WO2013059360A1

WO2013059360A1 - Ultrasonic measurement of particle size distribution

Info

Publication number: WO2013059360A1
Application number: PCT/US2012/060667
Authority: WO
Inventors: Steven A. Africk; Clark K. Colton
Original assignee: Prodyne Corporation
Priority date: 2011-10-17
Filing date: 2012-10-17
Publication date: 2013-04-25

Abstract

A method and apparatus to measure the particle size distribution of particles in suspension provides generating an interrogating ultrasonic signal consisting of tone bursts of a defined frequency into a fluid suspension, wherein the fluid suspension is in motion or is caused to become in motion by the interrogating signal or other methods wherein induced particle velocity is a unique function of particle size; measuring the backscattered ultrasound from the interrogating signal; converting the backscattered ultrasound to a high resolution, backscattered spectrum represented by a narrow bin- width histogram in terms of the Doppler shift of frequency away from that of the interrogating signal; assigning a particle size to each bin of the spectrum by reference to a separately constructed calibration curve or relationship of particle size as a function of Doppler frequency shift; and transforming the value of the ordinate of each bin in the backscattered spectrum to a measure of the relative particle concentration in each bin by scaling using functions of the particle size associated with that bin and of the value of the ordinate of that bin to produce a particle size distribution relating the relative concentration of particles in suspension to particle size.

Description

This patent application describes apparatus and method for measuring particle size distribution using, as modified herein, the ultrasonic pulsed Doppler (USPD) apparatus and method described previously in US Patents No. 7,543,480, 7,844,405, and 7,984,642, Additional materials describing this apparatus and method are provided in the publication, Africk, S. A., Coiton, C.K., Dalzell, VVJI, Wu, D.T,, Albritton, j,L, Daum, L.R, "Ultrasonic Pulsed Doppler (USPD): A Backscaiter Technique for Characterization of Particles and

Nanoparticles. Non-invasive measurement of fluid flow velocity," in Robert Muratore, ed._f

12- 14. 2010, Cambridge. MA. pp. 1-7, 2010.

Reference is also made to the priority precursor of this application, U.S. provisional patent application Serial No. 61/547,836 filed October 17, 201 1. All these materials are incorporated herein by reference as though set out at length here, The full apparatus and method described and claimed herein enable measurement of size distribution of

monodisperse or polydisperse suspension of particles (including inorganic and organic particles) in a fluid suspension.

USPD is a system for the characterization of particles from the nano to micron scales suspended in fluids, it can also measure flows containing scattering objects including particles. Unlike other ultrasonic technologies, it can measure backscatter from particles and consequently in the majority of applications requires only a single transducer to launch the interrogating waves and to capture the scattered energy radiated hack to the transducer. The magnitude of the backscattered signals can be very small, with ampli tude varying as the cube of the particle radius, and their measurement is difficult. Therefore, it is commonly thought that use of backscattered energy in an ultrasonic particle measurement system is too difficult if not impossible for making useful measurements. The patents/publications cited above show apparatus and method overcoming these perceived limitations and enabling the use of ultrasonic backscatter to characterize a desired parameter, for example, particle concentration, particle size, viscosity of suspension, flow rate of suspension, etc., including, among others, in samples containing islets of Langerhans, cells, nanoparticles and the like. Some embodiments may use an interrogating signal itself to produce velocities and Doppier shifts. The processes of creating velocities of the particles and the fluid medium by forces on the particles and/or the suspending medium by the interrogating ultrasound will be referred to herein as

"streaming.^"' Signal processing methods that generate high resolution, very narrow bin-width backscatter pressure or power spectra, which may allow determination of detailed spectral shape of the baekscattered energy, makes possible measurement of, for example,

concentration by adding up the power in the spectra at Doppier shifted frequencies (separate from the main peak due to interrogating signals in the backscatter spectrum) representing the particles in motion, and particle size by measuring the velocities generated by streaming. For example, the velocities that can be induced by a given level of stirring or acoustical streaming depend on the viscosity of a sample. Likewise, under the influence of streaming alone, particles of different size may attain different velocities depending on particle interactions with the interrogating acoustic fields and/or differing particle drag coefficients. In such cases, the backscatter spectrum may includ one very sharp peak associated with monodisperse suspensions or a broad spectrum with one or more peaks associated with polydisper.se particle size distributions. It is an object of the invention to extend USPD apparatus and method capabilities to measure particle size distribution of monodisperse or poiydisperse particle samples in fluid suspension.

SUMMARY OF THE INVENTION

The object of measuring particle size distribution (PSD) is met by apparatus and method described below using relatively high levels of ultrasound and backscatter from moving particles to generate return signals at Doppler-shifted frequencies. The dynamic range and signal to noise ratio can be adequate for many measurements, including that of particles as small 10 nanometers or less.

The apparatus and method include features similar to those of the above cited patents but modified to include methods of signal acqui sition/processing and analysis that make use of the detailed information in the backscatter spectrum in order to determine the PSD of the particles in suspension. The modified method makes use of means to calibrate the USPD measurement system. Calibration consists of (1) measurement of the backscatter spectrum for a sample of particles in suspension; (2) measurement of the PSD by using independent means with a sample of particles that are the same as or sufficiently similar to the particl es examined in (1 ); (3) transformation of the PSD (using information about particle concentration and particle size contained in the PSD) to generate a distribution having the same relative shape as would be expected for the backscatter spectrum that would result from a US PD measurement of the same particles in suspension, termed the transformed PSD; (4) alignment of the measured backscatter spectrum with the scaled PSD using comparable numbers of bins; (5) identification of common, features in the measured backscatter spectrum and transformed PSD to enable associations between a specific particle size with a specific Doppler shift; (6) repetitions of this procedure with like particles spanning the size range in question; (7) Combining pairwise associations between particle size and frequency shift to establish an overall calibration curve relating particle size to Doppler frequency shift,

Likewise, a processing and analysis method is defined to extract particle size distribution from a measured US D backscatter spectrum. This consists of: (1 ) measurement of the backscattered spectrum expressed as a function of frequency of an unknown sample by USPD; (2) assignment of particle size to each bin of the USPD spectrum by reference to the previously constructed (or otherwise determined) calibration curve of particle size as a function of Doppler frequency shift; (3) conversion of USPD spectral pressure or power levels to relative particle concentrations by appropriate transfomiation in the inverse manner to that used for calibration, thereby generating a PSD for the sample. Steps (3) in the previous paragraph and in this paragraph require transformation of the particle size distribution in the calibration step and the backscatter spectra in the USPD measurement by functions of the particle concentration in each size increment and powers of the particle siz as described herein.

