WO2012158121A1

WO2012158121A1 - Method and arrangement for determining decay rates of pulse-stimulated signals

Info

Publication number: WO2012158121A1
Application number: PCT/SE2012/050541
Authority: WO
Inventors: Andreas Ehn; Joakim BOOD; Olof Johansson
Original assignee: Andreas Ehn; Bood Joakim; Olof Johansson
Priority date: 2011-05-16
Filing date: 2012-05-16
Publication date: 2012-11-22
Also published as: SE535980C2; SE1100371A1

Abstract

The present invention relates to a method and a arrangement for determining a decay rate of a first signal originating from a pulse-stimulated sample. The method comprises the steps of: a) amplifying at least two electrical decaying signals derived from said first signal with functions of different temporal characteristics, wherein at least one of said functions has an increasing or decreasing ramp-like temporal shape, for forming at least two processed electrical signals, b) integrating said processed electrical signals, c) forming at least one ratio using said integrated processed electrical signals, d) calculating said decay rate from said at least one ratio.

Description

Method and arrangement for determining decay rates of pulse-stimulated signals

Technical field

The present invention relates to a method and arrangement for determining a decay rate of a first signal originating from a pulse-stimulated sample.

Background art

Temporal analysis of decaying electronic-response signals from pulsed input stimulation is undertaken in a number of measurement apparatuses. If the temporal pulse width of the input stimulation is of the same order or shorter than the decay time of the response signal, the response signal can be addressed as the impulse response function of the investigated system.

In nature there are several systems that have impulse response functions that have a nearly exponential decay, which means that the decay rate is proportional to the signal intensity. Examples of such systems could be luminescence signals emitted from atoms, molecules and more complex structures such as quantum dots, rare earth metals embedded in crystalline structures, etc.

In case of analyzing electromagnetic signals the photons are converted into an electric signal using electro-optic sensors. Decay rates of such luminescence, mentioned above, sometimes includes information about the luminescent object, such as temperature, pressure, luminescent particle size, ambient molecule concentrations, physical nature of the luminescence, luminescent species, and so forth. Such parameters are not only of great importance in a number of scientific fields such as medicine, biology, physics and chemistry, but also in engineering and commercial applications where tools are developed to provide information of such parameters. Such applications could be where; phosphorescence decays are analyzed to determine its temperature, fluorescence signals are analyzed to provide medical, biological, chemical and physical properties of medical and biological samples, auto fluorescence from different types of tissues could be mapped, studies of mixing in fluid dynamics, to determine authenticity of classic art objects described in the patent WO2004/001400 A1 .

Commonly, decay signals are analyzed as exponential decays, and a significant effort has been made to provide evaluation algorithms that determine the decay time of such signals.

There are several different approaches to evaluate lifetime signals especially if spatial information in one or two dimensions is of interest. In general, two different techniques to perform imaging are; imaging using one or two-dimensional detectors (array or camera detectors) or by scanning the excitation over the sample, thus collecting signal from each pixel separately. Independent of how the image is formed, three concepts are used to evaluate signals in order to obtain the luminescence lifetimes:

1 . Analysis in the frequency domain (FD)

2. Analysis in the temporal domain (TD)

3. Time correlated single-photon counting (TCSPC)

Below a brief description of each lifetime evaluation technique is given.

FD

Lifetime determination of optical signals in the frequency domain utilizes an intensity modulated excitation source. It is usually a light emitting diode (LED), laser diode or a laser, and the modulation frequency is generally in the kHz-GHz range, depending on the range of lifetimes to be measured. The detector can be either a photomultiplier tube (PMT), an array of PMT:s or an intensified charged coupled device (ICCD). After the signal has been converted from photons to electrons, the detected signal is compared to the excitation modulation. This comparison could be done by either modulating the intensifier with the same frequency as the excitation source or using a lock-in amplifier. Emitted luminescence is phase shifted and demodulated, with amounts depending on the lifetime of the signal. The phase shift and demodulation between excitation source and detector intensifier can be measured. Thus, phase shift and demodulation due to the lifetime of the optical signal can be obtained from recorded data, and the lifetime can be extracted.

A drawback of this approach is the modulation frequency of the excitation light which is optimal for a fairly narrow range of decay times.

Thereby, knowledge of the fluorescence lifetime has to be gained before choosing modulation frequency. Furthermore, the demand on quality of the modulation is fairly high, so if compromised, will introduce errors in the determination. Thus, the characteristics of a camera has be to precise and repeatable. Frequency based schemes in general need a certain amount of time, since a number of time periods need to be recorded. Hence, rapidly varying measurement objects cannot be investigated. If the measurement object is illuminated for quite some time, the sample may be saturated and the measurement object is then affect by the measurement procedure, which obviously introduces a problem. Especially since a number of consecutive measurements has to be performed.

