Method and system for performing time-correlated single photon counting measurements

Abstract

The disclosure pertains to a method of analyzing a time-correlated single photon counting measurement, the method comprising the steps of a) exciting the sample (10) by a plurality of successive excitation light pulses or any other form of periodically modulated light (11), b) detecting the radiation originating from the sample (10), thereby generating an electrical signal (12), out of which at least one detection event (13) is generated, each detection event (13) indicative of at least one photon originating from the sample (10) and having a measured relative time (tp), c) providing extended information for at least one of said detection events (13), preferably for each of said detection events (13), the extended information being representative of at least one of the size and shape of the electrical pulse associated with the detection event (13) within the electrical signal (12), and d) generating a distribution of relative times reflecting one or more properties of the sample (10) based on said signal (12) and said extended information, wherein a corrected relative time (t'p) is assigned to at least one detection event (13) which is based on the measured relative time (tp) of the detection event (13) and on the extended information associated with the respective detection event (13) and / or a weight factor (w(t)) is assigned to at least one detection event (13) which is based on the measured relative time (tp) of the detection event (13) and on the extended information associated with a plurality, in particular all, detection events (13) within a domain of interest (DOI).

Description

[0001]PPROS003EP2 / 01.05.2025 1 u2fyj2jnMethod and system for performing time-correlated single photoncounting measurements The present invention relates to methods and systems for per-forming time-correlated single photon counting measurements.In the context of scientific measurements based on fluorescence, various techniques can be employed, including but not limited to spectroscopic measurements using solutions in cuvettes, fluores-cence microscopy in all its flavors, fiber photometry, and flowcytometry. These experiments make use of instrumentations com- prising some main elements: ^an excitation source, for example a lamp, a laser, or an LEDused to excite a sample; ^excitation and detection optics;^ detectors to produce an electrical response upon detection oflight, in particular a current or a voltage);^ detection electronics, to measure the electrical signal fromthe detector and transform it into digital data suitable for further analysis; ^control software.The detection and quantification of photons can be performed us- ing two main techniques: analog integration and single-photon counting: Analog integration is based on the quantification of the elec-trical signal produced by a detector in a certain interval oftime, which is proportional to the number of detected photons. Single-Photon Counting (SPC) is based on the measurement of fast electrical pulses produced every time a single photon hits a suitable detector. The technique detects the moment in time inwhich the electrical pulse crosses a predefined threshold andPPROS003EP2 / 01.05.2025 2 u2fyj2jnassigns a time stamp (hereinafter called "absolute time") to theelectrical pulse (and therefore one or more detected photons),corresponding to its arrival time from the start of the experi- ment, and deduces the intensity of light hitting the detector bycounting the total number of electrical pulses (and thereforeone more photons) detected in a certain time interval.SPC offers superior noise performance with respect to analog in- tegration, due to the absence of background analog electronic noise. Moreover, SPC can be used to gather additional infor- mation rather than the intensity of light alone. In particular,when a periodically modulated (e.g. pulsed) excitation source isused, the time between the excitation event and the detection ofa photon generated due to such excitation (hereinafter called"relative time") can be measured using a reference signal thatis produced in a synchronized fashion with respect to the tem- poral profile of the excitation source. This method is called Time-Correlated Single-Photon Counting (TCSPC) and is used intechniques such as time resolved Fluorescence Spectroscopy, Flu-orescence Lifetime Imaging (FLIM), Fluorescence Lifetime FiberPhotometry (FLIP), and in other technological applications.Lifetime-based techniques are particularly advantageous in com- parison to intensity-based ones as they offer additional infor- mation to separate different components of a mixture of fluores- cent species, and they are not dependent on the total number of detected photons (above a minimal signal-to-noise ratio thresh- old), offering robust quantitative readout in the presence of intensity losses due to scattering or absorption, as typical of many in vivo and ex vivo biological measurements. Besides fluorescence techniques, TCSPC is a general method for the detection of photons referenced to a synchronization signal (usually the emission of light from a laser source) and extends,for example, to techniques that measure the same light emittedPPROS003EP2 / 01.05.2025 3 u2fyj2jnfrom the laser source (e.g. optical tomography or LIDAR rang- ing).Modern TCSPC measurements utilize a detection strategy namedTime-Tagged Time-Resolved (TTTR) detection that could include one or more of the following steps: 1. A pulsed excitation light or any other form of periodi-cally modulated light is used to illuminate the sample.2. The excitation instrument, or another suitable instru-ment, transmits an electrical signal (comprising, in par- ticular, pulses, periodic waves or other) that reports on the periodicity of the excitation source (the synchroni-zation signal). 