other ROI selection tools from context menu. In this case better to use ''<CTRL>'' or ''<Shift>'' buttons in order to remove pixel with a different or add pixels with similar fast lifetime. Ideally try to select an ROI with 10000 to 100000 counts in peak for getting the optimum statistics. ROIs with lower intensities can also be fitted, but in case of a more-exponential decay, some components might not be resolved.\\
		+
		+
		+	* In order to select an additional ROI, click "New" ROI.\\
		+
		+	{{ howto:addroi.png?400 \|}}
		+
		+
		+	Response:\\
		+	The software assigns sequential numbers to selected ROIs.The whole preview image will appear again.\\
		+
		+	* For the next ROI, first we use the same tool, "Magic Wand" but adapt its threshold to 20.
		+	{{ howto:tubul_magicwand20_3.png \|}}
		+
		+	* Repeat the last two steps in order to select the cell nuclei as the last ROI.\\
		+
		+	{{ howto:nuclei_magicwand30_3.png \|}}
		+
		+	Response:\\
		+	Now you can see fast FLIM (preview) images of "ROI 0", "ROI 1" and "ROI 2" when selecting them in the ROI-list In the Region of Interest-Menu, as well as their corresponding decays in TSCPC window in grey when selecting the different decays in the list.
		+
		+
		+	==== Perform an Initial Lifetime Fit on the Selected Regions (ROIs) ====
		+
		+
		+	* In the forth box, "Decay Fitting", from the Fitting Model drop-down list select "n-Exponential Reconvolution Fit".\\
		+
		+	{{ howto:nexpon_fitmodel.png?400 \|}}
		+
		+	Response:\\
		+	In the TCSPC window, the IRF is displayed in bright red, the data fitting limits are moved to the border of the TCSPC window.\\
		+	The new fitting parameters "Shift IRF" and "Bkgr IRF" (=background IRF) appear in the fitting parameter table.\\
		+
		+	Note:\\
		+	The software offers the possibility to fit the data using an n-exponential tailfit, n-exponential reconvolution or rapid reconvolution fit. A tailfit can be used when the fitted lifetimes are significantly longer than the instrument response function. A reconvolution fit is usually preferable, because the complete decay is fitted, while for a tailfit, the start of the fitting range is usually a bit arbitrary. A rapid reconvolution fit is suited, if the image was measured with a very high countrate and a system with a dead time significantly above the pile-up-limit or when the image has been acquired with a repetition rate, which is normally too high for the lifetime of the dye, so that the decay is not at the background level at the end of the decay window. The rapidFLIM-fitting is explained in another tutorial.\\
		+
		+	For explanation about the fitting model and the used equations, click on the "Help" button next to the selected model. This opens a help window containing the fitting equation and the explanation of the different parameters.\\
		+
		+
		+	* From "Decay" drop-down list select ''ROI 0'' and click "Initial Fit" (marked in orange).\\
		+	{{ howto:inner_monoexpo_3.png \|}}
		+
		+	Response:\\
		+	A single exponential reconvolution fit is performed. In the TCSPC window, the fit is displayed as a black line. Below, the residuals (= difference between raw data and fit values) are displayed.\\
		+	* Fit values appear in the fitting table. Check the fitting curve, residuals and χ².\\
		+
		+	Note:\\
		+	Usually, a decent fit is characterized by the following criteria:\\
		+	The fitted curve overlays well with the decay curve. In the residual window, the values spread randomly around 0.\\
		+	The χ²-value approaches 1.\\
		+	The calculated fitting values are reasonable.\\
		+	The fitting model with least parameters is preferred.\\
		+
		+
		+	* In this example it is obvious that the applied single exponential reconvolution fit is not suited to fit the decay curve. Increase the "Model Parameters" to n = 2. Again, click on "Initial fit".\\
		+
		+	{{ howto:inner_biexpo_3.png \|}}
		+
		+
		+	Response:\\
		+	The fit quality increases. But if it still doesn't look sufficient. One sees a trend in residuals and not a random distribution around 0. Increase number of "Model Parameters" to three.\\
		+
		+	{{ howto:inner_3expo_3.png \|}}
		+
		+	* Here the fitting model shows a satisfying result. A 3-exponential fitting model should be used for ROI 0.\\
		+
		+	* Try the last two steps with "ROI 1".\\
		+
		+	{{ howto:tubul_3expo_3.png \|}}
		+
		+
		+	* Find the best fit for "ROI 2" in a same manner. It is better always to start from monoexponential and try to find the fitting model with a lower number of components.\\
		+	{{ howto:nuclei_3expo_3.png \|}}
		+
		+	* Three components exponential decay seems to be suitable for all three ROIs. If all ROIs can be fitted with the same model, you can also click on "Fit All" to get all curves fitted with the same model.\\
		+	* Clicking on "Fit All" will fit all active data sets with the same model, using the start parameters of the active data set. If you do not want to fit the complete decay (dataset 1) and the decay of a single pixel (Dataset 2), press "Show All" button:
		+
		+
		+	{{ howto:showall.png \|}}
		+
		+	* Uncheck the first two datasets on top of the parameter table and press "Fit All" again.
		+
		+	{{ howto:deselectdataset1_3.png \|}}
		+
		+
		+
		+
		+	==== Compare the lifetimes and save results ====
		+
		+
		+
		+
		+	* In order to compare the lifetime of these three compartments, apart from fitting parameter table shown above, you can plot them by selecting the "Parameter Plot" on the right side of TCSPC window.\\
		+
		+	Note:\\
		+	The X-Axes is showing the "Dataset Number" corresponding to the dataset listed in Decay drop-down menu (in Dcay Fitting Panel). This means by default "Overall Decay" and "Pixel (0,0)", and then selected ROIs.\\
		+	For the Y-Axes one can select one or multiple fit parameters.\\
		+
		+	* Tick the "tau_Av_Int" checkbox for Y-Axes and zoom in to be able to see the lifetime differences better.\\
		+	{{ howto:parameterplot_3rois_3.png \|}}
		+
		+
		+
		+	* At the end, click on "Save Result" button in parameter panel.\\
		+
		+
		+	{{ howto:saveresultbutton.png?300 \|}}
		+
		+
		+	Response:\\
		+	A result file "FLIM.pqres" is stored under the raw data file ''Kidney_Cell_FLIM.ptu''.\\
		+
		+	* Later, clicking on the result file reopens the file in the same way as it was stored.

