Time-Resolved Fluorescence Wiki

pile-up_effect

Anonymous (anonymous@undisclosed.example.com) — 2015-06-03T15:09:55+00:00

2015/06/03 17:09		current
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-	{{tag>pile-up TCSPC pile-up dead_time}}	+	{{tag> TCSPC pile-up dead_time}}
	~~TOC~~		~~TOC~~

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]]))

t3-mode

Anonymous (anonymous@undisclosed.example.com) — 2015-02-10T16:27:57+00:00

2015/02/10 17:27		current
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	- the arrival time of the event pair on the overall experiment time scale (the time tag).		- the arrival time of the event pair on the overall experiment time scale (the time tag).

-	The latter was originally obtained from an independent asynchronous clock. This made it difficult to combine the start-stop timing with the time tag or to know the sync period the event belonged to. For the PicoHarp's T3 Mode a smarter approach was chosen:\\	+	The latter was originally obtained from an independent asynchronous clock. This made it difficult to combine the start-stop timing with the time tag or to know the sync period the event belonged to. For the *Harp's T3 Mode a smarter approach was chosen:\\
	The time tag is now obtained by simply counting sync pulses. From the T3 Mode event records it is therefore possible to precisely determine which sync period a photon event belongs to. Since the sync period is also known precisely, this furthermore allows to reconstruct the arrival time of the photon with respect to the overall experiment time.		The time tag is now obtained by simply counting sync pulses. From the T3 Mode event records it is therefore possible to precisely determine which sync period a photon event belongs to. Since the sync period is also known precisely, this furthermore allows to reconstruct the arrival time of the photon with respect to the overall experiment time.

tttr

Anonymous (anonymous@undisclosed.example.com) — 2015-02-10T16:42:50+00:00

2015/02/10 17:42		current
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	The [[Products:TimeHarp 200]] (also the [[Products:TimeHarp 100]]), the [[Products:PicoHarp 300]] [[Products:HydraHarp 400]] support TTTR mode measurements. With the the [[Products:PicoHarp 300]] a slight shift in the nomenclature was introduced. Due to its capability of simultaneously recording both signal inputs (in interactive mode used as 'Start' and 'Stop') as two separate TTTR traces with a time resolution of 4ps, a new TTTR mode was introduced, the so called T2-mode. The traditional recording as with the [[Products:TimeHarp 200]] / [[Products:TimeHarp 100]] is called [[T3-mode]]. In [[T2-mode]] both signal inputs are functionally identical.		The [[Products:TimeHarp 200]] (also the [[Products:TimeHarp 100]]), the [[Products:PicoHarp 300]] [[Products:HydraHarp 400]] support TTTR mode measurements. With the the [[Products:PicoHarp 300]] a slight shift in the nomenclature was introduced. Due to its capability of simultaneously recording both signal inputs (in interactive mode used as 'Start' and 'Stop') as two separate TTTR traces with a time resolution of 4ps, a new TTTR mode was introduced, the so called T2-mode. The traditional recording as with the [[Products:TimeHarp 200]] / [[Products:TimeHarp 100]] is called [[T3-mode]]. In [[T2-mode]] both signal inputs are functionally identical.

-	Today recording of [[glossary:T3-mode]] and T2 mode files is possible with all recent PicoQuant TCSPC devices ([[Products:TimeHarp 260]], [[Products:PicoHarp 300]] and [[Products:HydraHarp 400]] and their included software, analysis is supported mainly by the [[software:SymPhoTime]] software package.	+	Today recording of [[glossary:T3-mode]] and [[glossary:T2-mode]] files is possible with all recent PicoQuant TCSPC devices ([[Products:TimeHarp 260]], [[Products:PicoHarp 300]] and [[Products:HydraHarp 400]] and their included software, analysis is supported mainly by the [[software:SymPhoTime]] software package.

	Due to its capability of including external TTL pulses as markers in the stream of photon events TTTR mode is suitable for [[FLIM]] measurements. The markers are used to synchronise the photon events with a scanning process allowing to sort the photons into image pixels.		Due to its capability of including external TTL pulses as markers in the stream of photon events TTTR mode is suitable for [[FLIM]] measurements. The markers are used to synchronise the photon events with a scanning process allowing to sort the photons into image pixels.

dead_time

Anonymous (anonymous@undisclosed.example.com) — 2015-06-03T15:04:41+00:00

2015/06/03 17:04		current
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	In TCSPC the term dead time refers to the time the TCSPC system needs armed again after detecting an event. During the dead time the TCSPC system is blind.		In TCSPC the term dead time refers to the time the TCSPC system needs armed again after detecting an event. During the dead time the TCSPC system is blind.

