Particle size meter

Apparatus for determining the size of particles in Brownian motion by measurement based on analysis of fluctuations in the intensity of light diffused by the particles when they are illuminated by a ray of coherent light waves. The parameter(s) of interest is (are) determined in dependence on at least two double integrals R.sub.1, R.sub.2 having the general form ##EQU1## where the values .tau.a, .tau.b, .tau.c, .tau.d define the integration ranges in the delay-time .tau. region and where .DELTA.t represents an integration range with respect to time from an initial instant .tau..sub.o. Means are provided for forming signals representing the double integrals R.sub.1 and R.sub.2. A computer unit receives the signals and generates an output signal corresponding to the aforementioned parameter(s) of the autocorrelation function.

BACKGROUND OF THE INVENTION 
The invention relates to a method and device for determining parameters of 
an autocorrelation function of an input signal V(t), the autocorrelation 
function being defined by the general formula: 
##EQU2## 
and the form of the function .psi.(.tau.) being known. More particularly, 
the invention relates to the processing of electric or other signals in 
order to determine certain parameters of their autocorrelation function 
provided that the form of the function (e.g. an exponential form) is known 
in advance. The invention also relates to a device for performing the 
method and relates further to the application of the method and device to 
determining the size of particles in Brownian motion, e.g. particles 
suspended in a solvent, by a method of measurement based on analysis of 
fluctuations in the intensity of light diffused by the particles when they 
are illuminated by a ray of coherent light waves. 
In the aforementioned method of determining the size of particles, it has 
already been proposed to determine the size of particles by a method in 
which an electric signal is derived corresponding to the fluctuations in 
the intensity of light diffused at a given angle, and the size of the 
particles is determined by analysis of the electric signal (B. Chu. Laser 
Light scattering, Annual Rev. Phys. Chem. 21 (1970) page 145 ff). 
In order to analyze the electric signal it has already been proposed to use 
a wave analyzer to determine the size of the particles in dependence on 
the bandwidth of an average frequency spectrum of the electric signal. 
When a wave analyzer is used which operates on only one frequency at a 
time, by scanning, the aforementioned method has the serious disadvantage 
of requiring a good deal of time, so that not more than six or eight 
measurements can be made per day. If it is desired to reduce the measuring 
time by using a wave analyser which measures spectra over its entire width 
simultaneously, the disadvantage is that the apparatus becomes 
considerably more expensive, since such rapid analysers are complex and 
expensive. 
In an improved method of analysing the electric signal, an autocorrelator 
for deriving a signal corresponding to the autocorrelation function of the 
electric signal is used together with a special computer connected to the 
autocorrelator output in order to derive a signal corresponding to the 
size of the particles by determining the time constant of the 
autocorrelation function, which is known to have a decreasing exponential 
form. This improved method can considerably reduce the measuring time 
compared with the method using a wave analyser, but it is still desirable 
to have a method and device which can determine the size of particles by 
less expensive and less bulky means. In this connection, it is noteworthy 
that commercial autocorrelators and special computers (for determining the 
time constant) are relatively expensive and bulky. 
The previously-mentioned disadvantage, which was cited for a particular 
case, i.e. in determining the time constant of an exponential 
autocorrelation function, also affects the determination of other 
parameters of an autocorrelation function having a known form, e.g. linear 
or a Gaussian curve. As a rule, therefore, it is desirable to have a 
method and a device which can determine such parameters while avoiding the 
disadvantages mentioned hereinbefore in the case where the parameter to be 
determined is a time constant. 
SUMMARY OF THE INVENTION 
An object of the invention, therefore, is to provide a method and device 
which, at a reduced price and using less bulky apparatus, can rapidly 
determine at least one parameter of an autocorrelation function having a 
known form. 
The method according to the invention is characterized in that the 
parameter is determined in dependence on at least two double integrals 
R.sub.1, R.sub.2 having the general form: 
##EQU3## 
where the values .tau.a, .tau.b, .tau.c, .tau.d define the integration 
ranges in the delay-time .tau. and where .DELTA.t represents an 
integration range with respect to time from an initial instant t.sub.0. 
The invention also relates to a device for performing the method according 
to the invention, the device being characterized in that it comprises 
means for forming signals representing double integrals R.sub.1 and 
R.sub.2 and a computer unit which receives the aforementioned signals at 
its input so as to generate an output signal corresponding to the 
aforementioned parameter of the autocorrelation function. 