TD

Lifetime determination of optical signals in the time domain is performed with gateable cameras able to provide lifetime images, such as intensified CCD cameras, C-MOS cameras etc. The excitation source is short pulsed LEDs or lasers of various types. The shutter/gate of the camera is set as open or closed at different time intervals during the signal-decay curve. Most often, commercial systems contain one camera. Therefore, at least two images have to be recorded to evaluate the lifetime of the optical signal. There are several schemes to acquire and analyze the pixels in the images.

Algorithms that provide fast evaluation are called Rapid Lifetime

Determination (RLD) algorithms, providing decay times in every pixel in an image. These algorithms make use of the detector shutter/gate to control the integration time of the sign

here D is the total number of integrated counts, t_open is the time when the shutter is opened, t_C|_0Se is the time when the shutter is closed, and the integrand is the exponential decay signal with the decay constant τ. By using RLD a substantial part of the signal is thrown away, making the signal-to-noise ratio low. To compensate for low signals the data has to be averaged, which takes time and rapidly varying measurement objects cannot be measured on. Also, the efficiency of the RLD algorithm is strongly dependent on the fluorescence lifetime that is measured. Hence, the range of the lifetimes that is of interest has to be known in advance. Additionally, ICCD cameras do not have square gate functions, hence RLD will predict erroneous lifetimes.

TCSPC TCSPC is an acronym for time-correlated single photon counting, performing point measurements. An image is formed by scanning the detection and illumination over the area of interest. The difference in time between the laser pulse excitation and the incoming photons are determined and saved in a memory. The evaluation of the luminescence lifetime is most often performed by fitting the data with a least-square method.

If applying TCSPC only one photon is collected per excitation, making the acquisition time of the measurement very low. This makes the scheme time consuming and rapidly varying measurement objects cannot be measured on. Furthermore, the image has to be built up by point

measurement data, making this technique limited in terms of measurements on varying objects.

Summary of the invention

In view of the above, an objective of the invention is to solve or at least reduce one or several of the drawbacks discussed above. Generally, the above objective is achieved by the attached independent patent claims.

According to a first aspect, the present invention is realized by a method for determining at least one decay rate of a first signal originating from a pulse-stimulated sample. The method comprises the steps of: a) amplifying at least two electrical decaying signals derived from said first signal with functions of different temporal characteristics, wherein at least one of said functions has an increasing or decreasing temporal shape, for forming at least two processed electrical signals, b) integrating said processed electrical signals, c) forming at least one ratio using said integrated processed electrical signals, and d) calculating said at least one decay rate from said at least one ratio.

Using a signal originating from a pulse-stimulated sample is

advantageous in that the sample does not fade compared to using a continuous light source for stimulating the sample since the sample is exposed to a smaller amount of light. Furthermore, the method is applicable to almost all types of decay rates. This can be compared with when operating in the frequency domain, wherein one most approximately know the decay rate and adjust the switching frequency accordingly.

The increasing or decreasing temporal shape may be ramped.

Ramped can be interpreted as triangular and having a constant slope.

The increasing or decreasing temporal shape may be rampe-like.

Rampe-like can be interpreted as triangular and having an exponential function or similar.

The functions of different temporal characteristics may comprise at least one function having substantially linearly increasing temporal shape and at least another function having substantially linearly decreasing temporal shape.

The first signal may be an optical signal and the method may further comprise splitting the optical signal into at least two optical signals, converting said at least two optical signals for forming said at least two electrical decaying signals.

The first signal may be an optical signal, and the method may further comprise converting said first signal to an electrical, and splitting the electrical signal into at least two signals for forming said at least two electrical decaying signals.

The method may further comprise detecting different spatial parts of said first signal through at least two optical pathways for forming said at least two electrical decay signals. This is advantageous in that the first signal does not need to be divided in at least two signals which is capacity efficient.

The first signal may comprise optical signals originating from at least two pulse-stimulations of a sample, and the method may further comprise converting said optical signals originating from at least two pulse-stimulations of a sample into electrical signals for forming said at least two electrical decaying signals. This is advantageous in that only one sensor is necessary.

The step of calculating may be replaced by the steps of: a) preparing a set of library signals with different library decay rates, b) multiplying said set of library signals with said functions of different temporal characteristics, and forming a set of processed library signals, c) integrating said set of processed library signals forming a set of integrated processed library signals, d) inputting said set of integrated processed library signals in said at least one ratio, forming at least one set of library ratios, e) forming a decay-rate function by finding an unambiguous relation between said at least one set of library ratios and said different library decay rates, f) determining said at least one decay rate by inserting said at least one ratio from said first signal in said decay-rate function.

These steps are advantageous when the functions used for amplifying the at least two electrical decaying signals have a shape that does not provide analytical expression for the formed ratio.