3. An electronic device records the synchronization signal,extracts the time of each excitation event (the Excita-tion Time) and optionally increases a counter of the to-tal number of excitation events (Excitation Event Num- ber). Each excitation event corresponds to the emissionof an optical pulse from the light source or to a prede-termined value of a periodically modulated excitation light intensity. The temporal interval between two adja-cent excitation events is defined as Excitation Cycle. 4. The light emitted (fluorescence) or scattered (tomogra-phy, LIDAR) by the sample is collected by one or moresuitable photodetectors, which produce an electrical pulse every time a photon is detected. 5. Each photodetector produces a constant baseline electri-cal signal (current or voltage) possibly comprising ana- log noise, and electrical pulses of predefined size and shape (with variability on those parameters dependent on detector technology) every time a photon is detected. Electrical pulses generated by the detection of a single photon are defined as Single Photon Response (SPR) of thePPROS003EP2 / 01.05.2025 4 u2fyj2jndetector. A generic electrical pulse can be composed of one or more SPRs. 6. The electrical signal from the detector(s) is transmittedto the electronic device as described in item 3 above. 7. A predefined criterion, such as the signal crossing apredefined intensity threshold, is used to determine whenthe detector has received a photon. 8. The electronic device records a detection event with thefollowing information: a. Absolute Time: time between the start of the experi-ment and the crossing of the threshold by the elec- trical signal. b. Relative Time: time between the latest ExcitationTime and the crossing of the threshold by the elec- trical signal. Alternatively, the Excitation Time or the Excitation Event Number can be recorded, and the Absolute Time re- constructed during data analysis from those values and the Relative Time. 9. The information on the collected detection events istransmitted to a computer. 10. A temporal distribution of the detected photons (e.g.fluorescence decay for FLIM) is assembled by composing ahistogram where each detection event contributes to the intensity value of a discrete temporal bin that corre-sponds to its relative time. In practical implementations, TCSPC suffers from specific arti- facts that may distort the final temporal distribution of pho- tons, such as:PPROS003EP2 / 01.05.2025 5 u2fyj2jn^ Classic Pile-up: In classic TCSPC (not using the TTTRmethod), sampling of the exciting laser beam initiates a voltage ramp that is interrupted as soon as a photon has been detected. The voltage value is correlated with the time spent between the excitation and detection events, and after multi- ple excitation cycles, a histogram of the distribution of relative times can be composed. If more than one photon ar- rives at the detector within one single laser cycle, any pho- ton after the first is discarded. ^Dead time (DT): Either the detector or the electronics remain"blind" for a certain amount of time after the detection of aphoton, preventing the correct detection of other photons ar- riving in close time proximity. ^Pile-up (PU): In modern systems using the TTTR method, clas-sical pile-up is avoided. However, when two or more photons arrive on the detector in close time proximity, the generated electrical pulse (composed of the sum of the individual SPRs), might be counted as a single photon event in the pho-ton counting electronics.To avoid these distortions, experiments are traditionally con-ducted at photon count rates roughly below 1–5% of the laser ex- citation rate. However, even when using high-repetition rate la-sers (for example 40–80 MHz), the total number of collected pho-tons is limited to a few million counts per seconds (Mcps, also corresponding to counts per microsecond). While this count rate might be appropriate for some applications, in others, such asfluorescence lifetime imaging, it is strongly limiting in termsof accuracy and / or acquisition speed. While the exact values de- pend on many factors, a typical FLIM image collected in theseconditions might require an acquisition time in the order ofminutes to be suitable for accurate analysis.PPROS003EP2 / 01.05.2025 6 u2fyj2jnThus, increasing the count rate in TCSPC while avoiding distor- tion has become a primary goal in modern TCSPC. While DT remains a problem for certain detection technologies, such as individual Single-Photon Avalanche Photodiode (SPAD) de- tectors, systems like photomultipliers (PMTs), hybrid photode- tectors (HPDs), large SPAD arrays, and silicon photomultipliers (SiPMs) are virtually free of detector DT. With the progress infast Time-to-Digital Converters (TDCs) and Analog-to-DigitalConverters (ADCs), the electronics DT has also been shrunk to sub-ns levels or fully suppressed, de facto eliminating its con- tribution as well. Thus, pile-up remains the main obstacle to achieving undistorted TCSPC at high count rate. As of today, the most advanced TCSPC instruments use a threshold-based method to assign the time ofarrival of a photon. When an electrical pulse produced by thedetector crosses a certain threshold, the time stamp is as- signed. When the electrical signal drops below the threshold again, the system is ready to measure a new pulse. If a new pulse arrives before the first one has fallen again below the threshold, the second one cannot be detected, causing the dis- tortion of the decay due to a lack of appropriate pulse resolu- tion.The smaller the full width at half maximum (FWHM) of the elec-trical pulse generated when the photon hits the detector, the higher will be the pulse resolution power of the electronics. Due to their very sharp (sub-ns FWHM) pulses and low noise, HPDs are the gold standard in the field and the de facto technology for FLIM. Even using state-of-the-art electronics and detectors, the ef- fect of pile-up is still important, and even if detection ratesaround 80–100 Mcps have been demonstrated, the resulting decaysPPROS003EP2 / 01.05.2025 7 u2fyj2jnare heavily distorted, as can be seen in the example in Fig-ure 3. To add to the complexity of the problem, the degree ofdistortion depends on the fluorescence lifetime and laser repe- tition