Practical considerations in photon correlation experiments

Practical considerationsin photon correlation experiments

Robert G. W. Brown and Anthony E. Smart

Obtaining true and beautiful data from any photon correlation experiment demands serious attention tooptimizing both the measuring system and experimental conditions. The laser must have sufficientpower, be stable under all likely conditions, and usually be restricted to a single transverse mode. Thebeam-delivery optics must be carefully designed, built, and verified. The scattering medium mustcontain a proper concentration of suitably sized scatterers with appropriate characteristics. Surfacessurrounding the point of measurement must not introduce optical noise. Flare reduction in the receiveroptics may be improved with ghost analysis, spatial and spectral filtering, and careful choice of stops,baffles, and surface coatings. The photon detector must have adequate speed and sensitivity withsuitably low internal correlations and noise. The choice of correlator is crucial. Sometimes the equip-ment must be small to reach inaccessible places. Performance may be compromised by thermal, me-chanical, or electrical instabilities caused by exposure to environmental excesses. Errors may even beintroduced by preprocessing hardware and software before proper information is extracted. With somany conditions and potential problems, how does one obtain beautiful data, leading to correct resultsand enlightening information? That is the focus of our work. © 1997 Optical Society of America

Key words: Photon correlation, dynamic light scattering, laser velocimetry.

1. Introduction

The common-sense practical considerations thatshould have preceded any successful experiment be-come obvious often only in retrospect. Photon cor-relation experiments1,2 typically demand anunderstanding and assurance of many details thatmay be taken for granted in simpler and less de-manding applications. One major danger is that ofsuboptimization, in which one achieves flawless per-formance in the areas one knows about while the lesswell-understood areas receive less attention! To ob-tain the best from any photon correlation experiment,every part of the sensing system and its interfacewith the measured phenomenon merits attention.

Any successful experiment must be preceded by aclear intention of what is to be measured, how accu-rately, and over what range. This intention must besupported by a credible sequence of processes for its

R. G. W. Brown is with the Department of Electronic and Elec-trical Engineering, University of Nottingham, University Park,Nottingham NG7 2RD, UK. A. E. Smart’s address is 2857 Eu-ropa Drive, Costa Mesa, California 92626-3525

Received 13 January 1997; revised manuscript received 29 April1997.

0003-6935y97y307480-13$10.00y0© 1997 Optical Society of America

7480 APPLIED OPTICS y Vol. 36, No. 30 y 20 October 1997

realization. Dynamic light-scattering ~DLS! experi-ments typically investigate a continuum of macromo-lecular or particle properties.3 Laser Dopplervelocimetry4 ~LDV! and laser transit anemometry~LTA!, collectively described as laser velocimetry~LV!, usually measure the motion of scatterers fromwhich may be inferred velocity and perhaps turbu-lence of the fluid in which they are assumed to berigidly embedded. As we discuss throughout thispaper, the acquisition of true and beautiful5 data ~im-plying data that are meaningful, useful, and of thehighest quality! from any photon correlation experi-ment demands serious attention to optimizing boththe measuring system and, so far as they may becontrolled, the experimental conditions. Photon cor-relation measurements in laser speckle,6 astronomy,7quantum optics,8 and other areas may also be im-proved by the techniques outlined below. This pa-per summarizes selected opinions on how to make thebest possible measurements in the real world.

The information in any photon correlation experi-ment lies only in the time intervals between the ar-rivals of detected photons and their statisticalproperties.1 If any property or process associatedwith the equipment degrades the accuracy withwhich these intervals can be measured before theinformation can be fully exploited, then the experi-ment is irretrievably compromised. No subsequent

processing techniques, however ingenious, can re-cover what is lost. Because so much can destroy ordegrade the information borne by the sequence ofphotodetections, we emphasize how to retain its in-tegrity and completeness until correlation and sub-sequent processing.

2. Experiment Definition

Comprehensive experiment definition specifies thedesired measurements and also describes optimalways to retain all the information available from agiven physical situation. The exploitation of all po-tentially available information, without compromiseof its integrity even before correlation and later pro-cessing, demands specification and control of designvariables, not all of which are immediately obvious.

Photon correlation experiments fall mainly into thetwo categories of DLS and LV. Under DLS, a widerange of experiments encompasses the study of mac-romolecules in chemistry, biochemistry, and biotech-nology9 and, more recently, the study of surfacefluctuations and experiments in space.10 Under LV,the range of applications includes well-known exam-ples in aerospace,11 automobile engines,12 wind tun-nels,13 full-scale ships,14 model submarines,15 retinalblood flow,16 and the atmosphere.17 Astronomersuse photon correlation for optical aperture synthesisto create extremely high-resolution pictures of theobservable Universe.18 Each application requiresspecial considerations.

A. Environment

1. Laser VelocimetryThe main failure modes of LV ~Refs. 4 and 19! areinadequate concentration or diameter of the scatter-ing or seed particles, perturbations from extremes oftemperature, pressure, and vibration effects, and op-tical flare, typically unwanted reflections or straylight in the optical system or from the probed config-uration.

For LDV, inadequate scatterers alone can, and of-ten do, guarantee failure. Hostile temperature ex-tremes in the measurement volume or vibration inthe equipment bay, such as are incurred in engineexperiments, can impair data. Inherent optical ab-errations are often worsened by laser beam wave-front distortions incurred in flames and other densityfluctuations, specifically an inhomogeneous refrac-tive index. Only rarely does increased laser powerimprove the signal. Indeed, the performance of thelaser itself can be altered by the conditions of itsenvironment, not necessarily suspected when theequipment is originally set up and tested in the lab-oratory. This type of problem can plague real-worldapplications, which nevertheless can have a high fi-nancial pay-off if made correctly. Such applicationsinclude axial and radial compressors or turbines,20

rotating machinery in general,21 and complex com-bustion facilities22 involving extremes of tempera-ture, pressure, velocity, and turbulence.

For LV the original provision and the preservation

of optical access with clean, undamaged andbirefringence-free windows are often mandatory, butcan be nontrivial, particularly when transmissivemedia can degrade the optical wavefront. We haveknown windows and optical access ruined by localmelting, stress cracking, surface crazing, ablation,soot deposition, surface pitting by molten particles ofstainless steel, and ~once and accidentally! a ball-peen hammer. In many extreme industrial applica-tions, for example, turbocompressor and automobileengine studies, some ancillary method of keepingwindows clean or of intermittently cleaning them23 isunavoidable, as is an occasional need for cooling toavoid damage or heating to avoid condensation. Ifwindows or any intervening media introducerefractive-index fluctuations, then data integrity maybe compromised by distortions of optical phase, byunintended modulation, or even by beam-pointingdrift, which may reduce coincidence of the probebeam and the observed volume.

