Background correction in electron-ion coincidence experiments using a self-optimizing, pseudorandom count generatorIvan Powis and Peter Downie Citation: Review of Scientific Instruments 69, 3142 (1998); doi: 10.1063/1.1149074 View online: http://dx.doi.org/10.1063/1.1149074 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/69/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in An Improvement of (X, eX) Spectrometer for Coincident Measurement of Compton Scattered Photon andRecoiled Electron AIP Conf. Proc. 705, 1001 (2004); 10.1063/1.1757966 Calibration of a multiple microchannel plate detectors system by α-induced secondary electrons Rev. Sci. Instrum. 71, 2367 (2000); 10.1063/1.1150622 Preset count moving average digital algorithm with faster response to an increasing count rate Rev. Sci. Instrum. 70, 3765 (1999); 10.1063/1.1149990 A versatile electron detector for studies on ion-surface scattering Rev. Sci. Instrum. 70, 1653 (1999); 10.1063/1.1149647 Statistics and dead time correction of two-particle time-of-flight coincidence experiments Rev. Sci. Instrum. 68, 2347 (1997); 10.1063/1.1148117

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Background correction in electron-ion coincidence experimentsusing a self-optimizing, pseudorandom count generator

Ivan Powisa) and Peter DownieDepartment of Chemistry, The University of Nottingham, Nottingham NG7 2RD, United Kingdom

~Received 14 April 1998; accepted for publication 22 June 1998!

A technique is described whereby an estimate of the false coincidence signal, suitable forbackground correction of data acquired in a coincidence experiment, is obtained by using apseudorandom pulser to generate a stream of ‘‘false’’ start events. The statistical properties of thissimulated source are adjusted to mimic those of the real source of electron start events. False ioncoincidences with the simulated starts are measured concurrently with the real coincidence signal,with the mean count rate of the pseudorandom pulse source automatically tracking that of the trueelectron start events. In this manner any long term instrumental drifts during the course of anextended experimental measurement will similarly affect both the real and simulated coincidencedata. Subtraction of the simulated background of false coincidences from the real coincidence datathen yields an improved estimate of the true coincidence signal. ©1998 American Institute ofPhysics.@S0034-6748~98!03509-6#

Electron-ion coincidence experiment, and derivativetechniques are widely used. In a typical arrangement the de-tection of a fast particle~electron! is used to start a timedgate interval during which a delayed coincidence with theslow particle~ion! can be registered. This is inherently suitedto use with time-of-flight~TOF! ion mass and velocity analy-sis, accomplished by precise timing of the delayed ion arrivalwithin an extended coincidence window of perhaps sometens of microseconds overall width. The design of such ex-periments requires proper consideration of the statistics ofthe coincidence counting.1,2 A common problem is the re-cording of noncoincident ions, created in unrelated ioniza-tion events, which just happen to arrive at the detector withinthe period of the coincidence resolving window. These ionsgive rise to a background of false~sometimes also calledaccidental or fortuitous! coincidences, which can seriouslydistort a measurement if not properly allowed for. Addition-ally, there is a need to correct for paralysis losses of thedetector/recording system when more than one ion mightarrive within the instrumental deadtime, and this requires aknowledge of the statistics of both the true and false coinci-dence signals.3,4

Correction of coincidence TOF spectra recorded underconditions of a continuous source extraction field is com-paratively straightforward: the false coincidences are uncor-related with the true start signals and so give rise to a uni-form background, with Poisson statistics, across thecoincidence window. The constant mean background rate isreadily identified from the recorded baseline away from anytrue coincidence peaks and is straightforwardly subtracted~with necessary paralysis corrections! to yield an estimate ofthe true coincidence signal. However, the design of electron-ion coincidence experiments frequently demands the use of a

