Electrophoretic light scattering with plural reference beams, apparatus and method

Multichannel electrophoresis apparatus employing electrophoretic light scattering as a means for characterizing the particles under study. The apparatus is characterized by the ability to measure light scattered simultaneously using a plurality of local oscillators incident at different angles from the same population of particles being subjected to electrophoresis. The apparatus is used with data processing means to analyze the large amount of scattering data which provide information on electrophoretic mobility, particle size, particle charge, electrophoretic mobility, zeta potential. An important aspect of the new apparatus is a markedly improved capability to segregate data related to diffusion effects from data relating to heterogeneous effects.

BACKGROUND OF THE INVENTION 
The invention relates to improved apparatus for measuring, by 
light-scattering techniques, the characteristics of particles subjected to 
electrophoretic processes. 
In general electrophoretic light scattering (ELS) is a process described as 
follows: Particles, light-scattering entities often molecular in nature, 
are dispersed in a transparent liquid medium which is placed between 
positive and negative electrodes and subjected to an electric field. 
Depending upon the size, shape, and electronic natures of these particles, 
they tend to react differently to the electric field, particularly in 
terms of movement, and this reaction can be interpreted in 
analytically-useful ways by the use of light scattered from the particles. 
There is a large body of literature relating to such work. A chapter 
entitled "Electrophoretic Light Scattering" by Ben R. Ware and Daniel D. 
Haas which appeared in Fast Methods in Physical Biochemistry and Cell 
Biology edited by R. I. Sha'afi and S. M. Fernandez (Elsevier, 1983) gives 
a good bibliography of literature relating to, and forming the basis for, 
the electrophoretic light scattering art. 
Electrophoretic light scattering measurements utilizing a doppler shift 
detected by comparing the scattered light to a "local oscillator" (which 
is light from the original source which has not undergone scattering and 
may be viewed as a light-scattering control or standard against which 
other scattered light is referenced) have evolved in recent years. One 
advantageous embodiment of a doppler-type apparatus is described in a 
co-pending patent application Ser. No. 415,581 entitled Light Scattering 
Apparatus and Method and filed on Sept. 7, 1982 by Norman C. Ford. 
A number of patents have been published relating to electrophoretic 
measurements. Some of these, including U.S. Pat. Nos. 3,984,533; 
4,011,044; 4,102,990 and 4,217,195; are among those listed in a Summary 
Report entitled Laser Doppler Spectroscopy Technology dated October 1980 
and prepared by the Technical Marketing Operation of the General Electric 
Company. 
Electrophoretic light scattering (ELS) has been applied with success to the 
characterization of biological particles from small proteins to large 
living cells. A principal advantage of the procedure has been the ability 
to characterize the properties of many particles at the same time. 
Nevertheless, it has been difficult to distinguish, in some cases, between 
random movement of particles being characterized and movement which is 
more characteristic of the electrophoretic mobility. 
Particles to be evaluated in any test sample, will usually be heterogeneous 
in some important respects. For example, particles in a sample system will 
probably differ with respect to size-related polydispersity and 
electrophoretic mobility in a given electrophoretic environment. In many 
samples, and especially those with large particles such as blood cells, it 
becomes particularly difficult to analyze scattered light information and 
interpret it in terms of the characteristics of all particles in the 
population being measured. 
Thus it has remained to find a more convenient and practical way to vary 
the conditions of light scattering effects under a large variety of 
conditions so that the various light scattering effects can be more 
definitely evaluated and related to the nature of particle sample under 
study. 
SUMMARY OF THE INVENTION 
It is a principal object of the present invention to present an apparatus 
for characterizing electrophoretic light-scattering, call "ELS", from 
particles being characterized, and most particularly an apparatus that is 
capable of distinguishing heterogenous electrophoresis effects from 
diffusion effects on particles subjected to an electrophoretic field. 
Another object of the invention is to provide data-processing means whereby 
the superior detection characteristics of the electrophoretic apparatus 
can be rapidly analyzed. 
