Description of parameters

General fluorescence parameters

Convolution parameters

Parameter name	Abbreviation	Description	Type	Recommendation
Convolution type	-	In the periodic mode the model is periodically convolved with the instrument response function (IRF) (imported at high laser repetition rates). In the "exp" mode (faster) the model is only convolved once.	Selector	For most cases the periodic mode is recommended. At low repetition rates (4-8 MHz) and short fluorescence lifetimes, the "exp" mode can be used.
Repetition rate	r[MHz]	The repetition rate of the laser	float	Determined by the measurement settings.
Fluorescence decay bin width	dt	The bin width between the counting channels	float	Determined by the instrument and the measurements settings (fixed)
Dark counts/background of the instrument response function (IRF)	lb	The instrument response function may have a background that should be subtracted before convolution. The parameter lb is the number of counts that is subtracted in each counting channel of the IRF.	float	Depends on the count rate when of the IRF measurement
Start of convolution	start	The starting channel of the convolution. All detection channels in the IRF before this channel are not considered.	float	Depends on the IRF. In some IRFs, there may be a reflection visible that can be masked.
Stop of convolution	stop	The stop channel of the convolution. All channels after this channel are not considered.	float	Depends on the IRF. Ideally, the model can be convolved with the entire IRF.
Scaling parameter that is used to match the model function to the experimental data. This number is related to the detected excited molecules at the time point of excitation	n0	The number of detected molecules that were initially excited.	float	If this value is fixed, the area of the model fluorescence decay is matched to the experimental decay. This behavior is recommended for standard analysis. If n0 is "fixed/checked" the area of the model function is matched to the experimental data on every model update.
Time shift of the IRF	ts	Due to differences in the count rate when measuring the IRF and the fluorescence decay, the IRF can be shifted. This parameter shifts the IRF. The number corresponds to the number of channels.	float	This number should be determined by the fit.

Nuisance parameters

Parameter name	Abbreviation	Description	Type	Recommendation
Background pattern	Background file	In single-molecule experiments the fraction of scattered light and the background are related. For such measurements, a background file can be used to decrease the number of unknown parameters.	fluorescence decay file	Not recommended for standard ensemble TCSPC measurements. Can be used for single-molecule TCSPC analysis to relate the background and the fraction of scattered light.
Contribution of scattered light	Sc	Sc is a factor that is multiplied to the IRF before it is added to the convolved model function. This way, scattered light can be described.	float	This parameter should be free unless a background pattern relating Sc and Bg is used.
Background counts per counting channel	Bg	Due to dark counts of the detector uncorrelated signals can be found in the measured decay. This is described by a constant offset. In some setups, also after-pulsing can be described by a constant offset. This offset is added to the model function after convolution.	float	In standard analysis, this number should be free. It can be estimated by the counts before the IRF peak.
Measurement time of background pattern	tBg	When using a background file, the measurement time of the background file and the measurement time of the experiment should be provided. Both are used to calculate the contribution of the background pattern.	float	This time is used together with tMeas to determine the background and the fraction of scattered light. If no background file is loaded this parameter is not used. In standard ensemble TCSPC, this parameter should be fixed.
Measurement time of fluorescence decay	tMeas	See description of tBg	float	See recommendation above.

Fluorescence lifetimes

Parameter name	Abbreviation	Description	Type	Recommendation
Number of fluorescence lifetimes	add / del	By clicking on add and del the number of fluorescence lifetimes and corresponding species fractions of the model can be changed.	NA	The number of fluorescence lifetimes should be deleted to the noise of the data. Aim for the least number of fluorescence lifetimes that describe the data sufficiently well.
Fluorescence lifetime of a species	tau(L,i)	The characteristic time of a fluorescence component.	float	This value is ideally determined by fitting. However, is known from other experiments, this value can be linked or fixed.
Species fraction of fluorescence lifetime component	x(L, i)	The species fraction of a fluorescence lifetime component. This is NOT the contribution of a lifetime component to the total signal!	float	This value is ideally determined by fitting. However, ais known from other experiments, this value can be linked or fixed.

