Abstract:
Two arrangements are disclosed to provide high resolution measurement of sub-micrometer and micrometer particle size distributions. In a first arrangement, scattered light is measured over a wide range of scattering angles. At the same time, light scattered at low scattering angles is measured with high angular resolution. In the second arrangement an improved Polarization Intensity Differential Scattering (PIDS) measurement is made possible by providing an interrogating light beam of selected wavelength including a first component parallel to the scattering plane and a second component perpendicular to the scattering plane. Photodetecting arrangements detect light scattered by the particles at least at two scattering angles.

Description:
BACKGROUND OF THE INVENTION 
     This invention relates generally to systems for measuring the size of particles, and, more particularly, relates to apparatus and methods for high resolution measurement of sub-micron and micron particle size distributions using polarization intensity differential scattering. 
     There are several prior art techniques for measuring the size and distribution of sizes of particles in a sample by using light scattering. Generally, to measure the sizes of individual particles, for example, in a flowing stream of a liquid or gas, the particle-containing sample stream is illuminated by a constant light source and the intensity of light scattered by each particle is detected. 
     A particle scatters the light by an amount related to the particle size. In general, larger particles scatter more light than do smaller particles. The relationship between the amount of scattering and particle size can be determined either from theoretical calculations or through a calibration process. With a knowledge of this relationship, for a single particle at a time, the detected scattered light intensity provides a direct measure of the particle size. 
     The distribution of particle sizes in a sample can be determined by individually passing each particle in the sample, or a portion of the sample, through the scattered light detection apparatus, and tabulating the sizes of the various particles. In practice, this method is generally restricted to particles larger than 0.5 microns. Moreover, this method is relatively slow, because particles must be presented and detected individually. This technique is referred to in the prior art as optical particle counting. 
     Another prior art technique of particle sizing by light scattering is referred to as static or &#34;classical&#34; light scattering. This method is based upon illumination of a sample containing the particles to be sized, followed by the measurement of the intensity of scattered light at several predetermined angles. The intensity of light scattered from a particle is a function of the size of the particle, the wavelength of incident light, and the angle at which the scattered light is collected relative to the incident light. This method of particle sizing based upon the angular dependence of the scattered light intensity can be employed to determine the size distribution of a group of particles. 
     In particular, for particles larger than approximately one micron, scattering in the near-forward direction is well described by Fraunhofer diffraction theory. The Fraunhofer principle yields the angular distribution of scattered light in the focal plane of a lens. For a given particle having a diameter d, the scattered intensity in the angular direction u is given by 
     I d , u =k 1  [(]d 2 )/4] 2  [2J 1  (k 2  du)/(k 2  du)] 2   
     where 
     k 1  =a constant; 
     k 2  =]g; and 
     cJ(k 2  du)/=a Bessel function 
     The Fraunhofer theory, upon which most conventional laser diffraction systems are based, shows that small particles diffract light at high angles while larger particles diffract light at smaller angles. Accordingly, by analyzing the composite diffraction pattern resulting from the scattering of monochromatic light beam by a given sample, and measuring the intensity of light scattered at predetermined angles, it is possible to deduce the size distribution of particles in the sample. This principle is widely used in laser diffraction methods and apparatus. 
     The following U.S. Pat. Nos. disclose examples of laser diffraction systems for measurement of particle size: 
     
         ______________________________________3,646,652          Bol et al3,758,787          Sigrist3,809,478          Talbot3,873,206          Willcock4,017,186          Shofner et al4,037,965          Weiss4,052,600          Wertheimer4,099,875          McMahon et al4,167,335          Williams4,274,741          Cornillault4,286,876          Hogg et al4,341,471          Hogg et al4,541,719          Wyatt4,595,291          Tatsuno4,648,715          Ford, Jr. et al4,676,641          Bott4,679,939          Curry______________________________________ 
    
     Certain prior art systems, among those disclosed in the above-identified U.S. Pat. Nos., utilize a single-optical-axis system, which may comprise a single lens or an assembly of lenses disposed along the same optical axis, for collecting forward scattered light--in a range of approximately 0.03-30.00 degrees from the axis of the incident beam--and directing the scattered light into 15-50 discrete detector cells, so that each detector cell is illuminated by light scattered from the particles at a particular scattering angle. 
     Other prior art systems utilize multiple collection lenses, disposed along different optical axes, the lenses being optically connected to a single photodetector via fiber optic or other optical coupling elements. 
     The configuration of a typical prior art laser diffraction instrument 110 for particle size analysis is illustrated in FIG. 1. The beam from a laser 112 is expanded by a conventional beam expander assembly 114, in order to cover a large number of particles in a sample and to reduce the divergence of the beam. This parallel beam then passes through the sample 116, typically a dispersion contained in a sample holder 118. The sample 116 can be stirred or pumped through the path of the laser beam in a re-circulation system, if the sample is a suspension or emulsion, or blown or sprayed through if the sample is a dry powder or spray. Light 122 scattered in the near-forward angles is collected by a Fourier transform lens configuration 120 and directed toward a multicell detector 124, arranged such that the position of a given particle in the path of the laser beam does not affect the point at which the light diffracted by that particle falls on the detector 124. 
     Discrete detector segments or cells on the detector 124 sense the intensity of light corresponding to that scattered at different angles to the incident beam. This intensity profile can be provided to a computer 126 where digital processing elements determine the size distribution of the particles passing through the laser beam. The computer 126 can be controlled by input from a keyboard 128, and can provide data output via a display unit 130 and printer 132. 