The invention also relates to use of the device for determining the size of 
particles in Brownian motion in suspension in a solvent by analyzing the 
fluctuations in the intensity of light diffused by the particles when 
illuminated by a ray of coherent light waves and/or for detecting changes 
in the size of the aforementioned particles with respect to time.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Let V(t) be a stochastic signal equivalent to the signal obtained at the 
output of an RC low-pass filter when the signal produced by a white noise 
source is applied to its input. The aforementioned signal V(t) has an 
exponential autocorrelation function of the form: 
EQU .psi.(.tau.)=.psi..sub.o e.sup..vertline..tau..vertline./.tau..sbsp.e (1) 
In order to determine the time constant .tau..sub.e of an exponential 
autocorrelation function such as (1) it has hitherto been conventional to 
use the method and device explained hereinafter with reference to FIGS. 1 
and 2. 
The input 13 of an autocorrelator 11 receives the previously-defined 
stochastic signal V(t) and its output 14 delivers signals corresponding to 
a certain number (e.g. 400) of points 21 (see FIG. 2) of the 
autocorrelation function .psi.(.tau.) of signal V(t). A computer 12 
connected to the output of autocorrelator 11 calculates the time constant 
.tau..sub.e (see FIG. 2) of the autocorrelation function and delvers an 
output signal 15 corresponding to .tau..sub.e. Of course, computer 12 may 
also make the calculation "off-line", i.e. without being directly 
connected to the output of autocorrelator 11. 
In general, the autocorrelation function of signal V(t) is defined by 
##EQU4## 
Since integral (2) cannot of course be obtained over a infinitely long 
time, the function .psi.(.tau.) obtained by the autocorrelator is subject 
to certain errors, which are due to the stochastic character of the 
physical phenomena from which the signal V(t) is derived. In order to 
reduce the effect of these errors, the time constant .tau..sub.e obtained 
by a computer program is usually adjusted by a least-square method so that 
it substantially corresponds with the experimental points given by the 
autocorrelation. FIG. 2 represents the function delivered by the 
autocorrelator (the set of points 21) and the ideal exponential function 
22 obtained by the aforementioned least-square method. 
In order to reduce the expense of the apparatus and time for determining 
the time constant .tau..sub.e, the invention aims to simplify the method 
of determining .tau..sub.e. The invention is based on the following 
arguments. 
Since it is known that the curve obtained .psi.(.tau.) is an exponential 
function, it is sufficient in theory to measure only two points on the 
curve, e.g. for .tau..sub.1 and .tau..sub.2. We shall then obtained two 
values .psi.(.tau..sub.1); .psi.(.tau..sub.2) from which we can deduce 
.tau..sub.e : 
##EQU5## 
The disadvantages of this method are clear. In order to obtain the same 
accuracy as for the least-square method, one must be sure that the 
measured values .psi.(.tau..sub.1), .psi.(.tau..sub.2) are subjected to 
only a very small error; this means that the integration time for 
calculating these two points on the autocorrelation function will be 
longer than when the method of least squares is used. Furthermore, if the 
measuring device produces a systematic error in the calculation of the 
autocorrelation function (resulting e.g. in undulation of the function), 
the two chosen measuring points .tau..sub.1, .tau..sub.2 may be 
unfavorably situated. A third disadvantage of the method (i.e. of 
calculating only two points on the autocorrelation function) is that the 
information in all the rest of the function is lost. 
The following is a description, with reference to FIG. 3, of a method 
according to the invention for obviating the aforementioned disadvantages 
and the disadvantages of the known method described hereinbefore with 
reference to FIGS. 1 and 2. 
The range of delay times .tau. is divided into two regions 31, 32. Region 
32 extends from .tau..sub.1 to .tau..sub.2, and region 32 from .tau..sub.2 
to .tau..sub.3. For simplicity, it is convenient to choose two adjacent 
regions having the same length, i.e. 
EQU .DELTA..tau.=.tau..sub.3 -.tau..sub.2 =.tau..sub.2 -.tau..sub.1 (4) 
However, the validity of the method according to the invention is in no way 
affected if the chosen regions 31, 32 have different widths or are not 
adjacent. 
It is known that curve .psi.(.tau.) is exponential. It can therefore be 
shown that: 
##EQU6## 
Equation (5) shows that the ratio .psi.-(.tau..sub.1)/.psi.-(.tau..sub.2) 
appearing in equation (3) can be replaced by the ratio between two 
integrals: 
##EQU7## 
This replacement largely eliminates the disadvantages of determining 
.tau..sub.e by simply measuring two points on the autocorrelation 
function. 