Installations, especially outdoor or field installa-tions, are often exposed to diurnal temperature cy-cling or steep temperature gradients, whether thefacility is running or not. Reflected sunlight, rain-water, and unsuspected fixed or pulsed magneticfields can introduce problems. Exposure to mois-ture or high humidity can age optical surfaces andinterference filters, also possibly causing fungusbuildup surprisingly rapidly. Any one of these iseasily averted or accommodated: avoiding them all,and also the unanticipated ones, can present a con-siderable challenge.

Perhaps the single most serious reason why LVmay fail to give the anticipated results, or indeed anyresults, is the inadequacy of natural or artificiallyintroduced seed particles.4 Critical properties re-quired of the particles are adequate concentration,ability to follow the flow, sufficient optical-scatteringcross section, and proper size distribution. The con-stancy of this distribution demands the avoidance ofsize changes by diffusion, collisional accretion, abla-tion, evaporation, or erosion. Additional importantproperties not obvious for the scientific requirementsare safety, with freedom from chemical toxicity orcarcinogenic properties, and economic availability.Occasionally obscure properties can cause problems,such as in atmospheric observations when, for exam-ple, tumbling microcrystallites of rock salt, commonin the lower atmosphere in littoral regions, introducea fluctuating scattered signal. It is perilous for anyLV experimentalist to disregard the bitter experi-ences of many observers,4,24 of which these referencesare mere examples of the large body of literature onthe subject of particles.

2. Dynamic Light ScatteringThe main failure modes of DLS are attributable tosample preparation, cleanliness, or condition, typi-cally macroscopic dirt or dust in the suspension ofparticles to be measured, multiple scattering, exceptin the limit of diffusing-wave spectroscopy,25 fluctu-ations in the laser power, sedimentation of particles,

20 October 1997 y Vol. 36, No. 30 y APPLIED OPTICS 7481

and temperature gradients in the sample cell thatcause convective flow across the laser beam.26

For DLS, most of the constraints and optimizationsof experimental conditions are different from those ofLV. Although temporal optical coherence in the il-luminating beam is still important, signals can nowalso be compromised by small temperature gradientsand by gravitational and vibrational effects in theobserved specimen. Measurements may be dis-torted by multiple scattering, critical phenomenathat are not the subject of the current experiment, orunsuspected polarization effects. The temporal andthe spatial mode characteristics and particularly sta-bility of the laser light source may assume great im-portance if these defects are comparable in scale orfrequency with the examined properties of the spec-imen. Not all manufacturers’ published specifica-tions are correct under all conditions of use, so it iswise to confirm the performance of the experimentalequipment.

Whether the scattering particles are plasticspheres for explorations of condensed-matter physics,or complex proteins, macromolecules, or aggregatestructures thereof for biological or biochemical re-search, the uniformity and the stability of the particleproperties affect the data. Typical systems are fre-quently so complex that it is often not easy to sepa-rate effects of interest from those that are incidental,inevitable, and possibly detrimental.

In addition to all the complex physical constraintsof the experiment that must be optimized as far aspossible, unrelated effects can ruin both DLS and LVmeasurements. For example, there are four aspectsof the controlling environment that are guaranteed tocause problems unless given serious attention.These are power supplies, software, schedule, andcost. Schedule and cost are important managementissues affecting the very existence or desirability ofthe experiment. Software and power supplies aremore likely to be ~or supposed to be! under your con-trol. Software should be tested on data for which theresults are already known and understood before anysignificance is attached to new information from un-known circumstances. Power supplies must be asstable and reliable as you can make them, especiallyfor photon correlation, in which ripples in the sup-plies for both lasers and detectors of even 0.01% caneasily be mistaken for a signal. This is especiallytroublesome if the fluctuation frequency is close tospectral features in the expected signal. For photoncorrelation experiments, 0.001% rms in the frequencyband of concern is a fair target for power-supply sta-bility, but confirmation of such a low level is nottrivial.

B. Measured Quantity

Two questions to ask are “What is to be inferred fromthe measured optical scattering?” and “How is theinterpretation to be made?”

Measured quantities may be based on particleproperties, velocity of an entraining fluid, or one ormore of many other parameters accessible with pho-


ton correlation measurements. An important pre-liminary question is how the basic photon statistics ofthe experiment affect the inferred values of the quan-tity to be measured, including confidence and accu-racy. Does the detected light from the scattererseven carry the required information? For LV, someuseful basic numbers can be calculated from expres-sions derived by Oliver.27 For DLS, the basic statis-tical equations have been summarized by Chu.28

Factors affecting inferences from LV measure-ments include flow stability, optical distortion andaberrations, optical and detection efficiencies, stabi-lization and constancy of everything except the pa-rameter to be measured, and the necessaryproperties of particles, as cautioned above. Briefly,this means that the measured properties of the scat-tered light must relate in a known and recoverableway to the quantity to be measured. This is neitheralways nor obviously true, as the whole subject ofinverse problems attests.29

Critical issues of DLS include the highest possiblequality of sample preparation, with special attentionpaid to the removal of dust and contamination. Al-though a covalent supporting fluid tends to clean it-self of suspended contaminants, no such fortuitousbehavior is to be observed with ionic suspensions,such as water-based colloids. Agglomerates and ag-gregation not intended as part of the measured phe-nomenology must be prevented: some techniques totry are particle surface treatment, dispersed surfac-tants, pH control ~buffering!, or ultrasonic dispersal.For large particles with a significant density differ-ence from the carrying medium, microgravity may bethe only feasible, if expensive, way to prevent sedi-mentation. Alternatively, slow sample rotation,centered on the measurement volume and about thelaser axis, can sometimes sufficiently average outgravitational effects. Thermal effects leading togravitational convection or those that induce revers-ible or irreversible changes of the specimen can dom-inate a measured quantity and mask and distort ordestroy the required information. Thermophoreticeffects can seriously mislead one, especially those in-duced by the focused laser beam itself if the productof laser power and local absorption is too great.30

Motion of the sample through the laser beam canintroduce particle-sizing errors unless the correct ge-ometry and flow rates are accommodated.31