     Diffraction-type particle size measurement instruments are widely used for measuring sample materials having a broad size distribution--i.e., a wide size range--such as dust or pigment particles. Because large particles scatter light at small angles to the axis of an incident beam, and smaller particles scatter light at large angles, particle size measuring systems utilizing scattered light detection must be capable of measuring scattered light intensity over a large range of scattering angles. Additionally, because large particles scatter light at small angles, and relatively large changes in their size produce only small changes in scattering angles, it would be advantageous to measure light scattered at small angles with relatively high resolution. 
     These two requirements pose conflicting demands on a single Fourier transform lens or lens system, such as lens system 20 shown in FIG. 1. The result, in conventional diffraction instruments, is compromised performance at large angles, small angles, or both. 
     A limited range of measurement angles --approximately 20-60 degrees--can be achieved in a conventional diffraction system for measurement of particle size, using a single Fourier lens and multiple detectors. Alternatively, a wide range of measurement angles, with sparse coverage within the angular measurement range, can be attained with multiple detectors, each coupled with a single lens or system of apertures to define the scattering angle, or by moving a single detector successively to different scattering angles. Each of these approaches has been implemented in certain prior art devices, and each has significant limitations. 
     In particular, when a single-axis optical system is utilized for collecting scattered light over a wide angular range, a short focal length system can provide detection at large angles, at the cost of compressing low-angle scattered light near the optical axis, where it may be obscured by laser spill-over or rendered unresolvable by the finite size of detector segments. 
     When attempts are made to overcome these deficiencies by utilizing lenses of longer focal length, further problems arise, especially in measurement of scattered light at higher angles. In particular, the longitudinal displacement of high angle detectors from the optical axis can require large dimensions, resulting in a cumbersome instrument package. The required displacement (R) of detectors from the optical axis is approximately 
     R=[FL]tan [theta] 
     where 
     [FL]=focal length of the lens 
     [theta]=scattering angle in the sample cell. 
     In addition, such a system would require large diameter lenses for collecting light scattered at large angles, thereby increasing spherical aberration and astigmatism and complicating the positioning of high angle detectors. 
     Systems which utilize elements for moving a single detector successively to different scattering angles are typically limited by low angular resolution, long measurement times and mechanical complexity. 
     Accordingly, it is an object of the invention to provide methods and apparatus for analysis of particle size based upon measurement of scattered light, which enable the measurement of scattered light over wide angular ranges. 
     It is another object of the invention to provide methods and apparatus for measuring particle size with high angular resolution at low scattering angles. 
     It is a further object of the invention to provide particle size analysis apparatus which is compact and mechanically reliable. 
     Moreover, although diffraction apparatus can be utilized to measure particles in the 0.1-0.4 micrometers size range, the resolution of conventional methods in this size regime is poor. The loss of resolution is a consequence of the similarity in the angular pattern of scattered light of all particles which are smaller than, or roughly equal in size to, the wavelength of the illuminating light. Since the angular scattering patterns of all particles in this size range are similar, conventional methods are unable to reliably distinguish between particles in this size range. 
     Another method to measure the sizes of particles in this size range is based on a phenomenon involving the scattering by small particles of light of different polarizations. For particles smaller than the wavelength of the incident light, for scattering at 90 degrees to the direction of the interrogating beam, the light component having a polarization parallel to the scattering plane is scattered much less efficiently that light polarized parallel to the scattering plane. The scattering plane is defined herein as the plane containing the incident light beam and the line connecting the detector to the illuminated part of the sample. 
     This phenomenon, which is illustrated by the intensity vs. angle plot of FIG. 8, is due to the transverse nature of light. In particular, the electric and magnetic field oscillations which comprise a light beam oscillate in a direction perpendicular to the direction of propagation of the beam. 
     The difference in the observed intensity of 90 degree scattering light, for a first component of light polarized perpendicular to the scattering plane and a second component of light polarized parallel to the scattering plane, is referred to herein as polarization intensity differential scattering (PIDS). PIDS has been used to measure sizes of particles in the 0.1-0.4 micrometers size range, and can be explained with reference to FIG. 9. 
     The abscissa on the graph of FIG. 9 represents particle diameter normalized by the wavelength of light. More particularly, the abscissa is a variable conventionally called alpha, given by: 
     alpha=pi*d/lambda 
     where d is the Particle diameter, and lambda is the incident light wavelength in the medium surrounding the particles. The ordinate in the graph represents the photodetected PIDS signal per unit mass of particles. The PIDS signal, given by 
     PIDS=Iperpen,90-Ipara,90 
     is the unnormalized difference between the scattering intensity at 90 degrees for incident light polarized perpendicular and parallel to the scattering plane. 
     The wavelength normalized diameter, alpha, is used on the abscissa because all scattering phenomena are dependent on the ratio of particle size to light wavelength, rather than on size alone. Thus the solid line in FIG. 9 can, for example, represent PIDS in the size range of 100 to 1000 nm with light of wavelength 600 nm, or particles in the size range of 200 to 2000 nm with light of wavelength 1200 nm. 