Consequently, equation (3) is converted into: 
##EQU8## 
FIG. 4 is a block diagram of a basic circuit of a device for working the 
method according to the invention. A signal V(t) is applied to the input 
of a store 41 and to one input of a multiplier 42 for forming the product 
P(t) of the input signal V(t) and the output signal M(t) of store 41. The 
resulting or product signal P(t) is in turn applied to the input of an 
integrator 43 which delivers an output signal corresponding to the 
integral R.sub.1 defined by equation (6) hereinbefore. 
In order to explain the operation of the circuit in FIG. 4, it is 
convenient to express R.sub.1 using equations (2) and (6): 
##EQU9## 
By inverting the two integrals and putting .tau..sub.1 =0 for simplicity, 
we can write: 
##EQU10## 
The circuit in FIG. 4 for determining R.sub.1 according to equation (9) 
operates as follows: 
The integral with respect to time t (from t.sub.0 to t.sub.0 =.DELTA.t) is 
obtained by an integrator 43 shown in FIG. 4. The integral with respect to 
the delay time .tau. is obtained by store 41 in FIG. 4, which samples 
signal V(t) at intervals of .DELTA..tau., i.e. during a time interval 
.DELTA..tau. the delay time .tau. between V(t) and the stored value varies 
progressively from 0 to .DELTA..tau.. 
As shown in FIG. 5, the instantaneous value of V(t) is stored at the time 
t.sub.0, and is again stored at the times t.sub.0 +.DELTA..tau., t.sub.0 
+2.DELTA..tau. etc. i.e. during the time interval between t.sub.0 and 
t.sub.0 +.DELTA..tau., the product P(t)=V(t). M(t) is the same as 
V(t).multidot.V(t.sub.0); This is precisely the product which it is 
desired to form in order to obtain R.sub.1 by equation (9). The integrator 
43 in FIG. 4 integrates P(t) during a time .DELTA.t. 
By way of example, in order to measure a time constant .tau..sub.e of 1 ms, 
we shall take .DELTA..tau.=1 ms and .DELTA..tau.=30 s. 
The integral R.sub.2 is calculated in similar manner to integral R.sub.1, 
except that the stored values are not delayed by a time which varies 
between 0 and .DELTA..tau. with respect to V(t), but by a time which 
varies between .DELTA..tau. and 2.DELTA..tau.: 
##EQU11## 
FIG. 6 is a block diagram of the complete device, and FIG. 7 illustrates 
its operation. 
At the beginning of the time interval [t.sub.0 +.DELTA..tau., t.sub.0 
+2.DELTA..tau.], store 61 stores the value V(t.sub.0 +.DELTA..tau.). At 
the same instant, a store 62 stores the value M.sub.1 (t)=V(t.sub.0) which 
was previously stored in store 61, i.e. during the time interval [t.sub.0 
+.DELTA..tau., t.sub.0 +2.DELTA..tau.] in question, we have 
EQU M.sub.1 (t)=V(t.sub.0 +.DELTA..tau.) 
EQU M.sub.2 (t)=V(t.sub.0) (11) 
During this interval, therefore the corresponding products P.sub.1 (t) and 
P.sub.2 (t) formed by multipliers 63, 64 are 
EQU P.sub.1 (t)=V(t).multidot.V(t.sub.0 +.DELTA..tau.) 
EQU P.sub.2 (t)=V(t).multidot.V(t.sub.0) (12) 
During the time interval to +.DELTA..tau., therefore, the delay between the 
two terms of the products P.sub.1 (t) and P.sub.2 (t) progressively varies 
between 0 and .DELTA..tau. for P.sub.1 and between .DELTA..tau. and 
2.DELTA..tau. for P.sub.2. 
The functions P.sub.1 (t) and P.sub.2 (t) are integrated in two identical 
integrators 65, 66; the results of integration R.sub.1, R.sub.2 are then 
transmitted to a computer circuit 67 which determines the time constant 
.tau..sub.e of the exponential autocorrelation function and gives an 
output signal 68 corresponding to .tau..sub.e. 
The circuit shown diagrammatically in FIG. 6 can be embodied in various 
ways, by analog or digital data processing. In the case of a digital 
embodiment, analog-digital conversion can be obtained with varying 
resolution (i.e. a varying number of digital bits). In the limiting case, 
the data can be processed by extremely coarse digitalization of one bit in 
one of the two channels (i.e. the direct or the delayed channel)--i.e., 
only the sign of the input signal V(t) is retained. The theory shows that 
the resulting autocorrelation function is identical with the function 
which would be obtained by using the signal V(t) itself, provided that the 
amplitude of the function V(t) has a Gaussian statistic distribution in 
time. A special case is shown hereinafter with respect to FIG. 8. In this 
example, only the signal from the delayed channel is quantified with a 
resolution of one bit. 
