Time-Resolved Fluorescence Wiki

measuring_quantum_yield

Anonymous (anonymous@undisclosed.example.com) — 2017-07-12T13:16:44+00:00

2015/02/25 13:52		current
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	====== Measuring the Quantum Yield with the Integrating Sphere Assembly for the FluoTime 300 ======		====== Measuring the Quantum Yield with the Integrating Sphere Assembly for the FluoTime 300 ======

-	Note: The integrating Sphere is made from Spectralon™. While this material provides excellent spectral reflectivity and spectral flatness it is also very sensitive to contamination and due to the porous nature of its surface collects impurities easily. Any impurities will change the reflectiveness of the integrating sphere and thus might influence the measurements.	+	Note: The integrating Sphere is made from Spectralon™. While this material provides excellent spectral reflectivity and spectral flatness it is also very sensitive to contamination. Due to the porous nature of its surface, it collects impurities easily. Any impurity will change the reflectivity of the inner walls of the integrating sphere and thus will influence the measurements.
-	Therefore, handle the integrating sphere carefully avoiding any exposure to dust or other impurities. Avoid spilling sample into the sphere or the sample holder.	+	Therefore, handle the integrating sphere carefully avoiding any exposure to dust or other impurities. Avoid spilling sample into the sphere or contamination of the sample holder.

	{{ youtube>JLiDnlS5BS8?large }}		{{ youtube>JLiDnlS5BS8?large }}

-	===== Setp-by-Step =====	+	===== Step-by-Step =====
-	* Insert the integrating sphere with caution in order not to hit any optical elements in the FluoTime 300. The integrating sphere assembly has an indexed lid to ensure proper orientation.	+	* Mount the integrating sphere carefully. Make sure you do not hit any optical elements inside the FluoTime 300. The integrating sphere assembly has an indexed lid to ensure proper orientation.

	{{ :howto:2013-12-19_at_14-30-03.jpg?600 \|}}		{{ :howto:2013-12-19_at_14-30-03.jpg?600 \|}}

novaflim_calculated_irf

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

2025/02/18 13:31		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.
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	* Height of Gaussian curve 2 (limited to the height of Gaussian curve 1)		* Height of Gaussian curve 2 (limited to the height of Gaussian curve 1)

-	This model is the result of extensive internal development, testing, and refinement. By optimizing these parameters, the IRF model can accurately represent the measured response of the system.	+	The IRF is determined only during the initial TCSPC fit, which means it may vary depending on the different exponential components. During the pixelwise fitting in FLIM, this IRF is applied without any modifications. Consequently, all image points are fitted using the same fixed IRF established during the initial fit.
		+
		+	This model is the result of extensive internal development, testing, and refinement. By optimizing these parameters, the IRF model can accurately represent the measured response of the system.

some_origins_of_multiexponetial_decays_for_single_dyes

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

fluorescence_correlation_spectroscopy-_a_short_introduction

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

2023/02/17 12:39		current
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-	{{tag>MT200 MircoTime LSM Theory SymPhoTime FCS Correlation}}	+	{{tag>MicroTime LSM Theory SymPhoTime FCS Correlation}}

-	~~TOC~~

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

2ffcs

Anonymous (anonymous@undisclosed.example.com) — 2015-11-04T09:41:00+00:00

2013/12/03 11:42		current
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-	====== 2FFCS ======	+	{{tag> 2fFCS FCS}}
		+	~~TOC~~
		+	====== 2fFCS ======


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	Correlation analysis that is applied to the fluctuations of the fluorescence intensity. The cross-correlation between the occurrence of events in two different detection volumes is used to introduce an absolute diffusion length into the analysis.		Correlation analysis that is applied to the fluctuations of the fluorescence intensity. The cross-correlation between the occurrence of events in two different detection volumes is used to introduce an absolute diffusion length into the analysis.
		+
		+	see [[glossary:FCS]] for a introduction on FCS.

	===== Experimental Setup =====		===== Experimental Setup =====
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	Occasionally, pinhole size can be used to adjust amount of photons to change the signal intensity and increase SNR. In addition to the "optimal" 1 AU, Pinhole 1-3 AU is the range of choice. Bigger pinhole give you stronger signal but with the compromised confocal effects.		Occasionally, pinhole size can be used to adjust amount of photons to change the signal intensity and increase SNR. In addition to the "optimal" 1 AU, Pinhole 1-3 AU is the range of choice. Bigger pinhole give you stronger signal but with the compromised confocal effects.

-	PQ usually uses a 50 micron pinhole (1.4 AU) to get maximum detection efficiency, somewhat sacrificing background rejection.	+	PicoQuant usually uses a 50 micron pinhole (1.4 AU) to get maximum detection efficiency, somewhat sacrificing background rejection.