rate.To overcome this problem in FLIM, two different approaches havebeen developed: ^A posteriori modelling: Based on analytical equations, it ispossible to introduce parameters that account for the pile-up effect in an exponential fitting equation, thus in principle retrieving the correct results. However, this approach works only for fitting analysis which, while being the most infor- mation-preserving one, is also more sensitive to noise than alternative estimation methods. Moreover, the total number ofdetected photons is underestimated in a sample-dependent way, preventing accurate intensity measurements. ^High speed FLIM filter: By using ADCs, it is possible to ob-tain information about the total number of photons per exci- tation cycle by integration rather than counting. In this way it is possible to remove from the photon counting analysis all excitation cycles (defined as the time between two con-secutive excitation events) that contain more than one pho-ton, thus effectively eliminating distortions. However, this technique discards a progressively large fraction of detectedphotons at progressively higher detection rates, limiting its ability to improve signal-to-noise ratio.While no other approach has been reported to the best of the in-ventors' knowledge to solve the pile-up problem, two interesting methods have been presented for the control and correction of detector dead time in single SPAD detectors, here defined as Matched Dead Time (MDT) and SPAD Dead Time Correction (SDTC): ^MDT: By adjusting the active quenching circuit of the SPADdetector, is it possible to set the dead time to be equal toPPROS003EP2 / 01.05.2025 8 u2fyj2jnthe excitation period (i.e., the time between two consecutiveexcitation events). Under this condition, a certain percent- age of photons are discarded, but the fluorescence decay is undistorted. ^SDTC: By measuring the behavior of the active quenching cir-cuit, it is possible to prepare a second temporal histogram(having the same time scale as the relative time histogram) reflecting the "state of the detector" that can be used tocorrect the decay. This is the only reported method to cor- rect both the decay and the total intensity (except for added statistical noise in certain areas of the decay) but can be used only with a specially designed SPAD detector. Importantly, SPAD detectors have active areas that are signifi- cantly smaller than HPDs or SiPMs, preventing their use in highly scattering samples, which prevents tight focusing of the light collected by an objective. SEBASTIAN ISBANER ET AL: ("Dead-time correction of fluorescence lifetime measurements and fluorescence lifetime imaging", OPTICSEXPRESS, vol. 24, no. 9, pages 9429-9445, DOI: 10.1364 / OE.24.009429) disclose a theory of dead-time effects on Time-Correlated Single Photon Counting (TCSPC) as used for fluores- cence lifetime measurements. A collection algorithm to remove these artifacts is developed and this algorithm is applied to fluorescence lifetime measurements as well as to Fluorescence Lifetime Imaging Microscopy (FLIM), where rapid data acquisition is necessarily connected with high count rates.EP 3 431 967 Al discloses a method for estimating and correctingdetector pulse pile-up effects in time-correlated single-photon counting applications, particularly in decay histograms. In view of the disadvantages inherent in the prior art, it is an object of the present invention to provide a method for perform-ing time-correlated single photon counting measurements in whichPPROS003EP2 / 01.05.2025 9 u2fyj2jndistortions (in intensity and / or shape) of the distribution of relative times can be reduced. In particular, this method should allow the use of standard commercial detectors such as HPDs, SiPMs, PMTs, etc. This and further objects are obtained by a method for performingtime-correlated single photon counting measurements that com-prises the steps of a) exciting a sample by a plurality of successive excitationevents, in particular successive excitation light pulses orany other form of periodically modulated light, b) detecting the generated radiation (fluorescence or scatter-ing), thereby generating an electrical signal, out of whichat least one detection event is generated, each detectionevent comprising at least one electrical pulse indicative ofat least one photon originating from the sample and having ameasured relative time, c) providing extended information for at least one of said de-tection events, preferably for each of said detection events, the extended information being representative of at least one of the size and shape of the electrical pulse within the detection event, and d) generating a distribution of relative times reflecting oneor more properties of the sample based on at least one de-tection event and said extended information,wherein, ^at least one detection event is disregarded based on themeasured absolute time, relative time, and / or extended information associated with one or more of the detectionevents within a domain of interest and / or ^a corrected relative time is assigned to at least one de-tection event which is based on the measured relativePPROS003EP2 / 01.05.2025 10 u2fyj2jntime of the detection event and on the extended infor-mation associated with the respective detection event and / or ^a weight factor is assigned to at least one detectionevent which is based on the measured relative time of thedetection event and on the extended information associ-ated with a plurality, in particular all, detected detec- tion events within a domain of interest.The excitation light pulses or the periodically modulated lightmay be produced by a laser source.In the context of the present application, an electrical signalis to be understood as a time-dependent electrical signal thatis obtained, in particular from the detector, within the domainof interest. The signal may be an electric signal, such as a voltage or an electric current. The detection of the electrical pulse occurs by measuring whether the signal crosses a prede- fined intensity threshold in a