The principle of this embodiment is as follows: a one-bit digital system is 
used to store the signal. It is simply necessary, therefore, for stores 
81, 82 to store the sign V(t) (FIG. 8) obtained by comparing V(t) with a 
reference value V.sub.R, which can be equal to or different from zero, in 
a comparator 84. for V.sub.R =0 the following values appear at the store 
outputs: 
EQU M'.sub.1 (t)=sign of M.sub.1 (t) 
EQU M'.sub.2 (t)=sign of M.sub.2 (t) (13) 
Next, V(t) is multiplied by M'.sub.1 and M'.sub.2 as follows: 
If M'.sub.1 (t) is positive, a switch 85 makes a connection to the correct 
input V(t). In the contrary case, i.e. if M'.sub.1 is negative, switch 85 
makes the connection to the signal -V(t) obtained by inverting the input 
signal V(t) by means of an amplifier 83 having a gain of -1. The two 
products P'.sub.1 (t) and P'.sub.2 (2) are obtained in the same manner: 
EQU P'.sub.1 (t)=[sign of M.sub.1 (t)]. V(t) 
EQU P'.sub.2 (t)=[sign of M.sub.2 (t)]. V(t) (14) 
Next, values R.sub.1, R.sub.2 are obtained simply by integrating P'.sub.1, 
P'.sub.2 using simple analog integrators 87, 88. The circuit 89 for 
calculating the time constant .tau..sub.e can be analog, digital or 
hybrid. 
The circuit shown in FIG. 6 is made up of two identical computer circuits, 
each comprising a store, a multiplier and an integrator as shown in FIG. 4 
and a circuit 67 for calculating the time constant. Each computer circuit 
in FIG. 4 can be generalized and given the form shown in FIG. 9 or FIG. 
10. 
The generalized forms shown in FIGS. 9 and 10 are equivalent, as will be 
shown hereinafter. 
At the time t.sub.0, the value of the input signal V(t) is stored in store 
91, i.e.: 
EQU M.sub.1 (t)=V(t.sub.0) for t.sub.0 &lt;t.sub.1 &lt;t.sub.0 +.tau.'(15) 
At the time t.sub.0 +.tau.', a new value of V(t) is stored in store 91. At 
the same time, the value previously contained in store 91 is transferred 
to store 92, i.e.: 
##EQU12## 
Similarly, in the time interval to +2.tau.'&lt; to &lt; to +3.tau.' we have: 
EQU M.sub.1 (t)=V(t.sub.0 +2.tau.') 
EQU M.sub.2 (t)=V(t.sub.0 +.tau.') 
EQU M.sub.3 (t)=V(t.sub.0) (17) 
During this time interval, the three multipliers 94, 95, 96 shown in FIG. 9 
output a signal 
EQU P.sub.i (t)=M.sub.i (t).multidot.V(t) (18) 
or, more precisely: 
EQU P.sub.1 (t)=M.sub.1 (t).multidot.V(t)=V(t.sub.0 +2.tau.').multidot.V(t) 
EQU P.sub.2 (t)=M.sub.2 (t).multidot.V(t)=V(t.sub.0 +.tau.').multidot.V(t) 
EQU P.sub.3 (t)=M.sub.3 (t).multidot.V(t)=V(t.sub.0).multidot.V(t) (19) 
The products P.sub.1 (t), P.sub.2 (t), P.sub.3 (t) are added in summator 97 
and the resulting sum 
EQU .SIGMA.P.sub.i (t)=P.sub.1 (t)+P.sub.2 (t)+P.sub.3 (t) (20) 
is applied to an integrator (e.g. 43 in FIG. 4) which delivers an output 
signal corresponding to R.sub.1 or R.sub.2. 
If we limit ourselves to a series of three stores per computer circuit (as 
in the example shown in FIG. 9) and if we put 
EQU .tau.'=(.DELTA..tau.)/3 (21) 
where .DELTA..tau.=computer time constant defined by equation (4) 
hereinbefore (compare FIG. 3), we obtain a result similar to that obtained 
with the simple version in FIG. 4 (using one store per computer circuit), 
but the accuracy of calculation is improved by dividing the single store 
in FIG. 1 into the three stores or more in FIG. 9. 
If expression (20) is re-written to show V(t) more clearly, we have: 
EQU .SIGMA.P.sub.i (t)=V(t).multidot.[M.sub.1 (t)+M.sub.2 (t)+M.sub.3 (t)](22) 
It can easily be seen that the thus-obtained expression (22) represents the 
product P(t) obtained at the outlet of the multiplier in the circuit shown 
in FIG. 10. We have thus shown that diagrams 9 and 10 are equivalent. 