     The large peak on the left hand side of the graph of FIG. 9 shows that the PIDS signal of particles below alpha=2 is the most significant source of PIDS. This means that that PIDS is sensitive principally to particles smaller than approximately 2/3 the wavelength of the incident light. If a series of PIDS measurements were made, each with light of a different incident light wavelength, a histogram of the particle size distribution could be produced as follows. The shortest wavelength PIDS measurement, for example, at 300 nm, would generally measure the mass of particles below approximately 200 nm. The next measurement might be made at lambda=600 nm. This measurement would be sensitive to particles smaller than approximately 400 nm. By subtracting the first measurement value from the second PIDS measurement value, the mass of particles in the 200-400 nm range could be determined. The third PIDS measurement might be made at 900 nm. By subtracting the second measurement value from the third measurement value, the mass of particles in the size range 400-600 nm would be determined. 
     This process could be extended indefinitely toward larger or smaller sizes, so long as sources of light of the proper wavelengths are available. In practice, however, conventional diffraction measurements are more suitable for particle sizing above around 1 micrometer and the absorption of UV light by quartz and silica limits the low range endpoint of wavelength to around 150 nm. 
     This conventional PIDS measurement technique, however, has several significant deficiencies relating to resolution and accuracy. In a measurement such as that described above, it has conventionally been assumed that the PIDS value at any wavelength is sensitive almost exclusively to particles below a certain size. However, the secondary, smaller peaks toward the right hand side of FIG. 9 show that conventional PIDS measurements have substantial response to particles over a range of sizes. Thus a PIDS measurement at, for example, a wavelength of 300 nm will actually be sensitive to a substantial portion of the mass of particles at sizes above 200 nm, with varying sensitivity to the various larger particles, as shown in FIG. 9. This lack of discrimination means that conventional PIDS measurements are subject to serious artifacts and inaccuracies. 
     A useful &#34;figure-of-merit&#34; (FOM) for evaluating the discrimination of a PIDS measurement is simply the ratio of the area under the curve in the major peak (small alpha value) to the total area under the first peak plus the areas under the subsequent smaller resonance peaks, typically out to five subsequent peaks. This FOM represents the ratio of the sensitivity to the particles of interest to the sensitivity to all particles--including those not of interest. A FOM of 1 would be ideal; a FOM of 0 would mean that the method had no particle sizing discrimination whatsoever. As can be seen from the FIG. 9, the FOM of the conventionally measured PIDS in FIG. 9 is approximately 0.3, indicating a low value of size discrimination. 
     It is thus a further object of the invention to provide PIDS apparatus and methods having enhanced particle size discrimination. 
     Other general and specific objects of the invention will in part be obvious and will in part appear hereinafter. 
     SUMMARY OF THE INVENTION 
     The foregoing objects are attained by the invention, which provides PIDS methods and apparatus for illuminating suspended particles in a sample cell along an interrogating axis with at least one interrogating light beam, having a selected wavelength, and including at least a first component polarized parallel to a scattering plane and a second component polarized perpendicular to the scattering plane. The invention includes photodetection methods and apparatus for detecting light scattered by the suspended particles in a scattering plane at two or more selected scattering angles. 
     One aspect of the invention includes photodetector elements for generating a first intensity signal representative of intensity of scattered light corresponding to the first interrogating component, and elements for generating a second intensity signal representative of intensity of scattered light corresponding to the second interrogating component. The signals are processed by an intensity differential processing element, which executes selected arithmetic transformations of the difference signal to generate a resultant signal representative of the particle size distribution in the sample cell. 
     The invention can include an array of photodetectors disposed at an angular position substantially centered about 90 degrees with respect to the interrogating axis. 
     The invention will next be described in connection with certain illustrated embodiments. However, it should be clear to those skilled in the art that various modifications, additions and subtractions can be made without departing from the spirit or scope of the claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a fuller understanding of the nature and objects of the invention, reference should be made to the following detailed description and the accompanying drawings, in which: 
     FIG. 1 is a schematic diagram illustrating a conventional laser diffraction apparatus for particle size analysis; 
     FIGS. 2A and 2B depict particle size analysis apparatus according to the invention; 
     FIG. 3 is a schematic diagram depicting an embodiment of a photodetector array utilized in connection with the apparatus of FIG. 2; 
     FIGS. 4A and 4B depict another embodiment of photodetectors which can be employed in the apparatus of FIG. 2; 
     FIGS. 5A and 5B depict a further example of photodetectors utilized in connection with the invention; 
     FIG. 6 is a schematic diagram illustrating a lens configuration employed in accordance with the invention; 
     FIG. 7 depicts a practice of the invention utilizing a selected optical axis offset. 
     FIGS. 8 and 9 are graphs of measured intensity vs. angle and particle diameter, respectively; 
     FIG. 10 depicts PIDS values for particles of various sizes, measured at various angles; 
     FIG. 11 depicts a PIDS measurement system constructed in accordance with the invention; and 
     FIGS. 12A and 12B depict a Projector module utilized in the embodiment of FIG. 11. 
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
     FIG. 2A depicts a particle size analysis system 2 constructed in accordance with the invention, for measuring the size distribution of particles 4 suspended in a fluid 6 and contained in a sample cell 8. In accordance with conventional engineering practice, the walls 10 of sample cell 8 can be constructed of a transparent material, such as glass or plastic, for admitting an interrogating beam 12 of light. Beam 12 can be a substantially parallel beam of monochromatic light, generated by a conventional light source including a laser, spatial filter, and collimator 14 of known design and construction. The beam 12 is transmitted through the walls 10 of sample cell 8, where particles 4 to be analyzed scatter a portion of the light 16 at various angles to the axis of the beam 12. As discussed above, the amplitude and angle of the scattered light is in part a function of particle size. 