predefined direction (either up- wards or downwards, depending on whether the photon detection produces positive or negative electrical pulses), and the time of such crossing is defined as the time of the detection event. The detection event terminates once the signal crosses thethreshold in the opposite direction as the crossing that deter-mined the detection event itself. Each excitation event may re-sult in zero, one, or more than one detection event. The meas- ured relative time is the measured time between the excitation event and the time of the detection event. Examples of the ex- tended information will be provided below. A domain of interest may encompass a time of interest or a time of interest and op- tionally a location of interest. As could be shown by the inventors, the method according to the invention allows to compensate distortions of the distribution of relative times in intensity and / or shape. It is thus possiblePPROS003EP2 / 01.05.2025 11 u2fyj2jnto determine accurate distributions at high detected light in- tensities. The method may comprise at least one step in which distortionsof the distribution arising from deviations of an electricalpulse generated by the detection of a single photon from an im-aginary perfect square pulse are corrected.In particular, by iteration over at least one, in particularall, ^ detection events ^ ∈ ^ = {^^, … , ^^} within the domain of in-terest, a subset ^^ = {^′^, … , ^′^} of all detection events ^ is de-termined, and corrected blind times ^^^^ , are calculated bythe following Algorithm 1:^ = 1^^^ = ^^^^^^^ = ^^^^ + ^^^For all ^ ∈ [2, ^]:If ^^^ < ^^^^ + ^^^^^: (Case B)Set ^^^^^ to ^^^ + ^^^^ + ^^^ − ^^^ ^Else: (Case AAdd 1 to ^ ^^^ = ^^^^^^^ = ^^^^ + ^^^Here, ^^^ is the absolute time of the detection event ^^ from thestart of the experiment, obtained by combining the time of the last excitation event before the detection event and the rela-tive time of the detection event. ^^^ is the pulse width of the^-th detection event, and ^^^ is a predefined blind time exten-sion parameter. The above step is referred to as AdditionalPPROS003EP2 / 01.05.2025 12 u2fyj2jnBlind Time (ABT) Algorithm. The measured data (e.g. an Event 1and an Event 2), the calculation for the two different cases Aand B and the resulting final result for the two cases A and B are schematically shown in Fig. 4. The method may comprise at least one step in which distortions arising from a photon pile-up are corrected. This may be achieved by calculating a blind time compensationweight ^(^^) for each discrete relative time bin ^^∀ ^ ∈ [1, ^^^^^] as wherein ^totalis the total number of excitations cycles within adomain of interest DOI and ^dead(^^) is the number of excitationcycles within the domain of interest DOI where the relative timebin ^ was within a blind time period B^^, and ^bins is the numberof discrete time bins within an excitation cycle. This step isreferred to as Blind Time Compensation (BTC). The weights may be used for generating the distribution of rela- tive times. Instead of adding a discrete count for each photon ^in the histogram, the weight ^(^) is added. This adjusts the con-tribution of each photon to compensate for the probability of being able to detect a photon with that relative time.The above-mentioned number of excitation cycles ^dead(^) can becalculated by the following Algorithm 2:Initialize ^dead at 0 for all ^ ∈ [0, ^las)For all ^ ∈ [1, ^]:For all ^ in range [^^^, ^^^ + ^^^^]:If ^ ≥ ^las^ = ^ − ^lasIncrement ^dead(^) by 1PPROS003EP2 / 01.05.2025 13 u2fyj2jnHere, ^las denotes the excitation period.For each detection event ^^ ∈ ^^, a corrected relative time ^^^^ may be calculated as wherein a correction function aiming at correcting theapparent difference in relative time of detection events featur- ing different size and / or shape of their associated electricalpulse (see Figure 8). RTC stands for Rising Time Compensation.^RTC can assume any suitable mathematical form, contain anysuitable number of correction constants, and depend on at leastone pulse parameter, in particular at least one pulse parameter of the electric signal (see Figure 7) selected from the group consisting of ^a width of the electrical pulse associated with a detectionevent from a first time of crossing a threshold in a firstdirection to a later second time of crossing the threshold in an opposite second direction, ^a slope of the electrical signal at a first time of crossinga threshold in a first direction, ^a slope of the electrical signal at a later second time ofcrossing the threshold in an opposite second direction, ^a maximum or minimum of the electrical signal at a time in-terval associated with the detection event, ^a maximum or minimum of the electrical signal within a prede-fined duration from a threshold crossing,^ an area defined by the electrical signal at a time intervalassociated with the detection event within a predefined dura-tion from a threshold crossing,PPROS003EP2 / 01.05.2025 14 u2fyj2jn^ at least one, in particular a plurality of, values of theelectrical signal at predefined time intervals before and / orafter a threshold crossing, ^at least one, in particular a plurality of, crossing timesand / or widths determined at secondary threshold level,^ a time between an excitation event and a secondary thresholdcrossing. In one example, may be used as correction function, wherein is a predefined correction constant, ^^^is a pulse height, and ^threshis a prede- fined threshold voltage. As alternative examples, or may be used as correction function, wherein Δt is a predeterminedtemporal interval starting at the time of threshold crossing^^^^^^^, and ^^  (Δt) and ^^(Δt) are correction constants, dependent onΔt. The correction constants can be predetermined e.g. by usingcalibration experiments and / or mathematical simulations of an experimental system featuring the same SPR (Single Photon Re- sponse) of the detector.A histogram of the distribution of relative times (see Figure 9)may be calculated as follows: Algorithm 2aPPROS003EP2 / 01.05.2025 15 u2fyj2jnInitialize the