Instrument for velocity and size measurement oflarge particles
Gabriel Laufer
A new instrument for velocity and size measurement of large particles in two-phase flows was introduced anddemonstrated. This instrument which is based on the laser interferometer technique uses two Ronchi grat-ings. The two separate diffraction modes formed by the gratings interfere with each other and generate thenecessary fringe pattern. The instrument can be continuously matched to particles from 100 ,m to the cen-timeter range.
1. IntroductionThe simultaneous flow of two phases (e.g., solid or
liquid particulates in gas or gas bubbles in liquidstream) is a common phenomenon in modern technol-ogy. Such flows are frequently encountered in thechemical or food industry. In nuclear or conventionalpower generation, for example, two-phase flow occursin the core of the nuclear plant and in the power gen-eration system. Spraying paints, injecting fuel intointernal combustion engines, or more generally theformation of aerosols are other examples of two-phaseflow. The flow of solid particulates in a gas streamoccurs in smoke stacks and in fluidized beds.
In many of these examples which are far from repre-senting an exhaustive list, the engineer is presented withthe need to determine the size distribution of the par-ticulates suspended in the flow and their concentration.This problem is certainly a daily challenge for the re-searcher in these fields.
There are only a few available techniques for particlesize measurement. They can be divided into two basicgroups. In the first group a direct measurement of oneor all the particle dimensions is done, i.e., the outcomeof the measurement depends on particle size only (andpossibly shape) but is independent of any other prop-erty of the particle. Examples for such techniques aremicroscopy or photography.
The second group uses indirect measurements todetermine the particulate size, i.e., a size-dependent
The author is with Technion-Israel Institute of Technology, Facultyof Mechanical Engineering, Haifa, 32 000, Israel.
property is measured and the size is deduced from theresult of that measurement. Examples of such tech-niques are the electric mobility analyzers where theelectric mobility is believed to be a measure for particlesize or intensity measurement,2 which clearly dependson particle shape and size as well as index of refrac-tion.
Techniques of the second group are usually calibratedusing standard particulates. It is assumed that thiscalibration holds for other particulates of different size,shape, or material. This assumption cannot always betrue. Thus, techniques of the first group, apart fromtheir own inherent drawbacks, are likely to yield moregeneral results.
The size resolution is another parameter which canbe used to group the various techniques. At the lowerlimit, the wavelength of the visible light (-0.5 Atm) canbe regarded as a convenient measure of size resolution.This is approximately the resolution limit of opticalmicroscopy3 and therefore should be the limit for all thedirect measurement optical techniques. Nonopticaltechniques are free from the limits of optical micros-copy. For example, it is not surprising that the mobilityanalyzer can yield a resolution as fine as 0.003 AIm.1
Most techniques which offer high resolution cannotbe applied to particles in the millimeter range and viceversa (e.g., see Refs. 4 and 5). Therefore, whenever alarge particle size is required, two separate systems mustbe used. Furthermore, very few of the available sizingtechniques can also be applied to simultaneous velocitymeasurement.
In this paper an optical instrument is described whichuses a direct size measurement technique, i.e., to thefirst approximation it is sensitive only to particle sizeand shape. It offers simultaneous measurement of sizeand velocity for particle diameters ranging from 0.5 Amto the centimeter range. This instrument is based ona derivative of the laser Doppler velocimeter techniques
which was formerly called the laser interferometer (LI)technique. 7,8
II. Laser Interferometer TechniqueWith the LI technique7 an ordered fringe pattern is
formed in the probed region by two intersecting laserbeams. The spacing s between two adjacent fringesdepends on the wavelength of the light X and on theangle 0 between the two intersecting beams, suchthat
S =~~~~~~~ ' ~~~(1)2 sinO/2
Particles passing through this grid of fringes scatterlight at a frequency which depends linearly on the fringespacing and the particle velocity. Thus, two scatteringintensities can be identified for every particle. Thefirst, Imax, is the peak intensity associated with the acmodulation of the signal while the second, Imin, is thetrough.
