OCTOBER 1994 NOTES AND CORRESPONDENCE 1409A Review and Discussion of Processing Algorithms for FSSP Concentration Measurements ,l. L. BRENGUIERMdt~o-France (CNRM/GMEI), Toulouse, France D. BAUMGARDNERNational Center for Atmospheric Research, Boulder, Colorado B. BAKERNew Me?:ico Institute of Mining and Technology, Socorro, New Mexico12 March 1993 and 7 March 1994ABSTRACT The forward-scattering spectrometer probe (FSSP) is an optical particle counter widely used for the measurement of cloud droplet size distributions and concentration. Previous studies have identified operationallimitations of these probes and a number of techniques have been developed to minimize the impact of theselimitations on the measurements. The majority of effort has been focused on accounting for droplets missedby the FSSP as a result of droplet coincidence and electronic dead time. This note reviews the algorithms thathave been developed to account for these losses, describes how and when to apply them to previously acquiredmeasurements, and recommends methods to improve the quality of future measurements.1. Introduction A great deal of information about cloud structurehas been acquired with the forward-scattering spectrometer probe (FSSP) manufactured by ParticleMeasuring Systems (Boulder, Colorado). Numerouspapers have been published that evaluate the limitations and accuracies of this instrument. Authors haveproposed corrections to total concentration (e.g.,Baumgardner 1983; Dye and Baumgardner 1984;Baumgardner et ai. 1985; Brenguier and Amodei 1989;Brenguier 1989) and to size distribution measurements(e.g., Cooper 1988; Baumgardner and Spowart 1990;Hovenac and Lock 1993). In general the FSSP providesrelatively accurate measurements of the size distribution of cloud droplets but only if appropriate corrections are applied to account for the recognized limitations. Failure to make corrections to FSSP measurements will lead ~o significant errors in sizing andconcentration. Baumgardner et al. (1990) estimate errors as large as 30% and 60% in measured sizes andconcentration, respectively, that can be reduced significantly when appropriate corrections are applied.The published information on these correction techniques, while useful to those already familiar with the Corresponding author address: Dr. Darrel Baumgardner, NCAR,Research Aviation Facility, P.O. Box 3000, Boulder, CO 80307.operational characteristics of the FSSP, do not necessarily lend themselves to easy implementation and thevariety of techniques leaves the investigator wonderingwhich technique is most appropriate for a specific setof data. The other problem is that most of the techniques require auxiliary information from the FSSPfor optimum implementation of the processing algorithms, but many of the earlier model FSSPs do notprovide this information. The processing algorithmscan still be used on measurements from these probesbut additional assumptions must be made. This notepresents a simplified explanation of how droplet concentration measurements are made, describes howdroplets are missed as a result of coincidence and deadtime, reviews the algorithms that account for theselosses, and discusses how and when to implement theseprocessing methods.2. Fundamentalsa. Derivation of droplet concentration The FSSP detects light scattered in the forward direction from droplets that pass through its laser beam.The concentration N is simply the ratio of the dropletrate n (s-~) through the sensing section of the probeto the corresponding volumetric flow rate of air. Thevolumetric flow rate is determined from the productc 1994 American Meteorological Society1410 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 11of the airspeed v and sensitive beam cross section S.Hence, n (1) ;v= However, not all droplet detections can be used forsizing because of the nonuniform intensity of the laserin both cross section and along its length. Only dropletscrossing close to the center of focus are selected by anelectro-optical discrimination in the probe and thecorresponding acceptance length is defined as the depthof field (DOF). Thus, one of the basic parameters provided by most FSSPs is a measure of the number ofparticles passing through the DOF, referred to as the"total strobes," or nr (the appendix lists a glossary ofall the variables discussed in this paper). To apply ( 1 )the droplet velocity through the sample volume, thebeam diameter ( ~ 0.2 mm) and DOF ( ~ 3 mm) mustalso be 'known (S = beam diameter x DOF). Theseparameters provide a primary evaluation of the dropletconcentration, but the correction algorithms discussedbelow require a measure of additional parameters; thatis, 1 ) the fast resets nf (droplets detected outside theDOF) or total resets/~/r (all