The finding can, e.g. be performed using a suitable numerical method. The steps of the first aspect can be performed by analog circuits, such as integrated circuits, for example operational amplifiers, performing multiplying, integrating and ratio-forming operations, as well as providing gain functions, such as linear ramp functions. The steps can also be performed by a general purpose computer or central processing unit programmed in a suitable manner, or by dedicated integrated circuits, such as a FPGA or a custom made integrated circuit.

According to a second aspect, the present invention is realized by an arrangement for determining at least one decay rate of a first signal originating from a pulse-stimulated sample. The arrangement comprises: at least one amplifier for amplifying at least two electrical decaying signals derived from said first signal with functions of different temporal

characteristics, wherein at least one of said functions has an increasing or decreasing temporal shape, for forming at least two processed electrical signals, at least one integrator for integrating said processed electrical signals, a first unit for forming at least one ratio using said integrated processed electrical signals, and for calculating said decay rate from said at least one ratio.

The first signal may be an optical signal, and the arrangement may further comprise an optical unit arranged to split the optical signal into at least two optical signals, and the arrangement may further comprise at least one photosensitive sensor for forming said at least two electrical decaying signals by converting said at least two optical signals.

The first signal may be an optical signal, the arrangement may further comprise a photosensitive sensor for converting said first signal to an electrical signal, and a second unit arranged to split the electrical signal into at least two signals for forming said at least two electrical decaying signals.

The arrangement may further comprise at least one photosensitive sensor for forming said at least two electrical decay signals by detecting different spatial parts of said first signal through at least two optical pathways.

The first signal may comprise optical signals originating from at least two pulse-stimulations of a sample, the arrangement may further comprises at least one photosensitive sensor for forming said at least two electrical decaying signals by converting said optical signals originating from at least two pulse-stimulations of a sample into electrical signals of similar temporal characteristics.

The photosensitive sensor may comprise at least one from the group of: photo diodes, photo multiplier tubes, array detectors of photo diodes, or array detectors of photo multiplier tubes.

The at least one photosensitive sensor may be arranged to replace the integrator and may be arranged for integrating said processed electrical signals.

Said at least one amplifier, said at least one integrator and said at least one photosensitive sensor may be replaced by at least one from the group of: an intensified CCD camera, electronmultiplying CCD cameras, or

electronmultiplying CMOS cameras. The advantages of the first aspect are equally applicable to the second aspect. The second aspect can be embodied in accordance with the embodiments of the first aspect.

According to a third aspect, the present invention is realized by a computer-readable recording medium having recorded thereon a program for implementing the method according to the first aspect when executed on a device having processing capabilities. The advantages of the first aspect are equally applicable to the third aspect.

Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise herein. All references to "a/an/the [element, device, component, means, step, etc]" are to be interpreted openly as referring to at least one instance of said element, device, component, means, step, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not have to be performed in the exact order disclosed, unless explicitly stated.

Brief Description of the Drawings

Further objects, features and advantages of the invention will become apparent from the following detailed description of embodiments of the invention with reference to the drawings, in which:

Fig. 1 is a schematic illustration of an embodiment of the inventive method for determining a decay rate of a first signal originating from a pulse- stimulated sample.

Fig. 2 is a schematic illustration of an embodiment of the inventive method of Fig. 1 .

Fig. 3 is a schematic illustration of an embodiment of the inventive method of Fig. 1 .

Fig. 4 is a schematic illustration of an embodiment of the inventive method of Fig. 1 .

Fig. 5 is a schematic illustration of an embodiment of the inventive method of Fig. 1 . Fig. 6 are graphs illustrating Monte Carlo simulations of exponential decays recorded with two different sets of gain functions.

Fig. 7 is a schematic illustration of an experimental setup used for fluorescence lifetime imaging in a gas-phase experiment.

Fig. 8 illustrates in (a_exp) and (b_exp)simultaneous, single-shot laser- induced fluorescence (LIF) images of a tolueneseeded air jet in a nitrogen co- flow, and in (a_Sj_m) and (b_Sj_m) the scheme for simulating the detection.

Fig. 9 is a diagram illustrating fluorescence lifetimes.

Fig. 10 is a schematic illustration of an embodiment of the inventive device.

Fig. 1 1 is a schematic illustration of the inventive arrangement for determining a decay rate of a first signal originating from a pulse-stimulated sample. Detailed description of preferred embodiments of the invention

Below, several embodiments of the invention are described. These embodiments are described in illustrating purpose in order to enable a skilled person to utilize the invention and to disclose the best mode. However, such embodiments do not limit the scope of the invention.

Moreover, certain combinations of features are shown and discussed.

However, other combinations of the different features are possible within the scope of the invention.

