In the study of combustion processes it is importantto know the concentrations of the species that areparticipating in the elementary reactions. Some ofthese species are critical for selection of the overallkinetic scheme that governs the combustion, andthey have to be quantified quite accurately. Thelaser-induced fluorescence technique1 offers the pos-sibility of detecting species at low concentrations non-intrusively. However, a problem in many cases isthat the measured fluorescence is quenched by colli-sions and that the concentration cannot be obtainedwithout knowledge of the quenching rate. There aretechniques, e.g., saturated fluorescence spectroscopy2
~SFS!, photoionization-controlled loss spectrometry,3and laser-induced predissociation fluorescence4 thatmake quenching-insensitive fluorescence measure-ments possible. In SFS the detection limit is thelowest because the fluorescence emission and absorp-tion rates are both saturated. Problems may arisein SFS because it is not possible to achieve completesaturation throughout the entire laser-beam profile
The authors are with the Department of Combustion Physics,Lund Institute of Technology, P.O. Box 118, S-221 00 Lund, Swe-den.
Received 7 July 1997; revised manuscript received 7 November1997.
and because the high electric fields required for sat-uration may induce disturbances such as photochem-ical processes. For photoionization-controlled lossspectroscopy and laser-induced predissociation fluo-rescence the signal yields are much lower than forSFS, as the emission rates are controlled by the dom-inating photoionization and predissociation lossmechanisms.
There are also techniques that correct for quench-ing. If the bimolecular quenching cross sections areknown, the quenching rate can be calculated frommeasurements of absorption5 or Raman scattering6 ofthe major quenching species, and finally the fluores-cence yield is obtained.
In practice, the most direct way to determine thequenching is to measure the effective lifetime of thefluorescence emission after a short laser-pulse exci-tation. The decay of the fluorescence emission for atwo-level system follows an exponential decay with adecay constant leff that is the same as that of thepopulation of the upper electronic state. The life-time of the fluorescence emission and the upper elec-tronic state is teff 5 1yleff.
The fluorescence yield in the regime of linear ab-sorption with respect to laser power is assumed to bethe same as the fluorescence quantum yield Ateff,where A is the Einstein A coefficient. If the length ofthe laser pulse is much less than teff it is possible toevaluate the lifetime by fitting a single exponentialfunction to the tail of the decay.7–10
In atmospheric flames the effective lifetimes are
20 April 1998 y Vol. 37, No. 12 y APPLIED OPTICS 2303
100–1000 times shorter than the radiative ones.They are approximately 1.5–2 ns for, e.g., NO andnonpredissociative states of OH ~Refs. 7–9! and liebelow 1 ns for, e.g., CO, H, and O ~Refs. 10–13! andfor OH in rapidly predissociating states,14 resultingin fluorescence quantum yields of 0.001–0.01. Inaddition, the effective lifetime can change, dependingon the burning conditions and the position in theflame; see, e.g., @Refs. 12–13#. In common gaseousflames the effective lifetimes are set mainly by therate of deactivating collisions that cause nonradiativerelaxation of the excited electronic states. Thestrong collisional quenching rate Q sets the total de-cay rate and the effective lifetime @teff 5 1y~A 1 Q! '1yQ#. Consequently, from measurements of teff, in-formation on the number of collisions taking placeand on the concentration can be obtained for the col-liding species in the probed volume.
Lifetime measurements are usually performed at apoint or along a line.15 Two-dimensional ~2-D! mea-surements of the lifetime of the fluorescence emissionare not common, but Ni and Melton demonstrated thepossibility of performing 2-D lifetime measurementswith gated intensifiers for lifetimes of 5 to 50 ns ~Ref.16! by measuring the emission intensity in two dif-ferent time windows after the laser pulse. In an-other experiment they were able to measure thelifetime distribution of the fluorescence emission in anisothermal turbulent fluoranthene-doped methane–air jet by using dual-gated image intensifiers coupledto a CCD detector. From a calibration measurementof oxygen quenching they were able to calculate theimage of the equivalence ratio of the jet.17 Also, ona later occasion they reported 2-D imaging of thetemperature of a naphthalene-doped nitrogen flow byfirst measuring the lifetime distribution and thenthrough a calibration procedure obtaining the tem-perature.18 Tsujishita and Hirano19 measured thefluorescence lifetimes of OH and NO ~ranging from1.5 to 2 ns! in flames with image intensifiers gated to3 ns. They recorded a sequence of accumulated im-ages after the end of the laser pulse with a delay thatincreased with a given step ~down to 1 ns! betweentwo sequential images. The lifetime distributionwas obtained from the logarithm of the pixel counts ofthe CCD images as a function of the time delay.Bormann et al.20 were able to make quenching-insensitive picosecond 2-D measurements by using470-ps-long laser pulses and a fast-gated ~;400-ps!intensified camera. In a recent publication21 theyreported 2-D lifetime measurements of OH in steadymethane–air and methane–oxygen atmospheric-pressure flames with the same laser and detectionsystem. 2-D fluorescence lifetime imaging is usedand has the potential of being used in variety of fieldsother than combustion; see, e.g., @Ref. 22#. In med-icine, Cubeddu et al. used gated cameras ~in the nano-second regime! for tumor demarcation.23 Lakowiczand Berndt demonstrated a radio-frequency modula-tion technique that uses a CCD camera to performlifetime-based measurements with a resolution of0.25 ns.24 Dowling et al. were able to perform mea-
2304 APPLIED OPTICS y Vol. 37, No. 12 y 20 April 1998
surements with a time-gated intensifier with a reso-lution of 185 ps.25 Progress toward higher temporalresolution promises the possibility of studying andmonitoring fluorescent species with lifetimes in thesubnanosecond regime. Autofluorescence from or-ganic samples is often in the range 0.1–2 ns,26 whichis why organic contamination on surfaces could berevealed by measurement of the lifetime. Confocalmicroscopy with two-photon excitation can be usedfor measurement of autofluorescence from organicmaterials such as paper, blades of grass, and ratliver.27 In biochemistry there are a number of fluo-rescent species that are used as probes for, e.g., Ca21
and pH; see Ref. 28, for example. Dyes employed inthe near infrared or the infrared often display life-times in the picosecond regime and are of interest formany laser-diode applications. Some dyes are alsoquenched by the presence of water, which could makethem interesting as probes for micelle analysis.