data_file_import

Anonymous (anonymous@undisclosed.example.com) — 2022-08-04T13:24:27+00:00

2022/08/04 14:53		current
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	\\		\\
	After expanding the data container:		After expanding the data container:
-	{{ :howto:et2_workspace2.png?340 \|}}	+	{{ :howto:et2_workspace2.png \|}}

	Two histograms have been imported. They are shown as "Decay" because EasyTau does not know their assignment yet.		Two histograms have been imported. They are shown as "Decay" because EasyTau does not know their assignment yet.
		+	\\
		+	\\
		+
		+
		+	==== Multiple File Import ====
		+
		+	Importing multiple data files is easy. Use CTRL + Click to select multiple files:
		+
		+	{{ :howto:et2_fileimport2.png \|}}
		+	\\
		+	\\
		+	Each input ''.phu'' file has got a dedicated ''.etc'' data container:
		+	{{ :howto:et2_workspace3.png \|}}
		+	\\
		+	\\
		+	Unlike ''Decay_Coumarin_6.phu'' containing two histograms, both ''Anthracene_EtOH.phu'' and ''IRF375.phu'' contains only one histogram. These two measurements actually belong to each other. In order to perform reconvolution fitting of the Antracene decay, the corresponding IRF measured at 375nm excitation wavelength will be needed.
		+

lifetime-fitting_using_the_rapid_reconvolution_algorithm

Anonymous (anonymous@undisclosed.example.com) — 2023-02-17T12:40:42+00:00

2021/06/12 07:05		current
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-		+	{{tag>howto tutorial FLIM analysis SymPhoTime MT LSM_upgrade reconvolution fitting}}
-	{{tag>howto tutorial FLIM analysis SPT SymPhoTime MT LSM_upgrade reconvolution fitting}}	+