-	If for example two photons are detected with the dead time of the TCSPC device the second photon will be lost. This leads to the so called [[glossary:Pile Up Effect]].	+	If for example two photons are detected with the dead time of the TCSPC device the second photon will be lost. This leads to the so called [[glossary:Pile-up Effect]].

	Note that not only TCSPC devices but also photon counting devices exhibit dead times.		Note that not only TCSPC devices but also photon counting devices exhibit dead times.

tcspc

Anonymous (anonymous@undisclosed.example.com) — 2014-01-28T13:06:31+00:00

2014/01/28 14:06		current
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	====== TCSPC ======		====== TCSPC ======

-	TCSPC stands for Time Correlated Single Photon Counting: A stream of photons is recorded, each photon with respect to a (often periodical) signal, e.g. a repeated laser pulse. The single photon events are sorted into histogram channels that correspond to the time that elapsed since the last excitation pulse. It is a time domain method of investigating time resolved fluorescence.	+	TCSPC stands for Time Correlated Single Photon Counting: A stream of photons is recorded, each photon with respect to a (often periodical) signal, e.g. a repeated laser pulse. The single photon events are sorted into histogram channels that correspond to the time that elapsed since the last excitation pulse. It is a time domain method for investigating time resolved fluorescence.

hybrid_pmt

Anonymous (anonymous@undisclosed.example.com) — 2015-11-03T15:00:37+00:00

2015/11/03 15:59		current
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	"The hybrid photodetector's structure is similar yet different from a conventional PMT. Like PMTs, the HPD is a vacuum tube with a photocathode that detects light, an electron multiplier that multiplies electrons, and an output terminal that outputs an electrical signal. But unlike PMTs which use multiple dynodes as electron multipliers, the HPD uses a silicon avalanche diode (AD) instead"((continue reading on the [[http://www.hamamatsu.com/us/en/community/optical_sensors/tutorials/what_is_hpd/index.html\|Hamamatsu]] website.))		"The hybrid photodetector's structure is similar yet different from a conventional PMT. Like PMTs, the HPD is a vacuum tube with a photocathode that detects light, an electron multiplier that multiplies electrons, and an output terminal that outputs an electrical signal. But unlike PMTs which use multiple dynodes as electron multipliers, the HPD uses a silicon avalanche diode (AD) instead"((continue reading on the [[http://www.hamamatsu.com/us/en/community/optical_sensors/tutorials/what_is_hpd/index.html\|Hamamatsu]] website.))

-	PicoQuant integrates various Hybrid PMT tubes into a convenient assembly called [[https://www.picoquant.com/products/category/photon-counting-detectors/pma-hybrid-series-hybrid-photomultiplier-detector-assembly\|PMA Hybrid]].	+	PicoQuant integrates Hybrid PMT tubes into a convenient assembly called [[https://www.picoquant.com/products/category/photon-counting-detectors/pma-hybrid-series-hybrid-photomultiplier-detector-assembly\|PMA Hybrid]].

	The PMA Hybrid is a compact single photon sensitive detector based on a fast hybrid photomultiplier tube with peltier cooler to reduce the dark count rate. The detector includes a high voltage power supply and pre-amplifier with overload protection and emergency shut down procedure if the detector count rate reaches a critical limit.		The PMA Hybrid is a compact single photon sensitive detector based on a fast hybrid photomultiplier tube with peltier cooler to reduce the dark count rate. The detector includes a high voltage power supply and pre-amplifier with overload protection and emergency shut down procedure if the detector count rate reaches a critical limit.

mcp

Anonymous (anonymous@undisclosed.example.com) — 2015-11-03T13:27:59+00:00

2013/08/05 13:45		current
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	====== MCP ======		====== MCP ======

-	Microchannel Plate PMT (MCP)	+	Microchannel Plate [[PMT]] (MCP)