The modulation depth or visibility V of the scatteredsignal is defined as
V Imax - Imn (2)
Imax + Imin
Several authors (e.g. Refs. 7-15) have demonstratedtheoretically and experimentally that the visibility canbe correlated with particle size. This is a complexfunction which depends on several optical parametersof the experimental setup. Nevertheless, it is generallyobserved that the particle size d can be deduced un-ambiguously from V only if d < s. Although this limitcan be somewhat enhanced (e.g., see Ref. 15), there isstill an upper bound for the measurable particle sizeassociated with the fringe spacing of the system. Thuss must be matched to fit the particle size range to bemeasured.
For a given s only a limited range of sizes can bemeasured. The particle size lower limit is the pointwhere the visibility V 1 and is almost independent ofthe particle size. The upper limit is where V yieldsambiguous values for the particle size.
These two limits have been estimated for a variety ofconditions, e.g., for large (d >> X) reflecting particlesobserved at 90° to the incident light they are9
d0.282f <- < 2.82f, (3)
S
where f is the collection optic f/No. These limits in-dicate that for a fixed value of s the dynamic range isrestricted to a factor of 10.
Both the upper and lower limits for particle sizing inEq. (3) depend on s. Obviously, the lower fringe spac-ing limit corresponds to the wavelength of the lightsource. Therefore, the lowest resolution limit of the LItechnique conforms with the optical microscopy limit.There is no upper bound for s and therefore there is noupper physical limit for the detectability of particle size.The fringe spacing can be increased without any limitby simply decreasing 0. However, from Eq. (1) it fol-lows that, when 0 is sufficiently small ( << 1),
where 5(s) represents a fluctuation in the fringe spacingdue to a random fluctuation of 60 in the intersectionangle.
With the LI technique (e.g., see Refs. 8, 10, 11, 13, and14), a single laser beam is usually split into two partswhich are then intersected to form the fringe pattern.The passage of these two beams through separate op-tical paths and their interaction with different opticalcomponents may cause, due to air currents or mechan-ical vibrations, minute random fluctuations in 0. Thesefluctuations when amplified by 1/6 cause a strong jitterwhen large fringes are to be formed. The Mach-Zehnder and the Jamin interferometers, where inter-ference fringes form between two beams intersecting ata shallow angle, suffer from such jitter. This jitter isinduced by disturbances which cause optical compo-nents to vibrate relative to each other. The problemis eliminated by isolating the optical system from me-chanical vibrations and unnecessary air currents. Thisis satisfactory for well-controlled laboratory conditions.However, in an industrial environment the LI techniqueis likely to fail when attempting to measure millimetersize or larger particles.
To avoid jitter and distortion in the fringe pattern dueto fluctuations in , it is proposed here to use an inte-grated optical arrangement to split and almost simul-taneously intersect the laser beams. In such a compactsystem, unlike ordinary LI systems, mechanical vibra-tions and air currents affect equally all componentsthereby eliminating all fluctuations in . In this wayit will be possible to extend the upper size measurementlimit into the centimeter range.
The integrated system is made of two Ronchi grat-ings. An expanded laser beam passing through onegrating is split into an attenuated undisturbed beamand a series of diffracted beams, i.e., diffraction modes.These modes lie in a plane normal to the grating lines.The angle On between the nth-order diffraction modeand the normal to the grating plane is3
sin4,n - sinO. = where n = 0,±14,2,....dg (5)
where 00 is the incidence angle and dg is the spacingbetween two adjacent grating lines. For the first gratingh = 0.
The second grating of the instrument is placed behindthe first grating. The planes of the two gratings areparallel, but the second grating is rotated around thenormal to the plane through an angle V/ (see Fig. 1). Alldiffraction modes of the first grating are transmittedthrough the second grating. The angle of incidence onthe second grating of the nth-order mode of the firstgrating is n. Thus, the diffraction angle of the mth-order mode in the second grating of the nth-order modeof the first grating, i.e., the ninth mode, will be
where m = 0,t14,2,.... When m = 0 and n:(6) is exact.
