circular-array optical-fiber probe for backscattering photon correlation spectroscopy measurements

Circular-array optical-fiber probe forbackscattering photon correlation spectroscopymeasurements

Massimo Brenci, Andrea Mencaglia, Anna Grazia Mignani, and Massimiliano Pieraccini

Aminiaturized probe comprising a circular array of optical fibers coupled to a graded-indexmicrolens hasbeen designed for analyzing colloidal solutions by photon correlation spectroscopy ~PCS!. The system’ssuitability for PCSmeasurements was validated by experimental testing performed in bulk solutions andsmall drops of monodisperse and bimodal test colloidal solutions. © 1996 Optical Society of America

Key words: Colloidal solutions, dynamic light scattering, optical fibers, particle size analysis, photoncorrelation spectroscopy.

1. Introduction

Photon correlation spectroscopy ~PCS! is a powerfultool for analyzing polyatomic and molecular aggrega-tions in complex liquids such as micelle solutions,biopolymer and protein dense solutions, fractal ag-gregations, and gel. Being able to measure the dis-tribution of particle sizes, which range from severalangstroms to hundreds of micrometers, is of para-mount importance in numerous applications:

• Medical: Early detection of cataract upsetachieved through measurements of the protein ag-gregation inside the eye lens.1,2• Biochemical: Aggregation dynamics study of

fibrinogen, an essential protein in human biochemis-try.3• Environmental: Size analysis of microorgan-

isms and detrital materials that play an importantrole in the functioning of marine ecosystems and bio-geochemical cycles.4• Aerospace: PCS monitoring of protein crystal

growth in a microgravity environment,5—a key pro-cess in synthesizingmaterials for new-generationmi-

M. Brenci, A. Mencaglia, and A. G. Mignani are with The Insti-tute for the Research on Electromagnetic Waves, National Re-search Council, Via Panciatichi, 64, 50127 Firenze, Italy. M.Pieraccini is with The Universita di Firenze, Dipartimento di In-gegneria Elettronica, Via di Santa Marta, 3, 50139 Firenze, Italy.Received 14 September 1995; revised manuscript received 16

February 1996.0003-6935y96y346775-06$10.00y0© 1996 Optical Society of America

croelectronics components.6 There are still majorproblems to be solved in aerospace applications.These are related to probe miniaturization and geo-metrical versatility and the capability to carry outmeasurements inside drops with diameters of only afew millimeters.

Optical fibers have been widely used for PCS mea-surements. Fiber miniaturization and flexibility al-low localized measurements without necessitatingsample drawing, thus enabling on-line, in situ mea-surements to be made, even in the most difficult ac-cess areas. Typically, fiber-optic systems for PCSuse two fibers,1,5,7,8 one for illumination and one fordetection. Linear-array optical fibers coupled to mi-crooptics components are also used.9This paper describes a coherent fiber-optic back-

scattering system for PCS measurements and its ex-perimental testing conducted with suspensions ofpolystyrene latex beads. The system has some novelfeatures, foremost of which are the original probedesign, adhering to the strictest optical specifica-tions10,11 and the capability to perform measure-ments in small drops of colloidal suspensions withhigh efficiency.

2. Theory

PCS is a noninvasive laser light-scattering techniquecommonly used for probing and characterizing thedynamic behavior of fluid systems.12–14 When par-ticles in a fluid suspension are illuminated by a col-limated monochromatic beam, the scattered lightintensity fluctuates because of the particles’ Brown-ian motion. The normalized intensity temporal au-

1 December 1996 y Vol. 35, No. 34 y APPLIED OPTICS 6775

tocorrelation function F~t! can be expressed as1

F~t! 5 1 1 bug~t!u2, (1)

where b is a measure of the self-beating efficiency~coherence factor! and g~t! is the first-order field au-tocorrelation function. The latter can be expressedas

g~t! 5 *0

`

G~G!exp~2Gt!dG, (2)

where G~G! is the G linewidth distribution, with

G 5 q2D (3)

being the relaxation parameter corresponding to theparticle species characterized by a translation diffu-sion coefficientD, and where q is the scattering vectormodule.Assuming that the particles are spherical and non-

interacting, the coefficient D is given by

D 5kT3pha

, (4)

where

h is fluid viscosity,a is particle diameter,k is the Boltzmann constant,T is temperature.

The task of PCS is to recover G~G! from the F~t!measurement. The diameter distribution for spher-ical and noninteracting particles, can be obtainedfrom G~G!, keeping in mind Eqs ~3! and ~4!. Themost widely used of the algorithms available for G~G!recovery are cumulant analysis, double exponentialand exponential sampling, and nonnegatively con-strained least squares and regularized nonnegativelyconstrained least squares analysis.15,16 For mono-disperse particles G~G! is approximately a d Diracfunction that specifies a single value of G.The efficiency of a PCS optical system can be eval-

uated with the b factor, ranging from 0, the worst, to1, the best. This factor can be obtained directly fromthe measured F~t! as

b 5 limt30

F~t! 2 1. (5)