Perhaps the two most damaging problems in DLSare laser instabilities in the same frequency domainas the probed phenomenon and flare, that is, anyunwanted scattered light, however, it arises. Theformer problem can be mitigated by careful attentionto the laser power supply and the design of mode andalignment control techniques for the laser itself. Re-ducing flare is more of an art, and a black art at that.The predominant aspect of this art is, of course, tomake everything in the equipment matte black—always desirable to absorb unwanted light. Geo-metric optical stopping is a preferred method of flarereduction32 but rarely sufficient, usually because ofconstraints of physical layout. A comprehensive

analysis and the removal or reduction of optical re-flection ghosts are always essential. Reduction ofsurface reflections by using standard antireflectioncoatings,33 however, can sometimes lead to increasedsurface scatter, depending on the coatings and thesupplier, so a good design trade must be attempted.Superpolishing34 can sometimes move a difficult de-sign closer to its ideally achievable performance but,depending on the exact geometry of the design, it caneasily be an expensive irrelevance. As soon as theoptical system exists physically, just looking throughit in the visible spectrum usually suggests sources offlare not imagined earlier, even with a well-analyzeddesign. These sources can often be reduced to be-come negligible.

3. Model

A numerical model or simulation can serve severalpurposes. These are summarized in the list below.Exercising a model also allows estimates of experi-ment times for given error bounds and statistics, andpredicts necessary computational resources, theirbottlenecks, and even, if we are really lucky, ways bywhich we might build confidence in the proper per-formance of software.

Purposes of a Model• Definition and quantification of the physics and

phenomenology.• Verification that specifications and constraints

are compatible.• An understanding of the interactions among pa-

rameters.• Optimization of a design configuration.• Prediction of ideal performance possible with

that design.• Prediction of performance deterioration when

implementation is not ideal.• Potential to diagnose anomalies found during

construction, testing, and use.• Building confidence in the technology used in

the experiment.

For modeling optical experiments, we have found itbeneficial to simulate the experiment by riding theray or constructing independent simulation modulesthat can be applied sequentially from the generationof the photons to the recovery of the numerical andthe graphical representations of the final measure-ment. This sequence of modules can usually repre-sent the physical phenomenology relatively well. Itmust, however, be augmented by other factors notrepresentable in the temporal or logical sequence ofinformation flow. These typically include thermal,electrical, acoustic, and optical flare noise, and me-chanical movements and vibrations that lead to mis-alignments. All these and more conspire to reducedata quality and may be injected at various points inthe linear model as quantifiable deteriorations.

For both LV and DLS experiments, a suitable mod-ule sequence is photon generator, illumination optics,scattering particles or medium, collection optics,

semiclassical detection, and statistical processing.Detrimental intrusions must include at least lasernoise, the optical imperfections of aberrations andflare, incomplete separation of intended from unin-tended effects of the phenomenon, detector limita-tions, effects of real-time data-compressionalgorithms, which are often erroneously assumed tobe perfect and usually other factors specific to theindividual experiment. A more detailed discussionof the mathematical processes and implementation ofan LV model for photon correlation has been de-scribed by Mayo.35 An approach to DLS modelinghas been described by Edwards.36

With a clear overview of the needs and limitationsof the experiment, the choice of laser, optics, andphotodetector, on which success may fundamentallydepend, can be made with rationality and confidence.Trade-offs can be quantified objectively. Even inreal life, in which the choice of equipment is so oftenlimited by what can be temporarily borrowed, theexistence of a comprehensive model can produce astartling improvement in final results, primarily be-cause it permits the rapid and unambiguous correc-tion of errors made while the equipment wasconstructed and the experiment was performed.

4. Light Source

Most photon correlation experiments are active inthat they use a light beam to probe, although notusually intentionally to stimulate, a phenomenon ofinterest. The light source must have known, con-stant, and well-understood properties. Criticalproblems one must solve before believing experimen-tal results from photon correlation are the laser modequality and stability, mode hopping, and constancy ofthe power level, which often implies a better power-supply performance, as we have stressed above.

Often the first consideration in a light-scatteringexperiment is the necessary wavelength for adequateq or scattering-vector28 coverage in DLS, fringe spac-ing, or spatial discrimination in LV. The laser, cho-sen to have a wavelength appropriate to the plannedexperiment, must have sufficient power, acceptabletemporal and spatial mode structure, and adequatestability, both in fluctuations over the short term ofan individual correlogram and, in the longer term,drift over a series of experiments for which that maybe of concern. Despite manufacturers’ claims, it iswell, some would say essential, to characterize thelaser under the conditions of anticipated use. Thetemporal characterization may be simply performedby the monitoring of a suitable constant fraction ofthe raw laser beam with a stable detector whose out-put is captured by an analog-to-digital converter andanalyzed for modulation and drift. The understand-ing of the laser should be extended to include effectsof ambient temperature changes, power-supply mod-ulations, drifts and transients, mechanical vibrationsand shocks, contamination, and aging of constructionmaterials. With modern PC’s it is relatively cheapand easy to characterize such behaviors. To neglectto quantify at least the time record, rms, and peak-


to-peak fluctuations, together with the amplitudeand phase, or even power spectrum of the laser noiseand drift is courting poorly understood experimentaldata.

Visual confirmation of spatial properties of the la-ser beam is usually adequate. Purists may wish toquantify the spatial distribution and transversemode structure by a beam profiler or by image cap-ture and analysis, which requires an additional two-dimensional ~2D! sensor, sometimes for wavelengthsto which the eye is not sensitive. Our personal ex-perience of doing all these things is that one learnsmuch about the laser that is not available elsewhereand thereby gains confidence in subsequent measure-ments and some indication of the depth of conclusionsthat may be drawn without suspecting the measuringequipment.

Because photon correlation experiments almost al-ways demand coherence in the illumination, a laser isusually required as the light source. The laser itself,be it gas, solid state, or semiconductor, must havesufficient power to allow data acquisition in a timeover which the probed phenomenon is essentially sta-ble and constant and not take too long in objectiveterms—a week is a long time in correlation! It mustbe free from internal correlations and instabilities,have a TEM00 mode structure, and be stable andreliable. Typical output powers require a rangefrom milliwatt to watt levels, depending on the phe-nomenon. Essential criteria in the laser perfor-mance have been reviewed briefly by Chu.28 Herewe elaborate on his review and add consideration ofother effects.