We demonstrate a different way to measure the2-D distribution of the effective lifetime. The tech-nique employs a picosecond laser for excitation of thespecies and a streak camera with a CCD for the de-tection of the fluorescence, which in principle wouldpermit measurements of lifetime distributions con-siderably below 1 ns. There seems to be no theoret-ical hindrance to the system being extended tosubpicosecond resolution if a femtosecond laser and afemtosecond streak camera are used.
The streak camera is generally operated in such away that spatial and temporal coordinates of the out-put are independent @time-resolved method ~TRM!#,which means that it is possible to evaluate the life-time only along a line. Here a method is formulatedand demonstrated for the evaluation of lifetimes intwo dimensions. To separate out the spatial coordi-nate that is parallel to that of the time ~the directionof the streak! it is necessary to perform two measure-ments and then apply a numeric algorithm to obtainthe separation @separation algorithm method ~SAM!#.The two measurements are made with the streakcamera operating in different modes. One is per-formed in the streak mode ~with temporal deflectionof the image! and the other in the focus mode ~notemporal deflection of the image!.
The principle of the SAM is first given theoreticallywhen the numerical algorithms are defined; it is alsotested on streak and focus images constructed fromthe combination of different time-resolved imagesmeasured with the TRM. The SAM is applied andyields a distribution of lifetimes that are comparedwith the originally determined ones. The demon-stration is continued with the application of the SAMand the TRM to a fluorescing object, permitting in-dependent evaluations on the same object with bothmethods. The demonstration experiments are con-cluded with true 2-D measurements of an object of aknown distribution of fluorescence lifetimes. Fi-nally, the potential and limitations of the SAM fordifferent types of measurement are discussed.
2. Theory
The analysis of the rate equations that describe thedynamics of a two-level system of electronic states ina short laser-pulse interaction shows that in the re-gime of linear and low-level absorption, i.e., at lowlaser intensity, the number of excited states in anensemble is proportional to the Einstein A coefficient,the total number density ~N! of the species, and thelaser intensity ~Il!. The fluorescence quantum yieldY can be expressed as Ayleff, where leff is the totaldecay rate.
The intensity of the fluorescence emission is givenby
Ifl~t! 5 *2`
t
cNAIl~s!exp@2leff~t 2 s!#ds, (1)
where Ifl~t! is the fluorescence emission intensity, c isa constant, A is Einstein’s A coefficient, and Il~t! is thelaser intensity.
For a laser pulse starting at t 5 0 and with aduration tp approaching zero, i.e., much shorter thanteff, one can approximate Eq. ~1! as
Ifl~t! 5 cNAIl~0!exp~2lefft!. (2)
The total fluorescence emission is
I#fl ; *0
`
Ifl~t!dt 51
leffIfl~0!, (3)
and thus the total number of photons emitted is pro-portional to teffNIl~0!.
With a streak camera one can measure teff withpicosecond resolution. The camera can be operatedin two modes, the streak mode and the focus mode.The fluorescence image on the photocathode of theinput of the streak camera is transmitted to the out-put phosphor by the photoelectrons emitted from thecathode. In the focus mode the same image is trans-mitted to the output. In the streak mode, on theother hand, the photoelectrons are deflected sidewaysby a linearly increasing electric field. Consequentlythe electrons experience a displacement proportionalto the time ~elapsed after the trig of the streak cam-era! before hitting the output phosphor, and the re-sulting image appears blurred in the direction of thestreak ~x!.