3. Optical-Fiber Probe

A. Working Principle

The fiber-optic probe for PCS measurements consistsof a circular array of single-mode optical fibers cou-pled to a quarter-pitch graded-index ~1y4-p-GRIN!microlens. As illustrated in Fig. 1, two fibers, onefor illumination and one for detection, are used. The1y4-p-GRIN microlens enables the illuminating opti-cal fiber to provide a collimated beam and the detect-ing optical fiber to pick up the light from a narrowview cone. The scattering volume for backscattering

6776 APPLIED OPTICS y Vol. 35, No. 34 y 1 December 1996

PCS is defined by the superimposition of the illumi-nating beam and detecting view cone. The choice ofthe illuminating–detecting fiber pair is based on thefollowing requirements:

• Attainment of a high value of self-beating effi-ciency b,• Performance of measurements in the largest

scattering volume that is compatible with the dimen-sions of the cell where measurements are performed.

These requirements are satisfied when measure-ments are performed with large scattering an-gles,10,11 close to 180°. In addition, measurementsperformed close to backscattering condition minimizethe influence of multiple scattering.17

B. Design

An ST-type standard connector was used to couplethe optical-fiber circular array with the 1y4-p-GRINmicrolens. A suitable hole hosted the fibers, whichwere inserted, glued tight, and then polished so thefiber array termination coincided with the end face ofthe connector ferrule. The microlens was fixed in-side a slightly modified ST receptacle, one side ofwhich was connected to the connector holding thefiber array and one of which was in contact with thesolution. Only single-mode fibers were used in thearray, in keeping with ideal PCS specifications.10,11Two circular fiber arrays that were designed are

illustrated in Figs. 2 and 3. Figure 2 shows a 19-fiber bundle consisting of a central fiber with 2 con-tiguous rings of 6 and 12 fibers, while Fig. 3 shows an18-fiber bundle consisting of 2 central fibers and anexternal 16-fiber ring that are separated by a capil-lary tube. In the first array unjacketed fibers wereused, while in the second array the fibers were jack-eted. The two arrays made it possible to obtain dif-ferent scattering angle ranges, 172°–178° and 159°–176°, and consequently different shapes anddimensions of the scattering volume.

C. Advantages

With the GRIN diameter ~Ø 5 2 mm! theoreticallybeing the sole dimensional constraint, it was possibleto miniaturize the probe head notably. The use ofstandard components affords easy connection, clean-ing, and interchange of the GRIN’s and fiber arrays.In addition, measurements can be made in polysty-rene latex beads diluted in water with volume con-

Fig. 1. Sketch of fiber-optic probe for PCS measurements.

centrations as high as 10% since, in thebackscattering regime, the effects of multiple lightscattering occurring in dense solutions are mini-mized.The availability of more than one fiber coupled to a

single microlens also affords benefits:

• Illuminating–detecting fiber pairs can be se-lected to optimize the signal-to-noise ratio and toavoid detection of stray light in scattering cells of anyshape.• Since the measuring time is inversely propor-

tional to the number of separately processed detec-tion channels, measuring times can be reducedsignificantly when one fiber is used for illuminationand the others for simultaneous detection, providedthat the signals are processed by a multicorrelator.• There is no need for alignment between the

illuminating and detecting fibers because of the mi-crolens.

Fig. 2. Circular array consisting of a central unjacketed fiber withtwo contiguous rings of 6 and 12 unjacketed fibers. Fiber diam-eter, 125 mm.

Fig. 3. Circular array consisting of two central jacketed fibers andan external ring of 16 jacketed fibers. Fiber diameter, 250 mm.

• Integration of the illuminating and the detect-ing fibers in a single micro-optics component providesinsensitivity to vibrations.

Of note also is that non-PCS measurements ~ethero-dyne,18 cross-correlation,19 and laser Doppler veloci-metry20! can be performed with fibers arrangedaccording to the following criteria:

• Etherodyne: Two fibers, one for illuminationand one for detection positioned opposite each otherin the array.• Cross-correlation: Three fibers, one for illumi-

nation and two for detection.• Laser Doppler velocimetry: Three fibers, two

for illumination and one for detection; also, two com-ponents of the velocity vector can be measured simul-taneously by laser Doppler measurements with twopairs of fibers illuminated at different wavelengthsand a fifth receiving fiber coupled to a wavelengthdemultiplexer system.21

4. Experimental Setup and Results

The optoelectronic setup used for PCS measure-ments, which is schematically illustrated in Fig. 4,has been designed to allow easy interchange betweenseveral pairs of illuminating–detecting fibers, thusgiving much more measurement flexibility. The fi-ber bundle was divided into two sets, with the illu-minating fiber chosen from the first set and thedetecting fiber chosen from the second set. The il-luminating fiber was coupled to a 0.5-mW He–Nelaser tuned to the 543-nm spectral line ~Polytec!.The detecting fiber was coupled to the terminal fiber,and thus to the photomultiplier, by an ST-type con-nector. The terminal fiber, multimode graded-index50y125 to facilitate coupling, in no way alters the

Fig. 4. Optoelectronic setup used for fiber-optic PCS measure-ments.