Without limiting the scope of utilization of the invention, it can be incorporated into compact instruments with onboard or outside electronics or placed within process equipment. It can be used with suspensions of fluid volumes in which induced motion by gravity, acoustic streaming, electrostatic or magnetic fields or other excitation lead to motion of particles, the velocity of which is a function of particle size, The particles in suspension can include virtually any type of particl capable of being suspended in a fluid, for example, dendrimers, carbon nanotubes, colloids, micelles, Inkjet or electronic magnetic inks, drugs, living cells, food additives, alloying agents, crystallization growth inducers or inhibitors, catalysts, probing agents detectable by external radiation monitoring, and slurries used in semiconductor fabrication,

There is also a need to provide, on a stand-alone basis or complementing the above capabilities, a determination of particle size distribution as a research tool and for industrial process quality assurance and/or control it is an object of the present invention to provide such further capability,

important advantages of such apparatus and methods over existing ultrasonic measurement technologies include the ability to measure very small samples (because the bulk of the backscattered signals originate in a small focal zone in front of the transducer), the lack of a requirement for a special well-calibrated vessel in which to make the measurement, and the ability to incorporate a single USPD transducer into almost any vessel. It can thus be used in an on-line real time measurement system with existing equipment. It has advantages over optical systems including the ability to work with opaque (e.g. non-dilute) samples and to also measure particle mechanical properties such as density and compressibility.

Other objects, features, and advantages will be apparent from the following detailed description of preferred embodiments taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTIONS OF DRAWINGS

Figure 1 shows in schematic form an embodiment of a representative hardware and signal extraction and analysis system of a measuring apparatus to perform the measurement method in batch mode in a test cell.

Figure 2 shows in schematic form the application of the system to a suspension flowing in a conduit with the transducer in contact with the fluid or outside the vessel in which the flow is taking place, in a preferred mode, the transducer is oriented perpendicular to the direction of flow.

Figure 3 shows an individual USPD spectrum of backscattered pressure vs. frequency from a particle suspension generated by taking the Fast Fourier Transfomi (FFT) of the backscattered signal resulting from the imposition of a 40-msec long series of 50-cycle, 16-Mhz tone bursts separated by 7 usee. The resulting Fourier transform of this 40-msec time- domain signal is a power spectrum with 25 Hz bin width. This bin width is fractionally very small for signals with base frequencies in the Megahertz range, and it is deemed a high resolution power spectrum because it samples the spectra at a large number of finely spaced bins. While power spectra describe backscattered acoustic power, this spectrum has been s

converted to backscattered pressure by taking the square root of the power spectrum on a bin- by- bin basis. Many individual spectra of this type can be averaged to compute a smoother spectrum.

Figure 4 shows the left-hand side of an averaged USPD pressure spectrum for (nominal) 60 nm PS-COOH particles after LHS-RHS processing to remove noise.

Figure 5 show particle size distribution for (nominal) 60 nni Bangs Laboratories PS- COOH particles with images obtained by ΊΈΜ and analyzed using NiH~p.romujgated ImageJ particle counting software;

Figure 6 is the transformed TEM-derived PSD which has the same relative shape as the USPD backscatter pressure spectrum "expected" for Bangs Laboratories 60 nm PS-COOH particles based on the measured TEM PSD. This "expected" spectrum is formed by multiplying the particle number in each histogram bin by the cube of the average radius of the particles in that bin and dividing by the square root of the number of particles in that bin to correct for the efficiency of scattering due to particle size according to the Rayieigh scattering expression in the long wavelength limit.

Figure 7 shows correspondence of features between the transformed PSD derived from TEM and the USPD backscatter pressure spectrum for one particular sample of PS- COOH particles as determined herein.

Figure 8 shows the calibration curve between particle size and Doppler shift determined on the basis of comparison of the transformed TEM PSD and measured USPD backscatter spectrum over a range of particle sizes, the solid line therein being a power law fit relating particle size to USPD Doppler frequency shift.

Figure 9 shows USPD backscatter pressure spectrum for a mixture of nominal 24, 45. and 96 nm samples (each of which is actually polydisperse).

Figure 10 shows USPD-derived particle size distribution for the mixture of 24, 45 and 98 nm sample obtained from the backscatter pressure spectrum by utilizing the calibration curve in Figure 8 to identify the particle sizes in each frequency bin, followed by division of the backscattered pressure by the cube of these sizes to convert backscattered pressure to square root of relative particle number in each bin, followed by squaring of the ordinate value.

Figure 11 shows particle size distribution measured by image analysis with Image J of TEM images of the sample used in Figures 9 and 10. Figures 1 and 2 show generally the apparatus subject matter of our related U.S. patent 7,984,642 issued July 26, 201 1 previously and published February 4, 2010 (U.S. publication US2010/00317535 A 1), and reference is made to the '642 patent, incorporated herein by reference for details. That prior apparatus and method practiced thereby are modified as described below to achieve the purposes of this invention cited above.

The system of Figure 1 comprises a signal generator 101 for producing a series of narrow band electronic tone bursts to form an interrogating signal. A power amplifier 102 is provided to increase voltage of the interrogating signal if required. This signal is fed to a transducer 105 which generates ultrasonic pressure waves in the fluid consisting of narrow tone bursts. These waves cause the particle and fluids to flow by acoustic streaming and are also scattered by the particles to generate backscattered ultrasonic waves containing information about the particles. The backscattered ultrasonic waves from the suspended particles are detected by said transducer and an electronic signal consisting of the

interrogating pulses and the backscattered signal (separated in time) is fed to a pulser receiver 103 that provides gain to amplify the transducer signal and to limit the overall voltage to condition it for insertion into an analysis component (e.g. a deep memory oscilloscope) 104, or other processing device, that digitizes the incoming signals and performs Fourier

Transforms ( e.g. by FFT) to generate power spectra, to store individual power spectra, and to average them to generate an average power spectrum. Subsequent data analysis, including conversion of the spectra to particle suspension characteristics including particle size distribution, concentration, and mechanical properties, and display of results are provided by a processor (e.g. computer, iPad, smartphone) 1 15.

A fluid sample containing particles in an acrylic container insert 110 is embedded in chamber 1 13 (which includes a water jacket though which water at. constant temperature is pumped, exiting at outlet 1 1 1), for temperature control during batch measurement, when required, A magnetic stirring bar 107 located in the fluid suspension is driven by an electromagnetic stirring motor 108 to create motion of the suspension and hence of the particles therein when induction of such externally-driven motion is desired, e.g., for measurement of particle concentration. The transducer 105 is inserted into the chamber through a hole sealed with an o-ring.