The idea behind this invention is to amplify a decaying signal with different gain characteristics and thereafter integrate the amplified signals. One or several ratio(s) is/are then formed using the integrated values of the differently amplified signals. The amplification makes the signal ratio a function of the lifetime of the decaying signal. Thus, for each gain profile, it is possible to integrate the entire signal. The different gains should be known or measured along with the excitation pulse. The amplified signals can then be calculated for different signal lifetimes. First the simulated signal could be convolved with the excitation pulse. Such calculation could also be performed using more sophisticated methods, e.g. solving rate equations or density matrix equations. If the excitation pulse duration is sufficiently short, compared to the signal decay time, convolution is not necessary to perform. On the other hand, if the excitation pulse is of the same order or longer than the decay time, it is still possible to use this approach as long as the temporal shape of the decaying signals are known. Furthermore, typical signals could also be measured for a database/library of signals with different decay rates that would serve as input data in the calculations. Next the signal is multiplied with the gain functions and the same ratios are formed as for the measured data. The calculated signal ratios are then compared to the measured ones in order to find the lifetime/lifetimes of the measured data. This

detection/evaluation scheme can be applied for point measurements, measurements along a line as well as for two-dimensional measurements. The signal could be any kind of decaying signal; electrical, optical (infrared, visible, ultraviolet), radioactive particles etc.

The approach presented here could be implemented in TD and TCSPC since pulsed excitation is used. It should be emphasized though, that the present invention is not restricted to analysis of optical signals. In fact, it could be used to extract lifetimes out of any response function, which is converted to an electrical signal. Furthermore, the decaying signal does not have to be close to exponential. As long as signals have different decays this approach can distinguish between them, even if they are linear, multi-exponential, inverse, etc.

Even though the method described here is applicable in determining decay rates of response signals in general, we give examples of applications in analyzing optical signals. To provide an impulse response of luminescence an excitation pulse using electromagnetic radiation or charged particles is needed. Such excitation sources could be lasers, laser diods, or light emitting diodes. In case of analyzing electromagnetic signals, commercial detector systems are available to provide temporal information of the signal in zero dimension using point detectors; such as photo diods (PD), photo multiplier tubes (PMT) and such. In one dimension (along a line) sensors based on an array of PDs or PMTs are available and for two dimensions (images) ICCD, EMCCD, C-MOS-cameras and similar products are used. All such sensors that convert the decaying electromagnetic signal into electrons with a similar temporal shape can be used to determine the decay rate or at least distinguish one decay rate from another.

There are several detection and signal processing schemes that could be used when applying the current concept. These are summarized in Fig. 1 - 4.

Fig. 1 is a schematic illustration of an embodiment of the inventive method for determining a decay rate of a first signal originating from a pulse- stimulated sample. In a first step 100, a sample is pulse-stimulated.

In step 1 10, two electrical decaying signals that have been derived from the first signal are amplified thus forming at least two processed electrical signals. The amplifying is done by multiplying the first signal with functions of different temporal characteristics. At least one of said functions has an increasing or decreasing ramp-like temporal shape. It is to be noted that these functions are herein sometimes referred to as gain functions.

In step 120, the processed electrical signals are integrated.

In step 130, at least one ratio is formed using the integrated processed electrical signals.

In step 140, the said decay rate is calculated from the at least one ratio.

Figure 2 is a schematic illustration of an embodiment of the inventive method of Fig. 1 . In a step 10, the first signal, which is an optical signal, is split into at least two optical signals. In step 20, the at least two optical signals are detected by a photosensitive sensor for forming the at least two electrical decaying signals that are then amplified in step 1 10.

Figure 3 is a schematic illustration of an embodiment of the inventive method of Fig. 1 . In step 30, the first signal, which is an optical signal, is converted to an electrical signal of similar temporal shape using a

photosensitive sensor. In step 40, the electrical signal is split into at least two signals for forming the at least two electrical decaying signals.

Figure 4 is a schematic illustration of an embodiment of the inventive method of Fig. 1 . In step 50, different spatial parts of the first signal are detected through at least two optical pathways using at least one photosensitive sensor thus forming the at least two electrical decay signals. At least two detectors can be applied to detect the different spatial parts of the first signal. The different detectors can for example observe the sample from different angles. The different sensors apply different amplification functions.

Figure 5 is a schematic illustration of an embodiment of the inventive method of Fig. 1 .The first signal comprises optical signals originating from at least two pulse-stimulations of a sample. In step 60, these optical signals are converted into electrical signals of similar temporal shapes using a

photosensitive sensor thus forming the at least two electrical decaying signals.

In the below embodiments decaying fluorescence signals are observed following excitation using picosecond laser pulses. The presented detection and analysis scheme is, however, not limited to fluorescence decays. It could be any kind of decaying signal.

For brevity only two gain functions will be used in the below

embodiments. In reality the upper limit of gain functions that can be applied is set by hardware and software limitations. If linear functions are used, analytic expressions can be derived. It will, however, be shown that the invention is not limited to the application of linear or ramp-like functions.

Consider a situation where the effective decay time of a decaying signal is described by a single exponential decay curve and the two gain functions are denoted by G1 and G2 respectively. The single exponential decay, however, serves only as an example. It could in fact be any kind of decaying signal, but an arbitrary signal does not necessarily provide analytical solutions and is thus not suitable for illustration purposes.