pulsed source extraction field in order to satisfy conflictingrequirements: a zero or low field for good electron energyresolution, a much larger field for favorable extraction ofheavier ions. The heavy ions will have a much longer sourceresidence time than the lighter electrons, especially in theabsence of the pulsed extraction field. Inevitably also, theelectron detection, and consequent sweeping of the ionsource by the pulsed field, is less than 100% efficient. Anexcess of background ions can therefore accumulate in thefield free source. When, following the eventual detection ofan electron, the extraction fieldis applied these residual ionsfrom previous ionizations will contribute false coincidencesto the recorded TOF spectrum. Since both the genuine andaccidentally coincident ions are simultaneously acceleratedfrom adjacent, localized spatial regions of the instrument thefalse coincidence background may itself be structured, show-ing distinct time-of-flight mass peaks, etc. False coincidencesmay also be registered by ions formed shortlyafter applica-tion of the extraction pulse~particularly for higher overallionization rates!, and these will display another distribution.Successful subtraction of the false coincidence backgroundnow requires specific knowledge of its overall distribution atthe detector.

Separate experimental measurements are often used toestimate the false coincidence background in pulsed extrac-tion experiments. An electronic rate generator produces anindependent stream of ‘‘pseudostart’’ pulses which triggertiming and the extraction pulser, just as real electron startswould. Because of the arbitrary nature of the pseudostartpulseall coincidences recorded in such a fashion are neces-sarily falsecoincidences. In the simplest case the backgroundmeasurement is made sequentiallyafter completion of thereal coincidence experiment.5–7 However, two criticismsmay be leveled at this procedure: one stems from the factthat coincidence data rates are typically low, requiring aminimum of several hours of data acquisition. Inevitably

a!Author to whom correspondence should be addressed; electronic mail:Ivan.Powis@Nottingham.ac.uk

REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 69, NUMBER 9 SEPTEMBER 1998

31420034-6748/98/69(9)/3142/4/$15.00 © 1998 American Institute of Physics

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there will be long term drift in intensity of the ionizing ra-diation, sample gas pressures, etc. so that the overall ioniza-tion rate prevailing during the real experiment will fluctuateand not be faithfully reproduced in a subsequent backgroundmeasurement. Second, the pseudostart pulses do not have thesame Poisson distribution as the true start signals, often noteven the same mean rate.

A modified procedure8,9 partially addresses these prob-lems by a concurrent measurement of real and pseudocoin-cidence data. A second extraction pulse, automatically gen-erated a fixed interval~40–100 ms! after each true startevent, causes a false coincidence background spectrum to beaccumulated in a separate data buffer. But the statistics of thepseudocoincidence background still do not correctly mimicthose of the real coincidence measurement since a fixed in-terval elapses between real and pseudo extraction pulses.

After their creation the background ions accumulating inthe source region will slowly drift from the ionization vol-ume due to their thermal motion, any translational energyacquired in fragmentation from the parent, and any smallfields ~stray or intentional! which are present. So the numberand spatial distribution of background ions within the sourcewill depend on the time interval since the source was sweptclear by a previous extraction pulse. When triggered bygenuine electron pulses in the real experiment this intervalwill have a Poisson distribution.

In the course of developing a new coincidence experi-ment which uses imaging detectors to establish electron-ionrecoil vector correlations10 the problem of backgroundsubtraction has been re-appraised. The increaseddimensionality—(x,y,t) as opposed to just (t)—of the coin-cident ion dataset makes it the more important to reproducereliably thespatialas well as numerical distribution of back-ground ions in the source, since the longer the interval be-tween successive extraction pulses the more diffuse the im-age of false coincidences becomes.

We have adopted the solution of using a pseudorandompulse generator to create an independent, uncorrelated streamof pseudostart pulses with the correct Poisson distribution.The background pseudocoincidence data are acquired con-currently with the real coincidences. As the pseudopulse gen-erator is free running there is no correlation between real andpseudostart pulses, but the pseudorandom generator tracksthe real electron source and continuously adjusts itself tomaintain the same mean count rate at all times throughoutthe experiment.

A continuous, random ionization source will followPoisson statistics such that for a mean count rate ofl theprobability of n counts in the intervalt50→T is given by

P~n;T!5~lT!n/n! 3exp~2lT!.

Consequently the probability of there being an intervalt be-tween two successive pulses is

p~ t !5P~0;t !3P~1;dt!5exp~2lt !3~l dt!exp~2l dt!,

which after expansion gives, to first order

p~ t !5l exp~2lt !dt. ~1!