	=== Two Foci ===		=== Two Foci ===

align_beam_backreflection

Anonymous (anonymous@undisclosed.example.com) — 2022-08-29T11:17:12+00:00

2022/08/29 11:02		current
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	This is indeed normal, it is the result of using polarized light and interplay of various interference and diffraction effects.		This is indeed normal, it is the result of using polarized light and interplay of various interference and diffraction effects.

-	Perfect alignment is reached when the lobes are more or less symmetric, that means they have roughly the same intensity in each quadrant. To reach this, you have to precisely position the beam to enter at the center of the objective entrance pupil, and the beam must be of course aligned with the optical axis of the objective. (Note that parallel beam displacement, not tilting, is necessary.)	+	Perfect alignment is reached when the lobes are more or less symmetric, that means they have roughly the same intensity in each quadrant. To reach this, you have to precisely position the beam to enter at the center of the objective entrance pupil, and the beam must be of course aligned with the optical axis of the objective. (Note that parallel beam displacement, not just tilting, is necessary to achieve that.)

	{{:howto:backreflection_defocused1.mp4\|}}		{{:howto:backreflection_defocused1.mp4\|}}
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	Adding a drop of water on top of the coverslip reduces the back-scattering intensity by an order of magnitude or so, but the basic shape remains the same. Even if one removes everything extra from the beam path, these fringes remain there, they are universal. Note that all those images above are slightly defocused.		Adding a drop of water on top of the coverslip reduces the back-scattering intensity by an order of magnitude or so, but the basic shape remains the same. Even if one removes everything extra from the beam path, these fringes remain there, they are universal. Note that all those images above are slightly defocused.

-	Such images are used for the daily and fundamental alignment of the MicroTime 200. The detailed procedure is described in the user manual of MicroTime 200. Although the MicroTime is extremely robust we suggest to spend 5-10 minutes every day for verifying the quality of the alignment by inspecting the back-reflection pattern. Have a look how this is used also by watching the tutorial [[howto:exchange_dichroic_mt200\|How to exchange the main dichroic of the MicroTime 200.]]	+	Such images are used for daily and fundamental alignment of the MicroTime 200. A detailed procedure is described in the user manual of MicroTime 200. Although MicroTime is extremely robust, we suggest to spend 5-10 minutes every day for verifying the quality of the alignment by inspecting the back-reflection pattern. Have a look how this is used also by watching the tutorial [[howto:exchange_dichroic_mt200\|How to exchange the main dichroic of the MicroTime 200.]]

-	The classic paper by E. Wolf "Electromagnetic Diffraction in Optical Systems. II." shows some 4 lobed patterns for polarized light. http://rspa.royalsocietypublishing.org/content/253/1274/358	+	The paper by [[ http://rspa.royalsocietypublishing.org/content/253/1274/358\|B. Richards and E. Wolf: Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system]] shows such 4 lobed patterns for polarized light.
-	These figures are also reproduced in his text book if you have access to that instead. https://books.google.nl/books/about/Principles_of_Optics.html?id=aoX0gYLuENoC&hl=nl	+

		+	Similar figures can be found in this [[https://books.google.cz/books?id=kURdAAAAQBAJ\|classic textbook]].

diamond_nv_centers

Anonymous (anonymous@undisclosed.example.com) — 2018-04-19T12:11:55+00:00

2015/02/25 14:00		current

how_to_measure_the_instrument_response_function_irf

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

2023/09/07 22:49		current
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-	=== Low count rate during IRF measurements is important ===	+	==== Low count rate during IRF measurements is important! ====

-	Note: Make sure that the detection count rate is much lower than the count rate used for fluorescence decay measurement.Diluting the scattering solution is better than using grey filters. Ideal is when the decay and the IRF are recorded at the same [[glossary:differential count rate]] (and NOT at the same average count rates).	+	Make sure that the detection count rate is much lower than the count rate during a fluorescence decay measurement. Diluting the scattering solution is better than using grey (ND) filters. Ideal is when the decay and the IRF are recorded at the same [[glossary:differential count rate]] (and NOT at the same average count rate).

-	If the IRF should be measured on a microscope system with SPAD detectors, in the UV range also the Raman-scattering of water can be used. E.g. the Raman scattering can be recorded with a HQ480/40 bandpass filter, if a 405nm diode is used. This method is less suited for long wavelengths, as the Raman efficiency decreases. The water must be very pure in order not to capture any fluorescence.	+	If the IRF should be measured in the UV range on a microscope system with SPAD detectors, the Raman scattering of water can be used, too. E.g. the Raman scattering can be recorded with a HQ480/40 bandpass filter, if a 405nm laser diode is used. This method is less suited for long wavelengths, as the Raman scattering decreases. In order to avoid signal contamination by any fluorescence, the water must be very pure.