     The term &#34;scattering angle&#34;, as defined herein, denotes the angle between the direction of propagation of the interrogating beam and the direction of propagation of light scattered from the sample volume. In particular, a given portion of the scattered light will diverge from the direction of propagation of the interrogating beam by an angle theta. 
     The unscattered portion 18 of the beam 12 passes out of the sample cell 8 and into a set of optical components collectively referred to herein as lower optical train 3. The unscattered beam 18 is transmitted through a lower collecting lens 17 which focuses the beam 18 to a point on a mirror element 32 on the focal surface 20 defined by a photodetector array 22. Lens 17 can be a conventional Fourier lens constructed in accordance with known engineering practice. 
     Focal surface 20 can be inclined toward the sample cell 8, so as to be substantially tangent to the circumferential dashed line indicated in FIG. 2A. The focal surface 20 has associated therewith photodetector arrays 22 and 24, described in greater detail hereinafter in connection with FIGS. 3-5. In accordance with the invention, focal surface 20 is positioned so that the distance between the lens 17 and the focal surface 20 is equal to the focal length of the lens 17. 
     A portion of the light 16 scattered by particles 4 in the sample cell 8 also passes through the lens 17 and toward the focal surface 20. Those skilled in the art will appreciate that when focal surface 20 is positioned so that the distance between the lens 17 and the focal surface 20 is equal to the focal length of the lens 17, light scattered at angle 02 to the input axis of the beam 12, at any location in the sample cell 8, will fall on approximately the same point 26 at the focal surface 20. This is illustrated in FIG. 2A by exemplary light rays 28 and 30. 
     As a result, each location on focal surface 20 receives light scattered at a single, unique angle to the input axis of the beam 12 in the sample cell 8. By measuring light intensity at small discrete locations at the focal surface 20, the intensity/angle profile of light scattered by particles 4 in the sample cell 8 can be determined. Conventional light scattering theory, such as Fraunhofer or Mie scattering, can then be applied to determine the approximate particle size distribution in the sample cell 8, based upon this intensity/angle profile. 
     If the focal surface 20 is displaced forward or backward, the angle-mapping relationship between lens 17 and surface 20 no longer applies. Rays scattered at the same angle, such as rays 28 and 30, no longer fall on exactly the same point on surface 20, and a single detector point 26 will collect a mixture of light from different angles, thereby providing a less precise measurement estimate of particle size distribution. 
     Referring again to FIG. 2A, light scattered at higher angles in the sample cell 8 passes into a second set of optical elements, referred to herein as the upper optical train, denoted collectively by reference numeral 50 in FIG. 2A. The included light, illustrated by exemplary rays 05 and 06, is transmitted through a collection lens 52 to a second detection surface 54. This detection surface 54 is related to its collection lens 52 in the same manner that surface 20, in the lower optical train, is related to its respective collection lens 17. Specifically, the detection surface 54 is displaced from the collection lens 52 by a distance equal to the focal length of the lens 52. Preferably, the detection surface 54 is substantially spherical, rather than flat. 
     In the embodiment illustrated in FIG. 2A, the lowest angle of scattered light θ5 entering the upper optical train can be slightly smaller than the angle corresponding to θ4, and the highest angle of scattered light θ6 entering the optical train can be several times greater. Thus, the optical train 50 collects high angle light scatter over a wider angle than does the lower optical train. Moreover, because the smallest angle θ5 is less than the largest angle θ4 measured by the lower optical train 3, both optical trains measure a certain portion of light which is scattered at the same angles relative to the input axis defined by beam 12. A first portion of scattered light is defined herein to have the &#34;same&#34; or &#34;comparable&#34; scattering angle as a second portion, when the first portion diverges from the interrogating beam by an angle of the same magnitude as that of the second portion, and falls in the plane defined by the axis of the interrogating beam and the second portion. The overlapping angular ranges of the upper and lower optical trains permit the illustrated apparatus to measure a continuous, uninterrupted intensity/angle profile in the angular range between θ1 to θ6. 
     The focal length of collection lens 52 can be, for example, 118 millimeters, while that of collection lens 17 can be 2.5 times greater, or 293 millimeters. As a result, the detection surface 54 is 2.5 times closer to its respective lens than is surface 20, and the light scatter from θ5 to θ6 is compressed along the detection surface 54 by a factor of 2.5 compared with that along the surface 20. These values are provided solely by way of example, and other optical values can be utilized in accordance with the invention. 
     The invention has been described in connection with a &#34;binocular&#34; optical configuration utilizing two optical pathways for collecting scattered light and directing this light onto detector arrays. Those skilled in the art will recognize that the invention can be advantageously practiced in connection with apparatus utilizing a greater number of optical pathways, providing the advantages of measurement over a large angle and high resolution at small angles. 
     Moreover, the invention can be practiced in conjunction with a variety of photodetector array configurations, including certain conventional photodetectors. In accordance with a preferred practice of the invention, however, a low angle photodetector such as that depicted in FIG. 3 is utilized. The surface 20 has associated therewith a central mirror element 32 and two silicon detector arrays 22 and 24. The inner detector 22 is a monolithic silicon structure which can include sixty-two discrete silicon sectors 30 are substantially annular in form. As illustrated in FIG. 3, these sectors are disposed so as to radiate outward from central mirror 32, which defines the position upon which the light source is focused. 