Particularly important parameters are laser line-width, especially for DLS,37 and coherence length,which for LV must be long enough compared with themeasurement volume or optical-path mismatch to op-timize the signal, maximize fringe contrast, and re-duce noise. It is also helpful to know where the laserbeam waist is and to use the correct Gaussian formu-las to find the properties near the probe volume. Ap-proximations to waist positions derived fromgeometrical optics can be quite misleading for suchtypically narrow beams. Errors are especially seri-ous in LV as they can result in tapered fringes that inturn introduce artificially high turbulence estimates.

Perhaps the earliest and most fundamental de-scription of the deleterious effects of source fluctua-tions was given by Oliver38; compensation techniquesfor DLS were reviewed later by Chu.28 Here we seequantified the effects of instabilities on the correlo-grams from photon correlation experiments. Inten-sity fluctuations as small as 0.1% rms can bedeleterious. One frequent source of intensity insta-bility is a direct reflection of a small part of the laserbeam from one of the optical surfaces in the systemback into the laser cavity. This is especially prob-lematic when illuminating light passes throughsingle-mode optical fibers, whose end faces should bewedged by a few degrees to avoid the possibility: 7°is not uncommon for a wedge angle, but as high as 12°is not unknown.


Oliver38 also considered frequency fluctuations andtheir acceptable magnitude, concluding that the mea-sured frequency components must be considerablyless than the longitudinal mode separation of thelaser and that it is highly desirable to eliminate anytransverse modes, whose typical frequency separa-tion of only a few megahertz can easily distort mea-surements. Launching the illumination through asingle-mode fiber can mitigate this, because no trans-verse modes are transmitted.

Even small amounts of power in higher lasermodes, especially TEM01* from gas lasers, can in-crease beam diameter, which seriously affects DLS39

and destroys the uniformity and the contrast offringes in the measurement volume of LDV experi-ments. In photon correlation experiments, highermodes must be eliminated and restriction to a singleaxial laser mode is essential. Without this care, forexample in LDV, it is possible to mistake the beatingof two axial modes as a Doppler signal and thus re-port a spurious velocity.40 With semiconductor di-ode lasers, the unwanted splitting of the laser modefrom, say, TEM00 to TEM01 can give two outputbeams. Usually this is accompanied by reducedpower in the LV measurement volume, which maythen be a warning symptom.

Beam-pointing stability is important, particularlyin optical systems with high magnification. If thelaser beam direction changes sufficiently, the mea-surement volume may move from its intended posi-tion or even no longer overlap the sensitive cone of thecollecting optics. It is worth calculating the effectsof directional fluctuations quoted by the laser manu-facturers and then confirming them experimentally.

A major difference between semiconductor diodelasers and gas lasers is a higher tendency towardmode hopping caused by temperature changes of thelaser cavity. To avoid the typical mode hop for ap-proximately every 1 °C temperature drift, a laser di-ode must be temperature stabilized. When bothsupply voltage and temperature are adequately sta-bilized, diode lasers can perform photon statisticallyjust as well as the currently more common gas lasers.Their factorial moments can be close to the unityvalue expected from a perfect Poisson source, andthey exhibit virtually complete freedom from internalcorrelations.41 Sometimes it is desirable or neces-sary to circularize the beam cross section, which tra-ditionally is elliptical from the edge-emittinggeometry of a laser diode.42 Usually a beam of cir-cular cross section is required for photon correlationexperiments; one exception is LTA, in which an asym-metry of up to a factor of 200:1 from a multistripelaser emitting array has been exploited for both 2Dand three-dimensional ~3D! measurements.43 Inthe future, maybe vertical-cavity laser diode44 geom-etries will provide high-quality circular-cross-sectionbeams directly without astigmatic correction optics.

Residual laser performance parameters pertinentto light-scattering experiments are polarization pu-rity and orientation. These can be particularly im-portant when launching into polarization-preserving

single-mode optical fibers, in which an error as smallas 0.01° in polarization orientation at launch is sig-nificant in that it can confer excessive sensitivity totemperature changes and movement of the fiber. Inthe illumination, the total optical intensity noise fromall sources, including likely causes such as power-supply fluctuations or unlikely causes such as vibra-tions induced by fans or cooling water turbulence,should typically not exceed ;0.001% for high-qualityphoton correlation measurements.

Starting with a near-perfect laser is just a neces-sary preliminary step; during a real experiment, la-ser performance can degrade to introduce spuriousartifacts into the correlogram. Vibration effects inautomobile,12 ship,14 and aeroengines11 are exam-ples. In such hostile environments, temperaturechanges can misalign, introduce mode hopping into,or extinguish even gas lasers. Ambient pressurechanges can also have significant effects on laser per-formances as well as the more expected variations ofbeam propagation.

4. Optics

A. General ConsiderationsThe term optics conventionally describes the compo-nents whereby light is transmitted from the lasersource to the phenomenon of interest ~in photon cor-relation experiments the light-scattering process isusually elastic! and thence to a square-law detector.Ideally the detector yields an electrical signal thatcorresponds to individual quantizations of the inci-dent electric field under the semiclassical approxima-tion.45

Photon correlation systems almost always requireoptics, and the illumination is typically many ordersof magnitude brighter than the scattered light sub-sequently to become a photon-resolved signal. So-called bistatic configurations46 avoid most stray lightby physical isolation of illuminating and receivingsystems. For monostatic configurations46 or cases inwhich illumination and sensing are less than per-fectly isolated, as is often inevitable for small probeswith single-sided access to the phenomenon, morecare is necessary. Therefore, in addition to theusual mandatory optimization of conventional opticaldesign properties, special attention must be devotedto the avoidance or suppression of surface reflectionghosts, scattered flare, detrimental surface proper-ties, and contamination. Sometimes the antireflec-tion coating of a surface can increase its scattering,compromising the advantages otherwise gained bysuperpolishing or careful manufacturing control.

Any optical system for photon correlation meritsformal ghost analysis and establishment of optimizedstops and baffles, but, more than this, a careful studyof peripheral effects, often assisted by a tunnel dia-gram,47 can greatly improve stray light. For theless-common inelastic scattering, spectral filteringcan be beneficial, but the need for a narrow-bandfilter to be in a well-collimated beam can complicatethe receiver optics. Visual assessment of the system

is usually beneficial with respect to finding and cur-ing sources of stray light. This is particularly truefor systems at visible wavelengths, to which the dark-adapted human eye is almost as sensitive as typicaldetectors. For systems in which wavelengths out-side the visible range are used, the luxuries of visualalignment ease and stray-light diagnostics are notavailable.