	===== 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

2020/10/22 08:43		current
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-	{{tag>howto IRF tutorial analysis MT LSM_upgrade}}	+	{{tag>howto IRF tutorial analysis MicroTime LSM_upgrade}}


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-	1. First the measured IRF needs to be made accessible for being used in the analysis. Therefore, highlight the file with the measured IRF (single mouse click on the .ptu-file)\\	+	1. First the measured IRF needs to be made accessible for being used in the analysis. Therefore, highlight the file with the measured IRF (single mouse click on the .ptu-file)\\ An example measured IRF can be found in Tutorials workspace [[https://figshare.com/s/4957fcfa684daef86c23]].\\
	2. In Analysis tab, under TCSPC, find `TCSPC Decay`. Click Start;		2. In Analysis tab, under TCSPC, find `TCSPC Decay`. Click Start;

intensity_time_trace_analysis

Anonymous (anonymous@undisclosed.example.com) — 2014-06-19T08:12:32+00:00

2014/05/07 16:14		current
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	{{tag> tutorial howto time-trace analysis SymPhoTime}}		{{tag> tutorial howto time-trace analysis SymPhoTime}}

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

	======Intensity Time Trace Analysis======		======Intensity Time Trace Analysis======
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	This tutorial shows step-by-step, how to draw intensity time traces from a single molecule. The script requires a point measurement of an immobilized fluorophore. When applied to images, it can be used to check for line and frame marker presence and assignment.		This tutorial shows step-by-step, how to draw intensity time traces from a single molecule. The script requires a point measurement of an immobilized fluorophore. When applied to images, it can be used to check for line and frame marker presence and assignment.
		+
		+	{{ youtube>D4BBTLBvanQ?large }}
		+

	\\		\\

select_the_correct_pinhole_size

Anonymous (anonymous@undisclosed.example.com) — 2015-09-11T15:24:14+00:00

2015/09/11 15:20		current
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	====== How-to select the correct pinhole size ======		====== How-to select the correct pinhole size ======

-	The pinhole size should be slightly bigger than the image of the Airy disc at the position of the pinhole:	+	The pinhole size should be slightly bigger than the image of the [[wp>Airy Disc]] at the position of the pinhole:

	$$d_{Airy} = (1.22 * lambda / N.A.) * M$$		$$d_{Airy} = (1.22 * lambda / N.A.) * M$$

using_the_antibunching_script

Anonymous (anonymous@undisclosed.example.com) — 2014-06-19T07:40:32+00:00

2014/05/23 07:39		current
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	{{tag> antibunching howto tutorial correlation analysis SymPhoTime}}		{{tag> antibunching howto tutorial correlation analysis SymPhoTime}}
-	~~TOC~~	+	~~NOTOC~~

-	====== Using the Antibunching Analysis ======	+	====== Antibunching Analysis ======


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	This tutorial shows step-by-step, how to calculate an antibunching curve from a fluorescence time trace of a single emitter, in this example a nanodiamond NV center, excited with a pulsed 530 nm laser.		This tutorial shows step-by-step, how to calculate an antibunching curve from a fluorescence time trace of a single emitter, in this example a nanodiamond NV center, excited with a pulsed 530 nm laser.
		+
		+	{{ youtube>bEyhuWnmFC4?large }}

	===== Background Information =====		===== Background Information =====
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	* Here it is impossible to determine the number of emitters. In this measurement the luminescence stems from several emitters.		* Here it is impossible to determine the number of emitters. In this measurement the luminescence stems from several emitters.
-

symphotime64

Anonymous (anonymous@undisclosed.example.com) — 2015-01-22T14:39:59+00:00

2014/05/23 07:33		current
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-	The [[http://www.picoquant.com\|PicoQuant]] SymPhoTime 64 software package is an integrated solution for data acquisition and analysis using PicoQuant's time-resolved confocal microscope MicroTime 200, LSM upgrade kits or [[glossary:TCSPC]] electronics. Its clearly structured layout and powerful analysis routines allows the user to focus on the results rather than on the data processing. The software is designed for a 64 bit operation system and features a graphical user interface (GUI), which guides the user through all necessary steps for an individual analysis or measurement process. Data dependencies are directly visible in the underlying workspace concept. An integrated scripting language ("STUPSLANG") even puts the user in a position to freely add new analysis procedures or customize existing ones.	+	The [[http://www.picoquant.com\|PicoQuant]] SymPhoTime 64 software package is an integrated solution for data acquisition and analysis using PicoQuant's time-resolved confocal microscope [[products:MicroTime]], LSM upgrade kits or [[glossary:TCSPC]] electronics. Its clearly structured layout and powerful analysis routines allows the user to focus on the results rather than on the data processing. The software is designed for a 64 bit operation system and features a graphical user interface (GUI), which guides the user through all necessary steps for an individual analysis or measurement process. Data dependencies are directly visible in the underlying workspace concept. An integrated scripting language ("STUPSLANG") even puts the user in a position to freely add new analysis procedures or customize existing ones.