Figure 2 shows an embodiment of the transducer inserted into a conduit containing an external How of particles, as, for example in an industrial process including a flow pipe with a suspension flow therein, The transducer can be located outside the flow region and not in contact with the flow if it is in acoustic contact with the flow through an acoustic window. The external flow direction is indicated by the arrows 201 , A transducer 202 with an acoustic window 203 admits an interrogating acoustic wave beam 103 A at a target fluid volume 204. The electronics and processing devices are otherwise the same as in Figure I .

It is a further aspect of the present invention that the functionality described herein is also achievable with other functionality described in the '642 patent.

Measurement of backscattered energy from moving particles is preferred in the current invention because ultrasonic energy backscattered at frequencies other than the interrogating frequency is easier to detect than that at the same frequency. In the vessels containing the fluid there may be scattering or reflections from walls or other stationary structures that will be generated at the interrogating frequency and may be orders of magnitude greater than the backscattered waves, if these waves appear at times that overlap with those during which the backscattered waves from the particles appear, detection of the latter will be very difficult, if at ail possible. Likewise, there may be reileetions of the electronic signals at the interrogating frequency within the electronic system that overlap in time with the signal detected from the particles. These phenomena are referred to as "clutter" in radar and sonar applications.

However, when the backscattered energy is at frequencies that differ from that of the original interrogating signal, the detection is much easier because there will be no other energ present in the measurement system at these different (Doppler-shifted) frequencies, except for electronic or digitization noise which sets the lower limit of the dynamic range of the measurement. Consequently, weak backscatter from low concentrations of scattering particles as small as 10 or fewer nanometers may be measured in the presence of other signals such as strong wall reflections and electronic signals (including the interrogating signal itself), which may be many orders of magnitude stronger. This clutter-avoiding segregation of signals by frequency is intrinsic to Fourier analysis. In the application to determination of particle size distribution, it is the Doppler shifts resulting from velocities induced in the particles and fluid by acoustic streaming generated by the interrogating signal itself (or other applicable forcing functions) that allow this spectral separation of the backscattered energy from that of the interrogating signals.

Backscattered ultrasonic pressure waves (pressure vs. time) are incident on the transducer and are converted by it to electrical signals (voltage vs. time). By proper arrangement of the geometry of the measurement and time structure of the interrogating signal (pulse length and repetition rate), these electrical signals appear in the electronic signal sent to the pulser/receiver for amplification at times between the tone bursts comprising the interrogating signal. The entire signal received by the transducer (interrogating and backscattered parts) is amplified by the pulser/receiver, and the maximum voltage of the pulser/receiver output is limited to suppress the greatest values associated with the

interrogating signals to allow direct insertion of the signal into the oscilloscope. In the oscilloscope, the signal is digitized and then processed by a Fast Fourier Transform (FFT) to convert it from its time-domain, origin to a frequency domain power spectrum displaying acoustic (ultrasonic) power as a function of frequency in finite-width frequency bins. The width of these frequency bins is equal to the reciprocal of the time duration of the signal over which the FFT is taken. Spectra describing the backscattered pressure (rather than power) vs. frequency are computed by taking the square root of the pressure spectrum on a bin-by-bin basis,

When using embodiments of the present invention, backscatter from a suspension of particles may occur in a band of Doppler-shifted frequencies in the spectrum of the backscattered pressure, due in part to the distribution of velocities of the particles (or more precisely of the components of these velocities along the line between the scatterers and the transducer). The shape of the resulting power (or pressure) spectrum contains the information about the particles. For example, when particle velocities are driven, all or in part, by acoustic streaming, as in the present application, or by other means, the distri bution of energy as a function of Doppler frequency shift reflects the distribution of velocities of the particles and, because these velocities depend on particle size, the particle size distribution. For example, for monodisperse suspensions, there will be a single peak in the frequency spectrum, with the frequency of the backscattered peak indicating the single particle size; with increased polydispersity there will be a distribution over a range of frequencies with the energy peak corresponding to the largest number of particles and the width of the peak corresponding to the width of the distribution of particle sizes. In addition, a suspension of two distinct.

nionodisperse particles of different sizes will be represented by two distinct narrow peaks. The resolution of the measurement, system (the ability to deduce the existence of two distinct bu t similar particles sizes) will be a function of the narrowness of the analysis bin widths of the power or pressure spectrum. The ability to separate closely spaced spectral peaks (and resolve similar particle sizes) increases with decreasing bin width. Finally, for polydisperse suspensions there will be a broad range of frequencies detected. Methods to convert such spectra to particle size distribution are described below.

The foregoing apparatus and other like apparatus are adapted for calibrating the USPD system to enable measurement of particle size distribution of monodisperse or polydisperse suspensions of particles sizes ranging from below 10^" m to 10^" m and above. The USPD measurement system preferably includes a single transducer that interrogates a small volume of fluid (comparable to the focal zone of the transducer) diat is simultaneously set into motion by an external force (e.g., stirring, process flow), and/or by the USPD interrogating signal itself by acoustic streaming, If all of the particles move uniformly with the streaming-induced velocity associated with the adjacent fluid, the frequency of the backscattered energy would be shifted as a result of the Doppler effect relative to that of the interrogating signal by a single value. However, with polydisperse particles in suspension, a variety of Doppler shifted frequencies appear, representing the velocities determined by their size distribution. The apparatus and method described herein provides a means to establish a one-to-one correlation between (1) Doppler frequency shifts indicated by USPD backscattered spectral features and (2) particle sizes and a procedure for construction of particle size distribution from the USPD backscatter spectra. Such calibrations may be specific for certain particle types or may apply to a variety of particle types, depending upon the similarity of their physical properties, including density and compressibility. Other means to induce particle motion with velocities determined by their size (e.g. gravitational settling) can also be used.