reconvolution_fit

Anonymous (anonymous@undisclosed.example.com) — 2022-08-18T11:31:29+00:00

2022/08/18 13:30		current
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-	Clicking on (selecting) ''crv[0]'', the first histogram, the IRF in this particular case, updates the plot. Now, by a right-click on ''crv[0]'' opens a context sensitive dialog, where the "Curve type" can be changed from "Decay" to "IRF".	+	Clicking on (selecting) ''crv[0]'', the first histogram, the IRF in this particular case, updates the plot. Now, a right-click on ''crv[0]'' opens a context sensitive dialog, where the "Curve type" can be changed from "Decay" to "IRF".
	{{ :howto:et_fitwindow2.png \|}}		{{ :howto:et_fitwindow2.png \|}}
	\\		\\

measurement_hardware_instrumentation

Anonymous (anonymous@undisclosed.example.com) — 2018-06-25T07:18:07+00:00

2018/06/25 09:17		current
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	[[video_tutorials#Kurt Thorn: Optical Sectioning and Confocal Microscopy\|Confocal microscoy and optical sectioning by Kurt Thorn]]		[[video_tutorials#Kurt Thorn: Optical Sectioning and Confocal Microscopy\|Confocal microscoy and optical sectioning by Kurt Thorn]]

-	[[technical docs:Beampath of the Zeiss LSM880]]	+	[[Beampath of the Zeiss LSM880]]

	[[howto:check_overlap_of_different_color_confocal_volumes\|How to check the overlap of different color confocal volumes]]		[[howto:check_overlap_of_different_color_confocal_volumes\|How to check the overlap of different color confocal volumes]]

flim-fret_calculation_for_single_exponential_donors

Anonymous (anonymous@undisclosed.example.com) — 2020-05-06T09:38:57+00:00

2020/05/06 11:19		current
Line 85:		Line 85:

	Response: In the image, only pixels with higher photon counts are highlighted. Adapt the intensity maximum to see the highlighted pixels more clearly.		Response: In the image, only pixels with higher photon counts are highlighted. Adapt the intensity maximum to see the highlighted pixels more clearly.
-	{{ :howto:flim-fret-1expd_roi_from_thresh_2_v2.png?400 \|}}	+	{{ :howto:flim-fret-1expd_roi_from_thresh_2_v3.png?400 \|}}

	* In the lifetime fitting panel, keep the default Fitting model "Mono-Exp. Donor".		* In the lifetime fitting panel, keep the default Fitting model "Mono-Exp. Donor".

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.
-

applications

Anonymous (anonymous@undisclosed.example.com) — 2026-01-12T10:25:53+00:00

2023/02/23 09:12		current
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	[[howto:antibunching_measurements\|Photon antibunching measurements]]		[[howto:antibunching_measurements\|Photon antibunching measurements]]
		+
		+	[[howto:burst_duration_and_fcs_diffusion_time:burst_duration_and_fcs_diffusion_time\|Burst Duration and FCS Diffusion Time]]


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	[[howto:calculate_ratiometric_single_pair_fret_distributions\|Calculate ratiometric single pair FRET distributions]]		[[howto:calculate_ratiometric_single_pair_fret_distributions\|Calculate ratiometric single pair FRET distributions]]
		+
		+	[[howto:burst_duration_and_fcs_diffusion_time:burst_duration_and_fcs_diffusion_time\|Burst Duration and FCS Diffusion Time]]

some_origins_of_multiexponetial_decays_for_single_dyes

Anonymous (anonymous@undisclosed.example.com) — 2019-03-19T12:31:43+00:00

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.

visualizing_dynamics_with_the_multi_frame_flim_analysis

Anonymous (anonymous@undisclosed.example.com) — 2020-05-13T09:39:06+00:00

2015/11/03 15:33		current
Line 3:		Line 3:
	~~NOTOC~~		~~NOTOC~~

-	====== Visualizing Dynamics with the Multi Frame FLIM Analysis ======	+	====== Visualizing Dynamics Using the Multi Frame FLIM Analysis ======