FIG. 11 is a diagram of a detailed example of a digital embodiment of the 
block diagram in FIG. 6. 
An input signal V(t) is applied to an analog-digital converter 111. A clock 
signal H.sub.1 brings about analog-digital conversions at a suitable 
frequency, e.g. 100 kHz (i.e. 10.sup.5 analog-digital conversions per 
second). 
A second clock signal H.sub.2 periodically (e.g. at intervals 
.DELTA..tau.=1 ms=10.sup.-3 s) actuates the storage of the digital value 
corresponding to signal V(t) in a store 112. In the chosen example, the 
analog-digital converter 111 has a resolution of three bits and store 112 
is made up of three D-type trigger circuits. At the same time as a new 
value is being stored in store 112, clock signal H.sub.2 transfers the 
previously-contained value from store 112 to a store 113 which is likewise 
made up of three D-type trigger circuits. 
Consequently, a multiplier 114 receives the signal V(t) (the digital 
version of the input signal V(t) at the rate of 10.sup.5 new values per 
second, and also receives the stored digital signal M.sub.1 (t) at the 
rate of 10.sup.3 numerical values per second. Thus, output P.sub.1 of 
multiplier 114 is a succession of digital values following at the rate of 
10.sup.5 values per second. 
Registers 116, 117 are used instead of integrators 65, 66 in FIG. 6. Each 
register comprises an adder 118 and a store 119 which in turn is made up 
of a series of e.g. D-type trigger circuits. At a given instant, store 119 
contains the digital value R.sub.1. As shown in FIG. 11, value R.sub.1 is 
applied to one input 151 of adder 118, whereas the other input 152 
receives the product P.sub.1 (t) coming from multiplier 114. The sum 
R.sub.1 +P.sub.1 (t) appears at the output of adder 118. At the moment 
when the clock pulse H.sub.1 is applied to store 119, the store records 
the value R.sub.1 +P.sub.1 (t) (this new value R.sub.1 +P.sub.1 (t) 
replaces the earlier value R.sub.1). As already mentioned, in the chosen 
example the multiplier 114 delivers. 10.sup.5 new values of P.sub.1 (t) 
per second (due to the fact that it receives 10.sup.5 values of V'(t) per 
second from analog-digital converter 111, the rate being imposed by clock 
H.sub.1). Register 116 therefore will accumulate data at the frequency of 
10.sup.5 per second, under the control of clock H.sub.1. 
Register 117 is constructed in identical manner with register 117 and 
therefore does not need to be described. 
A control circuit (not shown in FIG. 11) resets the stores and registers to 
zero before the beginning of a measurement, delivers clock signals H.sub.1 
and H.sub.2 required for the operation of the device, and stops the device 
after a predetermined time. At the end of the accumulation phase (typical 
duration: 10 sec. to 1 min), the two values R.sub.1, R.sub.2 in registers 
116, 117 are supplied to a circuit (not shown in FIG. 11) which calculates 
the time constant. 
In an important variant of this manner of operation, the device does not 
have an imposed integration time, since it is known that the contents of 
R.sub.1 is always greater than the contents of R.sub.2. Consequently, 
integration can be continued as long as required for register R.sub.1 to 
be "full" (i.e. by waiting until its digital contents reaches its maximum 
value. The calculation of the time constant is thus simplified, since 
R.sub.1 becomes a constant. 
There are innumerable possible digital embodiments of the method according 
to the invention. Here are a few examples: 
Any kind of analog-numerical converter (unit 111 in FIG. 11) can be used, 
e.g. a parallel converter, by successive approximation, a "dual-slope", a 
voltage-frequency converter, etc. The number of bits (i.e. the resolution 
of converter 111) can be chosen as required. 
Stores 112, 113 and 119 can be flip-flops, shift registers, RAM's or any 
other kind of store means. 
The multipliers can be of the series of parallel kind. 
In an important variant, an incremental system is used; registers 116 and 
117 are replaced by forward and backward counters. In that case, a new 
product P(t) is added to the register contents by counting forwards or 
backwards a number of pulses proportional to P(t). In that case, the 
multipliers can be of the "rate multiplier" kind. 
FIG. 12 is a diagram of a hybrid embodiment similar to that shown in FIG. 
8. 
In the diagram in FIG. 12, the input signal V(t) is applied to the input of 
a comparator 122 which outputs a logic signal V'(t) corresponding to the 
sign only of V(t). For example, V'(t) will be a logic L when V(t) is 
positive, and 0 when V(t) is negative. The logic signal V'(t) is then 
stored in a trigger circuit 123 at the rate fixed by clock H.sub.2 (the 
same as in the digital case, e.g. with a frequency of kHz). The same clock 
signal H.sub.2 conveys the information from circuit 123 to a second 
trigger circuit 124. 