Two signals, and l₂, are obtained. A single signal could be detected and then split into two parts or two sensors could be used to obtain two signals or two signals could be obtained using a single detector in

combination with two excitations. The signals can be described by the following equations:

(1)

where τ is the signal lifetime, ti and t₂ are the gain delay times relative to excitation and δι and δ₂ are the time jitters of the gain profiles relative to excitation. The integration interval is set from -∞ to∞ for convenience because the integrand is nonzero only in a limited interval. Obviously shorter intervals are used in practice.

A signal ratio, R, can be formed in different ways. Three exampl equation (3), equation (4), or the inverse of equation (4), displayed in equation (5):

(3)

R

(4)

R

(5)

If the integrands, ^^fo ^ - '^{/ _ <5}) , in equations (1 ) and (2) are denoted ^i (*'^T) and ^ ( Ό, respectively, R can be written:

R

for equations (3), (4) and (5), respectively. Here, Fj(tj) could be interpreted as the (non-normalized) probability-density function of the time at which, for example, an electron emerges from the gain electronics. Taking the derivative of R with respect to τ while assuming the signal to be a convolution between a Gaussian function (the excitation pulse) and a single exponential decay, the following expressions are derived for equations (6), (7) and (8), respectively:

In equation (10), E,(t) is the expectation value in time of Fj(tj). Thus for equation (10) to have a determinate solution, the expectation values of Fi(t ) and F₂(t ) must not coincide. Similar conditions can be seen to hold for equations (9) and (1 1 ) although the distribution functions, Fj(t ), are not properly normalized. Apparently any choice of two dissimilar gain functions, including similar gain profiles with different ti, can be used. However, theoretically the optimal gain functions are Gi=At and G_∑=A for the ratio formed in equation (3). For equation (4), the optimal choice of gain functions are Gi=Bt and G₂- -Bt+B. With these choices of gain functions, the ratios in equations (3) and (4) both equal the lifetime τ, i.e. there is a linear relationship without any offset. For the ratio formed in equation (5), ramped gains lead to an inverse relationship between signal lifetime and formed ratio. Such ratio choice could under certain circumstances be advantageous if the signal lifetime is to be used for species concentration measurements.

Figure 6 are graphs illustrating Monte Carlo simulations of exponential decays recorded with two different sets of gain functions. The inventive method and arrangement are compared to prior art usually used in

fluorescence lifetime imaging microscopy (FLIM). Prior art uses gates of squared shape. An embodiment of the inventive method and arrangement uses triangular gates. The upper part of Fig. 6a illustrates exponential decay for prior art and the lower part of Fig. 6a illustrates exponential decay for the present invention. In Figs. 6b-d, the dotted lines relate to the prior art and the solid lines relate to embodiments of the present invention.

Fig. 6b illustrates the figure of merit for the two sets of gates. The solid curve corresponds to the linear gains, which is independent of the lifetime with a figure of merit less than 2. Fig. 6c illustrates the error in mean value of the determined lifetime. In Fig. 6d, the relative error in the measured lifetime of the detected signal is nearly constant for the linear-gains configuration contrary to the squared gains.

Theoretically, linear gain functions provide equally high sensitivity for any lifetime. This fact is illustrated in Fig. 6 where the choice of using two linear and two squared gain profiles are compared. The results shown are from Monte Carlo simulations involving 500 emitted particles that are Poisson distributed and decaying exponentially. The simulation was repeated 1000 times in order to generate statistics.

The squared functions shown in Fig. 6a comprise two consecutive time windows of 3 ns. AB is the amplitude of the signal and LIF is seen as the thick, solid, decaying curves. The linear gain functions are defined in a time window of 40 ns. Their slopes in this interval are equal in magnitude with opposite signs. Figure 6b shows the figure of merit for the two choices of gain functions. The figure of merit is defined (O_T/T) (N/ON), where o_T is the standard deviation in τ and o_N is the standard deviation of the signal; for poisson statistics σ_Ν = ^"v -^?\ It is a measure of the noise amplification of the system and should thus be as low as possible. Figure 6c shows the error in τ and Fig. 6d shows τ/σ_τ as a function of τ.

Besides providing equally high sensitivity for any lifetime, linear and ramp-like gain profiles are easier to realize than squared ones due to the high frequency components required to create the rising and falling edges of squared gain profiles. In addition, it is advantageous to be able to integrate the entire signal since it provides maximum signal-to-noise ratio. It should, however, be emphasized again that any set of dissimilar gain profiles can be used. Using linearly ramped gain curves is just the optimal choice for certain signal curves. Furthermore it should be stressed that the three ratios formed in equations (3), (4) and (5) are just examples. The skilled person realizes that there are other ways to form a ratio using two signals and all these ways are within the scope of the present invention.