     The innermost sector 42 measures light scattered at small angles to the beam 12, while the outer sectors 44 measure light scattered at greater angles. The innermost sector 42 can be located slightly outside the point of spillover from the light beam. This spillover is an effect well known in the art, and results from small imperfections in the optical elements In a preferred practice of the invention, sector 42 is constructed as small as manufacturing practices permit, to achieve optimum resolution. Thus, the radial width of the sector 42 can be, for example, approximately 15 microns, while the arc length of sector 42 can be approximately 50 microns. In the illustrated embodiment, the detector sectors increase progressively in radial width and arc length, providing an exponential increase in the areas of the sectors. 
     Preferably, sectors proximate the mirror 32 can be quasi-symmetrically disposed, to measure small, overlapping angular ranges of scattered light. Farther from mirror 32, the sectors can be symmetrically arranged, for measuring comparable angles of scattered light. Additionally, a single row of sectors 44, referred to as a &#34;tail,&#34; measures light scattered at progressively higher angles. In the embodiment illustrated in FIG. 2A, for example, the axis A--A (FIG. 3) of detector 22 can be oriented vertically with the &#34;tail&#34; sectors 44 extending upwards. 
     Moreover, in the embodiment illustrated in FIG. 2A, a second detector array 24 can be located on a vertical axis below detector 22. This array 24 measures light scattered at higher angles to the incident beam 12 than does detector 22. In particular, detector 22 measures scattered between θ1 and θ2 while detector 24 measures between θ3 and θ4. 
     This orientation is further illustrated in FIG. 4, which provides a front view of detector arrays 22 and 24. FIG. 4 also indicates that detector array 24 is an assembly of two monolithic, linear silicon arrays. Detector array 24 can, for example, include sixteen sectors, each 1.58 millimeters long and 1.22 millimeters wide. The arrays from which detector assembly 24 is constructed can include conventional detector elements manufactured by United Detector Technology, marketed as Part No. A2V-16. 
     In one embodiment of the invention, as indicated in FIG. 4, detector array 22 is asymmetrical, having tail sectors 44 extending outward on one side of central mirror 32. This configuration allows the inner sectors 46 of detector 24 to be positioned proximate to the optical center of mirror 32, and allows the innermost sectors 46 of detector array 24 to measure light scattered at angles near θ3 which are comparable to those angles --i.e. θ2--measured by the outermost tail sectors 44 of detector 22. The optical overlap of sectors 44 and 46 permits the particle size analysis system to measure a continuous, uninterrupted intensity profile from θ1 to θ4. 
     In accordance with this detector design, the employment of first sectors which increase exponentially in area, and other sectors which increase linearly or are of constant area, reduces the dynamic range required of associated signal amplifiers and signal conversion electronics utilized for processing sector signals. These signals typically have a wide dynamic range, and have heretofore posed significant difficulties in the design of signal processing electronics. 
     In particular, at small angles, where light scattered from large particles is of interest, observed light intensity falls off rapidly with angle. In this region, exponentially increasing sectors tend to yield signals of the same order of magnitude, thus simplifying subsequent electronic processing. At high angles, observed light intensity falls off in a substantially more linear manner. Accordingly, in this region, sectors which increase linearly in area, or which have constant area, tend to yield signals of the same order of magnitude, likewise reducing dynamic range requirements. 
     Additionally, at higher scattering angles, linear detectors have been observed to provide greater resolution. The resulting improved spectral detail associated with smaller particles is advantageous in quantifying anomalies associated with complex Mie light scattering effects, which occur when a particle size approaches the wavelength of interrogating light. 
     Detector geometry in accordance with the invention thus enables increased dynamic range of measurement and increased resolution, while reducing the dynamic range required of associated signal processing electronics. 
     In a further preferred embodiment of the invention, as illustrated in FIG. 4B, the detector arrays 22 and 24 are inclined inwardly, toward the collection lens 17, in order to maintain the forward surface of the detector sectors close to the surface 20. The surface 20 is preferably a substantially spherical surface corresponding to the surface of best focus of the collection lens 17. Positioning the active face of the sectors of the detectors on or near this surface 20 maximizes focus, and minimizes the mixing of light scattered at different angles at each sector&#39;s surface, thereby enhancing measurement precision. 
     The upper optical train detector arrays 56, corresponding to detection surface 54, are depicted in FIGS. 5A and 5B. In particular, FIG. 5B indicates that the detector arrays 56 are inclined toward the optical axis 58 of collection lens 52, in order to better conform to the spherical nature of the detection surface 54. Detector arrays 56 can include two United Detector Technology, Part No. A2V-16 silicon arrays as described above in connection with FIG. 4. These detector arrays 56 measure scattered light between θ5 and θ6 indicated in FIG. 2A. 
     The particle size analysis system of the invention can utilize a variety of lens designs for collecting scattered light. The high angle collection lens 52, as illustrated in FIG. 2A, can be a doublet, a configuration which provides a lens with a large aperture and short focal length. One configuration of the low angle lens 17 is a substantially spherical lens, having three sides 60, and truncated as illustrated in FIGS. 2A and 6. In order to minimize beam spillover, the interrogating beam is directed through the optical center of the lens. The sides of the lens perform no function, and thus can be removed. In addition, the upper portion of the lens 17 can be removed to facilitate positioning of the upper collection lens 52 so that both lenses 17 and 52 can collect light at comparable scattering angles from a given illuminated sample volume. 