In Fig. 1 the conventional one-dimensional lifetimetechnique with a streak camera is compared with themethod for 2-D measurements presented here. Nor-mally @Figs. 1~a! and 1~b!#, only one axis ~here y! canbe used for spatial resolution, because the other axis~x! corresponds to time when the camera is operatedin the streak mode @Fig. 1~b!#. The temporal depen-dence of the fluorescence emission can be obtaineddirectly from the streak image at any point on thespatial axis ~represented by A–D!. The intensitieson the focus image correspond to the time-integratedemissions I#fl; i.e., the areas under the time-dependentfluorescence curves. However, if the spatial infor-mation is in the direction of the streak ~x axis! as
shown in Figs. 1~c! and 1~d!, the time-dependentcurves that correspond to different positions ~A–D!overlap on the streak image, summing to a cumula-tive intensity curve @Fig. 1~d!#, so the decay constantsin A–D cannot be obtained in the way describedabove.
A simple mathematical relation between the inten-sities of the focus and the streak images can be ob-tained in a segment along the x axis that yields thedistribution of the effective lifetime of the fluores-cence emission. The intensity at equidistant pointsalong the segment, Isi in the streak mode is given by
Isi 5 (j51
i
I0sj expF2~i 2 j!lj
vG , (4)
where Isi is the intensity in point i in a given segmentof the streak image along the direction of the streak,li 5 1yti, v is the velocity of the streak as the inverseof the time separation between two adjacent points onthe output phosphor, and I0si and the intensity at thecorresponding position in the focus-mode image Ifiare interrelated through the normalization condition,which in the limit of infinitely close points or thecondition liyv 3 0 is given by
Ifi 5 *0
`
I0si expS2li
xvDdx3 I0si 5 Ifi
li
v(5)
and Ifi is the intensity in point i in a given segment ofthe focal image.
The distribution of the effective lifetime can be re-trieved by use of the following expressions obtainedfrom Eqs. ~4! and ~5!: for Ifi Þ 0
li 5vIfi (Isi 2 H(
j51
i21 SIfj
lj
vDexpF2~i 2 j!lj
v GJ) , i . 1,
l1 5 Is1
vIf 1
. (6)
The output of the streak camera can be imagedwith a CCD camera, so the direction of the streak ~x!is parallel to the rows. The intensity or number ofcounts in a pixel of a given row can still be expressedby Eq. ~4!, but we must modify the normalizationcondition that holds for Eq. ~5!, taking into accounteffects that are due to the discretization imposed bythe pixel representation. Infinitely high resolutionis not a valid assumption, and the condition liyv ,,1 is not necessarily satisfied. The new normaliza-tion condition defined by Eq. ~7! takes into consider-ation pixel width ~b! and separation between adjacentpixels ~expressed by the free spacing between adja-cent pixels, w!:
I0si 5 Ifi
1 2 expS2li
vDF1 1
wb
expSli
2vDG, (7)
20 April 1998 y Vol. 37, No. 12 y APPLIED OPTICS 2305
Fig. 1. Schematic focus and streak images for two cases: ~a!, ~b! conventional 1-D measurement and ~c!, ~d! measurement that requiresthe SAM. For ~a! and ~b! the coordinate for the spatial information ~y! is orthogonal to the direction of the time representation ~x! in thestreak image ~b!. The intensities at points A–D in the focus image ~a! correspond to the respective areas below the curves in the streakimage ~b!. The decay constants at A–D can be evaluated with the procedures normally used for lifetime evaluation. ~c! Intensities in thefocus image at points A–D distributed along the x axis, i.e., the second coordinate needed for 2-D spatial resolution. The correspondingintensity distribution in the streak image ~d! along the time axis ~x! no longer displays a simple decay because the time and spatial axesare no longer independent. The time-resolved curves overlap, and the bold curve in ~d! displays the sum of the curves. Therefore aseparation algorithm is needed to separate spatial from temporal information to yield the decay constants at points A–D.
where w is the free spacing between adjacent pixelsand b is the width of a pixel.
Generally wyb ,, 1, and Eq. ~7! takes the form
I0si 5 IfiF1 2 expS2li
vDG, wyb ,, 1. (8)
The effective lifetimes are obtained from Eqs. ~4! and~8! and yield the expressions
for wyb ,, 1, Ifi Þ 0
li 5 2v lnK1 21Ifi (Isi 2 H(
j51
i21
IfjF1 2 expS2lj
vDG3expF 2 ~i 2 j!
lj
vGJ)L , i . 1.
l1 5 2v lnK1 2Is1
If1L . (9)
2306 APPLIED OPTICS y Vol. 37, No. 12 y 20 April 1998
It is now possible to define a rigorous algorithm~RA! from Eqs. ~4!, ~8! and ~9!. However, Eqs. ~4!–~6!can still be used as an approximate algorithm, thelong-lifetime algorithm ~LLA!, when the lifetimes ful-fill the above given condition liyv ,, 1. The LLA isexact in the case of infinite resolution ~i.e., 1yv3 0!.