The intensity In of the nth mode of the firsttion grating is3
In = [sin(nrrw/dg)] 2
I, n rwldg
where Ii is the incident intensity, a is a coefficsociated with the attenuation of the grating, andwidth of the slit between two adjacent gratirThe transmission efficiency of the ninth modesecond grating is
I.I = H(n)H(m).
The diffraction through two gratings arratandem generates two sets of beams. One set i'by the diffraction modes of the first grating whtransmitted through the second grating as the 0mode. Modes within this set will be denoteinOth modes. The second set is formed by theorder modes of the second grating, which we]mitted as the Oth-order mode through the firstThese modes will be denoted as the Onth modifirst set lies in a plane normal to the lines ofgrating. The two planes intersect each other at1 along the incidence line, while all the diffractsintersect each other at the incidence point.
Although all diffracted beams form large antthe incident beam, pairs of beams exist with aintersection angle between the members of e,These are the Onth and the nOth modes. Sinccident beam is expanded, the beams within ewill copropagate through a relatively long distterfering with each other and generating a trnmodulation by interference fringes.
The intersection angle between the Onth andmodes can be found from simple geometrical ar(see Fig. 1):
0 nO/On = 4' sin¢nO
The spacing sno/on between the modulatingin the Onth and nOth modes is obtained frortogether with Eqs. (6) and (9):
oLar beam SnO/On - (10)0
nO/On n4.The spacing between the modulating fringes within
lerd* each pair depends on the rotation angle Q. Thus, thefringe spacing can be continuously adjusted to matchany particle size range by a simple angular adjustmentof the gratings. Unlike conventional interferometry,the spacing between the interference fringes is inde-pendent of wavelength. This property is useful whenoperating lasers in the multiline mode as it eliminatesthe need for calibration of fringe spacing for each laserline. Furthermore, although the various lines havedifferent phases, the fringes of all lines will overlap.This is because the phase difference between the in-terfering modes within each line is the same. It shouldbe noted that the fringe spacing within the pair of the1st-order mode (the 01th and the 10th beams) is iden-
= 0, Eq. tical with the fringe spacing of the moir6 pattern formedby the lines of the two gratings. However, the
diffrac- transverse modulation of the first pair is due to inter-ference of two plane wave fronts and is not the projec-tion of the moir6 pattern of the gratings.
(7) So far, the analysis has been concerned with the in-teraction between pairs of beams of the same order, i.e.,
cient as- the interaction between the Onth and the nOth orders.w is the As each of the modes of the first grating is also redif-ig lines. fracted by the second grating into higher-order modes,past the a cross interaction occurs. Most of the rediffracted
modes are of such low intensity that they have a negli-gible effect. However, some of the fundamental in-
(8) terfering pairs are strongly affected by additional red-iffracted modes. For example, consider the pair of the
nged in 20th and 02th modes. The fundamental fringe patternformed is described by Eq. (10) and the intensity by Eq. (8).
ich were However, the 11th-order beam (the 1st-order diffractionth-order mode in the second grating of the 1st-order diffractiond as the mode of the first grating) is diffracted at an angle olhigher- [Eq. (6)].
re trans-grating.
Bs. Thethe firstan angled beams
Oles withshallow
tch pair.e the in-ach pairance, in-ansverse
the nOthguments
(9)
g fringesi Eq. (1)
2Xsinl n_ sinPO2 sinO2O =--
dg(11)
Therefore, the 11th-order mode copropagates with thetwo 2nd-order beams. Since the angle formed betweenthe 11th mode and any of the two beams of the 2nd-order mode is
011/20 = 011/02 = 4' sinol , (12)
the fringe spacing due to the interaction of the 11thmode and the 20th and 02th modes is
s = dgl4. (13)
This spacing corresponds to twice the fringe spacing ofthe fundamental mode. It can be shown from Eq. (8)that for most practical cases the intensity of the 11thmode is comparable or higher than the combined in-tensities of the 20th and the 02th modes, and thereforetwo spatial frequency components are observed in themodulation pattern of the 2nd-order beams.