detected droplets, also thesum of nr and nf); 2) the activity A that measures the fraction of timethe FSSP is active detecting and processing droplets; 3) the electronic delay period ra following eachdroplet detection (typically between 2 and 10 t~s); 4) the time response of the FSSP amplifiers thatdetermine the effective droplet transit time. If these parameters are not available they can beestimated as will be discussed later, but the subsequentcorrections will be less accurate.b. Errors in derived concentration The concentration derived from ( 1 ) is correct underthe assumption that the FSSP measures n correctly andthat $ and v are accurately known. There is some uncertainty in v because of possible airflow distortionsand turbulence but the primary sources of error are in$ and n. The sensitive beam cross section is defined by thebeam diameter and the electro-optically defined DOF.Uncertainties in these dimensions have been discussedby Dye and Baumgardner (1984), and Baumgardneret al. (1990) estimate that the dimensions of the crosssection cannot be measured to an accuracy betterthan 15%. The measured droplet rate na is never identical to nsince all droplets in the sample volume are not detectedand the derived concentration will always be an underestimate of the true concentration. Two circumstances cause undetected droplets: coincidence anddead time. Droplets that are coincident in the FSSPsample area are measured as a single event. This [iappens each time a droplet enters the beam before theprevious droplet has left the beam. This causes an extended pulse width measured by the system. In thisevent the FSSP operates like a retriggerable counter. Each pulse is followed by a fixed electronic delay raneeded for accurate droplet sizing. During this delay,however, droplets will not be detected if they passthrough the beam and the length of the delay remainsfixed. In this, the dead-time loss case, the FSSP behavesas a nonretriggerable counter. These two distinctionsare important only because some of the correction algorithms that have been derived to correct for the twotypes of losses rely upon the mathematical descriptionof these two types of counters. The errors in concentration measurements that arisefrom uncertainties in the sample volume cannot beeasily eliminated without a new optical design. Algorithms have been developed, however, to account forthe droplet detection losses,c. Processing algorithms The processing algorithms that account for dropletlosses are statistically derived since coincidence anddead-time events are random events. These methodsare based on the hypothesis that the droplet-countingprocess is Poisson; that is, that droplet arrivals in thebeam are random and independent. In addition, if thedroplet concentration is uniform and the sampled volume remains constant during the accumulation period,the counting process is a stationary Poisson processand statistical procedures allow a calculation of theexpected value of the actual droplet rate. If the processis Poisson but not stationary (concentration inhomogeneities), the techniques discussed below still provideuseful information on the average rates and on thescales of inhomogeneities. There are two approaches to estimating actual droplet rate through the counter: 1 ) from measurements of counted rate and/or activity; 2) from measurements of the interarrival times between droplets, using either the slope of their frequencydistribution or the compensation method. 1 ) ACTUAL RATE FROM COUNTED RATE AND/OR ACTIVITY A particle is in the FSSP laser beam for a period rdetermined by its velocity v and the chord l of thebeam through which it passes; that is, r = l/v. If asecond particle enters the beam during r, the pulseduration T is lengthened and only one particle iscounted. It follows that the pulse duration is eitherequal to r, for single particles, or greater than r, forseries of coincident particles, and its mean value POCTOBER1994 NOTES AND CORRESPONDENCE 1411during the accumulation period is always greater thanr. The value of r, or single particle transit time, is acrucial parameter for the evaluation of coincidencelosses, since the probability of a coincidence is theprobability for a particle to enter the beam during r. The activity of the probe is measured by a clock thatis started as a particle enters the beam and remains onuntil the electronics are reset after the dead time; thatis, it is equal to the sum of the pulse durations andelectronic delays during the accumulation period: A = na(~+ ra) > nd(r + ra). (2) The probability of coincidence and dead-time eventshas been formalized by Baumgardner et al. ( 1985 ) andBrenguier and Amodei (1989). The latter investigatorstook a more theoretical approach, but their final solution