	For more information, latest version and download link see [[http://www.picoquant.com/products/category/software/symphotime-64-fluorescence-lifetime-imaging-and-correlation-software\|SymPhoTime64]].		For more information, latest version and download link see [[http://www.picoquant.com/products/category/software/symphotime-64-fluorescence-lifetime-imaging-and-correlation-software\|SymPhoTime64]].

burst_duration_and_fcs_diffusion_time

Anonymous (anonymous@undisclosed.example.com) — 2026-01-12T14:58:02+00:00

2026/01/12 10:06		current
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	~~NOTOC~~		~~NOTOC~~

-	====== Burst Duration and FCS Diffusion Time ======	+	====== Burst duration and FCS diffusion time ======
		+	Diffusion, flow, burst selection, and photobleaching in confocal single-molecule fluorescence

-	===== Overview =====	+	===== 1. Introduction =====

-	In single-molecule fluorescence experiments, two closely related time scales are commonly discussed:	+	In confocal single-molecule fluorescence experiments, molecular transport through the detection volume is commonly characterized using two different observables: the diffusion time extracted from fluorescence correlation spectroscopy (FCS) and the burst duration obtained from single-molecule detection (SMD) or burst analysis. Both quantities probe molecular motion through the same optical volume, yet they originate from fundamentally different experimental procedures and statistical definitions.

-	* the burst duration obtained from single-molecule burst analysis	+	The apparent similarity of their numerical values often suggests a direct equivalence. However, this impression can be misleading, because each observable responds differently to transport mechanisms, detection geometry, selection criteria, and photophysical processes. As a consequence, diffusion time and burst duration must be treated as distinct quantities whose relationship depends on the underlying physical assumptions and on how the experiment is performed.
-	* the diffusion time extracted from fluorescence correlation spectroscopy (FCS)	+

-	Although both quantities probe molecular transport through the same confocal detection volume and often have comparable numerical values, they differ fundamentally in their physical meaning, statistical definition, and sensitivity to experimental parameters.	+	In this article, we develop a unified theoretical framework to analyze the diffusion time and burst duration within a three-dimensional Gaussian detection model. We first derive both quantities independently using their full mathematical formalism. We then compare the two observables and establish their relationship under ideal diffusion conditions. Finally, we investigate how burst-selection procedures, directed flow, and photobleaching modify each observable and how these effects alter their mutual relation.

-	This article summarizes their relationship within the framework of a three-dimensional Gaussian detection model, explains the origin of the frequently cited relation between the two time scales, and discusses the influence of burst-selection thresholds and directed flow.	+	===== 2. Three-dimensional Gaussian detection model =====
-		+
-	===== Three-dimensional Gaussian detection model =====	+

	Both FCS and burst-based single-molecule experiments rely on a confocal detection volume that is well approximated by a three-dimensional Gaussian molecular detection function (MDF):		Both FCS and burst-based single-molecule experiments rely on a confocal detection volume that is well approximated by a three-dimensional Gaussian molecular detection function (MDF):

	$$		$$
-	\mathrm{MDF}(x,y,z) \propto	+	W(\mathbf r)
-	\exp\left(-2\frac{x^2+y^2}{w_0^2}\right)	+	=
-	\exp\left(-2\frac{z^2}{z_0^2}\right)	+
		+	\exp\left(
		+	-\frac{2(x^2+y^2)}{w_0^2}
		+	-\frac{2z^2}{z_0^2}
		+	\right)
	$$		$$

-	Here, $w_0$ and $z_0$ denote the lateral and axial $1/e^2$ radii of the detection volume.	+	where $w_0$ and $z_0$ denote the lateral and axial $1/e^2$ radii of the detection volume.

-	This model forms the basis of classical FCS theory and has been validated extensively in both theoretical and experimental studies.	+	This Gaussian MDF constitutes the standard model underlying classical FCS theory and most analytical treatments of single-molecule residence times. It provides a consistent geometric framework for comparing correlation-based and trajectory-based observables.