temporal dis- tribution ^ at 0 for all ^for all detection events in^^: Increment ^^^^^^ ^ by ^^^^^^Alternatively, a histogram of the distribution of relative times may be calculated as follows: Algorithm 2b Initialize the temporal dis- tribution ^ at 0 for all ^for all detection events ^^ in^^: Increment ^^^^^^ ^ by ^^^^^^ ^ The method may comprise at least one step in which distortionsof the distribution arising from a photon pile-up and / or fromdeviations of a one-photon detection event from an imaginary perfect square pulse are corrected. In particular, by iteration over at least one, in particularall, ^ detection events ^ ∈ ^ = {^^, … , ^^} within the domain of in-terest, a subset ^^ = {^′^, … , ^′^} of all detection events ^ is de-termined by selecting only events that correspond to an excita-tion period where only a single photon reached the detector.This selection is performed by applying Algorithm 3: ^^ = 0 ∀ ^ ∈ [1, ^total]For all ^ ∈ [1, ^]:PPROS003EP2 / 01.05.2025 16 u2fyj2jn^ = ^^^Increase ^^by 1 For all ^ ∈ [1, ^]: If ^^ = 1 and ^^^^ < ^^^:^^^ = ^^Add 1 to ^Here, ^total is the total number of excitations cycles within a do-main of interest DOI, ^^^ ∈ [1, ^total] is the index of the excitationcycle in which detection event ^^ was recorded, ^^^ is a prede-termined parameter that specifies the maximum pulse width for adetection event to be classified as a single photon response and^^results as a list of number of detection events for each exci-tation cycle. For this correction, the temporal distributionhistogram is computed as a standard histogram for all events in ^^. The method described above is referred to as the multi-photonfiltering (MPF)approach (Figure 10).^^^ is a parameter that depends on the pulse shape and a prede-fined threshold. Therefore, it can be estimated from the singlephoton response and / or calibration data.Alternatively, one can estimate a functional ^^^ value by compu-ting the mean squared error (MSE) between the area-normalizedtemporal distributions at different values of ^^^ and an area-normalized undistorted reference temporal distribution. The correction function may be determined on the basis of cali- bration data.To obtain an undistorted reference temporal distribution, onemay perform a second measurement with the same sample under ex- perimental conditions that ensure the same shape of the temporalPPROS003EP2 / 01.05.2025 17 u2fyj2jndistribution in the absence of pile-up effects, while keeping the detected photon flux at a level in which the effect of pile- up is negligible. Alternatively, one may obtain a reference tem-poral distribution by applying any other correction method, suchas discarding all excitation cycles containing more than one photon event (as determined by signal integration or any other method).Since the shape of the temporal distribution obtained with theproposed correction method depends both on parameter ^^^ and anyparameters of the correction function is preferred that an algorithm is implemented that optimizes all parameters.It is preferred to use the following procedure:1. Estimate a conservatively large value of ^^^, using themethod described above based on the known pulse shape (or any other value of conservatively large ^^^). 2. Minimize the mean square error (MSE) between the area-nor-malized corrected temporal distribution and an area-normal-ized undistorted reference temporal distribution using theconservatively large value of ^^^ and optimizing the param-eters of the above example, the value of a single constant may be determined due to the choice of using ^RTC,H(^). However, any other method for estimating any number of correction constants may be employed, depending on the mathematical form of ^RTC(^). 3. Minimize the MSE between the area-normalized corrected tem-poral distribution and an area-normalized undistorted ref-erence temporal distribution using the optimized form of^RTC(^) and optimizing the value of ^^^.Following this method, in the above example where ^RTC(^) has beendefined asPPROS003EP2 / 01.05.2025 18 u2fyj2jn one may first determine ^h using a conservatively large value for^^^. Successively, a one-dimensional parameter sweep may be per-formed to identify an optimized value After having determined an optimized value of ^h, one may perform an analogous procedure to determine an optimized value of ^^^.The present invention also pertains to a system for carrying outthe method. The system comprises^ at least one excitation source, in particular a laser, forexciting a sample, ^preferably excitation and detection optics,^ at least one detector for detecting the radiation emitted orscattered by the sample and generating an electrical signal,out of which at least one detection event is generated, each detection event comprising at least one electrical pulse be-ing indicative of at least one photon originating from thesample and having a measured relative time, ^at least one first computation unit for providing extendedinformation for at least one of said detection events, pref- erably for each of said detection events, the extended infor-mation being representative of at least one of the size and shape of the electrical pulse within the detection event, ^at least one second computation unit for generating a distri-bution of relative times reflecting one or more properties ofthe sample based on at least one detection event and said ex-tended information. The first and the second computation unit may coincide. As above, the first and / or the second computation unit mayPPROS003EP2 / 01.05.2025 19 u2fyj2jn^ assign a corrected relative time to at least one detectionevent which is based on the measured relative time of the de-tection event and on the extended information associated with the respective detection event and / or ^assign a weight factor to at least one detection event whichis based on the measured relative time of the detection eventand on the extended information associated with a plurality, in particular all, detected detection events within a domain of interest. In order to demonstrate the advantages of the