Batch interference granulometric process particularly applicable to poly-dispersed biological particles

A process for batch interferential granulometry applicable particularly to poly-dispersed biological particles. The process is characterized in that the positioning of the angular measurement regions is selected according to the criteria of representativity of the signals obtained with respect to the given granulometry sought, particularly for their alternative components, and in that the processing of the signals comprises successively a harmonic Fourier analysis of their alternative components, and the use of the results of this analysis in a computation leading to the parameters sought, namely, the numbers, mean dimensions, and granulometric distribution of the analyzed particles.

The present invention relates to the field of the granulometric analysis of 
particles, and has for its object a process for batch interference 
granulometry, applicable particularly to poly-dispersed biological 
particles. 
At present, the methods for the determination of granulometric 
characteristics, such as number, dimensions, and the granulometric curve 
of a group of particles in suspension in a fluid are generally of two 
categories, namely, flow processes, and batch processes. 
In the flow processes, the particles pass one by one through a measurement 
cell that furnishes upon the passage of each particle one information as 
to the size of the latter. Most often, there is performed a measurement of 
the resistivity of the particles in liquid medium (Coulter apparatus) or 
of their optical properties. In the latter case, the particle passes 
through an illuminated region, and the light absorbed or diffused is 
observed during its passage. 
The illumination is effected by a single beam or by two coherent beams 
producing interference fringes, the passage of the particle before the 
network of fringes producing in the latter case a periodic change in the 
diffused light. 
The frequency of this change is related to the speed of the particle, while 
the amount of the modulation is related to its size. 
The known flow processes have the advantage of permitting study of the 
particles one by one thereby favoring the determination of granulometric 
curves. However, the drawbacks of the flow process, which consist in 
providing high dilution to avoid the simultaneous passage of two particles 
through the measurement zone, and the circulation of the suspension to be 
analyzed, may be incompatible with certain determinations, such as, 
particularly, the mechanism of aggregate formation. Moreover, the 
measurement cell often operates at high frequencies to permit the 
observation of a significant number of particles, thereby limiting the 
quantity of data obtained per particle, and involving errors of various 
types that cannot always be compensated by computation. 
The batch processes comprise the simultaneous introduction of a large 
number of particles into a measurement cell, which provides batch 
information from which is determined the number, the dimensions and the 
distribution of the particles involved. The measurement techniques 
involved may be either mechanical, such as sedimentation, or primarily 
optical, such as diffractometry and nephelometry. 
These processes have, compared to the known flow processes, the advantage 
of requiring only one simple preparation of the specimens to be analyzed, 
particularly when they make possible the analysis of poly-dispersed 
granular populations, which is to say formed by mixtures of several 
families of mono-dispersed particles, the simultaneous analysis of some of 
these families being possible by these processes. The batch processes 
permit, moreover, obtaining an immediate measurement representative of the 
mean of a large collection of particles. However, the information 
furnished by the cell is the composite of the elementary informations 
concerning each particle, and if these bits of information are not 
sufficiently complete or differentiated from each other, their analysis is 
difficult, variations in size interferring particularly with variations in 
numbers, particularly in batch optical processes. These known processes 
therefore give only results that are limited as to scope and precision, 
except by the use of difficult and costly measures, which thus 
considerably restrict the field of use. 
It is in fact usual to count mono-dispersed populations, of a size 
distribution fairly well clustered about a normal mean value, in a 
satisfactory way, by a batch optical process in which the particles are 
illuminated by a single light beam, and the diffracted flux is measured in 
a particular solid angle called "stationary", so chosen that the 
diffracted flux there remains substantially stationary when the mean size 
of the particles to be counted varies within a certain range from its mean 
value. The measured flux is representative only of the number of particles 
to be counted, because it is independent of the variations in size of 
these particles. 
This process is therefore applicable to the counting of poly-dispersed 
granulometric populations with only one important restriction. Indeed, 
considering the mixture of two mono-dispersed populations of different 
mean sizes, there is for each population one stationary solid angle, which 
would permit effectively to count the considered population if this 
population were single. So, for two populations there are two distinct 
such stationary solid angles. As a result, in each stationary solid angle 
will be measured a total flux equal to the sum of a first flux that is 
stationary as a function of the size of the population to which that solid 
angle corresponds, and of a second non-stationary flux as a function of 
the size of the other population. To be able to use the process, it is 
thus necessary to be able to know simultaneously the sizes of the two 
populations in question, and the same is true in the case of a mixture of 
more than two populations. The restriction of the use of this process is 
therefore that the sizes of all these populations must be known and, 
moreover, must remain simultaneously completely stable, which is not the 
case in a great number of practical situations. 