     Referring again to FIG. 2A, those skilled in the art will recognize that the upper lens 52 can be further displaced upward, and that lens 52 can be positioned to collect light at angles as small as θ4. Displacement of lens 52 to this extent would preclude measurement over a comparable angular segment, but would provide a continuous measurement of the intensity profile to θ6. This configuration offers the advantages of further reduced spatial requirements and a physically smaller instrument package. 
     Alternatively, cutting of lens 17 can be avoided by directing the interrogating light beam 18 to pass, not through the optical center of the lower lens 17, but through a region of lens 17 offset from the optical center, as depicted in FIG. 7. This displacement permits upper lens 52 to be positioned for collecting light flux down to θ4, so that a continuous measurement of intensity is obtained. In this alternative embodiment, however, the focus of the beam 18 becomes non-optimal, and laser spillover will be increased, thus reducing low angle sensitivity. 
     In a preferred embodiment of the invention, as indicated in FIG. 2A, collection lens 17 can be a &#34;landscape&#34; or plano-convex lens oriented with its planar face facing the sample cell 8. Lenses of the plano-convex type ordinarily collect a substantially parallel bundle of light from each distant element in a landscape, and direct each such bundle onto a single position on a light-sensitive medium, such as a CCD array or the film of a camera. In the particle size analysis system of the invention, the light of interest is composed of rays scattered from the sample cell 8 at substantially the same angle, forming a bundle of parallel light. Because the precision of a diffraction instrument is improved by focusing all light scattered at a given angle to a single point, the plano-convex lens is advantageously utilized in the invention. 
     This employment of the plano-convex lens is contrary to conventional engineering practice. In conventional imaging devices, such as photographic apparatus, the distance from the object to the lens is much greater than the distance between the lens and the image, and sharp images are produced by orienting the planar surface of the lens toward the image. If a plano-convex lens were utilized in this conventional orientation in a diffraction instrument--i.e., with the planar surface facing the detector--the angular &#34;blur&#34; due to aberrations would be unacceptable. Designers of conventional diffraction instruments have therefore concluded that plano-convex lenses are of limited utility in such instruments, and have instead utilized expensive achromat lenses to obtain sufficiently sharp angular resolution. 
     We have found, however, that by positioning a suitable plano-convex lens in an orientation opposite that of the conventional orientation, angular resolution substantially equal to that attainable with an achromat can be achieved, with a less expensive plano-convex lens. This unexpected result arises because the plano-convex lens is applied herein for a different purpose--i.e., as a Fourier lens in a diffraction instrument, rather than to form an image, as employed conventionally. 
     In accordance with the invention, therefore, the plano-convex lens can be oriented with its planar surface facing the sample volume, and spaced sufficiently far from the sample volume so that spherical aberration and astigmatism are minimized. The configuration illustrated in FIG. 2A offers a combination of lens 17 and sample cell 8 offering minimum field curvature and astigmatism, and thus maximum resolution. 
     One deficiency of certain conventional laser diffraction apparatus used for analysis of particle size is a reduction in resolution due to interference by extraneous light. Thus, a preferred embodiment of the invention utilizes a light trap or &#34;beam dump&#34; module. Referring to FIGS. 2A and 2B, the interrogating light beam 18 can be directed onto mirror 32 and reflected into a light trap 34. As shown in FIG. 2B, the light trap 34 can be composed of two converging pieces of dark material 36, such as glass, and preferably, a photodetector 38 for monitoring the power of the reflected beam 18&#39;. The converging angle of the glass 36 can be approximately 9 degrees, an angle which causes the beam 18&#39; to make approximately seven reflections before re-emerging toward the surface 20. Because the glass is optically coated, each reflection reduces the intensity of the re-emerging beam 40 by a factor of approximately 10 2 . Seven reflections therefore yield a 10 14  reduction in the power of the emerging beam 40. Accordingly, the emerging beam 40 has an immeasurably small effect as it returns toward the surface 20. 
     The optically coated dark glass 36 can be, for example, three millimeter thick NGl glass manufactured by Schott Glass Technologies Inc. This material attenuates transmitted light by a factor of approximately 10 6 . In the light trap 34, where light passing into the glass 36 must pass through it, strike a wall 37, and then re-emerge through the glass 36, the power of emerging light is therefore reduced by a factor in excess of 10 12 . 
     The detector 38 can be, for example, a commercial silicon detector with a sensitive surface of about 0.4×0.8 inches in dimension. Such a detector is manufactured by EG &amp; G Vactec Division. The detector 38 can be positioned on one side of a dark glass element 37. 
     The invention thus provides a number of advantages over conventional particle size measurement methods and apparatus. As discussed above, certain conventional devices utilize a single optical train to provide measurements over a wide angle of scattered light. In these devices, a short focal length system permits detection to greater angles, but compresses low angle scatter near the optical axis, where it may be obscured by laser spillover or rendered unresolvable by the finite size of a detection segment. Other conventional devices attempt to address this problem by employing a longer focal length lens, at the expense of increased spatial requirements, greater spherical aberration and astigmatism, and increased complication in positioning high angle detectors. 