-	A microchannel plate PMT is a sensitive photon detector. It consists of an array of glass capillaries (10-25 μm inner diameter) that are coated on the inside with a electron-emissive material. The capillaries are biased at a high voltage. Like in the PMT, an electron that strikes the inside wall of one of the capillaries creates an avalanche of secondary electrons. This cascading effect creates a gain of 103 to 106 and produces a current pulse at the output. The timing jitter of MCPs is sufficiently small to perform time-resolved photon counting on a sub-nanosecond- scale, usually outperforming PMTs. Good but also expensive MCPs can achieve timing uncertainties as low as 20ps. Microchannel plates are also used as an intensifier for low-intensity light detection with array detectors.	+	A microchannel plate [[PMT]] is a sensitive photon detector. It consists of an array of glass capillaries (10-25 μm inner diameter) that are coated on the inside with a electron-emissive material. The capillaries are biased at a high voltage. Like in the PMT, an electron that strikes the inside wall of one of the capillaries creates an avalanche of secondary electrons. This cascading effect creates a gain of 103 to 106 and produces a current pulse at the output. The timing jitter of MCPs is sufficiently small to perform time-resolved photon counting on a sub-nanosecond- scale, usually outperforming PMTs. Good but also expensive MCPs can achieve timing uncertainties as low as 20ps. Microchannel plates are also used as an intensifier for low-intensity light detection with array detectors.

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.

mcs

Anonymous (anonymous@undisclosed.example.com) — 2014-01-21T16:39:04+00:00

2014/01/21 17:38		current
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	====== MCS ======		====== MCS ======

-	MCS stands for Multi Channel Scaler. At PQ this term is used in the following context: Single photon events, as originating from a [[TTTR]] measurement are sorted by means of their macroscopic time into equally spaced time bins. What immediately results is a time trace of the fluorescence intensity. In a subsequent analysis the binned ensemble of photons can be used to form [[TCSPC]] histograms, which in turn can be used for lifetime analysis, time-gated analysis etc.	+	MCS stands for Multi Channel Scaler. At PicoQuant this term is used in the following context: Single photon events, as originating from a [[TTTR]] measurement are sorted by means of their macroscopic time into equally spaced time bins. What immediately results is a time trace of the fluorescence intensity. In a subsequent analysis the binned ensemble of photons can be used to form [[TCSPC]] histograms, which in turn can be used for lifetime analysis, time-gated analysis etc.

spad

Anonymous (anonymous@undisclosed.example.com) — 2017-05-17T08:37:15+00:00

2013/08/06 16:53		current
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	SPAD means Single Photon counting Avalanche photo-Diode. It stands commonly for a complete module including an Avalanche Photodiode, working temporary above the breakdown voltage in reverse bias. One photon may trigger the avalanche process and generates a time-corresponding electrical pulse. The avalanche must be "quenched" in order to prevent destructive current flow. This is achieved by passive or active quenching circuits. Passive quenching requires basically just a resistor but is slow and causes longer deadtimes. Active quenching is standard for all modules used by PicoQuant.		SPAD means Single Photon counting Avalanche photo-Diode. It stands commonly for a complete module including an Avalanche Photodiode, working temporary above the breakdown voltage in reverse bias. One photon may trigger the avalanche process and generates a time-corresponding electrical pulse. The avalanche must be "quenched" in order to prevent destructive current flow. This is achieved by passive or active quenching circuits. Passive quenching requires basically just a resistor but is slow and causes longer deadtimes. Active quenching is standard for all modules used by PicoQuant.

-	/*
-	[[Howto:How to unmount a SPAD from the MT200]]
-	*/

t2-mode

Anonymous (anonymous@undisclosed.example.com) — 2015-02-10T16:24:41+00:00

2015/02/10 17:22		current
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	====== T2-mode ======		====== T2-mode ======

-	A special measurement mode of the [[Products:PicoHarp 300]]	+	A special measurement mode of the [[Products:PicoHarp 300]], [[Products:HydraHarp 400]] and [[Products:TimeHarp 260]]