Similar cross interaction occurs between the pairformed by the 1st-order mode and beams which wererediffracted from higher-order modes of the first grating
into this pair. However, with a proper selection ofgratings the intensity of the high-order rediffractedmodes can be made negligibly small, thereby leaving the1st-order pair unperturbed.
To adapt the LI technique to particle size measure-ment only the pair formed by the 01th and 10th modescan be used. This is the only pair modulated by a singlespatial frequency component. Particle detection isthen accomplished by a collection telescope directedoff-axis and a photodetector. The size of the probevolume is determined by the intersection of the modu-lated beam and the collection cone. The required pa-rameters, such as the collection f/No. and collectionangle, are determined according to experimental needs,while the transmission efficiency can be determinedfrom Eq. (8) as 2H(O)H(1). The effect of the opticalparameters on the collected signal is extensively dis-cussed in the literature, e.g., Ref. 9,10,15.
Ill. Experimental
The purpose of the experimental work was to dem-onstrate the feasibility of the instrument for particle sizeand velocity measurements in two-phase flow and todetermine its characteristics. In particular, the mod-ulation quality of the pair of the 1st-order mode and ofthe higher-order modes was evaluated, together with therelation between fringe spacing and the angular positionof the gratings.
The experimental setup consisted of a 2-W argon-ionlaser operating in the multiline TEMoo mode followedby a beam expanding telescope (see Fig. 2). The beamwas expanded to a diameter of 5 cm. Two Ronchigratings mounted on a rotational stage were placed inthe expanded beam. The Ronchi gratings were ruledon a 2.5- X 5-cm rectangular plate with a density of 500lines/in. A ratio of w/dg = 0.5 was selected which, ac-cording to Eq. (8), yields I02 = I20 = 0. This shouldleave the pair of the 1st-order mode unperturbed bycross interaction with the 2nd-order mode. The rota-tional stage had a resolution of 0.010.
The gratings were tested separately by measuring therelative intensities of the diffracted modes. The mea-sured relative intensities were H(O) = 0.21, H(1) = 0.09,and H(2) = 0.01. Deviations of H(1)/H(0) and ofH(2)/H(O) from the theoretical values are caused byimperfections of the gratings. The diffracted beamswere projected onto a screen 3 m away and their patternwas photographed (Fig. 3). Both the Oth-, 1st-, and
Fig. 3. Photograph of the fringe pattern within (from left) the Oth-,1st-, and 2nd-order modes. The spacing between fringes in the
1st-order mode is 2.05 mm.
12 0
10 5
E
. 75
4 5
3C
Is5
I I
- THEO
* EXP
I /
I I I I-3 -2 4 -1 8 -12 -6
I I I I I
I I I I0
, [1
6 1 2 18 24 3
Fig. 4. Comparison between experimental (+) and theoretical (solidline) results for fringe spacing vs angular position of the second
grating.
2nd-order modes are included in this photograph. Allthree modes are transversely modulated by grids offringes, but only the 1st-order mode is modulated by asharp single spatial frequency pattern. The Oth-ordermode is modulated by the projection of the moir6 pat-tern formed by the two gratings and is blurred out bydiffraction. The two spatial frequency components ofthe 2nd-order mode are evident. These are thefrequencies associated with the interaction of the 02thand the 20th modes and the interaction of the 11thmode with 02th and 20th modes.
As the laser was operated in the multiline mode, boththe 1st- and 2nd-order mode beams were multicolored.Despite the very clear color dispersion all fringes re-mained straight, and the interference patterns of alllines were perfectly superimposed, i.e., the fringe pat-tern was wavelength independent as predicted by Eq.(10).