The rates given by Eqs. ~6! and ~9! are not definedfor Ifi 5 0, i.e., either when the species concentrationis zero and li is limited or, less probably, when thespecies concentration is limited and li is infinitelyhigh. One has to discard those pixels where Ifi 5 0from the focus image. When Ifi 5 0 one has to useEqs. ~4! and ~5! or Eq. ~8!, which are still defined.Because I0si 5 0, the corresponding pixel i does notcontribute to the intensity of the streak image, Isi,and li is not defined. When we set li 5 0 in thosecases when Ifi is close to zero but nevertheless isconsidered 0 by definition of a discrimination level asdescribed below, the stability against errors appears
to be better. Together with this additional conditionin the case of Ifi 5 0, the SAM can be used on everyrow in the CCD image @with Eq. ~6! or Eq. ~9!# andthereby determine the effective lifetimes. The life-time distribution is independent of laser-induced ef-fects, e.g., absorption, power broadening, stimulatedemission, ionization, saturation ~either partial orcomplete!, and dissociation, which last only for theduration of the pulse ~assumed to be much shorterthan the effective lifetime of the fluorescence emis-sion!. The concentrations, on the other hand, can beobtained from the measurements once the lifetimesare determined, as long as the events during the laserpulse are known.
In the linear regime with respect to laser-pulseenergy and in the absence of laser pulse-dependentdisturbances, the concentrations can be obtainedfrom the focus image once quenching rates li havebeen determined. The intensity in a pixel element ofrow i and column j in the focus mode image can beexpressed as
If~i, j! 51
l~i, j!AN~i, j!Il~i, j!k~i, j!, (10)
where N is the species concentration in the corre-sponding volume element measured, Il is the laserintensity incident upon the projection area of the vol-ume element expressed in coordinates of the CCD,and k ~i, j! is a factor that depends on the probabilitythat the molecules in that particular volume elementhave absorbed an incoming photon. It also takesinto account the sensitivity of the multichannel plateand conversion factors in the intensity between theemitted fluorescence and the measured signal. k isnot necessarily the same for the focus and the streakimage, which complicates the retrieval of the concen-tration if k depends strongly on the elements orevents from the phosphor of the tube in the streakcamera to the CCD. If we assume that k~i, j! isconstant and that the incident laser radiation has aconstant amplitude throughout the image we obtainthe relation for the concentrations:
N~i, j! } If~i, j!li~i, j! (11)
To test the utility of the SAM we first calculatedstreak and focus images with Eqs. ~4! and ~8! forpredefined distributions of the effective lifetime, theconcentration, and a 19.63-ps time separation be-tween pixels ~v 5 5.094 3 1010 s21!. Several levelsof noise were then added to the calculated streak andfocus images, and the response of the SAM to thedynamic range of the focus image was investigated.The calculations were all performed in double preci-sion with seven-digit decimal number representationfor the streak and focus images.
Figure 2~a! shows the distribution of the effectivelifetime used in the calculations of the streak andfocus images. Figures 2~b! and 2~c! show the distri-butions of the concentrations used for moderate dy-namic range ~DG1! and high dynamic range ~DG10!.
The functions represented consist of a sum of twoGaussian functions with exponential powers of 1 inthe first case and 10 in the second case. In Figs.2~d!–2~e! we show the resulting streak and focus im-ages added with 5% random noise relative to themaximum intensity of the focus image.
Noise in the streak and focus images affects theevaluations of the lifetime and the concentrationsand can even inhibit the execution of the algorithms.It is sometimes necessary to set a level of discrimi-nation, εD, and to redefine the values in this regime ofpixels where Ifi , εDIfmax, where Ifmax is the maxi-mum value of the focus image. It is possible to set Ifi5 0 and li 5 0 in the same way as was describedabove.
Figures 3~a!–3~d! show the deviations of the re-trieved lifetimes from the true values at a 0.1% levelof noise ~εN 5 0.001! with respect to Ifmax in thecalculated focus images for DG1 and DG10 @see Figs.2~d!–2~e!#. In Fig. 3~a! no discrimination thresholdεD is used, whereas in Fig. 3~b! εD is 0.6%. To com-pare the dynamic behavior in the retrieved lifetimeswith respect to the intensity of the focus image, notethat the horizontal bars indicate the range, dε, inwhich If is greater than a certain level relative toIfmax. The levels ε increase in height in Fig. 3 from0.1%, to 0.6%, 10%, 20%, and 30%. The deviations ofthe retrieved lifetimes are higher in those regionswhere the intensity of the focus image is low, in par-ticular in the tails behind the maxima where even-tually the SAM fails even for the RA. Figures 3~c!and 3~d! show the corresponding results for the av-eraged effective lifetimes; i.e., when the retrieved val-ues are averaged over 11 pixels, the level of noise isstrongly decreased.
The upper limit of the resolution in the calculationsis ultimately limited by the dynamic range of theCCD camera. A representative example of a cameraused for experiments has a 14-bit dynamic range.The relative truncation or round-off error would thenbe ;3 3 1025. However, under experimental condi-tions realistic levels of noise are considerably higherthan 0.1%. In Figs. 3~e! and 3~f ! we give the relativedeviations for εN 5 2% obtained with the RA. Thestreak and focus images were averaged over a rect-angular window of 11 pixels before the SAM wasapplied. The retrieved lifetimes were afterward av-eraged over the same window. Further calculationsshow that the lifetimes obtained with the RA differless from those obtained with the LLA in most of thechannels at this level of noise than at the level of thenoise that is present in the finally averaged lifetimes.The results are better in the regions that correspondto the raising edge of the focus image than for thefalling-edge region. The root mean squares of therelative deviations ~RMSD! in the regions given by If. 0.3Ifmax, d0.3, are ;4% for DG1 and ;5% for DG10.