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	In T2 Mode both signal inputs of the PicoHarp 300 are functionally identical. There is no dedication of input channel 0 to a [[SYNC]] signal. Usually both inputs are used to connect photon detectors. The events from both channels are recorded independently and treated equally. In each case an event record is generated that contains information about the channel it came from and the arrival time of the event with respect to the overall measurement start. The timing is recorded with 4 ps resolution. Each T2 Mode event record consists of 32 bits. There are 4 bits for the channel number and 28 bits for the time-tag. Routing is not supported. If the time tag overflows, a special overflow marker record is inserted in the data stream, so that upon processing of the data stream a theoretically infinite time span can be recovered at full resolution. [[Dead time]]s exist only within each channel (95 ns typ.) but not across the channels. Therefore, cross correlations can be calculated down to zero lag time. This allows powerful new application such as [[FCS]] with lag times from picoseconds to hours. Autocorrelations can also be calculated at the full resolution but of course only starting from lag times larger than the [[dead time]].		In T2 Mode both signal inputs of the PicoHarp 300 are functionally identical. There is no dedication of input channel 0 to a [[SYNC]] signal. Usually both inputs are used to connect photon detectors. The events from both channels are recorded independently and treated equally. In each case an event record is generated that contains information about the channel it came from and the arrival time of the event with respect to the overall measurement start. The timing is recorded with 4 ps resolution. Each T2 Mode event record consists of 32 bits. There are 4 bits for the channel number and 28 bits for the time-tag. Routing is not supported. If the time tag overflows, a special overflow marker record is inserted in the data stream, so that upon processing of the data stream a theoretically infinite time span can be recovered at full resolution. [[Dead time]]s exist only within each channel (95 ns typ.) but not across the channels. Therefore, cross correlations can be calculated down to zero lag time. This allows powerful new application such as [[FCS]] with lag times from picoseconds to hours. Autocorrelations can also be calculated at the full resolution but of course only starting from lag times larger than the [[dead time]].

-	The 32 bit event records are queued in a [[FIFO]] (First In First Out) buffer capable of holding up to 256 k event records. The FIFO input is fast enough to accept records at the full speed of the time-to-digital converters (up to 10 Mcps each). This means, even during a fast burst no events will be dropped except those lost in the [[dead time]] anyhow. The FIFO output is continuously read by the host PC, thereby making room for fresh incoming events. Even if the average read rate of the host PC is limited, bursts with much higher rate can be recorded for some time. Only if the average count rate over a long period of time exceeds the readout speed of the PC, a FIFO overrun could occur. In case of a FIFO overrun the measurement must be aborted because data integrity cannot be maintained. However, on a modern and well configured PC with Windows 2000 or XP a sustained average count rate over 4 Mcps is possible. This total transfer rate must be shared by the two input channels. For all practically relevant fluorescence detection applications the effective rate per channel is more than sufficient.	+	The 32 bit event records are queued in a [[FIFO]] (First In First Out) buffer capable of holding up to 256 k event records. The FIFO input is fast enough to accept records at the full speed of the time-to-digital converters (up to 10 Mcps each). This means, even during a fast burst no events will be dropped except those lost in the [[dead time]] anyhow. The FIFO output is continuously read by the host PC, thereby making room for fresh incoming events. Even if the average read rate of the host PC is limited, bursts with much higher rate can be recorded for some time. Only if the average count rate over a long period of time exceeds the readout speed of the PC, a FIFO overrun could occur. In case of a FIFO overrun the measurement must be aborted because data integrity cannot be maintained. However, on a modern and well configured PC a sustained average count rate over 4 Mcps is possible. This total transfer rate must be shared by the two input channels. For all practically relevant fluorescence detection applications the effective rate per channel is more than sufficient.

-	For maximum throughput, T2 Mode data streams are normally written directly to disk. The current PicoHarp software 1.2 does not provide any immediate data visualization during a T2 Mode measurement, except count rate and progress display. However, using custom software it is also possible to analyze incoming data "on the fly". Even on-line correlation can be implemented. Obviously this requires efficient processing and possible restrictions in average count rate. The PicoHarp software installation CD contains demo programs to show how T2 Mode files can be read by custom software. The implementation of custom measurement programs requires the PicoHarp programming library, which is available as a separate option.	+	For maximum throughput, T2 Mode data streams are normally written directly to disk. The current Harp software does not provide any immediate data visualization during a T2 Mode measurement, except count rate and progress display. However, using custom software it is also possible to analyze incoming data "on the fly". Even on-line correlation can be implemented. Obviously this requires efficient processing and possible restrictions in average count rate. The PicoHarp software installation CD contains demo programs to show how T2 Mode files can be read by custom software. The implementation of custom measurement programs requires the Harp programming library, which is available as a separate option.