	===== Summary =====		===== Summary =====

flim_fcs_using_olympus_fluoview_fv3000_lsm_upgrade_kit

Anonymous (anonymous@undisclosed.example.com) — 2020-05-18T14:01:42+00:00

2020/05/18 16:01		current
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-	{{tag> video FLIM cquisition howto demo Olympus FV3000 LSM_upgrade}}	+	{{tag> video FLIM acquisition howto demo Olympus FV3000 LSM_upgrade}}

lsm710

Anonymous (anonymous@undisclosed.example.com) — 2016-07-21T13:31:38+00:00

2016/07/20 14:05		current
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-	====== FLIM Measurement Using a Zeiss LSM710 with a FLIM and FCS Upgrade ======	+	====== FLIM Measurement Using a Zeiss LSM710/LSM780/LSM880 with a FLIM and FCS Upgrade ======

	This tutorial shows the recording of FLIM images using an LSM upgrade kit, in this case a Zeiss LSM710.		This tutorial shows the recording of FLIM images using an LSM upgrade kit, in this case a Zeiss LSM710.
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	* to monitor concentration changes using a reporter dye		* to monitor concentration changes using a reporter dye

-	* To monitor interactions between two molecules via FRET.	+	* To monitor interactions between two molecules via FRET. \\
		+
		+
		+	\\
		+	{{ youtube>QXGqA2IsivM?large }} \\

	The data acquisition is analogous also for upgrades on an LSM780 or LSM880, and the general principles of the data acquisition are analogous in all LSM upgrade kits.		The data acquisition is analogous also for upgrades on an LSM780 or LSM880, and the general principles of the data acquisition are analogous in all LSM upgrade kits.
		+	\\ \\
		+	\\
		+	{{ youtube>vofLPLVmq-Q?large }} \\

-	{{ youtube>QXGqA2IsivM?large }}

advantages_and_disadvantages_of_two_photon_excitation_tpe

Anonymous (anonymous@undisclosed.example.com) — 2014-01-28T13:07:58+00:00

2014/01/28 14:07		current
Line 1:		Line 1:
-	{{tag>TPE}}
	====== Advantages and disadvantages of two photon excitation (TPE) ======		====== Advantages and disadvantages of two photon excitation (TPE) ======

fluorescence_correlation_spectroscopy-_a_short_introduction

Anonymous (anonymous@undisclosed.example.com) — 2024-10-11T08:30:57+00:00

2023/02/17 13:43		current
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	{{tag>MicroTime LSM Theory SymPhoTime FCS Correlation}}		{{tag>MicroTime LSM Theory SymPhoTime FCS Correlation}}

-	~~TOC~~	+

	====== Introduction to Fluorescence Correlation Spectroscopy ======		====== Introduction to Fluorescence Correlation Spectroscopy ======

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.

flim_measurement_using_a_nikon_a1_with_a_flim_and_fcs_upgrade

Anonymous (anonymous@undisclosed.example.com) — 2015-06-30T13:07:15+00:00

2015/06/16 13:47		current
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	The general principles of the data acquisition are analogous in all LSM upgrade kits.		The general principles of the data acquisition are analogous in all LSM upgrade kits.
-	The movie was recorded in 02/2014; the recording procedure may be somewhat different in older or newer	+	The movie was recorded in 02/2014 and shows the integration with Nikon A1 system with a NIS version lower than 4.3; the recording procedure may be somewhat different in higher or very old versions.
-	models.	+

	{{ youtube>1Tr9DZ-SkSQ?large }}		{{ youtube>1Tr9DZ-SkSQ?large }}

flim-fret_measurement_using_an_olympus_fv1200_with_a_flim_and_fcs_upgrade

Anonymous (anonymous@undisclosed.example.com) — 2020-05-18T12:53:40+00:00

2015/02/25 14:54		current
Line 11:		Line 11:

	The general principles of the data acquisition are analogous in all LSM upgrade kits.		The general principles of the data acquisition are analogous in all LSM upgrade kits.
-	The movie was recorded in 02/2014; the recording procedure may be slightly different in older or newer	+	The movie was recorded in 02/2018; the recording procedure may be slightly different in older or newer
	models.		models.