For example, the interrogation system can comprise a single transducer with a focused beam such that there is a small focal zone with a volume on the order of less than 1 mm³ situated, e.g., 1 to 2 mm from the transducer, in which zone the incident acoustic pressure and intensity are greatest. Particles within this zone are simultaneously accelerated by the interroga ting signal to velocities determined by particle diameter and create the bulk of the back-scattered signal received by the transducer. These velocities result from a combination of factors herein included in the term "streaming", including the velocity of the fluid excited into motion by the interrogating signal and the velocities imparted to the particles through forces generated on the particles by the interrogating signal, viscous drag, and possibly other forces. In a typical example, the interrogating signal consists of a 40~ms long series of tone bursts at 16 Mhz, 30 -50 cycles long, with each tone burst separated by 7 μβ. The backscattered signal received at the transducer as acoustic (ultrasound) pressure as a function of time is sent to a Fast Fourier Transform (FFT) or similar processing algorithm to produce a high resolution power spectrum in the frequency domain. By high resolution is meant that the frequency bin width of the backscatter spectrum, is small relative to the frequency range over which the backscattered signal extends so that there are many individual bins over the range associated with the velocities imparted to the particles. With a large number of narrow bins, it is possible to capture the details of the backscatter spectrum containing the information about the particles. In the examples described below, backscattered acoustic power (or pressure) is plotted as a function of the Doppler frequency shift away from the frequency of the incident interrogating signal, expressed in a histogram with frequency bins of width 25 Hz, (Bin width is the reciprocal of the length of the analyzed signal, in this example 40 s so that bin width equals 1/40 msec = 25 Hz.) Longer or shorter signals can provide a higher or lower resolution (e.g. a 1 -see signal can provide 1 Hz bin width). The present invention encompasses any bin width, for example, bin widths of from less than 1 Hz to 50 Hz or more. Typically, bin widths of 25 Hz are used in the example described here although bin widths as small as 1 Hz have also been used. The resolution of particle sizing varies inversely with bin width.

The backscattered spectra can also be represented by a continuous function constructed by, for example, fitting the ordinate values to an analytical function representing ultrasonic spectral level (backscatter pressure or backscatter power) as a function of backscatter frequency.

individual power spectra of the backscattered signal are computed for each 40-ms train of tone bursts in this example. Spectra from a number of these 40-ms trains are then averaged to obtain a smoother average spectrum. Typically, 250 individual spectra are combined in this fashion, but thousands may be required to obtain a representative average spectrum, depending on the signal to noise ratio and other factors. Pressure spectra can be formed by taking the square root of the power spectra on a bin-by-bin basis. An example of an individual pressure spectrum is shown in Figure 3, It represents the backscatter generated by all of the 16 Mhz tone bursts in one 40-ms train. The level in the main peak, which is centered at bin zero, is the (square root of) the power of the tone bursts in the interrogating signal. This energy at the interrogation frequency is not excluded from the measured spectra although in principle it could be by, for example, time gating out of the tone bursts before digitization or numerically zeroing out the signal at times con-esponding to the tone hursts at the transducer post-digitization. The bin at the center of this peak is herein referred to as bin number zero with bins to the left and right referred to by negative and positive integers. The left and right sides of the spectrum represent negative and positive DoppJer shifts due to velocities away from and toward the transducer. The bins on the left and right sides are numbered with negative and positive integers respectively.

The left-hand-side in Figure 3 has peaks at around bins -8 and -13 (and possibly at -5) that represent backscattered energy from particles moving away from the transducer with Doppier shifts of 200 and 325 (and possibly 125 Hz) and that correspond to velocities on the order of 0.9 and 1 .5 (and possibly 0.6) cm/sec according to the relationship between velocity and Doppier frequency shift Δί, which for the case of backscatter is where v is the particle velocity and <¾ is the speed of sound in the fluid. There are two equal shifts involved, that which reduces the frequency at which the particle is excited by the interrogating signal and the other due to the motion of the particle relative to the transducer in the backscatter direction. The jagged parts of the curve at about 2 mPa are due to electronic noise in the measurement system and digitization noise due io use of an eight-bit AID conversion in this example. Lower noise should be possible with quieter instrumentation and A/D processing with greater bit. resolution.

An example average pressure spectrum for a sample of carboxylated polystyrene particles claimed by their man facturer, Bangs Laboratories, to be monodisperse at 60 run is shown in Figure 4 with average backscatter pressure plotted in a frequency bin histogram, The graph represents the average over 1000 individual spectra, with one additional step: The pressure levels appearing in the bins on the right hand side of the spectrum have been subtracted binwise from their symmetrical counterparts on the left hand side (i.e., the level at bin 5 is subtracted from that originally measured at bin -5), This optional technique (referred to as LHS-RHS) presumes that the pressures or powers in bins to the right of the main peak represent system noise, so that by subtracting these values from the levels in the

symmetrically equivalent bins on the left side, the resulting levels will have enhanced signal- to-noise ratios. This technique can cause bins far to the left of the main peak to stand out, thereby emphasizing the contributions to the spectra by very small particles. There is a peak of back-scattered power at bin -9 that represents a Doppler shift of 225 Hz below the interrogating frequency of 16 Mhz and corresponds to a velocity of 1.1 cm/see. This spectrum has a single broad peak, suggesting that there is a wide distri bution of particle sizes about the size represented by the peak. There are also smaller secondary peaks around bins - 29, -33 and -39, indicating the possible presence of particles of additional sizes. As described below, in the long wavelength limit where particle size is very small compared to the acoustic wavelength, the scattered power is proportional to particle radius to the sixth power. Because of this strong variation, the lower backscatiered pressures in these large Doppler shift bins (representing smaller particles) do not necessarily represent fewer particles than are indicated by the larger peaks at smaller frequency shifts, which represent larger particles that are more efficient scatterers.

Calibration for a specific class of particles is carried out by comparing backscatter spectra of USPD with independent measures of particle size distribution modified to predict the relative shape of the spectra that would be expected if measured by USPD. This can be done by, e.g., employing an independent determination of particle size using a reliable method to establish the size distribution of a sample or beginning with a particle sample whose particle size distribution is known a priori by any other method, In the example shown here, transmission electron microscopy (TEM) was used for this purpose. Any other method that can provide accurate independent size distributions can also be used.

This technique described herein consists of combining USPD backscatter

measurements and independent PSD measurements made with one or more suspensions having particles that collectively cover a wide size range, i.e., the size range of interest, to develop a calibration curve relating Doppler frequency shift to particle diameter, in one embodiment, a preparation of a single sample particle suspension is divided into two parts, one each for TEM and USPD backscatter measurements. Sample preparation can include vortexing and sonication to minimize particle aggregation. One part of the so-prepared sample is then measured with USPD and spectra are computed as described above. The other part is appropriately prepared and imaged by TEM (or like technique). TEM photographs are processed by image analysis using, for example, ImageJ, public domain software developed at the US National Institutes of Health, to provide a reliable particle size distribution. An example TEM-determined size distribution for nominal 60 m PS-COOH particles from Bangs Laboratories, generated by ImageJ from the same sample that gave rise to the backscattered power spectrum in Figure 4, is shown in Figure 5, This histogram reveals particles at all diameters from 12 to 78 nm with a broad maximum centered at about 60 nm and a secondary peak of smaller particles around 12 nrn.