is in practice the same as found by Baumgardneret al. The algorithms derived by Brenguier and Amodei(1989) will be presented here. These authors haveshown that expected values of counted rate and activityare both functions of the actual droplet rate and r; thatis, na=f(n, r) and A = g(n, r). (3)Thus, the expectation of the actual droplet rate can bederived if either na or A are measured and - is known.Further in the text, the term "expectation of" will beomitted. The solution depends on the respective valuesof the r and of the electronic delay:for ra ~< r ~ = 1 - XXa ra nXfor ra > rA = 1 -XXa, (4) 1 -- X2 nX l, ld = 1 +nX(ra-r) X2 ,4 = I (5) I +nX(ra-r)'where X = e-"' and Xa = e-~'d. It is also possible to combine these equations toevaluate the homogeneity of the samples (Brenguier1990) and to check probe function (Brenguier et at.1993). These equations are strictly valid for a constantr, but Brenguier (1989) showed that they are still approximately valid for the FSSP when using the averagevalue of r. Two circumstances cause variations of ther: the location of the droplet trajectory through theFSSP's approximately cylindrical beam and the amplitude of the detected pulse. The actual duration of aparticle in the beam is determined by its location butthe electronic response time of the probe leads to alengthening of the measured pulse duration that variesas a function of pulse amplitude. Since the beam section is approximately circular andparticles will pass randomly through different chordsof the beam, it is easy to show that the average chordlength l is equal to ,r/4 of the beam diameter and theaverage r is 0.785 d/v. The average r is thus obtainedwith Eq. (3.3) in Brenguier ( 1989):7 = ,r ~-~ +-- n~mln -1 F/rn j=l ~0 '(6)where n j is the number of droplets in the size class j,nm is the total number of droplets that have been sized,V~ is the voltage corresponding to the class j, V0 is thedetection threshold, and 0 is the time response of theamplifiers (typically between 0.4 and 0.6 us for theFSSP). If these values have not been measured on theprobe, a value of 0.5 #s for the time response and thevoltage scale provided in the manufacturer's documentation are good estimates for the calculation of theelectronic lengthening. For a beam diameter of 0.2 mm, at an airspeed of100 m s-I, the maximum r is 2 tts, the average r is1.6 ~s, and the electronic lengthening can change from0 to 2 its, according to the proportion of big dropletsin the spectrum. The resulting r can range from 1.6 usto more than 3 t~s. The coincidence equations are sensitive to the r value; hence, it is crucial to correctlyevaluate the average r for an accurate correction. The distinction between (4) and ( 5 ) is an importantone to understand since it depends upon the conditionsunder which the FSSP is operated and the electronicsetup of the probe. The decision to select (4) or (5)will depend upon the particle velocity, the electroniclengthening--that is, the droplet spectrum--and theelectronic delay time. The newer-model FSS?s use twodelay cycles. If a droplet is detected in the DOF, itstransit is followed by a long delay (typically 6-10/~s),needed for size processing, while if it is detected outsideof the DOF, the electronics are more rapidly reset (typically 1-2 ~s). At a typical aircraft speed of 100 m s-I,the average r, as discussed above, will always be shorterthan the long delay but can be either longer or shorterthan the fast delay. The fraction of particles that pass through the DcF,f(or DOF fraction), and thus have been followed bya long delay, can be calculated directly if either the fastreset or the total resets are measured:f= ~lr nT (7) F/T q- /'/f F/r 'The coincidence equations must be combined according to this proportion:1412 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME II 1 oo0~ ~oo 800 70O._~ ~oog ~ooo ~oo 300 2'opg~ 100 0 0 SI d FastResetsI ........ Slow Reset Only 200 400 600 800 1000 1200 Actual Concentration (cm-3)F~G. 1. The measured and actual concentrations are compared inthis figure as a function of whether an FSSP has the electronics fora slow delay reset only or has both a slow and a fast reset delayinstalled. t= ~,(1--f)+ l=l-f+f nd ndl ha'2 .4 = nd( ~ + ~) ra = ra~(1 -f) + ra~f, (8)where ~, ~2, n,a, and n~ are the average pulse durations and counted r~/tes given by (4) or (5), forequal to ral and The choice of either (4) or (5) depends on the average r compared to rdl and ra~. The previous discussion showed that for ra2 (long delay), (5) always applies(ra > 7 ), while for r~2 (fast reset), the choice of (4)or (5) can be made only after calculation of 7. Examination of (4), (5), and (8) shows that they cannotbe solved analytically for n, but must be solved numerically. The effect of