In the last-mentioned embodiment, the input signal V(t) is multiplied by 
the delayed signal M.sub.1 '(t) or M.sub.2 (t) as follows: 
In the case where M.sub.1 '(t) is a logic 1 (corresponding to a positive 
V(t)), a switch 125 actuated by the output M.sub.1 '(t) of trigger circuit 
123 is connected to V(t). In the contrary case (M.sub.1 '(t)=0, and V(t) 
is negative), switch 125 is connected to the signal -V(t) coming from 
inventer 121. A second switch 126 operates in similar manner. 
It can be seen, therefore, that the two switches 125 and 126 can multiply 
the input signal V(t) by +1 or -1. 
In other words: 
EQU P.sub.i '(t)=V(t) if M.sub.i '(t)=1 
EQU P.sub.i '(t)=-V(t) if M.sub.i '(t)=0 (23) 
P.sub.1 '(t) and P.sub.2 '(t) are integrated by two integrators 127 and 
128. At the beginning of the measurement, the last-mentioned two 
integrators are reset to zero by switches 129 and 131 actuated by a signal 
133 coming from the control circuit (not shown in FIG. 12) which gives 
general clock pulses. After a certain integration time, which is preset by 
the means controlling the device (mentioned previously), integration is 
stopped and the values of R.sub.1 and R.sub.2 are read and converted, by 
means of a computing unit 132, into an output signal 134 corresponding to 
the time constant. 
Starting from the circuit in FIG. 12, various other embodiments are 
possible, i.e. 
(a) Exponential Averaging 
Integrators 128 and 128 are modified as in FIG. 13. As can be seen, the 
switch for resetting the integrator to zero has been replaced by a 
resistor 143 disposed in parallel with an integration capacitor 144. Thus, 
the integration operation is replaced by a more complex operation, i.e. 
exponential averaging, which can be symbolically represented as follows: 
##EQU13## 
where u.sub.1 =Laplace transform of the input signal 
u.sub.2 =Laplace transform of the output signal 
p=Laplace variable ("the differentiation with respect to time" operator) 
r.sub.a =value of resistor 143 
r.sub.b =value of resistor 142 
C=value of integration capacitor 144. 
r.sub.a is made much greater than r.sub.b and it can be seen intuitively 
that the output voltage of a modified integrator of this kind tends 
towards a limiting value (with a time constant equal to r.sub.a C). In 
this variant, the device for resetting the integrators to zero can be 
omitted and the integrators can permanently output the values R.sub.1, 
R.sub.2 required for calculating the time constant. 
(b) Increasing the Resolution of the Digital Part 
Comparator 122 and trigger circuits 123 and 124 can be replaced by a more 
complex analog-digital converter, i.e. having more than one bit and 
followed by stores of suitable capacity. The multipliers multiplying the 
analog signal V(t) by numerical values M.sub.1 '(t) and M.sub.2 '(t) will 
have a more complicated structure than a simple switch; multiplying 
digital-to-analog converters are used for this purpose. 
(c) Purely Analog Version 
The circuit comprising comparator 122 and trigger circuits 123 and 124 
(FIG. 12) can be replaced by a number of sample and hold amplifiers for 
storing the input signal V(t) in analog form. In the case of a purely 
analog voltage, switches 125 and 126 will be replaced by analog 
multipliers which receive the direction input signal V(r) and also receive 
the signal from the corresponding sample and hold amplifier. 
A particularly interesting application of the device according to the 
invention will now be described with reference to FIG. 14. 
It has already been proposed to determine the size of particles in 
suspension in a solvent, by means of a light-wave beat method using a 
homodyne spectrometer as shown diagrammatically in FIG. 14 (B. Chu, Laser 
Light scattering, Annual Rev. Phys. Chem. 21 (1970), page 145 ff). The 
specttrometer operates as follows: 
A laser beam is formed by a laser source 151 and an optical system 152 and 
travels through a measuring cell 153 filled with a sample of a suspension 
containing particles, the size of which has to be determined. The presence 
of the particles in the suspension causes slight inhomogeneities in its 
refractive index. As a result of these inhomogeneities, some of the light 
of the laser beam 161 is diffused during its travel through the measuring 
cell 153. A photomultiplier 154 receives a light beam 162 diffused at an 
angle .theta. through a collimator 163 and, after amplification in a 
pre-amplifier, gives an output signal V(t) corresponding to the intensity 
of the diffused laser beam. 