The differences in the results from the RA and theLLA are quite small for εN 5 5% and can almost bedisregarded with respect to the level of noise in theretrieved values. The RMSD’s are 11% for DG1 and16% for DG10.
20 April 1998 y Vol. 37, No. 12 y APPLIED OPTICS 2307
Fig. 2. Calculated streak and focus images. ~a! The predefined lifetime distribution used in the calculations at the distributions ofconcentration in ~b! and ~c!. ~b! Moderate ~DG1!, ~c! high ~DG10! dynamic ranges. ~d!, ~e! Resulting streak and focus images with 5% noiseadded with respect to the maximum of the corresponding focus images.
We performed calculations on DG1 with the sametype of lifetime distribution, maintaining the relativechanges within the distribution but changing the ab-solute values of the lifetimes. At εN 5 2% the life-times were in the 40-ps–4-ns range for a RMSD of610%, whereas for a RMSD of 64% the range wasfrom 100 ps to 2 ns. In theory, if the fastest streakis used, corresponding to a time separation betweenpixels of ;1 ps, lifetimes of 5–100 ps could be mea-sured with a relative error of 64%.
To investigate the precision of the algorithm con-cerning li as a function of the pixel number we de-fined li as
li 5 lcF1 1 B cosS2p
nelnp iDG , (12)
where lc is the baseline rate, B is the relative ampli-tude of the modulation, np is the spatial frequency~maximum, nely2!, and nel is the number of pixels.
The spatial resolution of li given by the algorithmis defined by the upper limit of the spatial frequency,np, for a retrieval that results in a given RMSD. Thedynamic range would result from the correspondingrange of lc. The lower and upper limits of B wouldgive the sensitivity of the algorithm at the given spa-tial variation. The investigation was limited to astudy of the dynamic range of the SAM with respectto the lifetime evaluation at a relatively large spatialdependence of the lifetime. We tested DG1 by add-
2308 APPLIED OPTICS y Vol. 37, No. 12 y 20 April 1998
ing 2% noise to the streak and focus images calcu-lated for different values of lc. B was maintained at0.5 and np 5 28, which corresponds to a periodicity of;20 pixels.
Table 1 shows the root mean square of the relativedifference between the retrieved lifetime and the truevalue in different domains of lc in d0.3. The streakand focus images were averaged over 5 pixels in mostof the runs. From these tests relative deviations of610% can be reached for the RA when vylc; i.e., theextension of the lifetime in terms of pixels is between2 and 50. The LLA, on the other hand, works bestbetween 50 and 75, and we do not recommend usingit below 20. The optimal range for RA seems to bevylc 5 3–25. From the evaluations we see that anincrease in the window of averaging from 5 to 11pixels in the streak mode image is favorable for vylc. 20.
So far the discussion has concerned pure theoreti-cal aspects. Experimental conditions require fur-ther considerations. The pulse position is the shiftin the x direction of the streak image with respect tothe focus image that appears during a measurementand depends on electronic delays and the trig level setfor the start of the streak. Once the streak imagehas been compensated for, this shift yields the correctpixel identification between streak and focus images.Background and different sensitivities for the streakand focus images can introduce errors into the eval-uation. A check on the model distribution of DG1
that was treated first shows that an offset of 1%
Fig. 3. Sensitivity of the retrieved lifetime distribution with respect to noise. ~a! Relative deviation from the true value of the lifetimeretrieved with the RA at 0.1% random noise on streak and focus images at DG1. ~b! Corresponding results for DG10, where the horizontalbars represent, from the bottom to the top, the range of pixels dε for ε 5 0.1, 0.6, 10, 20, 30%. ~c!, ~d! Corresponding deviations after theretrieved lifetimes are averaged over 11 points. ~e!, ~f ! Deviations for the RA at 2% noise on both streak and focus images. Afteraveraging over the streak and the focus images the lifetimes were evaluated and then averaged over 11 pixels.
introduces a RMSD in d30 of 613% and that a differ-ence in the sensitivity of 2% yields an error of 612%.Consequently, background is of great importance foraccuracy of the evaluation under experimental con-ditions.
Table 1. Sensitivity to Noise of the Retrieved Lifetime in VariousDomains of lc
av 5 5.094 3 1010 s21, B 5 0.5, np 5 28, εN 5 2%.bThe streak image was averaged over 11 pixels, whereas the
focus image was averaged over 5 pixels. The retrieved lifetimeswere averaged over 5 pixels ~those marked with an asterisk, over11 pixels!. Values in parentheses were obtained without smooth-ing on the retrieved lifetimes.