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	{{topic>howto +IRF &nodate&nouser}}		{{topic>howto +IRF &nodate&nouser}}
	{{topic>howto +FLIM +FRET +analysis &nodate&nouser}}		{{topic>howto +FLIM +FRET +analysis &nodate&nouser}}
-	{{topic>howto +FLIM +Nikon}}

separation_of_2_species_with

Anonymous (anonymous@undisclosed.example.com) — 2014-06-18T12:22:45+00:00

2014/06/18 12:57		current
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	{{tag> howto tutorial FCS FLCS analysis SymPhoTime}}		{{tag> howto tutorial FCS FLCS analysis SymPhoTime}}

-	~~TOC~~	+	~~NOTOC~~

	====== Separation of 2 Species with Different Lifetimes Using FLCS ======		====== Separation of 2 Species with Different Lifetimes Using FLCS ======
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	This tutorial shows step-by-step, how the FLCS analysis can be used to calculate separate autocorrelation curves for the two components of a mixture of ATTO655 and Cy5 based on their different lifetimes.		This tutorial shows step-by-step, how the FLCS analysis can be used to calculate separate autocorrelation curves for the two components of a mixture of ATTO655 and Cy5 based on their different lifetimes.

		+	{{ youtube>xx-WzT5TgqA?large }}

	===== Background Information =====		===== Background Information =====
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	* Click on "Save result" to save this curve. Rename the generated file as "Cy5-FLCS".		* Click on "Save result" to save this curve. Rename the generated file as "Cy5-FLCS".
	* These curves can now be fitted by selecting "Transfer to fit". The process of how to fit a FCS curve is explained in the tutorial [[howto:Calculate and Fit FCS Traces with the FCS Script]].		* These curves can now be fitted by selecting "Transfer to fit". The process of how to fit a FCS curve is explained in the tutorial [[howto:Calculate and Fit FCS Traces with the FCS Script]].
-

fluofit

Anonymous (anonymous@undisclosed.example.com) — 2015-11-03T14:07:12+00:00

2015/11/03 15:07		current
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	====== FluoFit ======		====== FluoFit ======
-	The FluoFit software package is a powerful global analysis software for fluorescence decay and anisotropy measurements. Tail fitting as well as a numerical reconvolution algorithm to account for the finite Instrument Response Function ([[IRF]]) can be applied. The FluoFit software is available in two versions (Basic and Professional) with different functionalities to meet individual needs.	+	The FluoFit software package is a powerful global analysis software for fluorescence decay and anisotropy measurements. Tail fitting as well as a numerical reconvolution algorithm to account for the finite Instrument Response Function ([[glossary:IRF]]) can be applied. The FluoFit software is available in two versions (Basic and Professional) with different functionalities to meet individual needs.

	see [[https://www.picoquant.com/products/category/software/fluofit-global-fluorescence-decay-data-analysis-software]]		see [[https://www.picoquant.com/products/category/software/fluofit-global-fluorescence-decay-data-analysis-software]]

2019/03/06 13:44		current
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-	The fluorescence lifetime of a dye measured with a TCSPC spectrometer can be multiexponential due to many reasons. The most obvious cases are due to scattering or presence of impurities. Although less obvious, it is also widely known that in an inhomogeneous media a pure dye will also exhibit a multiexponential decay. Advanced users know that if the decay is not measured with polarizers at magic angle, the rotation correlation time shows up as a second exponential in the decay (the second exponential is in fact the product of the rotation correlation time by the fluorescence lifetime, divided by their sum). And they also know that measuring without polarizers is not equivalent to measure at magic angle... But suspicion may arise when even a pure dye measured at magic angle in a homogeneous media exhibits a multiexponential decay. Is the spectrometer properly adjusted? Are the polarizers properly calibrated? A typical mistake is to measure the [[glossary:IRF]] at the nominal laser wavelength instead of measuring at the ideal wavelength for that specific laser head. Note that all diode lasers heads emit at slightly different wavelengths and each of them have an optimum at which the IRF should be measured. As little as 0.5 nm displacement from their optimum may induce a "non perfect" [[glossary:deconvolution]] fit.	+	The fluorescence lifetime of a dye measured with a TCSPC spectrometer can be multiexponential due to many reasons. The most obvious cases are due to scattering or presence of impurities. Although less obvious, it is also widely known that in an inhomogeneous medium a pure dye will also exhibit a multiexponential decay. Advanced users know that if the decay is not measured with polarizers at magic angle, the rotation correlation time shows up as a second exponential in the decay (the second exponential is in fact the product of the rotation correlation time and the fluorescence lifetime, divided by their sum). And they also know that measuring without polarizers is not equivalent to measuring at magic angle... But suspicion may arise when even a pure dye measured at magic angle in a homogeneous medium exhibits a multiexponential decay. Is the spectrometer properly adjusted? Are the polarizers properly calibrated? A typical mistake is to measure the [[glossary:IRF]] at the nominal laser wavelength instead of measuring at the ideal wavelength for that specific laser head. Note that all diode lasers heads emit at slightly different wavelengths and each of them have an optimum at which the IRF should be measured. As little as 0.5 nm displacement from their optimum may induce a "non perfect" [[glossary:deconvolution]] fit.