The TEM data can also be converted to a continuous function by, for example, fitting the particle count data to an analytical function.

An important additional step is required to relate an independently measured sample PSD to a USPD backscatter spectrum because the latter represents the backscattered power and not the particle size distribution, In order to perform this comparison, the TEM-derived PSD must be converted to a. transformed distribution that has the same relative shape as the backsca ttered spectrum that would be "expected" if the sample analyzed by TEM was suspended and subjected to USPD as described herein, The relationship between the number of panicles and the backscattered power is derived as follows. Under the assumptions of incoherent scattering from particles very small with respect to the wavelength of the incident pressure wave, the backscattered intensity I (proportional to power) from a sample is proportional to the number of particles N per unit volume and the square of the backscatter form factor Φ. The latter parameter is given by Eq. (2), which is the Rayieigh expression for scattering from a particle in the long wavelength limit in which particle size is very much smaller than the wavelength of the interrogating signal,

wherein

r is the distance from the transducer to the focal volume in which the backscatter from the particles originates,

i is the incident plane wave,

s is the radially scattered wave,

ko is the wavers umber of the incident wave = ω/co, Co is the speed of sound in the suspending medium,

a is the particle radius,

Ko and ι are the compressibilities of the medium and the particle, respectively, and po and p_¾ are the densities of the medium and the particle, respectively.

Θ is the angle of the scattered signal referenced to the direction of incidence.

For backscatter, Θ = 180° and cose ^:::: -.1. While the preferred embodiment of the invention is measurement of the backscattered signal with the same transducer that provides the interrogating signal, measurement of the scattered signal at other angles by one or more other transducers is also included in the invention. For scattering at an arbitrary angle, the Doppler shift (for small values of v/c) is given by Af/f ^::- (cosO ···· l)v/c, and the velocity in the direction of motion is calculated from the Doppler shift by v =c(Af/f}/ (cosG - 1).

Because the form factor is proportional to the cube of the particle radius a, the intensity (or power) is proportional to the sixth power of radius:

Furthermore, tlie backscatter pressure P is proportional to the square root of the intensity.

Consequently, the expected backscattered pressure is proportional to the square root of the number of particles per unit volume and the cube of the particle radius, in a PSD, the ordinate of the histogram is the number of particles N in the volume represented by each size increment. Therefore to transform the PSD so that it gives the expected relative shape of the backscattered pressure spectrum that would be measured, the ordinate must be multiplied by a' / ^1,2. To transform the PSD so that it gives the expected shape of the backscattered power spectral density, the ordinate must be multiplied by a⁶.

For a PSD in the form of a histogram with bins representing the increment of particle radii (or diameter), the transformed PSD is obtained by multiplying the number in each histogram bin by the cube of the measure of particle size represented by that bin and di viding by the square root of the number of particles in that bin.

The result of the conversion of the TEM-derived PSD histogram in Figure 5 to a transformed distribution having the shape of the "expected" baekscatter pressure spectrum is shown in Figure 6. The general shape of the transformed PSD differs from the measured PSD in Figure 5 because the levels for the larger particles are increased relative to those of the smaller ones due to the multiplication by a³. As a result, the peak region of the distribution has shifted over by one bin and the levels associated with the smaller particles are suppressed, although evidence for particles all the way down to very small size remains visible in the iransforrned PSD. This stresses the need to pay attention to small peaks in the USPD spectra at all, especially large, Doppler shifts because they can represent significant numbers of small, weakly scattering, particles.

The resulting transformed PSD reflecting the expected baekscatter pressure spectrum (Figure 6) can then be compared directly with the measured USPD baekscatter pressure spectrum (Figure 4) in order to establish the relationship between Doppler frequency shift and partic le size. The comparison consists of identification of common features in both curves and association of a corresponding particle size with the Doppler shift at these features. This is facilitated by plotting PSD histograms in bin widths chosen so as to provide shapes

comparable to the USPD spectra.

The same methodology of identifying common features in both curves and

association of corresponding particle size with Doppler shift, can be carried out analytically if both measured spectra and TEM values are converted to continuous functions.

Continuing with the example above, this comparison produces several correlations summarized in Table I and plotted on Figure 8 relating particle diameter to USPD Doppler shift. Table Ϊ: Correspondences between transformed TEM-derived PSD and measured

USPD backscattered specterum in Figures 4 and 6, resepectively.

USPD: Bins to the Left of the Main Peak

12.5

67,5 9

70 8

7.5

Full calibration for a specific type of particle over a wide range of sizes may require repeating this process with several samples of particles that collectively span the full range, in this way a calibration curve relating Doppler shift to particle size can be constructed extending over a wide range of particle sizes. This curve allows identification of particle size associated with each frequency bin in a USPD backscatter measurement. A calibration curve using carboxylated polystyrene beads from 10 to 100 run is shown in Figure 8. This curve was generated by combining results from 5 samples (the 60 nm from Bangs Laboratories and four others) of beads from two manufacturers with different particle size distributions that together span the range shown. Each symbol in Figure 8 represents a Doppler shift/particle diameter combination derived from associating features on the transformed PSD and

measured backscattered pressure spectra, This type of calibration curve forms the basis for measurement of particle size distribution for future samples of similar particles.

While each USPD frequency bin represents a range of Doppler shifts and particles sizes, this method assigns a single size to each bin that is representative of the range of sizes within the finite bandwidth bins. The smaller the spectra) bin width the better the precision of the size determination by this method.

Fits of analytical expressions to this empirical data can be generated by nonlinear regression for future use. For example, the best fit relating USPD bin number (B) away (to the left) from the main peak as a power law function of particle diameter is

Equation (5) is shown as the smooth curve in Figure 8, Inversion to give diameter as a function of USPD bin number yields

This calibration curve was constructed for polystyrene-COOH beads, The same process can be repeated for other particle types. It is possible that the calibration curve

constructed with polystyrene-COOH beads applies to other types of particles with similar or different properties, especially similar particle density and compressibility, all of which are wi thin the scope of this invention.