-	===== Diffusion and transit-time distributions =====	+	===== 3. Diffusive transport and transit-time distributions =====

-	For freely diffusing molecules, transport is governed by the three-dimensional diffusion propagator:	+	For freely diffusing molecules, transport is governed by the three-dimensional diffusion propagator

	$$		$$
-	P(\mathbf{r},t) = (4\pi D t)^{-3/2}	+	G(\mathbf r,t \mid \mathbf r_0,0)
-	\exp\left(-\frac{\|\mathbf{r}\|^2}{4Dt}\right)	+	=
		+	\frac{1}{(4\pi Dt)^{3/2}}
		+	\exp\left(
		+	-\frac{\|\mathbf r-\mathbf r_0\|^2}{4Dt}
		+	\right)
	$$		$$

-	A crucial point is that the transit time through the confocal volume is not a single well-defined quantity, but a random variable with a broad distribution.	+	where $D$ is the diffusion coefficient.

-	This distribution depends on the diffusion coefficient $D$, the molecular entry position, and the spatial weighting imposed by the MDF.	+	A crucial point is that the time a molecule spends in the detection volume is not a single well-defined quantity but a stochastic variable with a broad distribution. This distribution depends on the diffusion coefficient, the entry position of the molecule, and the spatial weighting imposed by the MDF. Any experimentally extracted time scale therefore corresponds to a specific statistical functional of this distribution rather than to a unique physical residence time.

-	===== FCS diffusion time $t_D$ =====	+	===== 4. FCS diffusion time $t_D$ =====

-	==== Definition ====	+	==== 4.1 Definition ====

-	In FCS, the fluorescence intensity autocorrelation function for pure diffusion can be written as:	+	In FCS, the normalized fluorescence intensity autocorrelation function is defined as

	$$		$$
-	G(\tau) =	+	G(\tau)
		+	=
		+
		+	\frac{\langle \delta I(t)\,\delta I(t+\tau)\rangle}{\langle I\rangle^2}
		+	$$
		+
		+	For pure diffusion, this can be expressed as
		+
		+	$$
		+	G(\tau)
		+	\propto
		+	\int d^3r \int d^3r_0\,
		+	W(\mathbf r)\,W(\mathbf r_0)\,
		+	G(\mathbf r,\tau \mid \mathbf r_0,0)
		+	$$
		+
		+	For a three-dimensional Gaussian MDF, this integral yields
		+
		+	$$
		+	G(\tau)
		+	=
	\frac{1}{N}		\frac{1}{N}
-	\frac{1}{(1+\tau/t_D)\sqrt{1+\tau/(S^2 t_D)}}	+	\frac{1}{(1+\tau/t_D)\sqrt{1+\tau/(\kappa^2 t_D)}}
	$$		$$

-	where $S = z_0 / w_0$.	+	with

-	==== Physical meaning ====	+	$$
		+	t_D = \frac{w_0^2}{4D},\qquad
		+	\kappa = \frac{z_0}{w_0}
		+	$$

-	The diffusion time $t_D$ is not the mean residence time of an individual molecule.	+	==== 4.2 Physical interpretation ====

-	Instead, it is a correlation-derived time scale determined by the spatial extent of the detection function. Formally, it can be related to the second spatial moment of the MDF.	+	The diffusion time $t_D$ is not the mean residence time of an individual molecule. Instead, it is a correlation-derived geometry time scale governed by the quadratic spatial weighting of the MDF in the autocorrelation function.

-	Thus, $t_D$ reflects ensemble-averaged transport properties rather than individual molecular trajectories.	+	Formally,

-	===== Burst duration $t_B$ =====	+	$$
		+	t_D
		+	\approx
		+	\frac{\langle r^2\rangle_{W^2}}{6D},\qquad
		+	\langle r^2\rangle_{W^2}
		+	=

-	==== Definition ====	+	\frac{\int r^2 W(\mathbf r)^2\,d^3r}
		+	{\int W(\mathbf r)^2\,d^3r}
		+	$$

-	In burst analysis, individual molecular events are identified by applying an intensity threshold.	+	For a Gaussian MDF, the lateral contribution evaluates to

-	A burst is defined as the time interval during which the detected signal remains above this threshold.	+	$$
		+	\langle r^2\rangle_{W^2} = \frac{3}{4}w_0^2
		+	$$

-	As a consequence, bursts begin and end on iso-intensity surfaces of the MDF rather than at the geometric boundary of the confocal detection volume.	+	which directly leads to the expression $t_D = w_0^2/(4D)$.