present invention,simulations of fluorescence decays featuring a 1 ns fluorescencelifetime with a 100 Mcps incident count rate were performed. The single photon response used in the simulation follows a Gaussianshape with a FWHM of 1 ns as shown in Figure 8. The number ofphotons in the simulation is approximately 1 million, whereinvariations are due to the random nature of the simulation. The proposed method is able to correctly retrieve both the intensity (Figure 11) and lifetime (Figure 12) information with a high de- gree of accuracy.Figure 1 shows an exemplary embodiment of a system 50 for carry-ing out the method. Such a system comprises an electronic device capable of measuring an electronic signal originating from a de- tector, detect electronic pulses and assign to each detected event: ^a relative time,^ an absolute time, or in alternative a value of an excitationevent number, ^one or more of any of the extended information mentionedabove, as for example a width of the detection event from a first time of crossing a threshold in a first direction to a later second time of crossing the threshold in an oppositePPROS003EP2 / 01.05.2025 20 u2fyj2jnsecond direction, a slope of the electrical signal at a firsttime of crossing a threshold in a first direction, a slope of the electrical signal at a later second time of crossing thethreshold in an opposite second direction, etc.Such system 50 is able to produce a data stream of informationabout temporally ordered detected events, possibly including ad- ditional events not originating from detected photons, and transmit it to an external computer. Figure 2 shows a typical electronic signal originating from the detector, with electrical pulses composed of one or multiple single photons responses. The times of detection of the excita- tion events are indicated as vertical dashed lines. Figure 3 depicts the distribution of relative times of fluores-cence photons calculated using simulated detection events in ab-sence (ground truth) or presence of pile-up distortions.In Figure 4, it is demonstrated why a blind time is preferablyextended when an event is removed from consideration. Case (A)shows the result of adding a blind time shorter than the separa-tion between any two events while (B) shows the result of a sec-ond event (event 2) falling within the added blind time of aprevious event (event 1). The result for case (B) shows how thetotal blind time for event 1 must be extended to encompass theremoved event.Figure 5 demonstrates the advantage of the concept of additionalblind time (ABT): If the blind time of pulse 1 (A) is set to itspulse width, then pulse 2 should be detected (B). However, ifpulse 2 is present, the measured analog signal does not go belowthe threshold and pulse 2 is not detected (C). Therefore, theblind time of pulse 1 is increased to account for this effect.Figure 6 shows the histograms of the weights used in the BTC correction to calculate the relative time histograms, for dif- ferent photon count rates.PPROS003EP2 / 01.05.2025 21 u2fyj2jnFigure 7 depicts an electrical signal 12 comprising a detectionevent 13, the two standard TTTR parameters, 0 and 1, and fiveparameters, 2 to 6, that form extended information:^ 0: the number of the excitation event,^ 1: the relative time of the threshold crossing,^ 2: the maximum of the electrical signal 12 within a prede-fined duration from an upward threshold crossing time,^ 3: the width of the electrical pulse associated with a detec-tion event 13 from a first time of crossing a threshold inan upward direction to a later second time of crossing the threshold in a downward direction, ^4: the slope of the electrical signal 12 at an upward thresh-old crossing time, ^5: the time between the excitation event and a secondarythreshold crossing, ^6: the area defined by the electrical signal within the de-tection event 13 within a predefined duration from an up-ward threshold crossing time.Figure 8 demonstrates the different threshold crossing timemeasured for electrical pulses comprising one or more single photon responses for photons arriving essentially at the same time. While the theoretical relative times should be the same for all detected pulses, the measured ones, measured at thresh- old crossing, differ.As shown in Figure 9, the method of the invention yields a dis-tribution of relative times that closely resembles ground truthdata (denoted by a circle). In this plot, the histogram denotedby a triangle (ABT+BTC) is obtained by the introduction of ablind time extension and by blind time corrections, whereas inPPROS003EP2 / 01.05.2025 22 u2fyj2jnthe histogram denoted by a rectangle (ABT+BTC+RTC) all correc-tions, included the correction of relative times, are applied. The difference plot in the bottom shows that the sources of biasmentioned before have been nearly completely removed from thehistogram denoted by a rectangle, leaving only the statisticalvariation as the main source of error. Comparing the differencecurves for the uncorrected histogram (denoted by a rhombus) andthe histogram denoted by a triangle illustrates that the major-ity of the distortion in intensity is generated by the blind time, whereas the temporal distortion is still present after ap- plying the blind time correction.Figure 10 visualizes a correction step in which all excitationcycles containing more than one photon are excluded from the analysis (Algorithm 3).Furthermore, as can be recognized in Figure 11, the linearity ofintensity is maintained. The crosses represent the count ratecorresponding to the total counts reported in the corrected his-togram when using the combined correction. The count rate of de-tection events that are used to compute the relative time histo-grams depends on the total blind time (BT) used.As visible in Figure 12, the lifetime estimate ^^ is virtuallyundistorted for all count rates evaluated. The four graphs werecreated from simulations of monoexponential decays correspondingto 0.5, 1, 2, and 4 ns lifetime, from left to right. The life-time values were obtaining through exponential fitting.