Improvement in the results of the process can be provided by the use of 
supplemental measures determining the sizes at the same time as the 
numbers. However, the cost of the apparatus would then be excessive with 
respect to other methods, for comparable results. 
The present invention has for an object to overcome these difficulties 
while giving access to batch information in which the influence of size 
and numbers is better differentiated than in known processes, to permit 
characterizing poly-dispersed granulometric populations or to determine 
the granulometric curves with greater precision, by simple calculations 
and under more economical conditions.

It thus has for its object a batch interferential granulometric process 
applicable particularly to poly-dispersed biological particles, 
characterized by a combination of steps consisting in: 
suspending the particles to be analyzed in a fluid in which they are 
distributed at random 
moving said particles and fluid with uniform speed through a fluid pathway 
including one measuring volume (3) in which the particles may be 
illuminated when they cross said volume 
illuminating said particles simultaneously by at least two beams of 
coherent light with convergent axes, beams produced by a light source (1) 
and a splitter (2), thus producing in the measuring volume (3) a network 
of interference fringes 
measuring by a photodetector (4) the light flux diffracted by said 
illumianted particles in at least one solid angle 
setting the concentration of said particles in said fluid so that at each 
instant a group of particles are simultaneously illuminated in said 
measuring volume 
setting the angles between said coherent beams, and thus the interference 
fringe distances, at values defined according to an iterative computation 
process 
setting the position and the limits of said solid angles as a function of 
the granulometric measurement to be made, these position and limits being 
obtained by said special iterative computation process involving also the 
said interference fringe distances 
using only the alternative components of the measurement signals 
representing the flux diffracted by said particles in said solid angles 
treating, when the particles are illuminated by more than two beams, these 
alternative components by a Fourier Analysis device (5) in order to 
separate the various frequencies which are present in these components 
treating the obtianed results in a treatment module (6) in order to 
calculate the sought granulometric characteristics. 
Processes utilizing similar means, particularly means for performing a 
Fourier harmonic analysis on signals representing the diffracted flux 
created by particles illuminated by several coherent intersecting beams, 
are known, but they are used for velocimetry, which is the determination 
of the particle speed or of the distribution of the speeds of the moving 
particles. Such velocimetric processes may also be used in an extension of 
their original purpose for particle sizing but only if the sizes are 
homogeneous or the size distribution very narrow, and for measuring number 
densities when the size of the particles is known. In that field their 
accuracy is not high, these velocimetric processes being essentially 
different from that of the present invention not only by the results 
sought and obtained, but also by the combination of means employed. 
Particularly, their results are not influenced in a determinative way by 
the choice of the solid angle where the diffracted flux is collected and 
measured. 
The interference of two coherent light beams of wavelength .lambda., whose 
axes intersect at an angle .theta., permits obtaining an interference 
fringe whose value is .delta.=.lambda./2 sin (.theta./2) 
From the simultaneous interference of K beams with convergent axes, there 
are l=K (K-1)/2 different couples of beams which may be considered as 
combined in this condition, to which there correspond a maximum of l 
different angles .theta. and thus as many interference fringe values. 
Designating these values of interference fringes .delta..sub.1, 
.delta..sub.2,-.delta..sub.i . . . and .delta..sub.l, and considering V to 
be the speed of flow of the particles in front of the fringes, which is 
taken to be constant, it will be seen that to the various possible 
combinations of couples of bundles it corresponds l modulation frequencies 
on the diffracted flux equal to: 
EQU f.sub.1 =V/.delta..sub.1, f.sub.2 =V/.delta..sub.2 . . . f.sub.i 
=V/.delta..sub.i . . . and f.sub.l =V/.delta..sub.l. 
From the simultaneous interference of all these beams the harmonic analysis 
of the resulting modulation leads to l frequencies f.sub.1, f.sub.2, . . . 
f.sub.i, . . . f.sub.l and gives a corresponding amplitude for each. These 
amplitudes indicated by e.sub.1, e.sub.2, . . . e.sub.i, . . . and e.sub.l 
are a function of the numbers and sizes of the illuminated particles and 
of the solid angle of measurement of the diffracted flux. 
This method therefore permits obtaining, in the measured signal, a number l 
of superposed separate data, from a single measurement in a single solid 
angle of collection, while in the absence of a fringe, as is usual in 
prior art methods, a measurement in l different solid angles would have 
been necessary to obtain the same amount of information. 