We next introduce a numbert5lt, and substitute to yield

p~t!5exp~2t!dt. ~2!

It is well known that a series of values with exponentialdistribution and unit mean as described by Eq.~2! can begenerated ast i52 ln(Ri) where the random numbersRi areuniformly distributed on the interval 0→1. Subsequently aseries of real time intervals with an appropriate random dis-tribution and the desired mean ratel is obtained from

t i5t i /l. ~3!

A schematic of the key features of a hardware imple-mentation of the tracking random pulse generator is shown inFig. 1. An AM9513 device, containing five 16 bit program-mable mode counter/timer units, a 5 MHz oscillator, andprescaler circuitry, provides the required timing functionsunder control of a microprocessor. Some minimal additionalinput/output ~I/O! @two binary coded decimal~BCD!switches, 4 digit alphanumeric light emitting diode~LED!display driver# and a 4 Mbyte erasable programmable read-only memory ~EPROM! are also provided. A single pro-grammable array logic~PAL! device provides the requiredglue logic. None of these component choices is critical,though the AM9513 is particularly convenient because of itshigh degree of integration, and the flexibility of its config-urable counter/timer functions.

The timing functions are implemented as follows.Counter C3 is used to divide down the prescaled 5 MHzclock to provide a 1 Hzprocessor interrupt and a special gatefor counter C4. This is configured to count and store theincoming true electron pulses during each 1 s gate intervaland is read by the processor to obtain the instantaneous trueelectron count rate. A running exponential average of thisrate is computed using a time constant in the range from 1 to256 s ~selected in binary steps by one of the BCD inputswitches! and a continuously updated value of the resultingmean count rate is displayed on the LED display as a con-venient ratemeter. This mean count rate is also used to setthe mean rate of the pseudorandom pulse generator.

The divisiont i /l @Eq. ~3!# required to obtain the ran-dom interpulse time interval is conveniently achieved byloading the valuet i into a count-down timer which is

FIG. 1. Schematic of hardware implementation of pseudorandom pulser.

3143Rev. Sci. Instrum., Vol. 69, No. 9, September 1998 I. Powis and P. Downie

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clocked at a ratel. In practice, to achieve both acceptableprecision and use only fixed point arithmetic, a commonmultiplier, N, is applied to scale botht i and l. C2 is thenprogrammed to divide down the system clock to a rateNlwhich in turn clocks timer C1, operating in a count-downmode. Each end-of-count pulse of C1 is fed out as the de-sired random start pulse and causes the next random interval,int(Nt i 11), to be transferred into C1 from a processor-maintained cyclical queue. Tracking variations in the truemean count ratel is then simply a matter of adjusting thefrequency of C2 to a revised value ofNl while loading ofthe sequenceNt i into C1 continues with no additional inter-vention.

For this implementation a fixed value ofN(51000) wasassumed. A random number sequence,t i , was computedfrom Eq.~3!, using a pseudorandom generator ofRi , and thesequence int(Nt i) stored in a memory resident lookup table.The system performance relies critically on the quality ofthis sequence which depends on:~i! the quality of theRi

generator;~ii ! length of the sequenceRi ; and ~iii ! roundingerrors in computing and storingt i . For example, in the datato be presented below~Fig. 2! the recorded total of trueelectron starts was 4 343 780, and that of pseudostarts was4 260 546. The 1.9% discrepancy is readily attributed to themean value t&eff recovered from the 1500 member storedsequence, int(Nt i), which at 1.019 93 exceeds the ideal of 1.We have subsequently demonstrated that effective compen-sation is achieved by increasing the C2 generated clock rate,Nl, fed to C1 by an additional factor^t&eff with a commen-

surate increase in the generated mean pseudopulse rate. Withthe foregoing data it is easily estimated that the recordednumber of pseudostarts would thereby have increasedby this factor~to 4 345 459!, with the remaining discrepancy(21679) falling within the estimated Poisson standard de-viation (6ANe) of 2084 in the real count.