Regardless of the gain functions used, it is advantageous to apply a detailed characterization of the excitation and detection systems. If the gain profiles and the excitation function are known or can be measured, the lifetime can be obtained with virtually no approximations involved in the analysis. A library of signal ratios can be calculated for different lifetimes by calculating the signal that would be obtained for different signal lifetimes using the applied gain profiles and excitation function. Forming a decay-rate function by finding an unambiguous relation between said at least one set of library ratios and said different library decay rates. By comparing measured signal ratios with the calculated library, the decay rate of the signal from the sample is obtained. In this process it is imperative that a ratio is formed since the initial value of the exponential decay function will cancel, which is necessary in order for the calculated values to be readily compared to the measured ones. A library of signal ratios could alternatively be obtained by calculating the ratios using measured decay functions. For example, if the functional behavior of the decaying signal is known and the excitation pulse has been measured along with the amplification functions that are used, the signal convoluted with the excitation pulse and then multiplied with the gain functions can be simulated for different decay rates. Another approach would be to use a set of measured decay signals with different decay rates in the generation of the library. After multiplication with the gain functions, the signals are integrated and at least one ratio is formed in the same way as for measured data. The ratios obtained from the measured data are then compared to the calculated ratios in order to extract the at least one decay time of the signal from the sample.

The general procedure is illustrated below:

Figure 7 is a schematic illustration of an experimental setup used for fluorescence lifetime imaging in a gas-phase experiment. The laser beam is expanded using a spherical telescope (ST) and then focused to a laser sheet above the measurement volume with a cylindrical lens (CL). A trig pulse (TP) is sent to the two ICCD cameras and to a trig box (TB) which triggers both the streak camera and the MCP-PMT.

Two intensified CCD (ICCD) cameras are used when the optical signal is split, and a picosecond excitation laser source is used. Briefly, the fourth harmonic (266 nm) of a pulsed (10 Hz repetition rate) Nd:YAG laser with 30 ps pulse duration was focused into a laser sheet aligned into the probe volume. Toluene-seeded gas was ejected through a 2.2 mm diameter jet tube inserted at the center of a porous plug, which provides a controlled co-flow of gas shielding the central jet. Mass flow controllers were used to provide oxygen/nitrogen gas mixtures to the jet and co-flow through separate gas- supply systems. Two ICCD cameras were positioned in a right-angle configuration with a 70/30 beam splitter directing the signal to the two cameras. The choice of beam splitter can be adjusted to maximize the signal- to-noise ratio for the two detectors, i.e. to compensate for differences in for example sensitivity, detector noise and signal collection efficiency. A gated MCP-PMT detected the laser pulses before they reached the probe volume. The time separation between the MCP-PMT signal and a camera's gate monitor pulse was logged using a 3 GHz digital oscilloscope, allowing single- shot jitter correction in the data analysis. Lifetime images were verified along a horizontal pixel row through the gas jet by comparison with streak-camera measurements. A streak camera is a commercially available detector that in one dimension can resolve events happening on picosecond time scales. Grid images were recorded prior to each measurement in order to overlap the two camera images. An in-house Matlab code based on simulated annealing was used to find an image transform that pixel overlapped the two camera images.

Figure 8 illustrates in (a_exp) and (b_exp) simultaneous, single-shot laser- induced fluorescence (LIF) images of a tolueneseeded air jet in a nitrogen co- flow. From one single excitation, two LIF images were recorded with different camera gate characteristics. Typical experimental results using 2 ns and 400 ns camera gate widths are seen in Fig. 8a_exp and 8b_exp, respectively. The thick solid gray curves are simulated LIF signals, the dashed light gray curve in (a_Sim) is the 2 ns camera gate function while the rising flank of the 400 ns gate function is seen in (b_Si_m)- The areas are the simulated signals detected by the two ICCD cameras, using equations (1 ) and (2). The laser pulse was measured with the streak camera and the temporal profile was found to be well described by a bell-shaped curve with 30 ps FWHM. The gate functions were measured by sequentially stepping the gate-delay time between the camera gate and the laser pulse, while recording Rayleigh scattering from a flow of dust-free air. The recorded gate functions were corrected for differences in wavelength sensitivity at the Rayleigh and LIF wavelengths. To do this correction, sequential stepping of the gate delay time was performed while recording the Rayleigh and LIF signals. Ratios between these signals for each camera were formed and multiplied with the gate functions.

Graphical descriptions of the signal simulations are shown in Fig. 8a_Si_m and Fig. 8b_Sim- The thick solid curves show the LIF signal, which is modeled as a single exponential decay convolved with the laser pulse. The gain functions of the cameras, Gi and G₂ are seen as the dashed curves. The exponential decay multiplied by the gain functions are displayed as the thin black lines at the boundaries of the solid gray areas, and the solid gray areas illustrate the integrated signals, i.e. the values obtained in a single pixel pair of the two cameras.