A further object of the invention is to provide a particularly advantageous 
optical arrangement for transmitting light to the sample cell in such a 
way as to allow optimal processing and analysis of light leaving the 
sample cell. 
Still another object of the invention is to provide a rapidly-replaceable 
electrophoretic cell means which further complements the capability of the 
invention to provide rapid comprehensive testing. 
Still other objects of the invention will be recognized by those skilled in 
the art on their reading of this disclosure. 
"Particles" as described herein are defined as light-scattering entities in 
a fluid medium. They are frequently molecular species or other such 
entities not always strictly viewed as particulate in nature. Most work 
has been done with light-scattering particles in the range of from 0.1 to 
one micrometer in average diameter, but there is no reason to believe that 
successful measurements cannot be carried out with other particles, e.g. 
particles of a magnitude larger or smaller than the indicated range. A 
range from 0.01 to 30 microns is satisfactory. 
The above objects have been substantially achieved by construction of 
electrophoretic light-scattering, or ELS, apparatus of the Doppler 
shift-measuring type which utilizes a highly advantageous multiple array 
of scattered light receptors in combination with means to introduce a 
local-oscillator portion of the light source which is not scattered during 
passage through an electrophoretic sample cell. Other light detecting 
means are so placed as to receive light scattered at a plurality of angles 
from the particles being characterized. In order to provide a simultaneous 
analysis of the immense amount of data which such an apparatus may 
provide, a computer control means is advantageously used to aid analysis 
and also to control and modulate the electrical supply to the 
electrophoretic cell. Such light-evaluating apparatus are already 
available in commerce and are readily adapted, with manufacturer's 
instruction, for use with the present invention. One such device is sold 
by Langley Ford Instruments of Amherst, Mass. under the designation the 
1096 digital correlator. 
The new apparatus may be used with data processing means to analyze 
scattering data and provide information on electrophoretic mobility, 
particle size, particle charge, electrophoretic mobility and zeta 
potential. 
The light scattered at different angles (and the reference beams which act 
as local oscillators) is received on different photodiodes. It is 
convenient to use photodiodes with a built-in operational amplifier to 
improve the signal/noise ratio. Such photodiodes are readily available and 
can be obtained from EGG company under the designation HUV-1100BQ. The 
output signals from the output of the photodiodes are readily processed on 
the available digital correlators such as described above. 
The usual computer control procedure can be carried out by those of 
ordinary skill in the ELS art following the instructions of the Equipment 
supplier and, preferably, utilizing readily-available computer hardware 
and software. Alternately, software can be developed by a capable 
programmer familiar with the ELS art. 
It is to be understood that the apparatus is readily configured for 
utilizing differently shaped sample cell chambers, different laser 
sources; different light beam configurations, as long as they are 
compatible with the selected sample chamber; or including beams crossing 
one another in the sample chamber. Moreover, the apparatus allows an 
operator to view the scattering volume and to move that volume with 
respect to the light source to suit a particular experiment. 
It is to be stressed that it is important to carry out the multi-angular 
testing on a given sample simultaneously. This is not only because of the 
relative inconvenience of conducting multiple tests. For example, in many 
materials to be tested, there will be sufficient statistical variations, 
e.g. as to size, occurring among particle populations of sequential "cell 
loads" of the same material to make interpretation of results under 
various test conditions difficult or impossible. However, if those 
measurements are taken from the same cell load, the unavoidable 
statistical variation in sample loads is avoided. 
THE DOPPLER SHIFT 
In ELS processes of the type described in this application, one measures 
electrophoretic velocities through the Doppler shifts of laser light 
scattered from the particles. By analogy with sound waves from a source 
moving towards the detector at speed v, the Doppler shift of the frequency 
for either light or sound is given by: 
EQU .DELTA..nu.=(v/c).nu..sub.o 
where .nu..sub.o is the original frequency in the source's inertial frame 
of reference and c is the characteristic speed of the wave (i.e., the 
speed of light for light scattering). If the source is moving at some 
angle .theta. with respect to the detector, the magnitude of the Doppler 
shift is diminished by a factor of sin .theta.. 