As already explained, Brownian motion of particles in suspension produces 
fluctuations in the brightness of the diffused beam 162. The frequency of 
the fluctuations depends on the speed of diffusion of the particles across 
the laser beam 161 in the measuring cell 153. In other words, the 
frequency spectrum of the fluctuations in the brightness of the diffused 
beam 162 depends on the size of the particles in the suspension. 
Let V(t) be the electric signal coming from photomultiplier 154 followed by 
preamplifier 156. Like the motion of the particles in suspension, the 
signal is subjected to stochastic fluction having a power spectrum given 
by the relation 
##EQU14## 
In the second member of equation (25), the first term represents 
shot-noise, which is always present at the output of a photodetector 
measuring a light intensity equal to I.sub.s. The second term is of 
interest here. It is due to the random (Brownian) motion of the particles 
illuminated by a coherent light source (laser). 
a and b are proportionality constants, I.sub.s is the diffused light 
intensity, and 2.GAMMA. is the bandwidth of the spectrum which is 
described by a Lorentzian function. .GAMMA. is directly dependent on the 
diffusion coefficient D of the particles. We have 
EQU .fwdarw.=DK.sup.2 (26) 
where 
##EQU15## 
is the amplitude of the diffusion vector (n, .lambda. and .theta. 
respectively are the index of refraction of the liquid, the wavelength of 
the laser and the angle of diffusion). The diffusion coefficient D for 
spherical particles of diameter d is given by the Stokes-Einstein formula 
##EQU16## 
where k, T and .eta. respectively are the Boltzmann constant, the absolute 
temperature and the viscosity of the liquid. 
Consequently, if .GAMMA. is determined experimentally, the size of the 
particles can be calculated from the previously-given relation. In the 
case of non-spherical particles, the average size is obtained. 
As explained in the reference already cited in brackets (B. Chu, Laser 
Light scattering, Annual Rev. Phys. Chem. 21 (1970), page 145 ff), the 
determination can be made by ananyzing the fluctuations of the signal 
V(t), using either a wave analyzer or an arrangement 158 comprising an 
autocorrelator and a special computer. 
The second method is usually preferred today, since the fluctuations are 
low frequencies (of the order of 1 kHz or less). The information obtained 
by both methods is identical, since the autocorrelation function 
.psi.(.tau.) is the Fourier transform of the power spectrum, i.e. 
##EQU17## 
(Wiener-Khintchine theorem) 
In the special case of the diffusion spectrum, we find: 
EQU .psi.(.tau.)=aI.sub.s .delta.(.tau.)+bI.sub.s.sup.2 e.sup.-2.GAMMA..tau.( 
30) 
The first term is a delta function centered at the origin=0 and represents 
the shot-noise contribution. The second term is an exponential function 
having a time constant 
EQU .tau..sub.e =1/2r (31) 
Using relations (26), (27), (28) and (31), we can write 
##EQU18## 
In the case where water at 25.degree. is used as solvent, a time constant 
.tau..sub.e of 1 millisecond corresponds to a particle diameter d of 0.3 
.mu.m. 
It can be seen from relation (32) that the size of the diffused particles 
can be determined by measuring the time constant .tau..sub.e of the 
autocorrelation function of the signal V(t) coming from the photodetector. 
It has already been proposed to measure .tau..sub.e using the method and 
arrangement described hereinbefore in detail with reference to FIGS. 1 and 
2. The disadvantage of the known arrangement is that the units used (i.e. 
an autocorrelator and a special computer) are relatively expensive and 
bulky. 
FIG. 14 shows the particle size meter including the new device 158 which 
overcomes the disadvantages of the prior art. 
As the preceding clearly shows, the method and device according to the 
invention can considerably reduce the cost and volume of the means 
required for determining the time constant. As can be seen from the 
embodiments described hereinbefore with reference to FIGS. 4-13, the means 
used to construct a device according to the invention are much less 
expensive and less bulky than an arrangement made up of commercial 
autocorrelator and special-computer units for calculating the time 
constant of an autocorrelation function. It has been found, using 
practical embodiments, that a device according to the invention can have a 
volume about fifty times as small as the volume of the known arrangement 
in FIG. 1. 
Although the previously-described example relates only to the use of the 
invention for determining the diameter of particles suspended in a liquid, 
it should be noted that the invention can also be used to detect a gradual 
change in the dimension of the particles, e.g. due to agglutination. For 
this purpose, it is unnecessary to determine the absolute particle size as 
previously described, since a change in the size of the particles can be 
detected simply by using double integrals such as R.sub.1 and R.sub.2. In 
addition, the invention can also be used for continuously measuring the 
dimension of the particles, so as to observe any variations therein. 