Test simulations of the LIF signal were performed for moderate excitation intensities with density matrix equations (DME) and rate equations (RE), neglecting spectral overlaps and detuning. The difference in evaluation of fluorescence lifetimes when using the convolution, rate equation or density matrix equation approaches was less than 0.1 %, justifying the choice of the convolution which is the least complicated of the three. The easiest alternative would be to simply use the single exponential function without convolution with the excitation pulse.

Figure 9 shows fluorescence lifetimes measured in single shot in single camera pixels along a line in these two-dimensional gas-phase measurements. Two mixtures of oxygen and nitrogen were used as ambient quenching molecules; 10.5/89.5 (open circles and dashed line) and 17/83 (filled circles and solid line). The detection and evaluation scheme described above was used (ratio according to equation (4)) with the gain functions shown in Fig. 9. Also displayed in the figure are the results from 900 averaged single shots using the streak camera. The streak camera

measurements were performed in order to validate the method described in this patent application. However, the fact that this method provided two- dimensional single-measurements of lifetimes in below 1 ns with 120 ps standard deviation without using optimal gain functions illustrates its significantly higher sensitivity compared to a comparable, available instrument such as the streak camera. It should also be stressed that the streak camera only provided lifetimes along a line, while the method described here provided data in two dimensions.

An apparatus for luminescence lifetime determination is schematically illustrated in Fig. 10. A sample is excited using a pulsed radiation source, with a laser, a laser diode or a light emitting diode. The focusing/collection optics could be a microscope, fiber-coupled optics, lenses etc. Suitable filter sets are used. Emitted luminescence is detected in two acquisitions by a single sensor or in single acquisition by two or more sensors. The optical signals are converted to electrical signals of similar temporal decays as the optical decay from the sample and the electrical signals are amplified using either at least one detector-integrated amplifier or at least one external amplifier. The gain functions multiplied with the signals have different temporal characteristics; at least one is described by a ramp-like function. The amplified signals are integrated and at least one ratio is formed. The at least one ratio is used for extraction of the at least one decay rate of the signal from the sample. The formed ratio is compared to calculated ratios, calculated either through analytic expressions or through simulations (Fig. 5). The simulated signal ratios have been calculated using the same gain functions as are used to amplify the signals and the decay rate of the signal from the sample is modeled as single exponential, i.e. it can at least approximately be described by a single exponential decay. There could either be an analytical relationship between the at least one ratio and the decay rate or the at least one ratio could be simulated for different decay rates of the optical signal prior to comparison with at least one measured ratio.

Fig. 1 1 is a schematic illustration of an embodiment of the inventive arrangement 300 for determining at least one decay rate of a first signal originating from a pulse-stimulated sample. The arrangement 300 comprises an amplifier 310 for amplifying at least two electrical decaying signals derived from said first signal with functions of different temporal characteristics, wherein at least one of said functions has an increasing or decreasing ramplike temporal shape, for forming at least two processed electrical signals. The amplifier 310 can be gain in a CCD, a photo diode, a photo multiplier tube, array detectors of photo diodes, array detectors of photo multiplier tubes, an intensified CCD camera, electronmultiplying CCD cameras, or

electronmultiplying CMOS cameras. Alternatively, the amplifier 310 can be an operational amplifier. As another alternative, a photo diode, a photo multiplier tube, array detectors of photo diodes, array detectors of photo multiplier tubes or the intensifier in an intensified CCD camera can be used as the amplifier 310. Even though Fig. 1 1 illustrates one amplifier the skilled person realizes that the arrangement 300 can comprise a plurality of amplifiers.

The arrangement 300 further comprises an integrator 320 for integrating said processed electrical signals, and a first unit 330 for forming at least one ratio using said integrated processed electrical signals and for calculating said decay rate from said at least one ratio. The first unit 330 can, e.g., be a Central Processing Unit (CPU). Even though Fig. 1 1 illustrates one integrator the skilled person realizes that the arrangement 300 can comprise a plurality of integrators.

The arrangement 300 can comprise an optical unit 350 arranged to split the optical signal into at least two optical signals. The optical unit 350 can, e.g., be a beam splitter. Even though Fig. 1 1 illustrates one optical unit the skilled person realizes that the arrangement 300 can comprise a plurality of optical units. The arrangement 300 can comprise a photosensitive sensor 360 for forming electrical decaying signals by detecting optical signals. The

photosensitive sensor 360 can, e.g., be a photo diode, a photo multiplier tube, array detectors of photo diodes, array detectors of photo multiplier tubes. Even though Fig. 1 1 illustrates one photosensitive sensor the skilled person realizes that the arrangement 300 can comprise a plurality of photosensitive sensors.

The arrangement 300 can comprise a second unit 340 arranged to split the electrical signal into at least two signals for forming said at least two electrical decaying signals.