The fact that the Doppler shift impressed upon the scattered light by a 
moving particle is directly proportional to that particle's velocity may 
give the misleading impression that the light scattering spectrum will 
simply be a histogram of the sample particles' instantaneous velocities. 
In addition to the electrophoretic drift, the particles undergo the 
jostling motions of random Brownian diffusion. These random components 
have velocities which are orders of magnitude greater than the 
electrophoretic drift velocities at the usual electric field strength. 
However, in actual practice, the electrophoresis causes a 
well-characterized spectral peak at the proper Doppler shift frequency, 
with a linewidth dependent upon a particle's diffusion constant. This 
primary dependence of the spectral shift upon electrophoresis rather than 
upon random motions can be reconciled with the Doppler shift explanation 
by interpreting the Doppler shift in classical terms as a continuously 
increasing phase shift impressed upon light of the original source 
frequency by the particle's motion, causing an apparent frequency shift in 
the observed light. Only those motions which carry the particle a 
substantial fraction of the wavelength of the illuminating light can cause 
a noticeable change in the time required for successive crests of the 
scattered light wave to reach the detector, thereby affecting the 
perceived frequency of scattered light seen by the detector. Individual 
steps in the random walk executed by the sample particle are much too 
small (only a few angstroms) to be detectable with light of optical 
wavelengths. The cumulative effects of many steps in a particle's 
diffusion are only noticeable as a secondary contribution to the 
electrophoresis peak in an ELS spectrum because diffusion broadens the 
distribution in times required for sample particles to migrate roughly a 
wavelength of light while being forced through solution by an applied 
electric field. 
INTERFERENCE PHENOMENA AND THE PRINCIPLE OF BEATING 
Although in theory the Doppler shift produced by an electrophoresing 
particle could be detected directly, this shift is so small (about 100 Hz 
shift on a carrier frequency of about 10.sup.15 Hz) that no optical 
filters of sufficient resolution are available. The only practical way to 
detect the shift is by optically beating the Doppler-shifted scattered 
light with a portion of the original illuminating light. This situation 
can be analyzed by simply considering the simultaneous observation of 
light scattered from two particles: (1) the test particle which is moving 
under the influence of the electric field and might also be executing 
random Brownian movement or any other motion of interest; and (2) a 
stationary particle, referred to as the local oscillator, which might be 
rendered immobile by attachment to the wall of the sample chamber. Most of 
the important effects seen in light scattering experiments can be 
explained with the aid of this simple system. 
The oscillating electric field of the illuminating light forces the 
electron distributions of each of the molecules constituting these two 
model particles to oscillate slightly about their normal motion with 
respect to their associated atomic nucleii. In accordance with the 
classicial Drude model (The Theory of Optics, Longmans Green & Co., NY, 
1907), the frequency of the electrons' oscillations is the same as the 
driving frequency of the illuminating light seen in the rest frames of 
each particle; and the phase of the electrons' oscillations with respect 
to the light's electric field oscillations is determined by the proximity 
of the light's frequency to the resonance frequencies of the electrons 
(i.e., the absorption frequencies of the particles). These electron 
oscillations in turn cause the particles to appear as secondary sources 
radiating light of the same frequency as the incident light, although with 
amplitude and phase shift with respect to the illuminating light as 
prescribed by the particles' positions and constituent matter. 