The correlation between the angular tuning of thegratings and the fringe spacing s was measured. Itcan be seen in Fig. 4 that the experimental and theo-retical values [Eq. (10)] are almost indistinguishable.
The largest value for s in this experiment was limitedto 2 cm by the width of the grating. The smallest
Fig. 5. Typical oscillogram for a free falling 1-mm glass bead.
measured value for s was 200 um. Still smaller valuescould be observed. But, as s was decreasing, the in-tersection angle between the interfering beams was in-creasing. Thus, the area of overlap between the beamswhere modulation can be observed was relatively smalland settings which yield s < 200 um were consideredimpractical. Fringe periods smaller than 200 Aum canbe obtained by relay lenses.
The instrument performance was demonstrated forparticle size and velocity measurement of free fallingglass beads of 1- and 3-mm diam. An f/10 collectionoptics was placed in the backscatter position at an off-axis angle of 20°. The light scattered by the free fallingparticles was detected by a photomultiplier and re-corded on a digital oscilloscope. The fringe contrast ofthe first-order mode was estimated as better than 0.96by measuring the visibility of a glass bead with d/s = 0.5.An example of what was obtained for a 1-mm glass beadis shown in Fig. 5. The pattern appeared very regularwith a slight asymmetry. The asymmetry varied inmagnitude and shape from bead to bead and thereforewas attributed to irregularities in the glass bead shapeitself. Yet, the visibility function in Fig. 5 could bedetermined to an accuracy of better than 10%. Due tolack of previous data which correspond to the presentexperiment, the measured visibility could not be com-pared with any expected data. The velocity as evalu-ated from the known fringe spacing and the scatteredsignal frequency was compared within 2% of the calcu-lated velocity of a free falling body.
IV. ConclusionsA double grating interferometer was developed for
measuring the size and velocity of large particles. Ac-cording to theoretical analysis the spacing between
fringes formed by the device is wavelength independentand depend only on the rotation angle between thegratings and the ruling density. Only the fringe patternformed by the 01th and 10th modes is accessible for sizemeasurement. It was demonstrated that the fringespacing can be tuned continuously from 200 gum to 2 cmand the instrument can be used for measuring particlesas large as 3 mm.
Portions of this work were done in the facilities of theUnited Kingdom Atomic Energy Authority, AERE,Harwell. This support and hospitality is gratefullyacknowledged.
This work was partially supported by the StanleyLangendorf Research Fund.
References1. B. Y. H. Liu, K. T. Whitby, and D. Y. H. Pui, J. Air Pollut. Control
Assoc. 24, 1067 (1974).2. D. Holve and S. A. Self, Appl. Opt. 18, 1632 (1979).3. M. Born and E. Wolf, Principles of Optics (Pergamon, New York,
1975).4. R. Semiat and A. E. Dukler, AIChE J. 27, 148 (1981).5. W. J. Glantschnig, M. W. Golay, S. H. Chen, and F. R. Best, Appl.
Opt. 21, 2456 (1982).6. L. E. Drain, The Laser Doppler Technique (Wiley, New York,
1980).7. W. M. Farmer, Appl. Opt. 11, 2603 (1972).8. W. M. Farmer, Appl. Opt. 13, 610 (1974).9. W. M. Farmer, Appl. Opt. 19, 3660 (1980).
10. W. D. Bachalo, Appl. Opt. 19,363 (1980).11. D. M. Robinson and W. P. Chu, Appl. Opt. 14, 2177 (1975).12. W. P. Chu and D. M. Robinson, Appl. Opt. 16, 619 (1977).13. D. W. Roberds, Appl. Opt. 16, 1861 (1977).14. R. J. Adrian and K. L. Orloff, Appl. Opt. 16,677 (1977).15. C. R. Negus and L. E. Drain, J. Phys. D 15, 375 (1982).