	But it is worth noting that even at magic angle in a perfectly aligned spectrometer pure dyes in homogeneous media may exhibit a multiexponential decay. The origin may be physical, like solvent relaxation, or chemical, when the fluorescent molecule undergoes a ground or excited state reaction. In this brief article a few examples are described.		But it is worth noting that even at magic angle in a perfectly aligned spectrometer pure dyes in homogeneous media may exhibit a multiexponential decay. The origin may be physical, like solvent relaxation, or chemical, when the fluorescent molecule undergoes a ground or excited state reaction. In this brief article a few examples are described.
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-	The electronic redistribution of electrons due to optical excitation leads in many cases to a different reactivity in the ground and excited states. In other words, a fluorescent molecule which is boring under the dark may become reactive upon excitation. Common excited state reactions are redox (electron transfer) and acid-base (proton transfer) reactions. Depending on the rate of the excited-state rection relative the the original fluorescence lifetime, the observed decay time measured with a TCSPC spectrometer may be single- or multiexponential.	+	The electronic redistribution of electrons due to optical excitation leads in many cases to a different reactivity in the ground and excited states. In other words, a fluorescent molecule which is mostly inert in the dark may become reactive upon excitation. Common excited state reactions are redox (electron transfer) and acid-base (proton transfer) reactions. Depending on the rate of the excited-state reaction relative the the original fluorescence lifetime, the observed decay time measured with a TCSPC spectrometer may be single- or multiexponential.

	Let us consider the reaction in Scheme 2 in different situations:		Let us consider the reaction in Scheme 2 in different situations:
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	Scheme 2		Scheme 2

-	//Starting point: The molecule A is promoted to the excited-state where it can react with a molecule X to form the compound B, through a rate constant $k_{AB}$. Once the compound B is formed the back-reaction can occur, with a rate constant $k_{BA}$. Compounds A and B are fluorescent with original fluorescence lifetimes $\tau_A$ and $\tau_B$. Once B decays to the ground state the back-reaction takes place. Hence the system is always in its starting position $(A + X)$ prior to any excitation pulse.//	+	//Starting point: The molecule A is promoted to the excited-state where it can react with a molecule X to form the compound B, through a rate constant $k_{AB}$. Once the compound B is formed, the back-reaction can occur with a rate constant $k_{BA}$. Compounds A and B are fluorescent with original fluorescence lifetimes $\tau_A$ and $\tau_B$. Once B decays to the ground state, the back-reaction takes place. Hence the system is always in its starting position $(A + X)$ prior to any excitation pulse.//

	//Case A) The constant kAB is too slow with respect to $\tau_A$ and $\tau_B$.// In this case the compound A would decay to the ground-sate before the excited-state reaction could take place. The decay measured would be single exponential and coincident with $\tau_A$.		//Case A) The constant kAB is too slow with respect to $\tau_A$ and $\tau_B$.// In this case the compound A would decay to the ground-sate before the excited-state reaction could take place. The decay measured would be single exponential and coincident with $\tau_A$.
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	being $Z = \sqrt{(M-Y)^2 + 4 k_{AB} k_{BA}[x]}$		being $Z = \sqrt{(M-Y)^2 + 4 k_{AB} k_{BA}[x]}$