system’s reception coherence. The operation of thedetection unit was based on the photon-countingtechnique. The terminal multimode fiber was cou-pled to a Hamamatsu ~Model R2949! photomulti-plier, whose output was processed by a pulseamplifier-discriminator, followed by a PC-compatibleBrookhaven ~Model BI9000AT! correlator card.Brookhaven ~BI-ISDA! size distribution software wasused for processing.Probe performance was evaluated bymeasurement

of monodisperse and polydisperse colloidal solutionsmade of Sigma and Serva polystyrene latex beads ofvarious nominal diameters in purified water passedthrough a Millipore filtering system. Bead diame-ters of 70 and 90 nm exhibited a nominal polydisper-sion of ,15%, whereas bead diameters of 114, 303,440, 825, 2967, and 11,900 nm exhibited a nominalpolydispersion of ,3%. Wholly bimodal solutionswere obtained by mixing of the following monodis-perse solutions: 90–440 nm, 114–303 nm, 114–605nm, and 114–2967 nm.The probe was tested under the two conditions rep-

resenting the most significant cases of PCS measure-ments, test-tube solutions and small drops.

A. Test-Tube Solutions

Measurements were performed with the probe at-tached to the bottom of the test tube; the probe waskept tilted to avoid backreflection from the solution–air interface, as illustrated in Fig. 5. For these mea-surements the 19-fiber array ~Fig. 2! was used, withtwo close fibers for illumination and detection. Inparticular, the pair indicated with arrows in Fig. 2was used, allowing the highest scattering angle~178°! and hence the best value for b. The experi-mental results relative to measurements of monodis-perse solutions are plotted in Fig. 6, which shows acomparison of the measured and the nominal particlediameters. The error was computed as a standarddeviation on five measurements of approximately 5min each on the same particulate. The resultsshowed an accuracy of approximately 5%.

Fig. 5. Test-tube measurements.


The PCS system’s capability to analyze polydis-perse solutions was tested by analysis of wholly bi-modal solutions, as this measurement is a highlysevere test. Wholly bimodal solutions were obtainedby mixing of the following monodisperse solutionsmade of Sigma polystyrene latex beads in purifiedwater: 90–440 nm, 114–303 nm, 114–605 nm, and114–2967 nm. Measured particle size distributionsare plotted in Figures 7–10. Since the solutionswere wholly bimodal, the abscissa relative to the size

Fig. 6. Test tube measurements: comparison between the mea-sured and the nominal particle diameters.

Fig. 7. Bimodal colloidal solution of particles with nominal diam-eters of 90–440 nm. Measured diameters, 91–399 nm.


distribution peaks were assumed as measured parti-cle diameters.The value of b was calculated from Eq. ~5!: The

resulting value of 0.85 6 0.05 was extremely satis-factory.

B. Small Drops

Measurements in small drops were performed withthe probe’s GRIN lens vertically positioned to permita small drop to be retained on the flat lens surface, asshown in Fig. 11. In these measurements it is im-portant that the illuminating–detecting fiber pair beproperly selected to fit both requirements of largescattering angle and scattering volume inside thedrop. For this reason the 18-fiber array ~Fig. 3! thathas the largest range of available scattering angleswas used. In particular, for measurements in 3mmØ drops, the pair indicated with arrows in Fig. 3 wasa suitable choice as it allowed this configuration to


Fig. 10. Bimodal colloidal solution of particles with nominal di-ameters of 114–2967 nm. Measured diameters, 105–2716 nm.

Fig. 11. Measurements in a small drop.

obtain the lowest scattering angle together with thescattering volume inside the drop. In fact the cho-sen fiber pair ~scattering angle 168°! made it possibleto locate more than 99% of the scattering volumeinside the drop. The experimental results relativetomeasurements of monodisperse solutions, are sum-marized in Table 1.The calculated b was 0.67 6 0.04, a value that was

also extremely satisfactory. Previous experimentsin drops presented in the literature have reportedlower self-beating efficiencies. A case in point, anexperiment in drops performed by NASA in theSTS-26 space shuttle mission,5 exhibited a self-beating efficiency of ,0.4.

5. Conclusions

A coherent fiber-optic backscattering system for PCSmeasurements has been presented. Designed inkeeping with ideal optical specifications, it combinesthe illuminating and detecting functions in a singlelens, thereby eliminating the need for alignment. Inaddition, the highest versatility and constructivesimplicity has been obtained with a circular-arrayoptical fiber. Finally, backscattering extends its ap-plication range to high-density particulates. Thesystem was validated by experimental testing per-formed in monodisperse and bimodal test colloidalsolutions. The high self-beating efficiency obtainedis confirmation of its suitability for PCS measure-ments even when small drops of solution are sub-jected to analysis.

The authors are grateful to Waldemar Jeda of theWarsawUniversity of Technology, hosted at Institutefor Research on Electromagnetic Waves-National Re-search Council under the TEMPUS-TOSCA S JEP-08051 Project, for his invaluable contribution to theexperimental test campaign.

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Table 1. Measurements in Small Drops: Summary of theExperimental Results

Nominal~nm!

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~nm!

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circular-array optical-fiber probe for backscattering photon correlation spectroscopy measurements

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