The particular choice ofN determines the useful rangeof the instrument. With a 5 MHz system clock andN51000, as here, count rates ranging from,0.1 Hz up to 5kHz can be accommodated. The minimum interpulse intervalwhich can be generated is thentmin51/Nl. For our typicalcount rate ofl'100, tmin'10mS which is actually less thanthe effective dead time in the start channel~determined bythe width of the coincidence gate used for timing the ionTOF!. So in such circumstances there would be no resultingloss inregisteredstart counts. More generally, for a Poissondistributed count the probability ofn>1 events occurring inan intervaltmin is11

P~n>1!512P~n50!512exp~2ltmin!512exp~21/N!.

Hence forN51000 just 0.1% of expected counts are affectedby the restricted lower bound ont.

The otherwise spare C5 can in fact be configured as aprogrammable one-shot, triggered by the real electron pulses,whose output can be used purposely to disable all countingfunctions for a period following each real pulse. The widthof this disable function, computed from a Poisson distribu-tion as above, will reduce losses of genuine electron countsto a predetermined small percentage~selected with the sec-ond BCD input switch! while inhibiting spurious responsesto a non-Poissonian noise burst.12 It too can be optimized bythe processor in real time in response to changes in the meanelectron count rate, as described previously.11

The performance of this system can be demonstratedwith ‘‘worst-case’’ TOF results from a photoelectron-photoion coincidence measurement on the systemCF4→CF3

11F, recorded under conditions~pressure, light in-tensity, etc.! which resulted in a high background ion count~Fig. 2!. At the 21.2 eV photon energy employed, essentiallyall the ion yield is present as CF3

1 , so that both the true andfalse coincidences have a very similar TOF arrival distribu-tion making accurate subtraction more difficult. The durationof the measurement was 31.5 h. The uncorrected real andpseudocoincidence TOF curves are shown in Fig. 2~toppanel! while the estimated true coincidence TOF spectrumobtained by using a combined paralysis correction and sub-traction algorithm4 appears in the lower panel of Fig. 2. ThisTOF peak shape is in excellent accord with previous data13,14

and with other measurements made under more nearly opti-mal conditions.

1J. H. D. Eland, Int. J. Mass Spectrom. Ion Phys.8, 143 ~1972!.2J. H. D. Eland and V. Schmidt, inVUV and Soft X-Ray Photoionization,edited by U. Becker and D. A. Shirley~Plenum, New York, 1996!, p. 495.

3P. B. Coates, Rev. Sci. Instrum.63, 2084~1992!.4T. Luhmann, Rev. Sci. Instrum.68, 2347~1997!.5M. Richard-Viard, O. Dutuit, M. Lavollee, T. Govers, P. M. Guyon, and J.Durup, J. Chem. Phys.82, 4054~1985!.

6I. Powis, O. Dutuit, M. Richard-Viard, and P.-M. Guyon, J. Chem. Phys.92, 1643~1990!.

FIG. 2. CF4→CF311F coincidence TOF data. Top: real and pseudo~false!

data. Bottom: True coincidences estimated after paralysis correction andsubtraction of false coincidence background as described in Ref. 4.

3144 Rev. Sci. Instrum., Vol. 69, No. 9, September 1998 I. Powis and P. Downie

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7L. Ferrandtanaka, M. Simon, R. Thissen, M. Lavollee, and P. Morin, Rev.Sci. Instrum.67, 358 ~1996!.

8W. Goy, V. Kohls, and H. Morgner, J. Electron Spectrosc. Relat. Phenom.23, 383 ~1981!.

9K. Norwood and C. Y. Ng, Chem. Phys. Lett.156, 145 ~1989!.10P. Downie and I. Powis~unpublished!.

11I. Powis, J. Phys. E15, 151 ~1982!.12M. Arnow, Rev. Sci. Instrum.48, 1354~1977!.13J. C. Creasey, H. M. Jones, D. M. Smith, R. P. Tuckett, P. A. Hatherly, K.

Codling, and I. Powis, Chem. Phys.174, 441 ~1993!.14K. G. Low, P. D. Hampton, and I. Powis, Chem. Phys.100, 401 ~1985!.

3145Rev. Sci. Instrum., Vol. 69, No. 9, September 1998 I. Powis and P. Downie

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