-	$A_1= A_0 [M- (1/\tau_2)] / [(1/\tau_1 – 1/\tau_2]$	+	$A_1= A_0 [M- (1/\tau_2)] / [1/\tau_1 – 1/\tau_2]$

-	$A_2= A_0 [(1/\tau_1)- M] / [(1/\tau_1 – 1/\tau_2]$	+	$A_2= A_0 [(1/\tau_1)- M] / [1/\tau_1 – 1/\tau_2]$

-	$B_1= -A_0 k_{AB}[x] / [(1/\tau_1 – 1/\tau_2]$	+	$B_1= -A_0 k_{AB}[x] / [1/\tau_1 – 1/\tau_2]$

-	$B_2= A_0 k_{AB} [x] / [(1/\tau_1 – 1/\tau_2]$	+	$B_2= A_0 k_{AB} [x] / [1/\tau_1 – 1/\tau_2]$

	being $A_0$ the concentration of $A$ at $t=0$.		being $A_0$ the concentration of $A$ at $t=0$.
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	Note from $A(t)$ that, even if $B$ would not be fluorescent, the decay of $A$ will still be biexponential!		Note from $A(t)$ that, even if $B$ would not be fluorescent, the decay of $A$ will still be biexponential!

-	A situation like this may occur with molecules dissolved in an aprotic but hygroscopic media, like acetonirile. Water molecules may diffuse (diffusion happens in the nanosecond time scale) and react with fluorophores bearing proton-transfer groups like -OH or -NH2.	+	A situation like this may occur with molecules dissolved in an aprotic but hygroscopic medium, like acetonitrile. Water molecules may diffuse (diffusion happens in the nanosecond time scale) and react with fluorophores bearing proton-transfer groups like -OH or -NH2.

	//Case D) Interconversion rate constants $k_{AB}$ and $k_{BA}$ are very quick compared to the intrinsic lifetimes $\tau_A$ and $\tau_B$.// In this case the equations of case C would still apply. But in practice, a quick equilibrium between reactants and product would be established. This means that the concentrations of A and B with respect to each other would always be constant prior to their decay, and hence the whole system could be treated as a single dye. The decay would be single exponential, being an average of $\tau_A$ and $\tau_B$ weighted by their fraction in the equilibrium.		//Case D) Interconversion rate constants $k_{AB}$ and $k_{BA}$ are very quick compared to the intrinsic lifetimes $\tau_A$ and $\tau_B$.// In this case the equations of case C would still apply. But in practice, a quick equilibrium between reactants and product would be established. This means that the concentrations of A and B with respect to each other would always be constant prior to their decay, and hence the whole system could be treated as a single dye. The decay would be single exponential, being an average of $\tau_A$ and $\tau_B$ weighted by their fraction in the equilibrium.

-	This situation may happen if compounds A and X were directly in contact prior to excitation, for example throgh ground-state interactions.	+	This situation may happen if compounds A and X were directly in contact prior to excitation, for example through ground-state interactions.
	===== 3) Solvation dynamics =====		===== 3) Solvation dynamics =====


-	Even pure fluorophores in pure solvents may lead to multiexponential decays. This is the case of molecules with strong charge transfer character in polar solvents when undergoing solvation dynamics. In such cases the fluorescence spectra shifts to longer wavelengths in time. Measuring the decay in the blue edge of the steady-state spectrum will lead to a multiexponential decay. The ns lifetimes corresponds to the intrinsic fluorescence lifetime of the fluorophore, whereas the ultrafast components (ps) are related to the rate of the shift. Measuring in the red-flank of the steady-sate spectrum leads to multiexponential decays with positive (intrinsic lifetime, ns) an negative (rate of shift, ps) pre-exponential factors. This is depicted in Scheme 3.	+	Even pure fluorophores in pure solvents may lead to multiexponential decays. This is the case of molecules with strong charge transfer character in polar solvents when undergoing solvation dynamics. In such cases the fluorescence spectrum shifts to longer wavelengths on a picosecond time-scale. Measuring the decay in the blue edge of the steady-state spectrum will lead to a multiexponential decay. The ns lifetime corresponds to the intrinsic fluorescence lifetime of the fluorophore, whereas the ultrafast components (ps) are related to the rate of the shift. Measuring in the red-flank of the steady-sate spectrum leads to multiexponential decays with positive (intrinsic lifetime, ns) and negative (rate of shift, ps) pre-exponential factors. This is depicted in Scheme 3.