Once a calibration curve is constructed, the opposite procedure and the subject application of USPD technology— estimation of particle size distribution from a measured USPD backscattered spectrum— is possible. This operation begins by using the calibration curve to assign a particle diameter to each frequency bin in the USPD spectruin. The spectral pressure associated with each bin in the measured backseatter spectrum is then divided by the 3^!d power of the diameter associated with that bin to produce a plot of the square root of the relative number of particles as a function of size. Squaring the ordinate removes the square root and produces a conventional PSD histogram of number of particles in each size bin. Alternatively, the power spectra can be used instead of the linear pressure estimates, in which case the power levels are divided by a⁽' (determined in the same way bin by bin by reference to the calibration curve) to estimate relative numbers of particles,

if the measured power spectrum is expressed as a continuous function in the form Π = ri(f) and the calibration curve is expressed as continuous functions f = f(a), where f and a are frequency and particle radius, a contmous function representing relative numbers of particles as a function of radius can be constructed by the analytical transformation Π =II(f(a))/a⁰. If the backseatter spectrum is expressed in terms of pressure, P(f), the rela tive particle distribution can be constructed by the transformation [P(f(a))./a³]²

This particle sizing procedure is demonstrated by the following example. A sample containing a mixture of 24-, 45-, and 96-nm nominal diameter PS-COOH particles (each claimed [inaccurately] as monodisperse by the manufacturer) in the ratio of 1 :5:45 by volume was prepared. This sample was then split into two parts which were respectively evaluated by TEM using IMAGEJ software and measured by USPD as described above. The USPD backseatter pressure spectrum was converted to PSD by use of the calibration curve to determine the size associated wit each frequency bin, then performing the transformation algorithm consisting of dividing by the diameter cubed and squaring the ordinate,

The USPD baekscatter power spectrum for this sample is shown in Figure 9 and its conversion to PSD is shown in Figure 10. The latter has peaks around 12 nm, 14-15 rim, and 37.5 nm. 1 he first two peaks demonstrate that small contributions in bins far from the main peak (corresponding to smaller, weakly scattering particles) can be revealed once converted to PSD by the calibration. The peak in the derived PSD curve at 37.5 nm does not correspond to the peak in the USPD curve at 9 bins removed from the main peak, which corresponds to 55 nm. This difference is brought about by the bin-by-bin scaling, which involves division of the USPD backseat tered pressure by the factor of a^J. It illustrates that the particle size associated with a peak in the USPD spectrum does not necessarily coincide with the peak in the derived PSD.

A TEM-derived measurement of the PSD for this sample is shown in Figure 1 1. It is a good match to the USPD-derived PSD in Figure 10 below about 70 nm. The TEM-derived peak near 16 nm agrees wed with the second USPD-derived peak. The main peak on the TEM curve is at 32 nm, which agrees reasonably well with the USPD peak at. 37,5 nm.

The USPD-derived PSD also indicates a peak around 12 nm that does not exist on the TEM-derived PSD for this sample because particles as small as this size were not included in the TEM imaging of this sample, The calibration curve data at these small diameters were based on other comparisons using TEM measurements for 24 nm Magsphere and 60 nm

Bangs nominal sized particles that did include particles of this small size. US PD appears to provide greater information at the low end of the size dis tribution, but this part of the range has not been examined in great detail.

The USPD-determined PSD does not show all the particles in the range above about 70 nm. This limitation comes about because the data pertaining to these relatively large particles resides in USPD frequency bins that are closest to the main peak and it is difficult to separate the spectral features from the main peak when they are this close to it. This limitation is specific to the experiments and equipment described in the example and is not inherent to particle sizing with USPD. The upper limit will be increased if the main peak can be removed so that power in bins close to the main peak can better represent baekscatter from large and slow moving particles instead of energy in the interrogating signal, This can be accomplished by time gating out the interrogating signal from the electronic analysis or zeroing that part of the digitized signal known due to its timing to be due to the interrogating signal. Alternatively, higher power can be used, which may increase the velocities and shift the curves to the left and away from the main peak.

The resolution of the PSD determined from USPD backscatter measurements is essentially the difference between the sizes represented by contiguous frequency bins in the backscatter spectra, For uniform bin widths, the frequency difference is just the bin width. While the bin width is constant across the backscatter spectrum, the particle size differences between contiguous bins varies with the size because the number of bins per nm varies with the slope of the calibration curve, in Figure 8, for example, consider the smaller particle sizes w^fhere the slope is greatest. There are about 16 frequency bins between 10 and 20 run, providing an average resolution of 1.6 nm/bin. Resolution changes uniformly to about 5 nm/bin in the 50 nm range and close to 10 nm/bin near 70 ran diameter.

More generally, the resolution in the example shown can be represented by the differential form of equation 6

so that, for example, for bin 17 (corresponding to 28 nm), a one bin difference corresponds to ΔΒ =1 , B = 17, so thai Ad/d = 6% difference in diameter, or 1.7 nm.

One embodiment of the present invention provides a method to measure the particle size distribution of particles in suspension comprising the steps of: (1) generating, from a transducer, an interrogating ultrasonic signal consisting of tone bursts of a defined frequency into a fluid suspension, wherein the fluid suspension is in motion or is caused to become in motion by the interrogating signal or other methods wherein induced particle velocity is a unique function of particle size; (2) measuring the backscattered ultrasound from the interrogating signal; (3} converting the

backscattered ultrasound to a high resolution , backscattered spectrum represented by a narrow bin-width histogram in terms of the Dopp!er shift of frequency away from that of the interrogating signal; (4) assigning a particle size to each bin of the spectrum by reference to a separately constructed calibration curve or relationship of particle size as a function of Doppler frequency shift; and (5) transforming the value of the ordinate of each bin in the backscattered spectrum to a measure of the relative particle concentration in each bin by scaling using functions of the particle size associated with that bin and of the value of the ordinate of that bin to produce a particle size distribution relating the relative concentration of particles in suspension to particle size.

The method backscattered spectrum and particle size distributions may be converted to continuous functions. The backscattered spectrum may be expressed in terms of backscattered pressure, and the transforming procedure may comprise dividing the value of the ordinate (backscattered pressure] of each bin by the cube of the particle size associated with that bin to produce a value proportional to the square root of the number of particles in that bin and squaring its value so that it is proportional to the number of particles in that bin to produce a particle size distribution. The

backscattered spectrum may be expressed in terms of backscattered power; and the transforming procedure comprises dividing the value of the ordinate (backscattered power] of each bin by the sixth power of the particle size associated with that bin to produce a value proportional to the number of particles in that bin to produce a particle size distribution.