Moreover, the obtained values e.sub.i distinguish better the effects of 
size from the effects of number than the continuous diffracted flux 
measurements in non-interferential batch processes. Thus, although the 
continuous diffracted flux varies proportionally to the number of 
illuminated particles when the latter are of uniform size, the alternative 
component of the flux modulated by the fringes varies, under the same 
hypothesis, proportionally not to the number but to the square root of the 
number of illuminated particles. A relative amplification of the effects 
of size relative to the effects of numbers may thus be usefully made, 
particularly to count poly-dispersed particles and for the determination 
of granulometric curves. Moreover, the variation of the modulation ratio 
of the diffracted light by a particle is a function of the relation of the 
size of the latter to the interference fringe, as well as to the angle 
from which the particle is observed. 
Under certain simplified conditions, it is known that this modulation ratio 
varies according to the formula 
##EQU1## 
in which J.sub.1 is the first order Bessel function 
a is the radius of the particle 
.delta. is the interference fringe value. 
This formula, by way of example, is shown in FIG. 2. In the general case, 
the modulation ratio V (a, .delta., s) is given by a more complex 
expression which involves, moreover, the angle of observation s. However, 
the formula given above shows in a simplified way that there are 
particular values of the ratio a/.delta. for which the modulation ratio 
will be zero or at least substantially near from zero, that is to say for 
a given interference fringe .delta., there exists particle sizes for which 
the diffracted flux will have practically no modulation, which means that 
the particles do not contribute to the formation of the alternative 
component of the diffracted modulated flux. 
This property is particularly interesting in the case of analysis of 
poly-dispersed populations. In this case, the process according to the 
invention may be applied in a characteristic way by setting an 
interference fringe value so as to eliminate the influence of one 
population by annulling its contribution to the formation of the 
modulation of the diffracted flux, and using this interference fringe 
value in the computation of the associated solid angles to be used for the 
flux measurements. 
One important characteristic of the invention, consists in using solid 
angles computed so that, for a given population size and for an associated 
fringe value, the alternative component of the flux, which is diffracted 
by said particles population, remains stationary when the size of the 
particles varies around a mean value. 
In known non-interferential processes, similar stationary solid angles are 
also used, in which the continuous signal representing total diffracted 
flux remains stationary when the particle size varies around a mean value. 
But in the process according to the invention the stationarity is 
investigated only on the alternative component of the modulated signal 
measuring the diffracted flux, and the solid angles where this property 
exists are different from those where the total continuous signal remains 
stationary. This difference may be understood by reference to the 
influence, shown in FIG. 2 of the interference fringe related to the 
particle size on the modulation ratio. 
The new stationary solid angles thus defined have the advantage of 
providing in certain cases precise information as to the count of the 
poly-dispersed particles, these data being directly separated from each 
other by virtue of the aforesaid discriminatory properties. These new 
stationary interferential solid angles thus permit simultaneously counting 
mono-dispersed mixtures of particles of different sizes, contrary to the 
prior art processes. 
A characteristic example of the use of the process according to the 
invention concerns counting the figured elements of the blood, 
particularly simultaneously counting white corpuscles and platelets in the 
presence of stroma or lysed red corpuscles. In blood of normal composition 
comprising per mm.sup.3 N.sub.B =8,000 white corpuscles, N.sub.P =300,000 
platelets, and N.sub.S =5,000,000 red corpuscles or stroma, a continuous 
stationary solid angle for the white corpuscles receives a diffracted flux 
from 50% of the white corpuscles, 7% of the platelets, and 43% of the 
stroma. Because this solid angle moreover is not stationary for the 
platelets or for the stroma, the flux measured in it does not permit 
direct counting of the white corpuscles. 
A stationary solid angle for the white corpuscles, defined according to the 
invention for an optimum interference fringe value, receives, with the 
same ratio between N.sub.B, N.sub.P and N.sub.S, a diffracted flux whose 
alternative component comes from 99% of the white corpuscles, the 
influence of the other particles being negligible. Because in this solid 
angle, this component is independent of the variations of size of the 
white corpuscles, its amplitude directly represents their number despite 
the presence of other particles. 
The process according to the invention may be used for the determination of 
a granulometric curve in the following manner: 
Letting a.sub.1 and N.sub.1 represent the mean radius and the number of 
particles pertaining to class 1 and a.sub.2, N.sub.2, . . . a.sub.j 
N.sub.j, and a.sub.n and N.sub.n the mean radii and the numbers of 
particles of classes 2, j, and n, one can cause to intersect K beams 
defining l=K (K-1)/2 harmonic frequencies, provided l.gtoreq.n. 