For the cases in which the phenomenology, geom-etry, and boundary constraints may be defined andcontrolled, the concentration and properties of opticalscatterers, the containing medium, and the opticalaccess may all be chosen as part of the system opti-mization. Often, however, the phenomenon underexamination and its optical access are limited and somust be included as boundary conditions on the sys-tem optimization, which therefore has fewer degreesof freedom.

The interest of a phenomenon often seems to varyinversely with its accessibility, and typical con-straints for measurement equipment can include theneed for extremely small size and tolerance to envi-ronments that may have thermal, mechanical, chem-ical, or electromagnetic extremes. The so-calledimmunity to physical effects of a beam of light used asa sensing probe can be compromised by its optics andsupport equipment.

Fiber optics48,49 are extending the regimes of acces-sibility, but they are less easy to use than might beexpected. In addition to the obvious advantages, theexploitation of such discontinuous media as opticalfibers and graded-index optics has many hidden pit-falls. The list below contains a few important ques-tions worth asking before committing to the use ofoptical fibers. Proper answers to these and manyother questions require experience and often a mea-sure of good luck.

Important Optical Fiber Questions in Photon Corre-lation Experiments

• Is a single-mode or a multimode fiber necessary,and which of the many types is optimal, or even ad-equate?

• What control, if any, should be applied to polar-ization?

• How, and how well, is injection mode matchingto be established and maintained?

• Will the fiber be sufficiently sensitive to vibra-tion, bending stress, temperature, aging, and possibleother factors to compromise desired properties of thetransmitted signal?

• Is the fiber sheath opaque to ambient light?• Does the fiber itself have internal mechanisms

that can introduce signal fluctuations?• Must cladding modes be suppressed, and if so,

how?• Does any intended high light intensity induce

changes of transmission, cause nonlinear effects, orinitiate damage?

• What adhesives are usable or necessary for con-struction?


Optical fibers are finding increasingly important ap-plications in light-scattering systems. In DLS,single-mode optical fibers are widely used to exploitthe increased signal-to-noise ratio and highest possi-ble intercept g2~t!, which is automatically availablewith the perfect spatial coherence of the fiber.50 Asingle-mode fiber is the perfect transmitting aperturefor DLS.

In LV the ability to transmit different colorsthrough the same single-mode fiber allows up to 3Dflow-vector estimates. Single-mode operation cansimultaneously cover a range as large as a factor of 2in wavelength, for example, from as short a wave-length as the blue ~450 nm! to as long as the red ~900nm! before propagation cutoff or multimode trans-mission occurs. Lengths of as much as 100 m ormore of such fibers allow remote access to difficult ordangerous experiments and multiple measurementvolumes.

With their light weight and flexibility, optical fibersallow the creation of miniature optical assemblies toprobe phenomena with small-scale or difficult access.Even photon correlators themselves can be partiallyimplemented with optical fibers.51

B. Optical Components

Optical components for photon correlation experi-ments can include lenses, beam splitters, polarizingcomponents, fiber optics, graded-index devices, coat-ings, stops, filters, attenuators, acousto-optic or Fara-day effect devices, mounts, transparent adhesives,and a host of others. Simple, practical suggestionsconcerning the use of some of these components forphoton correlation experiments have been summa-rized previously.24

The choice of components should always be theminimum set of the simplest parts that will accom-plish the desired performance. Avoid moving parts;avoid unusual or nonstandard parts; where possible,avoid parts. Incidentally, once your light islaunched inside an optical fiber, do not let it out andthen try to get it relaunched — the power loss isalways worse than expected!

Requirements for most photon correlation experi-ments are to detect as much light as possible thatcarries information of interest without compromisingthe retrievable statistics after detection. This im-plies that increased illumination may give less infor-mation if the detector performance is degradedthereby. Detrimental effects include nonlinearitiesand distortions from pulse pileup, afterpulsing, gainproperties, and others. Although as muchinformation-bearing light as possible is required, theoptimal reduction of flare or light that does not carrydesired information, is also just as important, some-times more so, as too much can mask the desiredeffects or consume processing or bandwidth re-sources. Even with correlation techniques, whoseimmunity to flare is one of their most powerful at-tractions, the noise-on-the-noise can rapidly become alimiting feature.

In this sense, the optics of the system are crucial,


for once information is lost or swamped it can neverbe recovered. Here we must distinguish betweennoise from added optical power, which carries no de-sired information, and quantization noise, which isan intrinsic property of the signal itself, and henceneither avoidable nor indeed properly to be regardedas noise.

Several simple criteria dominate the choice of op-tical components. These include maximum trans-mission at the wavelength of interest, control ofaberrations ~implying that aberrations may be ac-tively exploited, for example, apodization!, surfaceplacement, and curvature designed to reduce ghostsand barrel reflections and treatments to reduce sur-face reflection and scattering.

Many LV ~Refs. 4 and 43! and DLS ~Ref. 28! geom-etries have been exploited to derive 1D, 2D, or 3Dinformation about velocity and turbulence, particlesizes, diffusion constants, viscosity, and many otherproperties of flowing gases, liquids, colloids, and sus-pensions. Observations with multiple detectors andcross correlation, especially in DLS, can yield mole-cule, particle, and structure sizes and shapes andother properties. For each of these, a well-designedand usually application-specific optical system is nec-essary. The suggestion that one design adequatelyserves all applications can be misleading: compro-mises must always be properly evaluated, eventhough it sometimes seems easier to take a tried-and-true design and apply it to a new experiment.