Claims

PPROS003EP2 / 01.05.2025 23 u2fyj2jnClaims 1. A method for performing time-correlated single photoncounting measurements, the method comprising the steps of a) exciting a sample (10) by a plurality of successiveexcitation events, (11),b) detecting the generated radiation, thereby generatingan electrical signal (12), out of which at least onedetection event (13) is generated, each detectionevent (13) comprising at least one electrical pulseindicative of at least one photon originating from thesample (10) and having a measured relative time (^^),c) providing extended information for at least one ofsaid detection events (13), preferably for each ofsaid detection events (13), the extended informationbeing representative of at least one of the size and shape of the electrical pulse within the detectionevent (13), andd) generating a distribution of relative times reflectingone or more properties of the sample (10) based on atleast one detection event (13) and said extended in-formation, wherein ^at least one detection event (13) is disregardedbased on the measured absolute time, relative time (^^), and / or extended information associatedwith one or more of the detection events (13) withina domain of interest (DOI), and / or^ a corrected relative time (^^^) is assigned to atleast one detection event (13) which is based on themeasured relative time (^^) of the detectionPPROS003EP2 / 01.05.2025 24 u2fyj2jnevent (13) and on the extended information associ-ated with the respective detection event (13), thecorrected relative time ^^^^ being calculated as ^^^^ =being a correction that depends onat least one pulse parameter and / or^ a weight factor (^(^)) is assigned to at least onedetection event (13) which is based on the measuredrelative time (^^) of the detection event (13) andon the extended information associated with a plu- rality, in particular all, detected detection events (13) within a domain of interest (DOI).

2. The method as claimed in claim 1,wherein in step d), distortions arising from deviations ofan electrical pulse generated by the detection of a singlephoton from an imaginary perfect square pulse are cor-rected.

3. The method as claimed in one of the claims 1 or 2,wherein at least one detection event (13) is disregarded byiterating over at least one, in particular all, ^ detectionevents ^ ∈ ^ = {^^, … , ^^} within the domain of interest, deter-mining a subset= {^′^, … , ^′^} of all detection events ^, andcalculating corrected blind times ^^^^ , … , ^^^^ by the follow-ing Algorithm 1:^ = 1^^^ = ^^^^^^^ = ^^^^ + ^^^For all ^ ∈ [2, ^]:If ^^^ < ^^^^ + ^^^^^: Set ^^^^^ to ^^^ + ^^^^ + ^^^ − ^^^ ^PPROS003EP2 / 01.05.2025 25 u2fyj2jnElse: Add 1 to ^ ^^^ = ^^^^^^^ = ^^^^ + ^^^wherein ^^^ is the absolute time of the detection event ^^from the start of the experiment, obtained by combining the time of the last excitation event before the detection event and the relative time of the detection event, ^^^is the pulse width of the ^-th detection event, and ^^^ is a predefined blind time extension parameter.

4. The method as claimed in one of claims 1 to 3,wherein in step d), distortions arising from a photon pile-up are corrected.

5. The method as claimed in one of the claims 1 to 4,wherein for each discrete relative time bin ^^ , ^ ∈ [1, ^^^^^], theweight factor (^(^)) is a blind time compensation weight (^(^)) calculated aswherein ^totalis the total number of excitations cycles within a domain of interest (DOI) and ^dead(^) is the numberof excitation cycles within the domain of interest (DOI) where the relative time (^) was within a blind time periodB^^.

6. The method as claimed in any of claims 1 to 5,whereindepends on at least one pulse parameter ofthe electric signal selected from the group consisting ofPPROS003EP2 / 01.05.2025 26 u2fyj2jn^ a width of the electrical pulse associated with the de-tection event (13) from a first time of crossing athreshold in a first direction to a later second time of crossing the threshold in an opposite second direc- tion, ^a slope of the electrical signal (12) at a first timeof crossing a threshold in a first direction within thedetection event (13),^ a slope of the electrical signal (12) at a later secondtime of crossing the threshold in an opposite second direction within the detection event (13),^ a maximum or minimum of the electrical signal (12) at atime associated with the detection event (13),^ a maximum or minimum of the electrical signal (12)within a predefined duration from a threshold crossing, ^an area defined by the electrical signal (12) at a timeinterval associated with the detection event (13)within a predefined duration from a threshold crossing, and ^any number of voltage values at predefined time inter-vals before and / or after a threshold crossing timewithin the detection event (13), at least one, in par-ticular a plurality of values of the electrical signal at predefined time intervals before and / or after a threshold crossing, ^at least one, in particular a plurality of, crossingtimes and / or widths determined at a secondary threshold level within the detection event (13),^ a time between an excitation event and a secondarythreshold crossing within the detection event (13).PPROS003EP2 / 01.05.2025 27 u2fyj2jn7. The method as claimed in claim 6,whereinis used as correction function, whereinis a predefined correction constant, ^^^is a pulse height, and ^threshis a predefined threshold voltage.