having the fast reset functionof the probe implemented is illustrated in Fig. 1, where(5) for the counted rate is plotted for a ra of 10 Its anda ~a of 3.6. This clearly illustrates the necessity of decreasing the amount of electronic delay to the minimum possible and of compensating for the losses. The question arises, What is the best evaluation ofthe actual rate, from counted rate or from activity?The activity in typical FSSPs is measured with a 1MHz clock, but the subsequent clock counts are divided by 1000 before transmission to the data system.The resolution of activity measurements is thus limitedto 1 ms in a standard probe (1024 counts at 100%activity) but can be improved by reducing the divider,for example, 65 000 counts at 100% activity providesa resolution of 15 Its. At very low concentrations it isobvious that the direct measurement of counted rateprovides the best evaluation, since counted rate is almost identical to actual rate, while the value of theactual rate derived from activity is directly affected bythe error in the evaluation of the r and the limitedaccuracy of the activity measurement itselfi As theconcentration increases, the situation reverses becausecounted rate reaches a maximum while activity is acontinuously increasing function of the actual rate. Thesimplified set of equations for a pure retriggerablecounter is sufficient to illustrate this transition: na=nX and A= 1-X. (9)Partial derivatives provide the sensitivity of the actualrate calculation to uncertainties in r, na, and A: dn - l dna + nr -~ )n 1 n r \ na (10)when n is derived from na, dn . -dr 1 - e-"' dA ---+-- (11) n r nre-n* Awhen n is derived from the activity. Equation (10) shows that when na approaches itsmaximum (at nr = 1 ), the sensitivity of the calculationto errors in na and r tends to infinity. If n is derivedfrom activity, the sensitivity of the calculation to errorsin r is constant, equal to r-I, and its sensitivity toerrors in A at n r --- 1 is equal to e - 1, which is lessthan 2. This is illustrated in Fig. 2, where the relativeerror in n is plotted as a function ofn for a typical dna/na = 1%, if n is derived from na (dashed line) and atypical value of dA/A = 5% if n is derived from theactivity (dotted line). In both cases, dr/r = 10%. Thecontinuous line represents the contribution of the ab 0 30~'~ 95. 20; i,_8g ~s.ID.~ 10.2 S.o 50 100 ~50 200 . 250 300 350 ~ I ~ I ' I ~ I ' ~1 , I ~ I ; Pure retriggemble [ t / / / oo ..... ~.................. / ~tt tt .t tt - - ~ ~ ~ ,0 50 100 !50~ for bA-lma.... for AA/A-5%--- for bnffn~l?l I , I ~ I , I200 250 .300 .350n (s-') x 1000 400, -- -30 20 15 10 5~ '0 400 F~O. 2. The relative error in determining n is plotted as a functionofn for dna/na = 1% ifn is derived from nu (dashed line) and fordA/A = 5% when n is derived from the activity A (dotted line). Inboth cases, dr/r = 10%. The continuous line represents the: contribution of the absolute error in A when n is derived from the activity.OCTOBER 1994 NOTES AND CORRESPONDENCE 1413'solute error in A that results from the limited resolutionof the clock and that is significant only at low n values.These values are typical of an FSSP with an activityclock set at 65 000 full range. Figure 2 shows that at rates below 150 000 s-l (concentration below 750 cm-3), the evaluation of the actual rate from counted rate is the more accurate. Atrates above this the solution using activity is the moreaccurate. The question arises, what if the total strobes, fastresets, or activity were not recorded? In this case, theconcentration correction must be derived from an estimate of na, since the activity correction shown aboveassumes a measured activity that already has the effectsof coincidence taken into account in its value. If theFSSP in question was an older model that used onlythe single reset delay period, then nothing else is required to use the measured na to solve for n. If theFSSP used both the low and fast reset delays, but nTand nf were not recorded, an approximation to fin(7) is 0.20. This has been verified experimentally inlaboratory studies and by airborne measurements (Dyeand Baumgardner 1984) from FSSPs that measure boththe total strobes and fast resets; however, this value isdependent on the size spectra and can vary from 0.1to 0.3.the next one. When the interarrival time distribution(IATD) is obtained from a standard FSSP, the timeinterval, measured between detections, consists of theinterarrival time plus the pulse duration and the electronic dead time. The electronic dead time, which isconstant, can be simply subtracted from the measuredintervals but variations of the pulse duration due tocoincidence effects are random and cannot be exactlysubtracted from the measured values. However,Baumgardner et