     The multiple optical pathways of the invention offer the advantages of compactness and enhanced optical resolution. In addition, multiple lens trains, even of the same focal length, offer economic advantages. While the low angle lens train must be of high quality to minimize scatter and spillover--which reduces low angle resolution--the high angle lens train need not meet this requirement. This is because the interrogating light beam does not pass through the high angle lens train. This lens can be manufactured to less stringent tolerances, and thus may be less expensive. 
     Moreover, lens fabricating costs are approximately proportional to lens area, or the square of lens diameter. Replacing a single, large-diameter lens with two lenses of approximately half the diameter can reduce lens cost by approximately 50%. 
     In addition to these general advantages, the utilization of optical trains having different focal lengths permits a wide measurement span at high angles, and high resolution at low angles. Different power optical trains permit the use of a common detector design for both high and low resolution measurements, and allow greater flexibility in the selection of detector arrays. The designer can select a low angle array with sector areas which grow exponentially to compensate for the rapid decay of intensity at high angles, and high angle arrays with sector areas that are constant or increase linearly to compensate to the slow decay of intensity in this region. 
     While the apparatus described above in connection with FIGS. 2-7 provides enhanced resolution in particle measurement, a preferred embodiment of the invention utilizes a novel polarization intensity differential scattering (PIDS) system to provide still greater enhancements in accuracy and resolution. 
     We have found that the accuracy and discrimination of a PIDS measurement can be substantially improved by using not only the PIDS data collected at an angle of 90 degrees to the interrogating beam axis, as in conventional systems, but also the symmetry of PIDS scattering around 90 degrees. The theoretical basis for this advantage can be explained with reference to FIG. 10, which shows PIDS values for particles of various sizes, for scattering angles of fifty degrees on either side of 90 degrees, measured with respect to the axis of propagation of interrogating light. As can be seen from FIG. 10, for small particles (i.e. particles having an alpha value less than 2), the pattern of PIDS around ninety degrees is a symmetric, roughly quadratic curve with a peak at exactly 90 degrees. 
     Again referring to FIG. 10, for very small values of alpha, the PIDS pattern will have exactly the same shape, but the peak amplitude will be lower because small particles produce less scatter per unit weight. As particle size increases above (alpha=2), the PIDS peak shifts toward lower angles and thus, although it is still roughly symmetrical, the center of symmetry shifts toward lower angles. Finally, for larger particles, the PIDS curves acquire a shape similar to a cubic curve--i.e., high amplitude at low angles, low at intermediate angles, followed by a local maximum, and then a decay at higher angles. 
     The data displayed in FIG. 9 could be generated from FIG. 10 by drawing a vertical line at 90 degrees, and plotting the value of the PIDS curves for the various alpha values shown. It should be noted that the smaller resonance peaks in FIG. 9 occur when the local maxima which occur at larger alpha values, as in FIG. 10, line up at 90 degrees. 
     FIG. 10 thus illustrates that conventional PIDS measurements use only a small part of the information potentially available from such measurements. A 90 degree PIDS measurement is not responsive to the shape of the PIDS curve as a function of scattering angle. Moreover, as the peak of the curve shifts toward lower angles--as alpha increases from approximately two--a 90 degree PIDS measurement measures the PIDS off-peak. The information, describing particle size, inherent in the peak shift, which is caused by larger sized particles, is not sensed by a 90 degree PIDS measurement. 
     By measuring the PIDS at a number of angles around 90 degrees, information can be obtained about the shift of peak position, which is manifested by a peak which becomes asymmetric about 90 degrees. As the PIDS curve increases its cubic character with still larger alpha values, this further information can be sensed with judiciously placed detectors, as discussed in greater detail hereinafter. 
     The symmetry information obtained by multiple photodetectors which measure PIDS values at angles between around 40-140 degrees increases the discrimination with which the invention can distinguish particles of different sizes. 
     In particular, the invention, in the embodiment illustrated in FIG.11, includes a PIDS module 2&#39; including a projector element 210 which produces a collimated beam of light 212 characterized by one of a plurality of selectable wavelength and polarization combinations. For example, the light beam 212 can have any of three wavelengths of light, each polarized either perpendicular or parallel to the scattering plane. The PIDS apparatus can also include a sample cell 8&#39; containing a stream of particles-to-be-measured, and a detector module 214. 
     Referring again to FIG. 11, the detector module 214 includes a plurality of photodetector elements 201-205, which can be, for example, photodiodes, for measuring scattered light at selected scattering angles, and a further detector 206 for monitoring the amplitude of the projector beam at approximately zero degrees to the axis of the incident beam. In the illustrated embodiment, the photodetectors 201-205 are mounted on a bracket 219 having pinhole apertures 207-209, 211 and 213 for admitting scattered light to detectors 201-205, respectively. The five photodiodes 201-205 are employed for detecting scattered light, and a sixth detector 206 is utilized for monitoring the projector beam 212&#39;. Those skilled in the art will appreciate that a greater or lesser number of photodetector elements may be employed. 
     In generating a PIDS measurement, the particles-to-be-measured are suspended in a suitable liquid, such as water, to form a sample system containing, for example, approximately 1.5 liters of liquid. This sample system is pumped continuously through the sample cell 8&#39;, at a pumping rate which can be selected such that during each 10-30 second interval, all, or a substantial portion of, the 1.5 liters of particle-containing liquid passes through the sample cell 8&#39; where the scattered light measurement is made. 