The calibration curve may be constructed by combining ultrasound

backscattered measurements of particle samples in suspension with particle size distribution measurements of the same or similar particles obtained by using an independent measurement means comprising the steps of: (1] measuring the

backscattered spectrum for a first sample of particles in suspension; (2) measuring the particle size distribution with a second sample of particles that are the same or sufficiently similar to the particles of the first sample by using independent means and expressing the result as a histogram; (3) transforming the value of the ordinate of each histogram bin of the particle size distribution of the second sample by appropriate scaling using functions of the particle size associated with the bin and the number of particles in the bin; (4] alignment of the measured backscattered spectrum of the first sample with the transformed particle size distribution of the second sample; (5] identification of common features in the measured backscattered spectrum of the first sample and transformed particle size distribution of the second sample to enable associations between a specific particle size with a specific Doppler frequency shift; (6) repetition of steps (2) -(5) with like particles spanning a desired size range; and (7) combining pairwise associations between particle size and Doppler frequency shift to establish an overall calibration curve relating particle size to Doppler frequency shift The transformed value of the ordinate of the particle size distribution of the second sample ma be expressed as a measure of relative backscattered pressure; and the transforming procedure may comprise multiplying the value of the ordinate of each bin of the particle size distribution histogram by the cube of the particle size associated with that bin and dividing by the square root of the number of particles in that bin. The transformed value of the ordinate may be expressed as a measure of relative

backscattered power; and the transforming procedure comprises multiplying the value of the ordinate of each bin of the particle size distribution histogram by the sixth power of the particle size associated with that bin. The step of alignment may use a

backscattered spectrum of the first sample and a transformed particle size distribution of the second sample, each with a comparable number of bins. The transducer may be placed within, or in acoustic contact with, a conduit through which the suspension is flowing. The transducer may be aligned substantiall perpendicular to the direction of flow of the suspension.

The backscattered pressure or backscattered power spectrum may be modified by subtracting the values of the ordinate of each bin on the right side of the peak representing the interrogating signal from the value of the ordinate of the corresponding symmetrical bin, by number, on the left side of the interrogating signal to correct for background noise and presence of the interrogating signal. The backscattering from the particles may be measured by the same transducer, or at other than the backscatter direction by a transducer other than the one generating the interrogating signal.

Another embodiment of the present invention provides a system for measuring particle size distribution of particles in a suspension, the system comprising: a transducer to transmit an ultrasonic signal toward the particles and to receive a return signal reflected or backscattered from the particles; a processor to generate a

backscattered spectrum by processing the return signal to determine ordinate values for each of a plurality of frequency bins; wherein the processor includes means for transforming the value of the ordinate of each bin in the backscattered spectrum to a measure of the relative particle concentration in each bin by scaling using functions of the particle size associated with that bin determined by reference to a calibration curve and of the ordinate of that bin to produce a particle size distribution relating the relative concentration of particles in suspension to particle size.

The backscattered spectrum may be expressed in terms of backscattered pressure; and the means for transforming may comprise means for dividing the value of the ordinate (backscattered pressure) of each bin by the cube of the particle size associated with that bin to produce a value proportional to the square root of the number of particles in that bin and squaring that value so that it is proportional to the number of particles in that bin to produce a particle size distribution. The backscattered spectrum may be expressed in terms of backscattered power; and the means for transforming may comprise means for dividing the value of the ordinate (backscattered power) of each bin by the sixth power of the particle size associated with that bin to produce a value proportional to the number of particles in that bin to produce a particle size distribution, The means for constructing a calibration curve may include

independent means for measuring the particle size distribution with a sample of particles that are the same or sufficiently similar to the particles in suspension. The system may further comprise a system for constructing a calibration curve or relationship of particle size as a function of Doppler frequency shift,

The system for constructing a calibration curve may comprise; (1) means for measuring a return signal for a first sample using the transducer and for generating a backscattered spectrum from the return signal to determine ordinate values for each of a plurality of frequency bins using the processor; (2) independent means for measuring the particle size distribution with a second sample of particles that are the same or sufficiently similar to the particles of the first sample and expressing the result as a histogram; and (3) processor means for; (a) transforming the value of the ordinate of each histogram bin of the particle size distribution of the second sample by appropriate scaling using functions of the particle size associated with the bin and the number of particles in the bin; (b) aligning the measured backscattered spectrum of the first sample with the transformed particle size distribution of the second sample; (c) identifying common features in the measured backscattered spectrum of the first sample and transformed particle size distribution of the second sample to enable associations between a specific particle size with a specific Doppler frequency shift; (d) repetition of elements (3a) through (3c) with additional like particles spanning a desired size range; and (e) combining pairwise associations between particle size and Doppler frequency shift to establish an overall calibration curve relating particle size to Doppler frequency shift,

Yet another embodiment, of the present invention provides a system for constructing a calibration curve for measuring particle size distribution in a suspension, comprising: (1) a transducer to transmit an ultrasonic signal toward the particles in a first sample and to receive a return signal reflected or backscattered from the particles; (2) a processor to generate a backscattered spectrum for the first sample by processing the return signal to determine ordinate values for each of a plurality of frequency bins: (3) independent means for measuring the particle size distribution with a second sample of particles that are the same or sufficiently similar to the particles of the first sample and expressing the result as a histogram; and (4) processor means for: (a) transforming the value of the ordinate of each histogram bin of the particle size distribution of the second sample by appropriate scaling using functions of the particle size associated with the bin and the number of particles in the bin; (b) aligning the measured backscattered spectrum of the first sample with the transformed particle size distribution of the second sample; fc) identifying common features in the measured backscattered spectrum of the first sample and transformed particle size distribution of the second sample to enable associations between a specific particle size with a specific Doppler frequency shift; (d) repetition of elements (4a) through (4c) with additional like particles spanning a desired size range; and (e) combining pairwise associations between particle size and Doppler frequency shift to establish an overall calibration curve relating particle size to Doppler frequency shift

Claims

What is claimed is:

1. A method to measure the particle size distribution of particles in suspension comprising the steps of:

(1) generating, from a transducer, an interrogating ultrasonic signal consisting of tone bursts of a defined frequency into a fluid suspension, wherein the fluid suspension is in motion or is caused to become in motion by the interrogating signal or other methods wherein induced particle velocity is a unique function of particle size;

(2) measuring the backscattered ultrasound from the interrogating signal;

(3) converting the backscattered ultrasound to a high resolutio , backscattered spectrum represented by a narrow bin-width histogram in terms of the Doppier shift of frequency away from that of the interrogating signal;

(4) assigning a particle size to each bin of the spectrum by reference to a separately constructed calibration curve or relationship of particle size as a function of Doppier frequency shift; and

(5) transforming the value of the ordinate of each bin in the backscattered spectrum to a measure of the relative particle concentration in each bin b scaling using functions of the particle size associated with that bin and of the value of the ordinate of that bin to produce a particle size distribution relating the relative concentration of particles in suspension to particle size,

2. The method of claim 1, wherein the backscattered spectrum and particle size distributions are converted to continuous functions.