al. (1993) have shown that rates derived by this method will be negligibly affected if derived only from time intervals greater than tin, wheretm is roughly the maximum pulse duration, plus deadtime, likely to occur. The value of t,, will increase withn. A value of 7 us is adequate for typical values of n. Coincidence and dead-time errors can also be eliminated from the droplet rate measurement using theindividual interardval times (Baumgardner et al.1993). A fixed time, t~, is subtracted from each interarrival time and any negative times and a fraction(about 1/2) of the zero times are ignored. The actualrate n is calculated from this new sequence of interarrival times by dividing the number of arrivals by thesum of their interarrival times. The first approach wecall the slope method and the second the compensationmethod. 2) ALTERNATIVE DERIVATIONS OF CONCENTRATION The algorithms discussed in the previous sectionpertain to measurements made with conventionalFSSPs and data systems. A number of investigatorshave been recording individual droplet sizes and thetime between particle detections in the FSSP. This isdifferent than the conventional systems that only recordaccumulated size distributions over fixed sampling intervals. The single particle measurements lead to newmethods of calculating the droplet rate and minimizeany effect of coincidence and dead time. Baumgardner (1986) suggested deriving n frommeasurements of the distribution of the interarrivaltimes between droplet detections. The Poisson statisticsimply that the probability distribution of an interarrivaltime At being greater than any given time t is exponential; that is, P(At > t) = e-n'. (12) When an interarrival time frequency distribution isconstructed the rote n is just the slope of the distribution(on a log scale). Under the Poisson hypothesis, thisexponential law characterizes any frequency distribution of time intervals measured between any time originand the arrival of the next droplet in the beam, as longas the time origin and the arrival of the next dropletare independent events. This is the case with the fastFSSP (Brenguier 1993) where time intervals arecounted from the end of a pulse to the beginning ofd. Examination of the Poisson assumption All of the above methods for deriving the actual rateare based on the assumption that the droplets are randomly and independently distributed in space. If thisassumption is not valid then solutions of the coincidence equations for counted rate and activity will notbe identical and the IATD will not be exponentiallydistributed. To varying degrees of sensitivity, the hypothesis of Poisson statistics can be tested. The coincidence equations may be combined (Brenguier 1989,1990), the IATD may be compared with an exponential (Paluch and Baumgardner 1989), or the Fishingstatistic (Baker 1992) may be applied to the sequenceof interarrival times. The latter method is a well-defined, sensitive, statistical test that also yields information on the scales of the inhomogeneities in thedroplet arrivals. Observations of non-Poisson statisticsare generally interpreted as an inhomogeneity of thedroplet spatial distribution. When stationarity does notapply, for example, when droplet concentrations fluctuate during a sample period, the rate derived by anyof the methods described above is not equal to theaverage concentration of the sample. The rate derivedfrom the coincidence equations (Brenguier 1989) andthe rate derived from the slope method (Paluch andBaumgardner 1989), both termed "local rates," aresomewhere between the maximum rate and the averagerate of the sample. The rate derived from the IATDusing the compensation method is less than the averagerate (Baumgardner et al. 1993 ). Thus, from the IATD,1414 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 11some idea of the range of rates involved in the inhomogeneous sample can be obtained as well as upperand lower bounds of the average rate.3. Summary Measurements of the concentration from the FSSPunderestimate actual droplet concentrations becauseof coincidence and electronic dead-time losses. Thedifference between measured and actual concentrationsincreases with increasing concentration and can easilyexceed factor of 2 differences. A significant fraction ofthese losses can be recovered with appropriate processing algorithms that use the assumption of Poissondistributed particles to apply statistical corrections tothe measurements. The FSSPs used by the scientificcommunity are not identical and the processing algorithms are highly sensitive to the operating characteristics and environment of the probe. First-order corrections can be applied if the only measured parameteris the particle rate, which is the most fundamental output of this