-	For a Gaussian detection function, this surface is an ellipsoid whose effective radius depends on the chosen threshold.	+	===== 5. Burst duration $t_B$ =====

-	==== Statistical meaning ====	+	==== 5.1 Definition ====

-	The mean burst duration is defined as:	+	In burst analysis, individual molecular events are identified by applying an intensity threshold $W_{th}$. A burst is defined as

	$$		$$
-	\langle t_B \rangle = \int_0^\infty t\,p_B(t)\,dt	+	t_B = t_{exit} - t_{entry},\qquad
		+	W[\mathbf r(t)] > W_{th}
	$$		$$

-	Because short, peripheral trajectories often remain below threshold, the burst-time distribution differs from the full transit-time distribution.	+	Bursts therefore begin and end on iso-intensity surfaces of the MDF rather than at a geometric boundary of the confocal volume.

-	Burst analysis therefore yields a threshold-selected first moment of molecular residence times.	+	For a Gaussian detection function, the effective threshold radius scales as

-	===== Relation between diffusion time and burst duration =====	+	$$
		+	r_{th}
		+	\propto
		+	w_0\sqrt{\ln(1/W_{th})}
		+	$$

-	For a three-dimensional Gaussian detection volume, pure diffusion, and moderate threshold conditions, analytical treatments show:	+	==== 5.2 Statistical interpretation ====
		+
		+	The mean burst duration is

	$$		$$
-	\langle t_B \rangle \approx \frac{4}{3}\,t_D	+	\langle t_B\rangle
		+	=
		+
		+	\int_0^\infty t\,p_{burst}(t)\,dt
	$$		$$

-	===== Origin of the factor 4/3 =====	+	where $p_{burst}(t)$ denotes the threshold-conditioned residence-time distribution.
		+
		+	Burst analysis measures a first moment of residence times with linear spatial weighting, modified by explicit event selection. Short, peripheral trajectories often do not exceed the detection threshold and therefore do not contribute to the measured distribution.

-	The appearance of this constant factor reflects the fundamentally different nature of the two observables:	+	==== 5.3 Burst selection procedure ====

-	* the FCS diffusion time is obtained from an autocorrelation function and therefore involves a quadratic weighting of the MDF	+	In practice, burst detection is a multi-step selection process.
-	* the mean burst duration corresponds to a linearly weighted residence time conditioned on being above a detection threshold	+

-	For a Gaussian detection profile, this mismatch in statistical weighting leads, under ideal conditions, to the universal ratio:	+	Intensity thresholding.
		+	Photon arrival times are binned into short intervals $\Delta t$ or processed using a sliding window. A burst is initiated when the photon count rate exceeds a predefined threshold

	$$		$$
-	\frac{\langle t_B \rangle}{t_D} = \frac{4}{3}	+	R(t)=\frac{N_\gamma(t,\Delta t)}{\Delta t}>R_{th}
	$$		$$

-	This interpretation is consistent with theoretical treatments of single-molecule photon trajectories and residence-time statistics and with early analyses of diffusion in confocal volumes.	+	which is equivalent, up to proportionality factors, to $W[\mathbf r(t)]>W_{th}$.

-	===== Influence of burst-selection thresholds =====	+	Temporal continuity and photon-number criteria.
		+	To suppress spurious threshold crossings due to shot noise, bursts are often required to satisfy

-	In experimental practice, the ratio $\langle t_B \rangle / t_D$ is not universal.	+	$$
		+	t_B \ge t_{min},\qquad
		+	N_\gamma \ge N_{\gamma,min}
		+	$$

-	Increasing the burst-selection threshold preferentially selects long, central trajectories, thereby increasing the mean burst duration relative to the FCS diffusion time.	+	Selection functional.
		+	The burst-selection procedure can be written formally as

-	Conversely, photophysical effects such as blinking or inappropriate binning can shorten apparent burst durations without significantly affecting the FCS diffusion time, provided these effects are properly modeled in the correlation analysis.	+	$$
		+	\mathcal S[\mathbf r(t)]
		+	=
		+	\Theta(W[\mathbf r(t)]-W_{th})\,
		+	\Theta(t_B-t_{min})\,
		+	\Theta(N_\gamma-N_{\gamma,min})
		+	$$

-	===== Flow effects: decoupling of burst duration and FCS diffusion time =====	+	leading to an observed distribution

-	==== Physical background ====	+	$$
		+	p_{burst}(t)
		+	\propto
		+	\left\langle
		+	\delta(t-t_B)\,
		+	\mathcal S[\mathbf r(t)]
		+	\right\rangle
		+	$$

-	In the presence of flow, molecular transport through the confocal detection volume is no longer governed by diffusion alone.	+	==== 5.4 Consequences of burst selection ====

-	Directed motion introduces an additional transport mechanism that modifies single-molecule trajectories.	+	Burst selection introduces intrinsic and controllable biases. The mean burst duration depends explicitly on the chosen thresholds, increasing thresholds bias toward central trajectories and increase $\langle t_B\rangle$, and bursts are defined by iso-intensity surfaces rather than geometric boundaries. Burst statistics are also sensitive to photophysical processes such as blinking and photobleaching.