3. Experiments and Results
A. Experimental Setup
In Fig. 4 we show the setup used in the experiments.Laser pulses from the fourth harmonic ~266 nm! of a10-Hz-repetition-rate picosecond Nd:YAG laser ~Qu-antel YG572-C, pulse duration 35 ps at 532 nm! ~1!were passed through a contracting telescope ~2! andthen led through a delay line ~;50 ns! ~3! to matchthe electronic response time of the detector. Thepulses passed a rectangular mask ~;6 mm 3 3.5 mm!~4! and a cylindrical or spherical lens ~ f 5 300 mm!~5! and were deflected by two quartz prisms ~6! beforethey were focused horizontally onto the static object~7! to be studied. The radiation emitted from theobject was collected vertically by an Al mirror ~8! anda quartz lens ~9! ~ f 5 150 mm! and focused onto thephotocathode of the streak camera ~Delli Delti Del-listrique III! ~10!. The output phosphor of the streakcamera was imaged by a relay lens system onto theCCD detector ~Princeton Instruments TEyCCD-576-TUV! ~11!. The data from the CCD were thenpassed through the controller unit ~Princeton Instru-ments ST-130! ~12! to a personal computer ~13! forstorage and further data analysis.
20 April 1998 y Vol. 37, No. 12 y APPLIED OPTICS 2309
B. Experimental Procedures and Results
To test the numerical algorithms for the retrieval ofthe effective lifetimes we defined experiments thatpermitted measurements under conditions in whichnoise, temporal fluctuations of the distribution of con-centrations, and the effective lifetimes in the mea-surement volume could be kept as low as possible.The measurements were therefore performed onstatic objects, and the streak camera was operatedwith a single image intensifier.
Figure 5 shows the principle of the technique usedfor comparison of the TRM and the SAM. In the firstmeasurement the object, aligned 90° with respect tothe direction of the streak, consisted of pieces of blackpaper soaked with solutions of various dyes obtainedfrom line-marker pens. The pieces were keptsoaked by contact with individual reservoirs. Thelaser radiation was focused onto the tips of the papersto an intensity of ;6 MWycm2. In front of the pho-
2310 APPLIED OPTICS y Vol. 37, No. 12 y 20 April 1998
tocathode of the streak camera we used a long-passfilter with a wavelength cut-on position at 305 nm~Schott WG 305! to discriminate the fluorescenceemission from elastically scattered radiation. Thetime separation between two adjacent pixels of thecamera and the CCD system was 19.6 ps during op-eration in the streak mode. The CCD had pixelsplaced in 576 columns and 384 rows and was oper-ated in the free-running mode with a gate duration of100 ms. One hundred laser shots were accumulatedin the CCD before the data were transferred to thePC. Background images were recorded for bothstreak and focus images and subtracted from the re-spective fluorescence images.
We used the background-compensated streak andfocus images of the paper tips to evaluate the life-times by the TRM. We obtained the lifetimes byfitting a segment of the streak image to the corre-sponding segment of the focus image, which was con-voluted with a single exponential decay.29 The bestfit yielded the evaluated lifetime as well as the pulseposition, which was the position that the focus modeimage had to have relative to that of the streak imageto yield a correct evaluation. Lifetimes of between0.3 and 4 ns were obtained for the various paper tips.We constructed images by superposing the respectiveimages from measurements from which different life-times were obtained. The SAM was then performedon the constructed images, and a distribution of thelifetime along a line parallel to the direction of motionof the streak was determined. The pulse positionused was the same as that which resulted from theTRM. Because the short and the long lifetimes wereeasily distinguished in both methods, measurementswere continued on real one-dimensional ~1-D! and2-D lifetime distributions.
These objects consisted of pieces of either plaincopy paper ~teff ; 1 ns! or originally low-fluorescentpaper dyed with the green line marker ~teff ; 1.7 ns!.
Fig. 5. Principle of the technique used for comparison of the TRM and the SAM. ~a! In a time-resolved 1-D experiment the lifetimedistribution of the fluorescence emission on the output of the streak appears orthogonal to the direction of the streak. In a 2-D experimentthere is also a lifetime distribution in the direction of the streak. ~b! Two independent time-resolved measurements ~the two topmostgraphs! are performed and the resulting images are superposed, corresponding to a measurement of the lifetime distribution along asegment in the direction of the streak. ~c! The SAM is performed and the resulting lifetime distribution along the segment is obtained.
Fig. 6. 1-D measurement: Comparison between the TRM and the SAM of the results obtained for the lifetime evaluation. ~a! Imageson a combined set of tips of paper with different lifetimes were recorded, with the spatially resolved axis 45° relative to that of the streakaxis. The same 1-D object was recorded once again, but with the spatially resolved axis parallel to the streak. The images are shownin an inverted gray scale. The TRM was applied to the two upper images at different points; the SAM was applied to the lower images.~b! Results from the TRM and the SAM compared as a function of channel number of the CCD. The positions for the TRM results werecorrected for the axis rotation in the upper images. The counts in the streak and the focus images were summed over 11 rows andaveraged over 11 columns. The difference in the results obtained with the two techniques was estimated to be 10%.