From one signal solid angle for flux measurement, the Fourier harmonic 
analysis of the measured signal thus gives l values of amplitudes of 
different frequencies e.sub.1 e.sub.2 . . . , e.sub.i . . . e.sub.l 
corresponding to the various frequencies f.sub.1, f.sub.2, . . . f.sub.l. 
The values e.sub.i are related to the numbers N.sub.j by relationships of 
the type: 
##EQU2## 
F(e.sub.i) being a function of e.sub.i, and .alpha..sub.i, j being a 
coefficient depending on the interference fringe value .delta..sub.i and 
on a.sub.j as well as on the position of the solid angle used. 
For l values of frequencies (or of interference fringes) and a single solid 
measurement angle, there will therefore be used l equations such as 
Equation 1. If l is greater than n, it will suffice to use n equations, 
among the l available, so as to be able to calculate the values of Nj. The 
best choice of these n equations is that which will provide a matrix 
connecting the Nj to F(e.sub.i) so as to be the most diagonal possible, 
which may be written in the matrix form 
EQU .vertline.F(e.sub.i).vertline.=M.multidot..vertline.Nj.vertline. 
and 
EQU .vertline.Nj.vertline.=M.sup.-1 .vertline.F(e.sub.i).vertline. 
M.sup.-1 being the most diagonal possible 
When using in an analogous fashion no longer a single solid measurement 
angle, but a number m of such angles, there will be obtained a number l.m 
of separate equations like equation 1, from among which can be chosen n to 
provide an optimum matrix M.sub.o.sup.-1 which will be, like the preceding 
one, the most diagonal possible. 
It will be understood that the process of the present invention is 
potentionally more discriminatory than the non-interferential batch 
processes by virtue of the fact that among the choice of conditions for 
its use, there are available two degrees of freedom instead of a single 
one, namely, on the one hand, the number of solid measurement angles used, 
and, on the other hand, the number of separate frequencies used, it being 
understood that the choice of the positions of these solid angles and of 
the values of the frequencies themselves, is also available. By means of a 
judicious choice of the whole of these parameters, one can immediately 
achieve information either directly representative of the granulometric 
characteristics sought, or connected to the same by a system of equations 
easier to solve in a sufficiently precise way than in other processes, the 
treatment module 6 shown in FIG. 1 being thus adapted to be quite 
simplified. 
To find optimum conditions of use of the process for the determination of a 
granulometric curve, that is to say to find the best combination of 
frequencies and solid angles to be used with the granulometric 
classifications in question, the computation process comprises first the 
programming in the computer, in a conventional manner, the calculations 
permitting determining the flux diffracted by the particles in all 
directions and taking into account the intersection of the pairs of 
incident beams from which the interference arises. 
Then the repeated use of this program is programmed by causing the 
interference fringe values and the limits of the sought angles in question 
to vary, for each granulometric class, so as to scan systematically all 
the conceivable conditions and compare the results obtained so as to 
arrive at the best conditions. 
Thus, the computation process requires indications relative, on the one 
hand, to the formulas to be used for the calculation of the alternative 
flux diffracted, and relative, on the other hand, to the interference 
fringe values at the outset to be used to begin the computation, the 
programming operation itself being adapted to be performed in known 
manner. 
The alternative flux diffracted in a region of solid angle .OMEGA. by a 
particle of a radius a for a value .delta. of interference fringe may be 
calculated according to the general expression 
##EQU3## 
in which I (a,s) is the intensity diffracted by a particle of radius a at 
an observation angle s, this angle completely sweeping the solid angle 
.OMEGA., when this particle is illuminated by two beams producing the 
interference fringe .delta. 
V (a,.delta.,s) is the rate of modulation of the diffracted light, which is 
a function, as indicated above, of the three parameters a,.delta.,s 
These elements I (a,s) and V (a,.delta.,s) may be calculated by formulas of 
approximation proposed particularly by 
Farmer (Applied Optics, November, 1972) 
Atakan & Jones (Applied Optics, January, 1982) 
Bachalo (Applied Optics, February, 1980) 
As a first approximation, one can use the following formulas: 
##EQU4## 
wherein k=(2.pi./.lambda.) .lambda. wavelengths of the light used 
I.sub.s.sbsb.1.sub.,s.sbsb.2 (a) is the intensity of the light diffracted 
in a zone limited by the two extreme angles s.sub.1 and s.sub.2 
J.sub.1 (X) is the first order Bessel function 
##EQU5## 
as indicated above. As to the choice of interference fringe values, it is 
appropriate to use as a starting value twice the radius of the particle, 
namely .delta.=2a and then preferably to examine the higher values of 
.delta.. However, in case of poly-dispersed particles, it is necessary to 
note two particularities: 
on the one hand, if it is desired to effect counting by eliminating the 
influence of a population of, for example, turbulence, one can preferably 
use a value .delta.=1.64a 
on the other hand, it is possible, as shown by the example hereinafter, 
that an interference fringe value adapted to one class of particles is 
equally applicable to another class of smaller size. 