3. The method of claim 1, wherein:

(1) the backscattered spectrum is expressed in terms of backscattered pressure;

(2) the transforming procedure comprises dividing the value of the ordinate (backscattered pressure) of each bin by the cube of the particle size associated with that bin to produce a value proportional to the square root of the number of particles in that bin and squaring its value so that it is proportional to the number of particles in that bin to produce a particle size distribution.

4, The method of claim 1, wherein:

(1) the backscattered spectrum is expressed in terms of backscattered power; and

(2) the transforming procedure comprises dividing the value of the ordinate (backscattered power) of each bin by the sixth power of the particle size associated with that bin to produce a value proportional to the number of particles in that bin to produce a particle size distribution.

5. The method of claim 1, wherein the calibration curve is constructed by combining ultrasound backscattered measurements of particle samples in suspension with particle size distribution measurements of the same or similar particles obtained by using an independent measurement means comprising the steps of:

(1) measuring the backscattered spectrum for a first sample of particles in suspension;

(2) measuring the particle size distribution with a second sample of particles that are the same or sufficiently similar to the particles of the first sample by using independent means and expressing the result as a histogram;

(3) transforming the value of the ordinate of each histogram bin of the particle size distribution of the second sample by appropriate scaling using functions of the particle size associated with the bin and the number of particles in the bin;

(4) alignment of the measured backscattered spectrum of the first sample with the transformed particle size distribution of the second sample;

(5) identification of common features in the measured backscattered spectrum of the first sample and transformed particle size distribution of the second sample to enable associations between a specific particle size with a specific Doppler frequency shift;

(6) repetition of steps (2) -(5) with like particles spanning a desired size range; and

(7) combining pairwise associations between particle size and Doppler frequency shift to establish an overall calibration curve relating particle size to Doppler frequency shift

6. The method of claim 5, wherein:

(1) the transformed value of the ordinate of the particle size distribution of the second sample is expressed as a measure of relative backscattered pressure; and

(2) the transforming procedure comprises multiplying the value of the ordinate of each bin of the particle size distribution histogram by the cube of the particle size associated with that bin and dividing by the square root of the number of particles in that bin.

7. The method of claim 5, wherein;

(1) the transformed value of the ordinate is expressed as a measure of relative backscattered power; and

(2) the transforming procedure comprises multiplying the value of the ordinate of each bin of the particle size distribution histogram by the sixth power of the particle size associated with that bin.

8. The method of claim 5, wherein the step of alignment uses a backscattered spectrum of the first sample and a transformed particle size distribution of the second sample, each with a comparable number of bins.

9. The method of claim 1, wherein the transducer is placed within, or in acoustic contact with, a conduit through which the suspension is flowing.

10. The method of claim 9, wherein the transducer is aligned substantially perpendicular to the direction of flow of the suspension.

11. The method of claim 1, wherein the backscattered pressure or backscattered power spectrum is modified by subtracting the values of the ordinate of each bin on the right side of the peak representing the interrogating signal from the value of the ordinate of the corresponding symmetrical bin, by number, on the left side of the interrogating signal to correct, for background noise and presence of the interrogating signal.

12. The method of claim 1, wherein backscattering from the particles is measured by the same transducer, or at other than the backscatter direction by a transducer other than the one generating the interrogating signal.

13. A system for measuring particle size distribution of particles in a suspension, the system comprising;

a transducer to transmit an ultrasonic signal toward the particles and to receive a return signal reflected or backscattered from the particles;

a processor to generate a backscattered spectrum by processing the return signal to determine ordinate values for each of a plurality of frequency bins:

wherein the processor includes means for transforming the value of the ordinate of each bin in the backscattered spectrum to a measure of the relative particle concentration in each bin by scaling using functions of the particle sociated with that bin determined by reference to a calibration curve and of the ordinate of that bin to produce a particle size distribution relating the relative concentration of particles in suspension to particle size.

14. The system of claim 13, wherein:

(1) the backscattered spectrum is expressed in terms of backscattered pressure; and

(2) the means for transforming comprises means for dividing the value of the ordinate (backscattered pressure) of each bin by the cube of the particle size associated with that bin to produce a value proportional to the square root of the number of particles in that bin and squaring that value so that it is proportional to the number of particles in that bin to produce a particle size distribution.

15. The system of claim 13, wherein:

(2) the means for transforming comprises means for dividing the value of the ordinate (backscattered power] of each bin by the sixth power of the particle size associated with that bin to produce a value proportional to the number of particles in that bin to produce a particle size distribution,

16. The system of claim 13, wherein the means for constructing a calibration curve includes independent means for measuring the particle size distribution with a sample of particles that are the same or sufficiently similar to the particles in suspension,

17. The system of claim 13, further comprising a system for constructing a calibration curve or relationship of particle size as a function of Doppler frequency shift

18. The system of claim 17, wherein the system for constructing a calibration curve comprises:

(1) means for measuring a return signal for a first sample using the transducer and for generating a backscattered spectrum from the return signal to determine ordinate values for each of a plurality of frequency bins using the processor;

(2) independent means for measuring the particle size distribution with a second sample of particles that are the same or sufficiently similar to the particles of the first sample and expressing the result as a histogram; and

(3) processor means for:

(a) transforming the value of the ordinate of each histogram bin of the particle size distribution of the second sample by appropriate scaling using functions of the particle size associated with the bin and the number of particles in the bin;

(b) aligning the measured backscattered spectrum of the first sample with the transformed particle size distribution of the second sample;

(c) identifying common features in the measured backscattered spectrum of the first sample and transformed particle size distribution of the second sample to enable associations between a specific particle size with a specific Doppler frequency shift;

(d) repetition of elements (3a) through (3c) with additional like particles spanning a desired size range; and (e) combining pairwise associations between particle size and Doppler frequency shift to establish an overall calibration curve relating particle size to Doppler frequency shift.

19. A system for constructing a calibration curve for measuring particle size distribution in a suspension, comprising;

(1) a transducer to transmit an ultrasonic signal toward the particles in a first sample and to receive a return signal reflected or backscattered from the particles;

(2) a processor to generate a backscattered spectrum for the first sample by processing the return signal to determine ordinate values for each of a plurality of frequency bins:

(3) independent means for measuring the particle size distribution with a second sample of particles that are the same or sufficiently similar to the particles of the first sample and expressing the result as a histogram; and

(4) processor means for:

(d) repetition of elements (4a) through (4c) with additional like particles spanning a desired size range; and

(e) combining pairwise associations between particle size and Doppler frequency shift to establish an overall calibration curve relating particle size to Doppler frequency shift,