The following examples shows that the method and device according to the 
invention can be applied not only to determining the time constant of an 
exponential autocorrelation function decreasing in the manner described, 
but can also be used to determine the parameters of any autocorrelation 
function whose form is known. In addition, the input signal V(t) can be of 
any kind. 
If, for example, the autocorrelation function .psi.(.tau.) is linear and 
decreases with .tau., it is defined by: 
EQU .psi.(.tau.)=A-B.tau. 
EQU with B&gt;0 (33) 
In the case where register 116 (with B&gt;0 in the circuit in FIG. 11) 
integrates over the range from .tau.=0 to =.DELTA.t (to obtain a signal 
representing the integral R.sub.1) and register 117 integrates from 
.tau.=.DELTA..tau. to .tau.=2.DELTA..tau. (to obtain a signal representing 
the integral R.sub.2), the parameters A and B in equation (33) are given 
by 
##EQU19## 
If, for example, the autocorrelation function has the form of a Gaussian 
function defined by: 
EQU .psi.(.tau.)=e.sup.-.lambda..tau..spsp.2 with .lambda.&gt;0 (35) 
and if registers 116 and 117 (in the diagram of FIG. 11) integrate over the 
ranges previously given in the case of the linear function, we have the 
relation: 
##EQU20## 
with erf=error function. 
.lambda. can be obtained by solving equation (36). Although this equation 
is transcendental and does not have a simple analytical solution, it can 
be solved by numerical or analog methods of calculation, using a suitable 
electronic computer unit. 
In the case where the device according to the invention is applied to 
photon beat spectroscopy, there are two important cases where the 
autocorrelation function is in the form 
##EQU21## 
where K=const. 
These two cases are: 
The measurement of very low levels of diffused light and 
One-bit quantification, i.e. the "add-subtract" method, with a reference 
level different from zero (as described hereinbefore with reference to 
FIG. 8). 
The method according to the invention can be modified so as to determine 
the time constant .tau..sub.e in the two previously-mentioned cases. For 
this purpose, it is sufficient to calculate at least a third double 
integral R.sub.3 having a similar form to R.sub.1 and R.sub.2 and defined 
by 
##EQU22## 
with .tau..sub.3 &gt;.tau..sub.2 &gt;.tau..sub.1. 
The integration time ranges for calculating R.sub.1, R.sub.2 and R.sub.3 
respectively [.tau..sub.1, .tau..sub.2 +.DELTA..tau.], [.tau..sub.2, 
.tau..sub.2 +.DELTA..tau.][.tau..sub.3, .tau..sub.3 +.DELTA..tau.]. 
Accordingly, the electronic computer unit must calculate .tau..sub.e and, 
if required, K from a knowledge of the integration limits and the 
accumulated values of R.sub.1, R.sub.2 and R.sub.3. .tau..sub.1, 
.tau..sub.2 and .tau..sub.3 can be chosen so as to obtain a simple 
analytical solution of the problem. Two possibilities will be considered: 
The case where 
EQU .tau..sub.3 -.tau..sub.2 =.tau..sub.2 -.tau..sub.1. (39) 
The time constant .tau..sub.e is: 
##EQU23## 
The case where 
EQU .tau..sub.3 &gt;&gt;.tau..sub.e. (41) 
In this case, the value accumulated in R.sub.3 is very close to 
K..DELTA..tau. and we obtain: 
##EQU24## 
The numerator of the fractions in the expressions (40) and (42) is a 
constant related related to the construction of the device; consequently 
the determination of .tau..sub.e is as simple as in the case of equation 
(7) hereinbefore. 
R.sub.1, R.sub.2 and R.sub.3 can e.g. be calculated as described with 
reference to FIG. 11, by adding the elements necessary for forming 
R.sub.3. 
However, it is not absolutely necessary to use an additional register to 
work the last-mentioned modified method. It is also possible, using two 
registers R.sub.1 ' and R.sub.2 ', to calculate the values 
EQU R.sub.1 '=R.sub.1 -R.sub.2 
and 
EQU R.sub.2 '=R.sub.2 -R.sub.3 (43) 
directly in case (39), or the values 
EQU R.sub.1 "=R.sub.1 -R.sub.3 
and 
EQU R.sub.2 "=R.sub.2 -R.sub.3 (44) 
directly in the case (41). 
These operations are particularly easy to carry out in an "add-subtract" 
configuration, in a forward and backward counting configuration or in the 
analog case. In case (41), for example, the products P.sub.1 (t) and 
-P.sub.3 (t) will be accumulated in the same register R.sub.1 ". 
The main advantage of the device according to the invention is a 
considerable reduction in the price and volume of the means necessary for 
making the measurement.