The pieces of paper were combined in different pat-terns and placed upon a blackened paper. In Fig. 6we show an example of a 1-D measurement and theresulting comparison between the TRM and theSAM. The setup that was used permitted indepen-dent TRM and SAM evaluations of the effective life-time distribution along the 1-D spatial coordinate.The TRM measurements were performed with theimage of the object aligned at 45° with respect to thestreak direction, permitting a spatial resolution ofthe object without the need to realign the laser-beamsetup and that of the receiving optics. The loss ofresolution with respect to 90° orientation was notconsidered to be significant for the purpose of thedemonstration. The streak and focus images weresummed over 11 rows and averaged over 11 columns.The difference in the results obtained with the twotechniques was estimated to be 10%. The deviationobserved in the region of the last pixels is not alwayspresent in the results; we believe that it depends onthe decreased stability of the recursive method whenthe signal level decreases in the final tailing edge, aswe demonstrated from the results in Section 2.
The object used in the experiments for 2-D evalu-ation had a size of 2.6 mm 3 2.4 mm and consisted ofcheckered papers composed of squares of alternatingfluorescence lifetimes. The cylindrical lens used forfocusing the laser radiation was replaced with aspherical lens and displaced along the laser beam sothat a cross section of the laser beam of 2 cm 3 1 cmwas obtained, resulting in an intensity of 5 3 104
Wycm2 at the measurement site. The 2-D object wastipped 20–30° with respect to the preceding measure-ments, where the objects were oriented in the direc-tion of the receiving optics.
The color of the fluorescence emission from the whitepaper appeared bluish to the naked eye, whereas thatfrom the dyed paper appeared greenish. The emis-
sion was assumed to be at slightly lower wavelengthsfor the white paper. The ratio of the emission inten-sities transmitted through a long-pass filter ~SchottGG 455! with the wavelength cut-on position at 455nm was complementary to that for the case when thefilter was a Schott GG 495 with the cut-on at 495 nm.Although the absolute values of the effective lifetimesfrom the plain and the dyed papers could change de-pending on the filter used, the plain paper was alwaysassumed to have a shorter lifetime than the dyed pa-per.
Figure 7 shows the results of these measurements.In Fig. 7~a! we show the 2-D distribution of the fluo-rescence intensity when a Schott GG 455 filter wasused. The small island that appears beside the 2-Dobject is from a target used for determination of thepulse position. The corresponding retrieved lifetimedistribution is shown in Fig. 7~b! in the domain givenby d0.3. The streak and focus images were averagedover 11 rows and 24 columns, and the resulting life-time distribution was averaged over 24 columns. Thelifetime evaluated on the target by the TRM was 0.9ns. Evaluation by the SAM on the 2-D object resultedin slightly higher lifetimes, 1.0 ns, for the correspond-ing white squares. The precision and the accuracy ofthe 2-D evaluation were both estimated to be 10–20%.
A Schott GG 495 filter yielded the distributionsgiven in Figs. 7~c! and 7~d!. Figure 7~c! shows afluorescence emission distribution that is comple-mentary to that in Fig. 7~a!. However, Fig. 7~d! hasthe same type of structure as Fig. 7~b!, which is ex-actly what had been expected. The lifetimes mea-sured are greater than those obtained from themeasurements with the other filter. Evaluation bythe TRM on the small target yielded 1.2 6 0.1 ns,whereas the corresponding result from the SAM onthe checkerboard was 1.5 ns. To reach a sufficientnumber of counts and signal-to-noise ratio we in-
20 April 1998 y Vol. 37, No. 12 y APPLIED OPTICS 2311
Fig. 7. 2D measurements of the lifetime distribution. ~a! Focus mode image of a 2-D object consisting of alternating squares withfluorescence lifetimes of ;1 and ;1.7 ns, respectively. The measurements were performed with a Schott GG 455 filter in front of the inputphotocathode of the streak camera. ~b! Resulting lifetime distribution obtained by application of the SAM to streak and focus images.The streak and the focus images were averaged over 11 rows and 24 columns, and the resulting distribution of the lifetimes was averagedover 24 pixels. Measurements were also done with another filter, a Schott GG 495. The corresponding focus mode image ~c!, obtainedat 300 accumulations, has a structure complementary to the previous focus mode image ~a! because of the difference in emissionwavelengths of the two types of paper. However, the resulting 2-D lifetime distribution ~d! is of the same kind as that shown in ~b!.
creased the number of accumulations three timesfrom those in the previous measurements. How-ever, inasmuch as the experiments were made for thepurpose of demonstration, no further effort was madeto optimize the setup for resolution and signal-to-noise ratio. Because of the decreased resolution andsignal-to-noise ratio, the accuracy was estimated tobe 25–30%.
4. Discussion
A method for determining the 2-D distribution of effectivelifetimes has been described theoretically as well as ex-emplified experimentally under practical conditions onstatic objects. In principle, the method permits the de-tection of the effective lifetime with the same resolutionas the time separation between two adjacent pixels in theCCD when the streak camera is operated in the streakmode. An upper limit of resolution for the receivingpart of the experimental setup corresponded to a lifetime
2312 APPLIED OPTICS y Vol. 37, No. 12 y 20 April 1998
covering 3 pixels, i.e., ;60 ps at the streak speed used or;3 ps at the fastest streak.