The next stage of calculation consists in determining the relations such as 
those of Equation 1, and to compare their interest with a view toward the 
formation of an optimum calculation matrix, while varying the parameters 
of interference fringe and of position and of extent of the solid angles. 
Here again, according to the simplified hypotheses used, one can use more 
or less complicated formulas. For a good approximation, one can use 
equations such as the following: 
##EQU6## 
or S.sub.i.sup.2 is the mean value of the square of the alternative flux 
of frequency fi received over the solid measurement angle 
E.sub.i.sup.j is the value calculated as seen above for the expression E 
(a) with a value .delta..sup.i of interference fringe corresponding to the 
frequency fi for a particle of the class j having a mean radius a.sub.j 
Nj is the number of particles in the class j 
It will be noted that this formula permits achieving the result stated 
above, in which S.sub.i varies as .sqroot.Nj, or more exactly 
S.sub.i.sup.2 as Nj. 
These elements permit the use of the process in a satisfactory manner of 
the determination of granulometric curves, the calculations being 
conducted using the mean dimensions of the particles, that is to say using 
the assumption that, in each class of particles, these all have the mean 
size of the class. 
One then seeks, for each class of particle of mean radius a.sub.j a couple 
(.delta.,.OMEGA.) such that the expression E (a) will be a maximum for 
a=a.sub.j and as small as possible for a .noteq.a.sub.j, which, as is 
shown by Equation 2, will result in the most diagonal matrix. 
Of course, one can also refine the computation to determine a granulometry 
with the highest precision by calculating not only E (a.sub.j) from the 
mean dimension a.sub.j, but more particularly the mean value assumed by E 
(a) in the interval corresponding to class j, by integrating E (a) across 
this interval. One can then take account of the granulometric distribution 
of the particles of the class j, assuming it is known in advance, to 
calculate a mean value of E (a) more pertinent to this class j. 
All these processes for calculation are given by way of example, without 
thereby introducing a limitation. 
For counting purposes, or for improved granulometry, the computation 
process may be so oriented as to determine the stationary solid angles 
evoked above. 
To this end, the computation process leading to the determination of said 
solid angles, for a given population, and for an associated interference 
fringe value, is defined in order to determine solid angles in which the 
alternative component of the flux diffracted by the particles remains 
stationary when the size of the particles varies around a normal value. 
In that purpose the computation process leading, for a particular given 
population of particles, and for an associated interference fringe value 
to the determination of one solid angle is defined in order to determine 
one solid angle in which the alternative component of the flux diffracted 
by the particles is proportional to the volume of these particles, that 
means that for such a solid angle, the expression E(a)/a.sup.3 remains 
stationary when the diameter of the particles varies between the extreme 
values for this population. 
The following example, calculated according to the approximate formulas 
indicated, illustrates an instance of use of the invention. One seeks to 
count three families or classes of particles intimately mixed, knowing 
that they are characterized by the following granulometric ranges: 
Family 1: diameters of 2 to 3 .mu.m Number N.sub.1 
Family 2: diameters from 5 to 6 .mu.m Number N.sub.2 
Family 3: diameters of 10 to 20 .mu.m Number N.sub.3 
The calculation leads, with .lambda.=0.6328 (helium-neon laser) to the 
following dimensioning: 
Three solid angles or "windows" are determined, each being alternatively 
stationary for one of the three families. 
The window F.sub.1 which is invariable for the first family corresponds to 
an interference fringe value of 3.2 .mu.m. Its position is given in FIG. 
3. 
To windows F.sub.2 and F.sub.3 (see FIG. 3) which are invariable for the 
respective families 2 and 3, correspond the same value of interference 
fringe, 25 .mu.m. One thus reaches the case set forth above in which the 
interference fringe associated with family 3 will be equally useful for 
family 2, which is of interest for simplifying the apparatus for 
practicing the method.