instrument. Further improvement is gainedas additional information is recorded from the probe.The most comprehensive corrections are possible if theactivity, total strobes, and fast resets are recorded fromthe FSSP. FSSPs whose individual droplet counts can be recorded, along with the arrival time, provide the mostrobust measure of concentration since the distributionof arrival times provides a measure of the concentrationthat is virtually unaffected by coincidence and deadtime. Many of the newer data systems being built byseveral organizations are now routinely recording thesearrival time distributions without the necessity of recording every droplet event. New developments are currently under way to improve the FSSP; for example, the fast FSSP (Brenguier1993) eliminates electronic dead time and providespulse amplitude, duration, and interarrival time foreach detected particle such that coincidence correctionscan be made more accurately. APPENDIXDefinition of Annotation Used in TextTerm DefinitionA DOFfprobe activity: the amount of time the probe spends processing droplets (s)depth of field (ram)actual rate of droplets in sample volume (s-1)DOF fraction: ratio of total strobes to total resets1)TTdTmeasured droplet rate (s-l)total strobe rate: rate of particles passing through the DOF (s-l)fast reset rate: rate of particles passing outside the DOF (s-l)total reset rate: rate of all particles passing through the beam (s-l)actual droplet concentration (cm-3)cross-sectional area of laser beam where droplets can be detected (cm2)velocity of droplets through the laser beam (m s-l)pulse duration (transit time) of a droplet in . the laser beam (s)a fixed electronic delay time after the passage of a droplet (s)pulse duration including coincident droplets REFERENCES'Baker, A. B., 1992: Turbulent entrainment and mixing in clouds: Anew observational approach. J. Atmos. Sci., 49, 387-404.Baumgardner, D., 1986: A new technique for the study of ,.'loud microstructure. J. Atmos. Oceanic Technol., 3, 340-343. , and J. E. Dye, 1982: Cloud particle measurement sympo:dum: Summaries and abstracts. NCAR Tech. Note TN-199+PROC, 103 pp. , and M. Spowart, 1990: Evaluation of the forward scattering spectrometer probe. Part III: Time response and laser inho mogeneity limitations. J. Atmos. Oceanic Technol., 7, 666-672. , W. Strapp, and J. E. Dye, 1985: Evaluation of the fox,yard scattering spectrometer probe. Part II: Corrections for coinci dence and dead-time losses. J. Atmos. Oceanic Technol., 2, 626 632. , W. A. Cooper, and J. E. Dye, 1990: Optical and electronic limitations of the forward-scattering spectrometer probe. Liquid Particle Size Measurements Techniques, Vol. 2, ASTM STP 1083, 115-127.--, K. Weaver, and B. Baker, 1993: A technique for the measure ment of cloud structure on centimeter scales. J. Atmos. Oceanic TechnoL, 10, 557-565.Breed, D. W., 1978: Case studies on convective storms: 22 June 1976: First echo case. NCAR .Tech. Note NCAR/T.N-130+STR, 41 43.Brenguier, J. L., 1989: Coincidence and dead-time corrections for particle counters. Part II: High concentration measuremenls with an FSSP. J. Atmos. Oceanic Technol., 6, 585-598.--, 1990: Parameterization of the condensation process in small nonprecipitating cumuli. J. Atmos. Sci., 47, 1127-1148.--, 1993: Observations of cloud microstructure at the centimeter scale. J. Appl. MeteOr., 32, 783-793.--, and L. Amodei, 1989: Coincidence and dead-time corrections for particle counters. Part I: A general mathematical formalism. J. Atmos. Oceanic Technol., 6, 575-584. , A. R. Rodi, G. Gordon, and P. Wechsler, 1993: Real-time detection of performance degradation of the forward-sca~Itering spectrometer probe. J. Atmos. Oceanic Technol., 10, 27--33.Cooper, W. A., 1988: Effects of coincidence on measurements with a forward scattering spectrometer probe. J. Atmos. Oceanic Technol., 5, 823-832.Paluch, I. R., and D. G. Baumgardner, 1989: Entrainment and fine scale mixing in continental convective clouds. J. Atmos. Sci., 46, 261-278.

## Abstract

The forward-scattering spectrometer probe (FSSP) is an optical particle counter widely used for the measurement of cloud droplet size distributions and concentration. Previous studies have identified operational limitations of these probes and a number of techniques have been developed to minimize the impact of these limitations on the measurements. The majority of effort has been focused on accounting for droplets missed by the FSSP as a result of droplet coincidence and electronic dead time. This note reviews the algorithms that have been developed to account for these losses, describes how and when to apply them to previously acquired measurements, and recommends methods to improve the quality of future measurements.