At the streak speed used in the experiments theactual resolution would decrease to 8 pixels if onetook into account effects of pulse duration. The la-ser pulses at the fourth harmonic of the Nd:YAG wereassumed to be Gaussian shaped, with a full width athalf-maximum of 25 ps. The width that defines 10%of the maximum would then correspond to 5 pixels.Effects of the resolution as a result of imperfect im-aging of the object are difficult to interpret, as theyalso depend on the true distribution of the effectivelifetime of the object. A resolution of ;200–250 psseems reasonable. Deconvolution of the laser pulsein the algorithm could significantly increase the res-olution of the measurements at the fastest streakspeeds.
The method described requires at least two meas-urements. Turbulence phenomena demand single-
shot applications, which, however, could be performedif two detectors, one a streak camera with a CCD op-erating in the streak mode and the other simply aCCD, were used simultaneously.
The equations used for lifetime evaluation with theSAM are not influenced by any effects that depend onlaser intensity, as the pulse length is assumed to bemuch shorter than the lifetime of the fluorescenceemission. However, when concentrations are to bedetermined, these effects have to be considered.
The algorithms assume a decay of the fluorescenceemission described by a single exponential functionat every spatial point of the object. When the streakcamera was operated in the focus mode each pixel ofthe CCD would then in principle contain informationabout only one single lifetime component. Applica-tions to several lifetime component decays have notbeen discussed. However, tests have been made atDG1 in which two sets of streak and focus imageswere calculated for distributions of lifetimes that dif-fered by a specific amount. The images were thensummed with different weights that corresponded tothe emission intensities described by the two focusimages, and the SAM was applied to the resultingimages. A 1:1 summation corresponded to sets withfocus images normalized to the total number ofcounts; i.e., they described the same emission inten-sity. When the short-lifetime component was 70% ofthe long one, the RMSD for an emission ratio of 1:1 ind0.3 was 1% and increased to 5% for a difference of50% with respect to the emission intensity weightedlifetime. This lifetime is longer than the mean life-time given by the respective concentrations andyielded higher RMSD’s of 3% and 12%, respectively.The SAM seems to follow an emission intensityweighted lifetime description rather well when thedifference of the lifetimes is of the order of tenths ofthe long lifetime. Results from experimental mea-surements in which the imaging resolution was notperfect did in practice yield the same effect as intro-ducing other lifetime components to the decay. Noinstabilities were observed from these effects in themeasurements. SAM tests when the short compo-nent was ten times shorter than the long one dis-played low RMSD values only when one lifetimecomponent dominated. For a ratio of 100:1 ~short tolong! the RMSD based on the emission intensityweighted lifetime and the concentration weightedlifetime were 5% and 9%, respectively, and for a ratioof 1:100 the corresponding values were 1% and 8%.
In comparison, the theoretical upper time resolu-tion of the present technique is considerably higherthan those employed by Ni and Melton,16–18 Tsu-jishita and Hirano,19 and Cubeddu et al.,23 whereas itis of the same order as that presented by Bormann etal.,20 Lakowicz and Berndt,24 and Dowling et al.25
Effects that are due to several lifetime components,such as trigger-pulse jitter, pulse width, spatial res-olution, and noise have to be analyzed more pro-foundly for a proper comparison to be made amongthe various techniques. A deconvolution scheme orthe employment of lasers with pulse widths compa-
rable with the time separation between pixels wouldpresumably increase the temporal resolution of thetechnique presented. A resolution of a few picosec-onds or even better than a picosecond could presum-ably be reached with a femtosecond laser and afemtosecond streak camera.
We intend to test the SAM on a species in gas-phase combustion with lifetimes below 1 ns, where abetter assessment of the potential of the techniqueversus other 2-D techniques can be made.
5. Conclusions
The separation algorithm method permits the deter-mination of the 2-D distribution of the effective life-time of fluorescence emission by use of a picosecondlaser as the excitation source and a streak camera asthe detector. The lifetimes obtained with the SAMdo not depend on effects that are due to changes inlaser intensity as long as they are the same for thestreak and the focus images. The retrieved concen-trations, on the other hand, are not insensitive tolaser-pulse changes.
The resolution in terms of precision of the tech-nique as used in these measurements can be esti-mated to be 10–15% based on the results fromtheoretical calculations of the influence of noise onthe evaluation. Under experimental conditions theresolution is limited by the streak speed and thelaser-pulse duration as well as by the resolution ofthe fluorescent image produced on the photocathodeof the streak camera. From some simple consider-ations a resolution of 200–250 ps for a laser-pulseduration of ;25 ps was estimated. The accuracy ofthe technique is estimated to be nearly the same asthe precision of the technique, i.e., 10–20%.
In theory, it is possible that one could make single-shot measurements of turbulent systems if the detec-tion were extended with another detector, with thedetectors operating in different modes simulta-neously during one measurement event.
Theory shows that it is in principle possible to per-form 2-D measurements of effective lifetimes shorterthan the temporal resolution of fast-gated image in-tensifiers once effects that are due to the length of thelaser pulse are compensated for.
This research was supported financially by theSwedish Research Council for Engineering Sciencesand the Swedish Board for Industrial and TechnicalDevelopments.
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