	{{:solvation_dynamics.png?800\|}}		{{:solvation_dynamics.png?800\|}}

-	Scheme 3. Left: energetic representation of solvation dynamics. The fluorophore is represented as a sphere with a pointing dipole. Solvent molecules are represented in gray around the fluorophore. Right up : Spectral consequence of solvation dynamics. The fluorescence spectrum shifts in time to lower energies. Right bottom: Decay traces measured in different spectral regions. Blue flanks are multiexponential with positive pre-exponentila factors, red flanks are multiexponential with rising components.	+	Scheme 3. Left : energetic representation of solvation dynamics. The fluorophore is represented as a sphere with a pointing dipole. Solvent molecules are represented in gray around the fluorophore. Right, top : Spectral consequence of solvation dynamics. The fluorescence spectrum shifts in time to lower energies. Right, bottom: Decay traces measured in different spectral regions. Blue curves are multiexponential with positive pre-exponentila factors, red curves are multiexponential with rising components.

-	Before the excitation, the fluorophore is in the ground state S0 , which has a characteristic dipole moment. Solvent molecules, which also have their characteristic dipole moment are oriented in such a way that the interactions dipole-dipole with the fluorophore are as favorable possible. When the fluorophore is prompted to the excited state, its electronic distribution switches almost instantly. At time zero after excitation the solvent molecules remain in their "original" orientation to solvate ground state . The resulting dipole -dipole interactions with the fluorophore are hence less favorable. As a result , the solvent begins to relax to solvate the S1 state and brings the system to a more favorable position. Spectroscopically, this is manifested by the time-shift of the emission spectrum to longer wavelengths. Consider that the Steady-State spectrum is the time integral of all those shifting spectra. Measuring in the blue flank (λ1) will lead to a multiexponential decay: the signal decreases because of the shift and the intrinsic decay. Measuring in the red flank (λ3) will lead to a multiexponential decay with a negative pre-exponential factor: the signal first rises due to the increase in signal due to the displacement, and then decays due to the fluorescence lifetime.	+	Before the excitation, the fluorophore is in the ground state S0 , which has a characteristic dipole moment. Solvent molecules, which also have their characteristic dipole moment are oriented in such a way that the dipole-dipole interactions with the fluorophore are as favorable as possible. When the fluorophore is prompted to the excited state, its electronic distribution switches almost instantly. At time zero after excitation the solvent molecules remain in their "original" orientation. The resulting dipole -dipole interactions with the fluorophore are hence less favorable. As a result, the solvent begins to relax to solvate the S1 state and brings the system to a more favorable position. Spectroscopically, this is manifested by the time-shift of the emission spectrum to longer wavelengths. Consider that the Steady-State spectrum is the time integral of all those shifting spectra. Measuring in the blue flank (λ1) will lead to a multiexponential decay: the signal decreases because of the shift and the intrinsic decay. Measuring in the red flank (λ3) will lead to a multiexponential decay with a negative pre-exponential factor: the signal first rises due to the increase in signal due to the displacement, and then decays due to the fluorescence lifetime.

	In fluid media, solvation dynamics can be described with a multiexponential function spanning from the femtosecond time-scale to tens of picoseconds. Hence, the tail of this process can be monitored with a TCSPC spectrometer equipped with fast detectors such as a [[glossary:MCP]] or a Hybrid-PMT. In viscous media or at low temperatures, the ps tail component slows down to ns, and the process can be monitored with slower detectors, such as standard [[glossary:PMT]].		In fluid media, solvation dynamics can be described with a multiexponential function spanning from the femtosecond time-scale to tens of picoseconds. Hence, the tail of this process can be monitored with a TCSPC spectrometer equipped with fast detectors such as a [[glossary:MCP]] or a Hybrid-PMT. In viscous media or at low temperatures, the ps tail component slows down to ns, and the process can be monitored with slower detectors, such as standard [[glossary:PMT]].