-	==== Effect on burst duration ====	+	===== 6. Comparison of diffusion time and burst duration =====

-	Burst analysis directly reflects single-molecule residence times.	+	Although both observables probe molecular motion through the same confocal detection volume, their statistical definitions differ fundamentally. The FCS diffusion time $t_D$ is determined by quadratic spatial weighting of the MDF and reflects the decay of concentration correlations. In contrast, the mean burst duration $\langle t_B\rangle$ is governed by linear spatial weighting combined with explicit selection rules.

-	Directed flow shortens these residence times by accelerating molecular passage through the detection volume.	+	Because of burst-selection thresholds, $\langle t_B\rangle$ can be smaller than, comparable to, or larger than $t_D$. There is no universal ordering between the two quantities, whereas $t_D$ is largely insensitive to burst-selection parameters.

-	Consequently, burst duration distributions shift toward shorter times even when the diffusion coefficient and optical geometry remain unchanged.	+	===== 7. Mathematical comparison and conditions for a fixed ratio =====

-	==== Effect on FCS diffusion time ====	+	Under the assumptions of pure diffusion, Gaussian detection geometry, moderate burst-selection thresholds, and negligible photophysical interruptions, a closed analytical relation can be derived.

-	In contrast, the FCS diffusion time remains essentially constant under moderate flow, as it is primarily determined by the optical geometry and diffusion coefficient.	+	For a Gaussian MDF,

-	==== Relation to the 4/3 factor under flow ====	+	$$
		+	\langle r^2\rangle_{W^2} = \frac{3}{4}w_0^2,\qquad
		+	\langle r^2\rangle_W = w_0^2
		+	$$

-	The relation above is derived under the assumption of pure diffusion.	+	Using $\langle r^2\rangle \approx 6Dt$,

-	The presence of flow violates these assumptions by introducing directed transport.	+	$$
		+	t_D = \frac{w_0^2}{4D},\qquad
		+	\langle t_B\rangle = \frac{w_0^2}{3D}
		+	$$

-	Deviations from the 4/3 ratio under flow conditions therefore reflect the fundamentally different sensitivity of burst-based and correlation-based observables rather than a breakdown of the Gaussian detection model.	+	Thus,

-	===== Summary =====	+	$$
		+	\frac{\langle t_B\rangle}{t_D} = \frac{4}{3}
		+	$$

-	Although burst duration and FCS diffusion time often appear numerically similar, they represent fundamentally different quantities.	+	This ratio represents a diffusion-limited reference case and is not universal.

-	The diffusion time is a correlation-derived, geometry-dependent time scale linked to the second spatial moment of the detection function, whereas the mean burst duration is a threshold-selected first moment of individual molecular residence times.	+	===== 8. Flow: advection--diffusion effects =====

-	Under ideal diffusion conditions, this distinction naturally leads to:	+	==== 8.1 Transport equation and time scales ====

	$$		$$
-	\langle t_B \rangle \approx \frac{4}{3}\,t_D	+	\frac{\partial c}{\partial t}
		+	+
		+	\mathbf v\cdot\nabla c
		+	=
		+
		+	D\nabla^2 c,\qquad
		+	\tau_v=\frac{w_0}{v},\qquad
		+	\mathrm{Pe}=\frac{vw_0}{D}
	$$		$$