Recent advances in components such as semicon-ductor diode lasers, fiber optics, graded-index op-tics,52 and avalanche detectors have permittedminiaturization of photon correlation opticalsystems.53–55 They have also replaced the bulk op-tical technology, which has become well understood,with a new realm of challenges and mysteries aboutthe way such miniaturized systems may be con-structed and may perform. In future years we ex-pect to see yet more new optoelectronic technologiesentering the domain of photon correlation experi-ments.56

Optical fibers, especially single mode, with or with-out polarization preservation, can often mitigateproblems of alignment, geometric access, flare rejec-tion, complexity, and size, and act as single-modefilters that increase signal coherence. However,they can introduce their own problems such as inser-tion loss, which can easily lose 20% when new, andbecome worse with trivial aging misalignment, dam-age from high light intensity, laser destabilization bycoherent feedback, and unwanted modulation fromenvironmental sensitivity. Contamination on theend faces can massively reduce the amount and thequality of transmitted power, and can even destroythe component. Such problems are easily recog-nized. Output damage is identified by the appear-ance of Airy rings or other intensity structure aroundthe ideally Gaussian laser beam in the far field. In-put damage may be less obvious because all that islost is power. In interferometric arrangements,single-mode fibers are especially temperature and vi-

bration sensitive, causing fringe drift and fluctua-tions in LV. The basic fibers are fragile, usuallyneeding one or more tough concentric outer sheathfor protection. Their use also demands high-precision optomechanical designs and mounts, typi-cally to micrometer and microradian tolerances.Finally, the modes in the outer part of the fiber, theso-called cladding must often be stripped out at theend of the fiber by suitable index matching to allowlaunch of the purest light from the core. Althoughthe removal of cladding modes is not always neces-sary, it is well to allow for it.

Many physical problems can be mitigated byproper adhesives, extreme cleanliness always and ev-erywhere, highest-quality fiber-end treatment, be itcleaved or polished, normal or wedged to avoid back-reflections and laser instabilities, and the properchoice of mechanical alignment and its retention.High-radiation environments can also degrade trans-mission by creating color centers in the germaniumused to dope the core of some types of single-modefiber. This is much more serious for short wave-lengths and high-power lasers. The danger is moreserious still for spaceborne experiments with incidentcosmic or gamma radiation. The restoration of per-formance by heating the fiber to reduce the blacken-ing is often inadmissible. In these cases it isdesirable or essential to use cores of pure silica, whichare less susceptible to degradation.

For monostatic systems the control of flare is al-ways a challenge that demands a full design under-standing of the optical geometry and componentproperties, to identify all sources of flare. For bi-static systems, the problem may be almost eliminatedin some simple systems by physical separation ofilluminating and receiving optical trains, but evenhigh multiple-order reflections and scattering cancontribute unwanted scattered light comparable withor in excess of the extremely low signal from whichinformation is traditionally extracted by DLS. Thisis markedly more difficult to suppress than the con-ventional veiling luminance that impairs the contrastof traditional optical imaging instruments. As weintroduced above, a tunnel diagram47 can give valu-able insight into the sources of stray reflections, andsometimes scattering, to improve stray-light control.

In any optical system, the Lagrange invariant usu-ally limits etendue, but within this as an upper limit,it is easy to incur more serious losses of light-gathering power. A common trap is failing to matchthe numerical aperture and the diameter every-where. This is of concern when one is couplingsingle-mode to multimode fibers, for example, at theentrance to an avalanche photodiode ~APD!, underthe impression that alignment criteria will therebybe relaxed. Typically the receiving optics, collectinglight scattered from the probed phenomenon, ismerely a photon bucket, but this does not necessarilymean that aberrations can be tolerated; for example,the proper performance of a stop may rely on itshigh-definition image at the scattering location.

For LV used with photon correlation, conventional

wisdom suggests as many fringes as possible in themeasurement volume to increase the accuracy of thevelocity estimator, fringes that are parallel and of thehighest contrast because of polarization purity.This is not quite as simple as it seems, however,because, for a circular probe region and a limitingupper frequency capability, more fringes imply lessscattered signal and hence potentially less accuracy.There are, however, special cases, such as with LTA,in which the light is concentrated into two sheets thatactually enhance velocity accuracy substantially ~1part in 10,000 is typical!, but at the expense of muchincreased optical difficulty.43 If velocity directionsense is required from a fringe system, as with highlyturbulent or unstable flows, electro- or acousto-opticfrequency shifting may be used.57,58 Whateverfrequency-shifting method is chosen, the range mustmatch the range of turbulence frequencies and alsolie within the capability of the photon correlator.Size, cost, transmission losses, typically exceeding25%, dynamic range restrictions, increased complex-ity, and potentially reduced data quality all indicatethat designing to avoid the necessity for frequencyshifting is highly recommended, if at all possible.

With any coherent illumination system, it is nec-essary to consider the potentially deleterious effectsof laser speckle.6 One technique for reducing oreliminating laser speckle from surfaces close to a LVmeasurement volume is to use fluorescent scatterers.Of course the inelastic scattering that downshifts thewavelength also eliminates any residual coherence,and this can be either good or bad, depending on theapplication.

Critical problems over which there may be lesscontrol include the perturbations of the laser beampassing through hot turbulent gases in an engine orflame, potentially leading to increases of the mea-surement volume size and its wandering in space andnonuniformity of fringe spacing in LDV or beam spac-ing in LTA or loss of contrast in either. Pressurefluctuations around the equipment can also causeproblems.59

For DLS the preservation of wave-front quality inthe incident beam is particularly important beforerather than after the scattering, except in heterodynegeometries. It can be even more important for casesfor which definition of the sample volume is a factorin understanding the signals, for example, close tothe onset of multiple scattering.60

In summary, critical optical problems to solve be-fore performing experiments include provision of suf-ficiently good, clean, and stable optics. Specks ofdirt can destroy fiber performance, mechanicalmounting must be tightly controlled and rigid with-out hysteresis, glues must not degrade, and fiber endfaces must be of the highest quality.

The basic optical design rules for the best photoncorrelation experiments are that losses of light, andparticularly of signal quality must be avoided to theextent that costs allow: the simplest optical systemis often the best. Everything should be carefullymodeled and calculated before committing to hard-


ware, particularly the system etendue, aberrations,flare, polarization, phase distortions, and losses.The optics should be easy to build, align, and main-tain. Detailed testing of the individual componentsand the completed optical system is essential to pro-vide a quantified baseline for analysis when things gowrong during operation. As the components arrive,test everything rigorously. Be especially sensitiveto curious effects that, although not completely un-derstood, tempt dismissal as insignificant. Thesewarnings, almost below the threshold of observation,are the seeds of major catastrophe if ignored.