     The PIDS measurement is made by sequentially projecting light of the selected wavelength/polarization combinations through the sample cell 8&#39;, and measuring the average intensity of light scattered by each of the selected configurations of light. The light is measured at each of the scattered light detectors 201-205. In one embodiment, for each of the six wavelength/polarization combinations of light, the scattered light is measured for a time period of between 10 and 30 seconds. Thus, most of the particles in the 1.5 liter sample system are sensed with each variety of projected light. 
     Detail of a projector module 210 for generating various wavelength/polarization combinations is provided in FIGS. 12A and 12B. The projector module 210 utilizes a conventional light source 220, which can be a tungsten halogen element. The output of source 220 is collected by condensor lens assembly 222, and passes through pinhole 224. The light beam is then modulated by a conventional bandpass filter 226, polarizer 228, and filter wheel 230. The orientation of polarizer 229 and filter wheel 230 can be selected, in accordance with known engineering practice, to provide varying polarization and filtering outputs. Projection lens 232 collects the polarized, filtered light and directs it toward the sample area 234. 
     Referring again to FIG. 11, a conventional microprocessor or computational device 126 can process the average scattered light intensities measured by detectors 201-205, together with information from detector 206 and projector module 210, to generate particle size distribution data. In one embodiment of the invention, for each wavelength of light, the average scattered intensity resulting from incident light polarized parallel to the scattering plane can be subtracted from that resulting from incident light polarized perpendicular to the scattering plane. The subtraction is performed for each of the five detectors, as described by the following expression: 
     I(lambda, theta --  i)=I(lambda, theta --  i, perpen)-I(lambda, theta --  i, para) 
     where i=1, 5 denotes the five detectors 201-205 located at five selected scattering angles in an angular range substantially centered at approximately 90 degrees; lambda is the wavelength of the incident light; and theta is the scattering angle, defined in accordance with conventional engineering practice. The I(. . . ) terms denote the various average scattered intensities. In accordance with the invention, a function I(lambda --  j,theta) is generated for each wavelength, lambda --  j. The beam strength monitor photodetector 206 (FIG. 11) is used to normalize the above signals for changes in the incident beam intensity. 
     We have found that the symmetries of the three I(lambda --  j, theta) terms about theta=90 degrees is characteristic of particle size for particles with diameters approximately equal to lambda (see FIG. 10). In particular, a particle size distribution can be extracted from the three terms I(lambda --  j, theta), j=1, 3 by matching the pattern of the measured I(lambda --  j, theta) to the pattern of I(lambda --  j, theta) calculated for particles of various sizes in the desired range. For example, using an apparatus such as that described above in connection with FIG. 11, the sizes of four polystyrene latex beads of known sizes were measured. The results are shown below in Table 1. 
     
                       TABLE 1______________________________________PIDS Measured Sizes of Polystyrene Latex StandardsNominal SizeDiameter .109 um   .175 um   .246 um .305 um(um)     Volume %  Volume %  Volume %                                Volume %______________________________________.08.09.11      93%.13       7%.15                100%.21                          82%.24                          18%     95%.28                                   5%.33.39.46Meas.    .11 um    .15 um    .22 um  .24 umSize______________________________________ 
    
     Apparatus employed for these measurements can utilize light of wavelengths centered at lambda=450, 600 and 900 nm, using conventional filters, such as filter wheel 230 of FIG. 12, which transmit light of approximately 40 nm to either side of the nominal wavelength center, and scattering angles of 70.5, 81.4, 90, 98.6 and 109.5 degrees. A conventional microcomputer 126 (FIG. 11) or other processing device, programmed in accordance with known pattern matching algorithms, can calculate the relative volumes of particles in, for example, twelve size categories, geometrically spaced, for example, between 0.08 and 0.5 micrometers. 
     Those skilled in the art will appreciate that the apparatus can be constructed to employ more or fewer scattering angles and wavelengths of light. The significant feature of the invention is the evaluation of the symmetry of the polarization difference signal about the 90 degrees scattering angle, this angle being measured with respect to the interrogating beam incident upon the sample cell. In order to measure the symmetry, a minimum of three scattering angles and two light wavelengths should be evaluated. 
     The invention has important advantages over conventional light scattering methods, including certain conventional laser diffraction devices. One advantage is that measurement accuracy is relatively insensitive to the often unknown refractive index of the particles-to-be-measured. The invention also has the advantage, over conventional polarization dependent sizing methods, of enhanced discrimination in rejecting effects of particles outside the desired measurement range. In particular, in conventional polarization dependent sizing methods, particles outside of, but adjacent to, the measurement range will distort the measured size distribution within the measurement range. The method of the invention is far less susceptible to such anomalies, and provides enhanced resolution and accuracy in particle size analysis. 
     It will thus be seen that the invention efficiently attains the objects set forth above, among those made apparent from the preceding description. 
     It will be understood that changes may be made in the above construction and in the foregoing sequences of operation without departing from the scope of the invention. It is accordingly intended that all matter contained in the above description or shown in the accompanying drawings be interpreted as illustrative rather than in a limiting sense. 
     It is also to be understood that the following claims are intended to cover all of the generic and specific features of the invention as described herein, and all statements of the scope of the invention which, as a matter of language, might be said to fall therebetween.