-	Threshold selection and directed flow introduce systematic deviations from this relation, further emphasizing the conceptual difference between burst-based and correlation-based observables.	+	==== 8.2 Effect of flow on FCS ====
		+
		+	With advection--diffusion propagator
		+
		+	$$
		+	G(\mathbf r,\tau\mid\mathbf r_0,0)
		+	=
		+
		+	\frac{1}{(4\pi D\tau)^{3/2}}
		+	\exp\left(
		+	-\frac{\|\mathbf r-\mathbf r_0-\mathbf v\tau\|^2}{4D\tau}
		+	\right)
		+	$$
		+
		+	The autocorrelation function factorizes as
		+
		+	$$
		+	G(\tau)
		+	=
		+
		+	G_{diff}(\tau)
		+	\exp\left(
		+	-\frac{(v\tau)^2}{w_0^2(1+\tau/t_D)}
		+	\right)
		+	$$
		+
		+	When flow is modeled explicitly, $t_D$ remains unchanged.
		+
		+	==== 8.3 Effect of flow on burst duration ====
		+
		+	Burst durations scale approximately as
		+
		+	$$
		+	\langle t_B\rangle \sim \frac{L_{eff}}{v}
		+	\qquad (\mathrm{Pe}\gg1)
		+	$$
		+
		+	and therefore decrease continuously with increasing flow velocity.
		+
		+	==== 8.4 Consequences ====
		+
		+	Flow selectively affects burst durations while leaving the FCS diffusion time invariant when modeled correctly.
		+
		+	===== 9. Photobleaching effects =====
		+
		+	==== 9.1 General model ====
		+
		+	$$
		+	P_{survival}(t)=e^{-k_{bl}t},\qquad
		+	\tau_{bl}=\frac{1}{k_{bl}}
		+	$$
		+
		+	==== 9.2 Effect on FCS ====
		+
		+	$$
		+	G(\tau)=G_{diff}(\tau)e^{-\tau/\tau_{bl}},\qquad
		+	\tau_{bl}\gg t_D
		+	$$
		+
		+	Bleaching primarily affects amplitude and long-delay behavior.
		+
		+	==== 9.3 Effect on burst duration ====
		+
		+	$$
		+	t_{B,obs}=\min(t_{transport},t_{bleach}),\qquad
		+	p_{obs}(t)=p_{trans}(t)e^{-k_{bl}t}
		+	$$
		+
		+	Burst durations are systematically shortened.
		+
		+	===== 10. Conclusion =====
		+
		+	The diffusion time extracted from fluorescence correlation spectroscopy and the burst duration obtained from single-molecule detection probe molecular transport through the same confocal detection volume, yet they represent fundamentally different observables.
		+
		+	The FCS diffusion time $t_D$ is a correlation-derived geometry time scale governed by quadratic spatial weighting of the molecular detection function, whereas the mean burst duration $\langle t_B\rangle$ is a residence-time observable governed by linear weighting and explicit burst-selection criteria.
		+
		+	Because of these differences, there is no general reason for $t_D$ and $\langle t_B\rangle$ to coincide. Depending on burst-selection thresholds, the mean burst duration can be smaller than, comparable to, or larger than the diffusion time.
		+
		+	Under ideal diffusion conditions--Gaussian detection geometry, moderate thresholding, and negligible photophysical interruptions--a fixed relation can be derived,
		+
		+	$$
		+	\frac{\langle t_B\rangle}{t_D}=\frac{4}{3}
		+	$$
		+
		+	This factor is a geometric consequence of Gaussian detection combined with diffusion statistics and specific selection conditions. It is not universal.
		+
		+	Directed flow and photobleaching systematically break this reference relation. Flow introduces an additional transport time scale that leaves the FCS diffusion time unchanged when modeled explicitly, while directly shortening burst durations. Photobleaching truncates bursts and biases burst statistics strongly, whereas its influence on FCS is largely confined to slow non-stationarity.
		+
		+	Diffusion time and burst duration should therefore be regarded as complementary rather than interchangeable observables. Deviations from the diffusion-limited reference ratio provide direct physical insight into burst-selection effects, directed transport, and photophysical limitations in confocal single-molecule fluorescence experiments.

	===== References =====		===== References =====

-	* Elson, E. L.; Magde, D. Biopolymers 1974, 13, 1--27.	+	Elson, E. L.; Magde, D. Biopolymers 1974, 13, 1--27.
-	* Rigler, R.; Elson, E. L. (eds.) Fluorescence Correlation Spectroscopy, Springer.	+
-	* Rigler, R.; Widengren, J. Bioscience Reports 1990, 10, 395--403.	+	Rigler, R.; Elson, E. L. (eds.) Fluorescence Correlation Spectroscopy, Springer.
-	* Gopich, I. V.; Szabo, A. Journal of Chemical Physics 2005, 122, 014707.	+
-	* Rüttinger, S. Dissertation, 2006.	+	Rigler, R.; Widengren, J. Bioscience Reports 1990, 10, 395--403.
-	* Dörr, D. Dissertation, 2014.	+
		+	Widengren, J.; Rigler, R. Bioimaging 1996, 4, 149--157.
		+
		+	Gopich, I. V.; Szabo, A. Journal of Chemical Physics 2005, 122, 014707.
		+
		+	Ruettinger, S. Dissertation, 2006.
		+
		+	Doerr, D. Dissertation, 2014.

2019/03/06 12:44		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.
Line 25:		Line 25:


-	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:
Line 34:		Line 34:
	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 $\tau_A$.
Line 60:		Line 60:
	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 $t=0$.
Line 72:		Line 72:
	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 kAB and kBA 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]].