5. Photodetectors

For photon correlation experiments, the mandatorysingle-photon-counting detector, usually a photomul-tiplier or APD, must have adequate speed and sensi-tivity with tolerably low levels of noise and internalcorrelations. This was formerly possible only withphotomultipliers,61,62 with their intrinsic limitationsof physical size, limited cathode sensitivity at inter-esting wavelengths, and requirements for high volt-ages. More recently, available solid-state detectors,particularly cooled silicon avalanche detectors oper-ated in the Geiger mode are capable of individualphoton detection with acceptable statistical biases,such as dead time and afterpulsing.63,64

The traditional photodetector for photon correla-tion measurements has been the single-photon-counting photomultiplier tube ~PMT!, which remainsthe workhorse of the business. These satisfy manyneeds but typically have quantum efficiencies of nomore than a few percent for wavelengths in commonuse, must be carefully shielded from stray light, mag-netic, and electric fields and exhibit the afterpulsingcaused by secondary, satellite electron pulses typi-cally of 0.02%. The noise levels are typically noworse than 100 counts per second ~cys!. Dynodechain resistors, to which it is usual to apply kilovoltbiases, can degrade to cause buzzing, introducingspurious correlations into the photodetection pulsetrain. This can occur at any time during the photo-multiplier lifetime. The power supplies for PMT’susually have volumes of ;1 liter and weigh ;1 kg.They must also be highly stable, typically in the mil-livolt region on applied voltages up to 1 or 2 kV.Because of their characteristically low quantum effi-ciency, PMT’s can particularly benefit from a reflec-tive structure on the faceplate to increase the chancesof a given photon being absorbed in the photocathode,thus increasing the quantum efficiency, although thisis not widely used. Good photomultipliers for photoncounting are typically expensive and moderatelyfragile, especially in high-vibration engineering envi-ronments.

In recent years APD’s have been successfully intro-duced into photon correlation experiments63,64 withthe advantages of quantum efficiency at least as highas 25%–50% or more, a volume of a few milliliters,and a marginal cost of a few hundred dollars. How-ever, they demand greater stabilization of tempera-ture ~0.05 °C! and bias voltage ~1 mV on the few


hundred volts applied!. As with photomultipliers,the APD noise level can be less than 100 cys whencooled to ;0 °C, typically by a Peltier device. Be-cause APD’s are so small, with an active region di-ameter of much less than 1 mm, thermoelectrictemperature control is relatively easy and economicalin power, although thermal stability is important.For a case in which a high photon flux is availablefrom the experiment, photons are not always sepa-rately detected, and we enter the gray area betweenphoton counting and analog detection. Under thesecircumstances, sub-Geiger APD performance65,66 canbe beneficial.

Although the APD is inherently more rugged thanthe photomultiplier and therefore more useful inhigh-vibration environments, sometimes APD’s cango to sleep temporarily if exposed to too great a lightlevel. The mechanism is poorly understood, butswitching them off for 10 min or so can reawakenthem! This may be best prevented by avoiding sus-tained high light levels.

For photon correlation, the APD electronics mustbe correctly adjusted to give minimum afterpulsingand thus reduce distortion of the correlograms, par-ticularly at small delay times. In practical applica-tions, APD’s can deliver better than 0.04%afterpulsing, which is adequate for most photon cor-relation measurements and comparable with mostphotomultipliers. Cross correlating the output oftwo detectors can essentially remove the effects ofafterpulsing, if necessary.67

Photon correlation experiments are typically con-ducted with photon count rates from a few thousandto a few million counts per second. When APD’s areused, simple passive quenching circuitry63 can dealwith count rates typically up to ;100,000 cys; butactive quenching is necessary to deal with count ratesup to a few million counts per second for correlatorswith sample times as short as 1 ns. For prolongedmonitoring of high photodetection count rates withAPD’s, care is necessary to avoid local heating thatmay impair photon-counting statistics.64

With any photodetector, it is advisable occasionallyto confirm the retention of performance parametersoriginally specified as adequate for an experiment.It is also desirable to characterize the detector assem-bly in real conditions before believing experimentalmeasurements, particularly if the intended environ-ment is hostile, to ensure that there are no deleteri-ous effects of induced noise pickup or other loss ofintegrity.

A final method of photodetection, p-i-n photodiodes,can be useful when the signals are no longer purelyphoton resolved. Such quasi-analog signals appearnoisy as a consequence of photon statistics, but p-i-nphotodiodes can sometimes be a desirable alternativeto PMT’s. However, APD’s may still be preferable inapplications such as LTA, in which individual parti-cles crossing the laser beam generate analog pulsesfrom groups of photons, and a pulse discriminatorestimates the centroid time of this cluster to producetwo pieces of information, signal level, and time of

occurrence sent to the digital correlator with modifiedarchitecture.43

6. Other Aspects of Photon Correlation Experiments

Our main message is nearly complete at this postde-tection stage. Considerations of the laser source, op-tics, detector, environment, and the specific nature ofthe experiment have retained as much as possible ofthe information available, unless unforeseen circum-stances have foiled our careful design. The choicenow is how best to process the raw data to retain andexploit all the relevant information they contain.The intrinsic data in the stream of detected photonpulses are now as accurate and complete as possible.Ancillary observations can sometimes be invoked tobetter extract information, but basically all that re-mains is a choice of signal processing that compressesthe data to extract desired information at the expenseof uninteresting aspects. Photon correlation is agood example of the selective and nonlinear discard ofirrelevant data to enhance the quality of the requiredinformation.

The brief subsections below follow the informationflow sequence of the properly configured experiment,summarizing points for consideration, assuming thatso far we have retained the best data quality.

A. Photon Correlators

Electronic correlators encompass many functions andimplementations. DLS usually involves only digitalphoton correlators. In many cases, the signalstream is not exclusively a sequence of purely andunambiguously identified quantizations, but con-tains signals that are neither clearly separated one-bit events nor the classical continuous signal withnoise. In this gray area, signal behavior is not al-ways easy to describe nor to understand.

Even after the detector has yielded discriminableelectrical pulses from each alleged quantum realiza-tion, the processing of the statistics of photon inter-vals by correlation requires some care. Althoughmany commercial correlators are readily available,most operate in ways different from each other andfrom the ideal mathematical formalism. Single-bitor multibit correlation, sampling time, and samplingstrategy ~linear, geometric, logarithmic, or individu-ally selectable! choices must be made before the ex-periment. Likely statistical properties must beanticipated in the experimental design. The opti-mal use and control of the chosen correlator to derivethe best, or even the acceptable, results from a givenexperiment can be challenging.