If the two particles are separated by a distance d, then their far-field 
intensity pattern is a series of interference maxima and minima at 
scattering angles determined by the interparticle separation, d, and the 
wavelength of the light. The interference pattern is caused by the phase 
difference in the superposition of the oscillating electric fields 
emanating from the two particles. Maxima of the interference pattern are 
located at observation angles for which the distance the light travels 
from the source by way of one particle to the detector is precisely an 
integral number, m, of illuminant wavelengths greater than the distance 
from the source via the other particle to the detector: 
##EQU1## 
Suppose the test particle moves slightly farther away from the stationary 
local oscillator, perpendicular to the direction of the illumination. This 
increase in d, the interparticle spacing, causes a decrease in the angular 
separation of the far-field interference maxima and minima. Upon 
sufficient test particle motion, a photodetector originally placed to 
observe an interference maximum would be receiving a minimum of 
interference intensity due to the overall contraction of the interference 
pattern. Monitoring the photodetector's output discloses a regular 
sinusoidal oscillation in photocurrent with time as the test particle 
moves at constant velocity away from the local oscillator, and successive 
interference maxima and minima of scattered light intensity sweep across 
the photosensitive region of the detector. This oscillation of the 
detector's output can be exemplified in the photocurrent-versus-time plot. 
The frequency of photocurrent oscillation is identical to the Doppler 
shift appropriate for the test particle's velocity; but the stationary 
local oscillator is needed to achieve this scheme of "beating", or 
"heterodyning", the test particle's scattered light. Presence of the local 
oscillator converts the Doppler-shifted light of constant amplitude from 
the moving test particle into a total scattered light flux of varying 
intensity at the detector, indirectly rendering the miniscule Doppler 
shift detectable. 
A particle moving upwards cannot be distinguished from a particle moving 
downwards by the intereference method, because the signal modulation is 
generated simply by the particle going from positions producing scattering 
maxima to positions producing scattering minima for either direction of 
travel. However, direct determination of the Doppler shift would readily 
show an increased light frequency observed for a particle moving down 
toward the detector, but decreased frequency for a particle moving upward. 
The insensitivity of the "beating" method to the sign of direction of the 
observed particle's motion is called the Doppler ambiguity, from a similar 
problem encountered in radar applications. However, by shifting frequency 
of local oscillator, one can remove Doppler ambiguity. 
ANGULAR DEPENDENCE 
A detector receiving light scattered perpendicular to the illumination 
direction (.theta.-90.degree.) would observe an interference maximum 
replacing a minimum for .lambda./2 translation of the particle 
perpendicular to the illumination direction. But note that for the same 
detector placement to receive 90.degree. scattering, no change in 
interference intensity is observed for particle motion at 45.degree. to 
the illumination direction. This is because, for any scattering angle, the 
loci of points of equal optical path length from the illuminator's phase 
via the point of interest to the detector's phase front constitute lines 
(actually, planes in three-dimensional space) which bisect the scattering 
angle. Motions which carry a particle from one point to any other within 
the same plane of constant optical path length will not alter the relative 
phases of the scattered light intensity reaching the detector from the 
particle and the local oscillator. Only the component of particle motion 
perpendicular to these planes will cause modulation of the observed 
scattering intensity and result in a detectable signal change. If the test 
particle is originally in a plane causing an interference maximum at the 
detector, translocation of the particle by: 
##EQU2## 
(wherein .lambda. is the wave length and .theta. is the angle of scatter 
normal to the original plane) will carry the particle to the next plane 
for maximum scattering intensity and the signal at the detector will pass 
from a maximum through a minimum to another maximum as a result of such 
motion. The separation between planes of equal scattering intensity is 
determined only by the wavelength of the illuminant and by the scattering 
angle selected for observation by the arrangement of the detector with 
respect to the illumination beam, not by any properties of the scattering 
particles. This definition of scattering plane spacing is a statement of 
the effect known as the Bragg condition. 
The periodic spacing of these planes permits them to be succinctly 
characterized by a vector called the K-vector or scattering vector, whose 
amplitude is inversely proportional to the spacing of its associated 
planes and whose direction is normal to that set of planes: 
EQU K=(4.pi./.lambda.) sin (.theta./2)K 
where K is the unit vector directed normal to the planes. The K-vector is 
simply the difference between vectors describing the illuminating beam, 
k.sub.o, and scattered light, k.sub.s : 
EQU K=k.sub.o -k.sub.s 
whose directions coincide with the propagation directions of their 
respective light waves (i.e., normal to their respective wavefronts) and 
whose amplitudes are inversely proportional to their respective 
wavelengths: 
EQU k.sub.o =(2.pi./.lambda..sub.o)k.sub.o 
EQU k.sub.s =(2.pi./.lambda..sub.s)k.sub.s 
in the same fashion as the K-vector is defined by the wavelength (i.e., 
periodic spacing) and normal of its planes of equal scattering intensity. 