8. The method as claimed in claim 6,whereinis used as correction function, Δt is a predetermined tem-poral interval starting at the time of threshold crossing ^^^^^^^, and ^^  (Δt) is a correction constant dependent on Δt.

9. The method as claimed in claim 6,whereinis used as correction function, Δt is a predetermined tem-poral interval starting at the time of threshold crossing ^^^^^^^, and ^^ (Δt) is a correction constant dependent on Δt.

10. The method as claimed in any of the previous claims,wherein a histogram of the distribution of relative times is calculated as follows: Algorithm 2a Initialize the temporal dis- tribution ^ at 0 for all ^for all photon events ^^in ^^:PPROS003EP2 / 01.05.2025 28 u2fyj2jnIncrement ^^^^^ ^ by ^^^^^11. The method as claimed in any of the previous claims,wherein a histogram of the distribution of relative times is calculated as follows: Algorithm 2b Initialize the temporal dis- tribution ^ at 0 for all ^for all photon events ^ in ^^:Increment ^^^^^ ^ by ^^^^^^ 12. The method as claimed in any of the previous claims,wherein distortions of the distribution arising from a pho- ton pile-up and / or from deviations of a detection event generated by the detection of a single photon from an imag- inary perfect square pulse are corrected by iteration over at least one, in particular all, N detection events ^ ∈ ^ ={^^, … , ^^} within the domain of interest,a subset ^^ = {^′^, … , ^′^} of all detection events ^ being de-termined by selecting only events that correspond to an ex- citation period where only a single photon reached the de- tector, the selection being performed by applying Algorithm3: ^^ = 0 ∀ ^ ∈ [1, ^^^^^^]For all ^ ∈ [1, ^]:Increase ^^by 1 For all ^ ∈ [1, ^]:PPROS003EP2 / 01.05.2025 29 u2fyj2jnIf ^^ = 1 and ^^^^ < ^^^:^^^ = ^^Add 1 to ^ a temporal distribution histogram being computed as a stand- ard histogram for all events in ^^^^^^^^being the total number of excitations cycles within a domain of interest DOI, ^^^ ∈ [1, ^^^^^^] being the index of the excitation cycle inwhich detection event ^^was recorded, ^^^ being a predetermined parameter that specifies themaximum pulse width for a detection event to be classified as a single photon response and ^^resulting as a list of number of detection events for each excitation cycle.

13. The method as claimed in any of the claims 3 to 12,wherein the BTE is determined on the basis of calibrationdata.

14. The method as claimed in any of the claims 6 to 13,wherein the correction function is determined on the basis of calibration data.

15. A system (50), in particular for carrying out themethod as claimed in any of the previous claims, the system comprising ^at least one excitation source, in particular a laser,for exciting a sample (10),PPROS003EP2 / 01.05.2025 30 u2fyj2jn^ preferably excitation and detection optics,^ at least one detector for detecting the radiation orig-inating from the sample (10) and generating an electri-cal signal (12), out of which at least one detectionevent (13) is generated, each detection event (13) com-prising at least one electrical pulse being indicative of at least one photon originating from the sample (10)and having a measured relative time (^^),^ at least one first computation unit for providing ex-tended information for at least one of said detection events, preferably for each of said detection events (13), the extended information being representa-tive of at least one of the size and shape of the elec- trical pulse within the detection event, ^at least one second computation unit for generating adistribution of relative times reflecting one or more properties of the sample based on at least one detec-tion event and said extended information, the first and / or the second computation unit ^disregarding at least one detection event (13) based onthe measured absolute time, relative time (^^), and / orextended information associated with one or more of the detection events (13) within a domain of interest(DOI), ^assigning a corrected relative time to at least one de-tection event which is based on the measured relative time of the detection event (13) and on the extendedinformation associated with the respective detection event (13), the corrected relative time ^^^^ being calcu- lated as ^ ^^^ = ^^^ +being a correction thatdepends on at least one pulse parameter and / orPPROS003EP2 / 01.05.2025 31 u2fyj2jn^ assigning a weight factor (^(^)) to at least one detec-tion event (13) which is based on the measured relativetime (^^) of the detection event (13) and on the ex-tended information associated with a plurality, in par- ticular all, detected detection events (13) within adomain of interest (DOI).

Images