Typically the original correlators, of which modelsK7023 and K7026 from Malvern Instruments Ltd.68

are examples, worked by chopping time into smallsegments ~50 ns at first and later 10 ns! and assign-ing input stream events to 1’s and 0’s based onwhether or not a photodetection was received in agiven time window. For practical electronic pur-poses, a derandomizer assigned the event to the endof the clock period, thus incidentally preventing theincrease of resolution available with other schemes.69

With such a dual-clipping system, with one-bit orhard clipping on both channels, saturation at highertransient bit rates is ameliorated by clipping or scal-ing the event stream.70 An obvious extension of theimplementation is to a multibit shift register and asmany multibit accumulators as there are displayedwindows in the output time domain. A hybrid usesa single-bit shift register with multibit accumulators.A second method of accommodating high data rates isburst correlation71 with a reduction in efficiency ofsignal use proportional to the markyspace ratio forwhich the input is active. If too short an inputbuffer is used then the information in the data is evenless well exploited.

For cases in which the data are intrinsically sparse,that is, the average event rate is below a few hundredthousand counts per second with a transient peakrate of no more than a few million counts per second,more efficient processing can be obtained by the so-called Correlex69 principle, whereby the correlogramis accumulated by electronically processing the mea-sured times between all possible pairs of events onboth channels. The time precision is now that of theclock: 200 MHz ~5 ns! was demonstrated69 in 1980with substantial further improvement from postpro-cessing of the correlogram statistics. With this tech-nique, both autocorrelograms and the crosscorrelogram for both positive and negative delaytimes are accumulated simultaneously from the twoinput signals. When this technique and laser tran-sit velocimetry sheet-pair optics are used together,velocity precision of better than 1 part in 104 is rou-tine with update rates many times per second.

More recent correlators72,73 have offered PC com-patibility and freedom to choose store spacing in thecorrelation domain, enhancing their applicability forphenomena whose interest spans a wide range oftime scales.74

Usually a correlator with linearly spaced channelsis chosen for LV, but for DLS it can be advantageousto choose geometrically or logarithmically spaced cor-relation coefficients because of the subsequent dataprocessing and nature of the kernel of the integraltransform involved, i.e., Laplace.75 With a geomet-ric sample–time spacing ~for example, =2 ratio ofsuccessive sample times! there is essentially no lossof information in the Laplace transform case.76 Anexample of this kind of correlator was the MalvernK7027 Log-lin.68

The considerable range of correlator speeds, imple-mentation topologies, costs, and availabilities makenontrivial a choice that optimizes the use of the datamade available by assiduous attention to optical de-sign and implementation.

B. Data Processing

Enormous quantities of data can be acquired rapidlyin photon correlation experiments. Although thecorrelation process is itself invoked primarily to com-press the incoming event stream, typically too rich tobe recorded in real time, the processing algorithmsmust be chosen to discard selectively only that which


is irrelevant to the use to which the data will be put.In a LV experiment in a wind tunnel, industrialflame, a ship’s wake at sea, transonic flow, or in anaeroengine, for example, tens of thousands of corre-lograms may be acquired, often at great expense. Abalance must be established between archiving allthat could be necessary later and a reasonable stor-age expense, either in time or money. Adequatedata as raw as possible, together with all systemhealth and status monitoring parameters, must bestored and backed up as comprehensively as can bearranged.

For a salutary ~and real! example, if we have anairborne experiment that acquires six incoming datastreams each at 20 Mbytesys that we must correlateto give three simultaneous channels, each of 20 64-store 32-bit correlograms per second, for a flight of 2hthat costs $100,000, how should we present indica-tions to the experimenter for real-time inspection,system monitoring, and perhaps control, and howshould the most detailed data possible be stored foroff-line analysis?43

C. Information retrieval

When distinguishing information retrieval, in whichthe results begin to have some interpretable signifi-cance to the experimenter, from data processing, inwhich we are just getting the data into a storableformat, the question of meaning arises. Again thereis a gray area encompassing many data-manipulation techniques, each with claimed advan-tages, for processing the raw correlograms. In LV,for example, the fast Fourier transform is appropri-ate for measurement volumes containing manyfringes, as explained by Abbiss.77 Curve fitting maybe more appropriate for less than ;20 fringes in LVor for other applications for which there is an avail-able theoretical model.78 With DLS, again many ap-proaches are possible, all basically trying to computethe Laplace transform. These approaches havebeen reviewed by Chu.28

The experimentalist must consider optimization ofthe information-retrieval algorithms, basing theanalysis on the intrinsic information content of thesignal and data, the limits of what information can beextracted, the boundaries of attainable resolutionand accuracy, and any problems of understanding theresults in terms of the experimental hypotheses.

In recent years, singular value decomposition hasbeen extensively researched as a mathematically bet-ter approximation to the real nature of DLS data.75

Wavelet analysis79 is currently fashionable and isappropriate for nonstationary processes. However,we know of no published theoretical basis for advan-tages in photon correlation experiments. Neverthe-less we expect to see this and other techniques evolveto explore the limits of optimal information retrieval.For an experimentalist, careful justification of new orinnovative approaches must be made before the re-sults may be generally validated.


7. Concluding Remarks

The essence of this paper is the preservation of theinformation content in the signal before correlationand postcorrelation processing. By preservation wemean retention of all that is useful, rejection of dilu-tion by that which is not useful, and the prevention ofdeterioration caused by additive or intrinsic noise,nonlinear distortion, overranging, or other initiallyunsuspected exigencies. Failing this, no subsequentprocessing, however clever, can recover what is lost.Such processing can, however, be less than optimaland lose or, more commonly, distort desired data. Akey point here is that light source~s!, optics, anddetector~s! must be optimized not only as subsystems,but as parts of a complete system designed to addressthe original intention of the experiment.

We have highlighted lessons from many years ofexperience, citing books and proceedings in whichmore detailed advice may be found.1–4, 9,14,19,23,28,37,69,78

Additional sources of information80–88 give more de-tails and practical considerations for different applica-tions.

Time spent with the supplier of the equipment andcomponents you wish to use to optimize their designor performance within your system is never wasted.Spending this time before committing to a final de-sign or assembly is even better repaid.

With so many boundary constraints and potentialproblems, of which some are outlined in this paper,the acquisition of high-quality photon correlationdata demands careful planning and sustained effort.For really beautiful data it takes a total commitmentto perfecting and verifying every aspect of the designof the experiment and of the measuring system.

We acknowledge discussions with C. I. Moir con-cerning the planning of the original presentation ofsome material in this paper at the OSA Topical Meet-ing on Photon Correlation and Scattering, in Capri,Italy, 21–24 August 1996.

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Practical considerations in photon correlation experiments