As mentioned earlier, the Doppler wavelength shift induced by 
electrophoresis of most sample particles is only one part in ten billion, 
so the wavelength of the scattered light is typically considered to be 
identical to the illuminant's wavelength for most purposes: 
EQU .lambda..sub.o .apprxeq..lambda..sub.s 
Since the illuminant and scattered light wavelengths and k-vector 
amplitudes are nearly equal, the amplitude of the K-vector is determined 
solely by the angular difference of the constituent light vectors which 
gives rise to sin (.theta./2) factor of Equation A. 
Diffusion 
In the above discussion, the test particle has been assumed to be moving at 
constant speed with respect to the local oscillator, so that the detected 
signal indicates intensity modulated at only a single frequency given by 
the appropriate Doppler shift. But in reality all matter possesses thermal 
energy which is manifested by submicron particles suspended in water as 
random Brownian motion. This diffusional motion superimposes a random walk 
on the persistent directed motion of an electrophoresing particle. An 
ensemble of electrophoresing particles initially located on one plane of 
maximum scattering intensity will require a distribution of times to reach 
the neighboring plane of maximum scattering intensity, resulting in a 
diffusion-broadened spectral peak at the Doppler shift. The peak width 
caused by diffusion exhibits an angular dependence proportional to the 
square of the amplitude of the scattering K-vector (K.sup.2 dependent) 
whereas the Doppler-induced peak shift is only linearly proportional to 
.vertline.K.vertline. (K dependent). Thus the analytical resolution of the 
technique may be improved, when diffusion is a significant contribution to 
the linewidth, by working at a lower scattering angle as suggested by Ware 
and Flygare. (Chem Phys. Lett. 12 81-83). 
Although these angular dependences can be derived mathematically, they are 
rationalized via the previous discussion of the scattering planes' 
separation. Diffusion is characterized by short, jerky motions in random 
directions which seldom carry the particle very far away from its starting 
position. Spectra obtained at small scattering angles (small 
.vertline.K.vertline., large plane spacing) respond primarily to the 
long-range directed motion of electrophoresis and are only slightly 
affected by the random Brownian motion. But at large scattering angles 
(large .vertline.K.vertline., small plane spacing), these random motions 
of diffusion are increasingly likely to carry a particle from one plane to 
the next, making the diffusion broadening larger in comparison to the 
electrophoretic Doppler shift. 
Sample Heterogeneity 
A sample may be heterogeneous in two important respects: (1) size 
(polydispersity); and (2) electrophoretic mobility. A polydisperse sample 
of small particles often exhibits peak broadening due to the dependence of 
electrophoretic mobility upon particle radius. A sample of large particles 
with identical surface charge densities may not show any direct evidence 
of polydispersity in a single ELS spectrum because all of the particles 
would be expected to electrophorese at the same velocity regardless of 
size. Comparison of ELS spectra collected at various angles often permits 
some inference about the behaviors of different-sized particles in a 
size-polydisperse sample, because particles much smaller than the 
illuminant's wavelength scatter an equal amount of light in all directions 
about the oscillation axis, whereas light scattered from different 
portions of a large particle will destructively interfere, causing the 
scattered intensity from large particles to taper off at higher scattering 
angles. 