	Note: From a mathematical point of view, the T2 mode should be able to store 28 bit = 228 = 268435456 time bin data before need to "wrap around". However, the real wrap around time as shown in the demo code is only 210698240. This discrepancy is due to the design of the TDCs. Briefly, the [[TDCs]] include a coarse scaler and an interpolator for the the short times. This interpolator is not working in a binary fashion, which finally leads to the fact that not the full available memory is used. This does not lead to any data loss. To reconstruct the full temporal time trace one only needs to follow the procedures shown in the demo code		Note: From a mathematical point of view, the T2 mode should be able to store 28 bit = 228 = 268435456 time bin data before need to "wrap around". However, the real wrap around time as shown in the demo code is only 210698240. This discrepancy is due to the design of the TDCs. Briefly, the [[TDCs]] include a coarse scaler and an interpolator for the the short times. This interpolator is not working in a binary fashion, which finally leads to the fact that not the full available memory is used. This does not lead to any data loss. To reconstruct the full temporal time trace one only needs to follow the procedures shown in the demo code

	see also [[.:t3-mode]]		see also [[.:t3-mode]]
-

fast_flim

Anonymous (anonymous@undisclosed.example.com) — 2015-11-03T14:29:58+00:00

2013/08/06 15:49		current
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		+	{{tag>FLIM fast_flim}}
	====== Fast FLIM ======		====== Fast FLIM ======

	[[FLIM]] image, using the [[fast lifetime]] calculation. The color-coded fast lifetime of each pixel represents the average photon arrival time with respect to the preceding laser pulse.		[[FLIM]] image, using the [[fast lifetime]] calculation. The color-coded fast lifetime of each pixel represents the average photon arrival time with respect to the preceding laser pulse.

		+	===== FLIM in this wiki =====

		+	{{topic>FLIM -open_source&nodate&nouser}}

bifl

Anonymous (anonymous@undisclosed.example.com) — 2015-02-10T16:34:08+00:00

2014/04/09 22:38		current
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	BIFL stands for Burst Integrated Fluorescence Lifetime: The photon events of a complete burst are accumulated into a [[TCSPC]] histogram which is used for lifetime analysis methods afterwards. Usually a burst is defined as a time interval for which the intensity of a time trace or [[MCS]] measurement is above a chosen threshold. Evaluation of all bursts present in an [[MCS]] trace, for example, results in a lifetime histogram.		BIFL stands for Burst Integrated Fluorescence Lifetime: The photon events of a complete burst are accumulated into a [[TCSPC]] histogram which is used for lifetime analysis methods afterwards. Usually a burst is defined as a time interval for which the intensity of a time trace or [[MCS]] measurement is above a chosen threshold. Evaluation of all bursts present in an [[MCS]] trace, for example, results in a lifetime histogram.

-	BIFL is supported by the [[products:SymPhoTime]] software, alongside with a variety of burst related techniques.	+	BIFL is supported by the [[software:SymPhoTime]] software, alongside with a variety of burst related techniques.

marquardt-levenberg

Anonymous (anonymous@undisclosed.example.com) — 2015-02-10T16:34:33+00:00

2014/04/09 22:38		current
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	====== Marquardt-Levenberg ======		====== Marquardt-Levenberg ======

-	The Marquardt-Levenberg method is a means of optimising parameters in a least squares fit. It is used in our [[products:FluoFit]], [[products:SymPhoTime]] and a variety of other products (online-Fitting, FluoLib...).	+	The Marquardt-Levenberg method is a means of optimising parameters in a least squares fit. It is used in our [[software:FluoFit]], [[software:SymPhoTime]] and a variety of other products (online-Fitting, FluoLib...).

	Basically it works by examining how changes of a certain parameter affect the residuals trace, that means, it calculates a pointwise gradient of the residuals trace for each parameter. Marquard-Levenberg optimisation is fairly efficient and is regarded as state-of-the-art in least squares fitting.		Basically it works by examining how changes of a certain parameter affect the residuals trace, that means, it calculates a pointwise gradient of the residuals trace for each parameter. Marquard-Levenberg optimisation is fairly efficient and is regarded as state-of-the-art in least squares fitting.