In one embodiment, at least one from the group of an intensified CCD camera, electronmultiplying CCD cameras, or electronmultiplying CMOS cameras is used for realizing the photosensitive sensor, the amplifier, and the integrator.

The arrangement 300 can be implemented as one device comprising at least one amplifier 310, at least one integrator 320, at least one

photosensitive sensor 360, the first unit 330 and the second unit 340.

Alternatively, the arrangement 300 can be implemented as at least one amplifier 310, at least one integrator 320, the first unit 330, the second unit 340, a optical unit 350, and at least one photosensitive sensor 360 all being separate and external units. Additionally, the arrangement 300 can be implemented as any combination of the above.

Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. A single processor or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope.

Claims

1 . Method for determining at least one decay rate of a first signal originating from a pulse-stimulated sample comprising the steps of:

a) amplifying at least two electrical decaying signals derived from said first signal with functions of different temporal characteristics, wherein at least one of said functions has an increasing or decreasing temporal shape, for forming at least two processed electrical signals,

b) integrating said processed electrical signals,

c) forming at least one ratio using said integrated processed electrical signals,

d) calculating said decay rate from said at least one ratio.

2. Method according to claim 1 , wherein said first signal is an optical signal, further comprising splitting the optical signal into at least two optical signals, converting said at least two optical signals for forming said at least two electrical decaying signals.

3. Method according to claim 1 , wherein said first signal is an optical signal, further comprising converting said first signal to an electrical signal, splitting the electrical signal into at least two signals for forming said at least two electrical decaying signals.

4. Method according to claim 1 , further comprising detecting different spatial parts of said first signal through at least two optical pathways for forming said at least two electrical decay signals.

5. Method according to of claim 1 , wherein said first signal comprises optical signals originating from at least two pulse-stimulations of a sample, and the method further comprising converting said optical signals originating from at least two pulse-stimulations of a sample into electrical signals for forming said at least two electrical decaying signals.

6. Method according to any one of claims 1 -5, wherein the step of calculating is replaced by the steps of:

a) preparing a set of library signals with different library decay rates, b) multiplying said set of library signals with said functions of different temporal characteristics, and forming a set of processed library signals,

c) integrating said set of processed library signals forming a set of integrated processed library signals,

d) inputting said set of integrated processed library signals in said at least one ratio, forming at least one set of library ratios,

e) forming a decay-rate function by finding an unambiguous relation between said at least one set of library ratios and said different library decay rates,

f) determining said at least one decay rate by inserting said at least one ratio from said first signal in said decay-rate function.

7. Arrangement for determining at least one decay rate of a first signal originating from a pulse-stimulated sample, comprising:

at least one amplifier for amplifying at least two electrical decaying signals derived from said first signal with functions of different temporal characteristics, wherein at least one of said functions has an increasing or decreasing temporal shape, for forming at least two processed electrical signals,

at least one integrator for integrating said processed electrical signals, a first unit for forming at least one ratio using said integrated processed electrical signals, and for calculating said at least one decay rate from said at least one ratio.

8. Arrangement according to claim 7, wherein said first signal is an optical signal, wherein the arrangement further comprises an optical unit arranged to split the optical signal into at least two optical signals, and wherein said arrangement further comprises at least one photosensitive sensor for forming said at least two electrical decaying signals by converting said at least two optical signals.

9. Arrangement according to claim 7, wherein said first signal is an optical signal, wherein said arrangement further comprises a photosensitive sensor for converting said first signal to an electrical signal, and a second unit arranged to split the electrical signal into at least two signals for forming said at least two electrical decaying signals.

10. Arrangement according to of claim 7, wherein said arrangement further comprises at least one photosensitive sensor for forming said at least two electrical decay signals by detecting different spatial parts of said first signal through at least two optical pathways.

1 1 . Arrangement according to claim 7, wherein said first signal comprises optical signals originating from at least two pulse-stimulations of a sample, wherein said arrangement further comprises at least one

photosensitive sensor for forming said at least two electrical decaying signals by converting said optical signals originating from at least two pulse- stimulations of a sample into electrical signals of temporal characteristics.

12. Arrangement according to any one of claims 8-1 1 , wherein said at least one photosensitive sensor comprises at least one from the group of: photo diodes, photo multiplier tubes, array detectors of photo diodes, or array detectors of photo multiplier tubes.

13. Arrangement according to any one of claims 8-1 1 , wherein said at least one photosensitive sensor is arranged to replace said integrator and is arranged for integrating said processed electrical signals.

14. Arrangement according to any one of claims 8-1 1 , wherein said at least one amplifier, said at least one integrator and said at least one photosensitive sensor are replaced by at least one from the group of: an intensified CCD camera, electronmultiplying CCD cameras, or

electronmultiplying CMOS cameras.

15. A computer-readable recording medium having recorded thereon program for implementing the method according to any one of claims 1 -6 when executed on a device having processing capabilities.