The spectrum from an electrophoretically heterogeneous sample is a 
superposition of Lorentzians centered at various frequencies, 
corresponding to the electrophoretic mobilities of each of the sample 
particles. Due to the small diffusion coefficients of large particles such 
as blood cells, their ELS spectra can usually be interpreted as histograms 
of the cells' electrophoretic mobilities; and surface-charge-density 
polydispersity is the principal cause of peak width, rather than 
diffusion. If the difference in electrophoretic mobilities is insufficient 
to produce individually resolvable peaks, apportionment of a single 
inhomogeneously broadened peak into its constituent population 
contributions is exceedingly difficult. Measuring peak width for several 
scattering angles is a good test for deciding whether a peak is broadened 
by diffusion or by electrophoretic mobility dispersion since width due to 
the latter is linearly proportional to K (i.e., sin (.theta./2)). Also, a 
linear increase in peak width with greater applied electric field may be 
an indication of electrophoretic heterogeneity.

FIG. 1 illustrates electrophoretic apparatus 10 which comprises a laser 
light source 12, through a focussing lens 14 and a diffraction grating 17. 
The diffraction grating 17 is advantageously selected such that one of the 
second order light beams schematically illustrated as 18 is the more 
intense than the other light beams 19, 20, 21 and 22 which serve as local 
oscillators. The light leaving grating 17 is further focussed by an 
appropriate lens system 24 to collimate and focus the light. Lens system 
24 pair consists of two 50 mm F1.7 camera lens 24a and 24b. 
The diffraction grating 17 produces a second order light beam 18 which is 
more intense than each of the other four light beams (19, 20, 21 and 22). 
This second order beam (18) is called the main beam. The four other beams 
(19, 20, 21 and 22) are called reference beams and act as local 
oscillators (19, 20, 21 and 22). As described below, the main beam (18) 
passes into the sample cell (40) with an intensity four approximately 
orders of magnitude greater than each of the four reference beams (19, 20, 
21 and 22). As a consequence, most of the light scattered by particles in 
the sample cell (40) is scattered from the main beam (18). The light 
scattered from the main beam is what is measured. 
Each of the four reference beams (19, 20, 21 and 22) acts as a local 
oscillator against which the light scattered from the main beam (18) in 
the sample cell (40) is referenced. A grating 17 with 250 lines per mm is 
convenient. Such gratings are known in the art and may be purchased from a 
number of suppliers including the American Holographic company. 
A 4-beam attenuator 29, consisting of two polaroid sheets, is placed within 
lens system 24. It is used to produce a polarized light output which is, 
in a typical application, reduced to about 10.sup.-4 of the light incident 
thereon. The attenuator serves to adjust downwardly the intensity of 
oscillator beams with respect to the main reference beam. All beams have 
been maintained in strict coherence; thus the collimated light rays 
leaving lens array 24 may enter an electrophoresis sample cell module 40 
through a focusing lens 38 which is characterized by the ability to focus 
light over an annular range of 30 degrees with minimal spherical 
aberration. A component of the local oscillator beams will, of course, 
proceed directly through the center of cell module 40 and be used as the 
local oscillators, or reference beams. 
Thus each light beam is passed into photosensitive receptors such as 
photodiodes 52,54,56 and 58 of sensor array 50. 
Also illustrated in FIG. 2 is an optional frequency-shifter means 70 
comprising a stationary prism 72 and a moveable prism 74. Prism 74 is 
moved at a constant velocity, v, along a path such that the distance 
separating the wedges is maintained constant and very small. 
FIG. 3 illustrates sample cell 40 which is comprised of electrode-bearing 
member 102 electrode-bearing member 104 and the cell insert member 106. It 
is to be noted that member 106 should be formed of clear cast acrylic 
resin, ASTM D702. The electrophoretic sample-holding cell itself, i.e. 
aperture 108 of cell insert member 106 must be formed with the utmost 
attention to obtaining a smooth surface. Low-speed, optical polishing with 
rouge in a grease binder, with a reamer, or with a special buffing tool of 
the type known in the art is recommended. It has been found useful to 
apply kerosene during polishing for cooling during this finishing step. 