Rotational times

Parameter name	Abbreviation	Description	Type	Recommendation
Number of rotational times	add / del	By clicking on add or del a rotational time can be added to the fluorescence decay	NA	The number of rotational times should be adapted to the noise of the measurements.
Polarization of the fluorescence decay	VM, VV, VH	The selector determines the type of the polarization of the fluorescence decay in a single photon excitation experiment. VM refers to vertical excitation and magic angle detection (default), VV vertical excitation vertical detection, VH vertical excitation, and horizontal detection.	Selector	The parameter should be adapted to the experimental settings.
Fundamental anisotropy of the dye	r0	The fundamental anisotropy is the anisotropy	float	Normally, this parameter is known for the used dyes and fixed.
G-factor of the experimental setup	g	Describes the relative sensitivity of the setup to detect vertically or parallel polarized light.	float	Separate experiments should determine this parameter for a given setup.
Parameters describing the anisotropy mixing in an microscope objective	l1 and l2	This parameter describes the mixing of VV and VH as it may happen in a microscope objective. For details: Koshioka, M.; Saski, K.; Masuhara, H.; Appl Spectrosc. 1995, 49, 224-228	float	This parameter should be determined by separate experiments for a given setup. In ensemble spectrometers both are usually set to zero.
Rotational correlation time of component i	rho_i	The rotational correlation time of component i in the anistropy decay. The total anisotropy decay is an amplitude b_i weighted sum of the individual components.	float	Not used in VM measurements can be delete in VM to decrease the number of optimized parameters)
Amplitude of component i in the anisotropy decay	b_i	The amplitudes are normalized and sum up to r0	float	Not used in VM measurements can be deleted in VM to decrease the number of optimized parameters)

Linearity corrections

Parameter name	Abbreviation	Description	Type	Recommendation
Correct pileup effects	Pileup	This option corrects pileup artifacts in measurements with high count rates. To correct the pileup in the measurements the instrument dead time needs to be specified. (see: Coates, P.B., 1968 J. Phys. E: Sci. Instrum. 1 878)	checkbox	First try to optimize your measurement to minimize the effect of pileup on the data. In standard measurements this should be disabled.
Correct differential non-linearity	Linearize	Many time-resolved fluorescence spectrometers exhibit a differential non-linearity DNL that becomes most evident in measurement with good counting statistics. Here, the DNL considered, by multiplying the convolved model function with an experimentally measured DNL (measured using uncorrelated light).	checkbox	In good experimental setups this correction is not necessary. If you see DNL in your data first check your cables. If you cannot fix it use an experimentally measured DNL to modify your model function.
Linearization table	Lintable	The experimentally measured DNL of the instrument.	Fluorescence decay file	Measure the DNL at the same count rate and to a similar noise level as the experimental data.
Linearization smoothing window function	Window	The exprimentally measured DNL file is smoothened to reduce its contribution to the noise of the model function. The smoothing is performed using a sliding window function. This selector determines the type of the window function.	Selector	This selector should only have minor effects for typical measurements and windows sizes. In most cases a flat window functions works (Default).
Dead time of the experimental setup	tDead[ns]	The dead time of the experimental setup, i.e., the time the setup cannot detect another photon once, a photon is detected.	float	This number should be provided by the manufacturer and depends on the detectors and the counting electronics.
Window size to smooth the linearization table	win-size	The number of points that are averaged to yield a correction for the DNL that is multiplied with the model function.	int	This number should be adapted to the noise in the DNL correction file and the number of TCSPC channels. For large numbers consider using a different window function.
Reversing the linearization table	reverse	Some instruments save the decays in reverse mode. By clicking on reverse, the linearization table is reversed.	checkbox	If you take care when saving your data, this option should be turned off.

Parameters

Donor in the absence of FRET

Parameter name	Abbreviation	Description	Type	Recommendation
Number of donor fluorescence lifetime components	Donor, add/del	By clicking on the add and the del button a donor species can be added.	NA	The number of donor fluorescence lifetime components should be determined using a separate sample without an acceptor.
Species fraction of species i	x(L,i)	The species fraction of a donor component that has a fluorescence lifetime tau(L,i) in the absence of FRET.	float	The fraction of a donor component should be determined using a separate donor sample.
Fluorescence lifetime of the species i	tau(L,i)	The fluorescence lifetime of the donor component i in the absence of FRET	float	The donor component should be determined using a separate donor sample.