FIG. 4 is a top view of an electrode member 102 and FIG. 5 is a side view 
of this electrode member. The cell comprises electrode access taps 112 and 
114 and one of the brass electrodes-bearing members 102 comprises a sample 
tap 116. An O-ring fits in grooves 120 and helps provide a good sealing 
action when the disposable cell insert member 106 is clamped between 
electrode bearing members 102 and 104 by bolts, not shown, through bolt 
holes 124. 
FIGS. 6 and 7 show clean out or flush passages 128 which allow cleaning of 
electrodes and flushing of the cells. 
The cell 40 is readily disassembled and the cell insert member 106 is 
designed to facilitate replacement or refurbishment when this is 
practical. In this connection, it is noted that the interior surface of 
the aperture 108 of the cell 106 described herein is subject to an 
electro-osmotic effect whereby the walls of the tube attract oppositely 
charged ions. This charge will effect the attitude and geometry of 
particles being studied and will interfere, in many cases, with the 
electrophoretic measurements being carried out on the apparatus. In order 
to avoid, or much reduce, any effect on the measurements, the wall of the 
aperture 108 of cell insert member 106 are coated with means to minimize 
surface charge under the solution conditions to be used. One suitable 
coating material is methyl cellulose. 
Normally such coatings must be replaced frequently and this is one 
incentive for the construction of a disposable cell member. Proper coating 
of a cell many take several hours to several days. Thus referring again to 
FIG. 2, it is seen that electrode bearing members 102 and 104 may be 
readily separated from the cell insert member 106 which can then be 
quickly replaced with a pre-coated member without any substantial loss of 
operating time. 
It is to be understood that, in the illustrated 4-angle analysis of the 
scattered light wave fronts, it will be convenient to operate a 
1096-channel correlator as 4 simultaneous 256-channel correlators. 
In such a system, FIGS. 8 and 9, may be used to illustrate an 
electrophoretic operating program relating voltages to time. The voltage 
will be, typically, between 50 and 300 volts and vary on the 2-second on, 
one-second-off cycle of FIG. 8 and the run-hold cycle of FIG. 9. In a 
typical situation, the dT equals N.DELTA.T, wherein 
N=number of channels used in correlator analysis of a light sample 
component; (256 in a preferred mode) 
dT=0.256 seconds (typically) 
.DELTA.T=correlator sample time, say 10.sup.-3 seconds 
A typical analysis program, one standard in commercial apparatus, has the 
following components. 
1. It measures the correlation function g (tau), as a function of tau. (See 
FIG. 10). 
2. It analyizes via a Fourier transformation generating P (.omega.) as a 
function of .omega., (See FIG. 11) 
3. Thereupon .omega..sub.o and .DELTA..omega. are found by fitting 
Lorentzian curves 
##EQU3## 
to the curve of analysis item 2 above. The (.DELTA..omega.) is found for 4 
different scattering angles .theta.: 
##EQU4## 
B is a measure of diffusion of the sample. A is a measure of the 
polydispersity characteristics of the particles of the sample subjected to 
electrophoresis. A is related to the mobility characteristics and 
distribution of mobilities. It is related to both size and charge 
properties. 
Other approaches may be utilized in the assessment of the multiple wave 
fronts, but the subject approach is found to be adequate for most 
applications. 
.omega.=angular frequency, the characteristic variable of the power 
spectrum, P, resulting from the Fourier transformation of the 
autocorrelation function. 
.omega..sub.o =the central angular frequency shift due to the 
electrophoretic motion of the particles. 
.DELTA..omega.=the broadening (around the central frequency shift, 
.omega..sub.o) due to both diffusion and sample heterogeneity as discussed 
under the section herein on Diffusion and Sample Heterogeneity. 
P(.omega.)=the power spectrum of the scattered light as a function of 
angular frequency, i.e. the Fourier transformation of g(.tau.) 
It is also to be understood that the following claims are intended to cover 
all of the generic and specific features of the invention herein described 
and all statements of the scope of the invention which might be said to 
fall therebetween.