Donor in the presence of FRET

Parameter name	Abbreviation	Description	Type	Recommendation
Förster radius	R0	The Förster radius that matches to the orientation factor kappa2 and the tau0	float
Orientation factor	kappa2	The orientation factor of the donor-acceptor pair. By default a dynamic averaging in assumed. Alternatively, a static averaging can be set up in the chisurf settings file.	float	For most cases (dynamic averaging) 2/3 should be used. For fluorescent proteins a static orientation factor distribution should be used by changing the chisurf setting files.
Fluorescence lifetime of the donor in the absence of FRET	tau0	The fluorescence lifetime used to calculate the Förster radius.	float	The numbers R0, kappa2, and tau0 are jointly used to calculate the FRET rate constants, kFRET.
Fraction of donor molecules lacking an acceptor molecule	x(D,0)	The species fraction of FRET inactive donor molecules. The faction is in the range of [0,1].	float	For large xD0 (xD0>0.7) consider analyzing additionally, the FRET sensitized acceptor decay.
Number of superimposed distributions, Gi	NA	By clicking on add and del distributions can be added to the total distance distribution	NA	The number of components depends on the data and the system. In a typical data set, depending on the separation of the components, usually 2-3 components can be resolved.
Parameter describing the position of a individual component.	R	Usually, the individual components are normal distributions. For normal distributions, R is the center of the distribution.	float	For short distances or very broad distributions, consider using a chi instead of a normal distribution.
Parameter describing the width of a component	sigma	For normal distributions, sigma is the standard deviation of the distribution. For a chi distribution, which is the distance distribution between two normal distributions, sigma is the width of the individual normal distributions.	float	For the organic dyes typically used in FRET experiments sigma is usually in the range of 5-12 Angström.

Homo FRET and FRET sensitized emission

Parameter name	Abbreviation	Description	Type	Recommendation
Prefactor of the amplitudes for the energy migration of the dye A to the dye B (A>B) and dye B to A (B>A)	A>B, B>A	This factor can be used to set if the model function is a homo FRET experiment or a hetero FRET experiment. In a homo FRET experiment A>B and B>A are both one. In a hetero FRET experiment either A>B or B>A is zero.	float	This value should be either 1 or 0 and be fixed depending on the type of experiment
The fraction incomplete molecules that contain only the dye A or dye B but not both dyes AB	pureA, pureB	In a hetero FRET experiment these numbers correspond to the fraction of a acceptor only and donor only molecules. Depending on the parameters either (see A>B and B>A parameter) pureA is either the donor or the acceptor fraction. For A>B=1 and B>A=0 pureA is the donor only fraction and pureB is the acceptor only fraction.	float	pureA can be linked in a global analysis to the donor only fraction of the donor decay in the presence of FRET.
Excitation probabilities of the dye	ExA, ExB	Factor scaling the fluorescence decays of A and B on the excitation side. If ExA=1 and ExB=0 only dye A is excited. If ExA=0 and ExB=1 only dye B is excited.	float	The excitation of A and B can be estimated based on the absoption spectra and the spectrum of the excitation source.
Emission probabilities of the dyes	EmA, EmB	Factor scaling the fluorescence decays of A and B on the detection side. This factor depends on the spectra of the dyes and the experimental setup.	float	This parameter can be estimated using the spectra of the indivudal components of the setup, the fluorescence spectra of the dyes, and the dyes fluorescence quantum yields.
Fluorescence lifetimes of the dyes in the absence of FRET	Lifetimes-A, Lifetimes-B	The fluorescence lifetimes of the dyes in the absence of FRET. Meaning, the fluorescence lifetimes of the donor without acceptor and the acceptor that is directly excited (for hetero FRET).	NA	The fluorescence lifetime of the donor in the ab