Abstract:
The refractive index, extinction coefficient, size and density of fluid suspended particles are simultaneously determined by combined transmittance and scattering measurements. The scattering measurements are preferably angle selective to obtain additional information about the scattered light. A charge-coupled device is employed for its high sensitivity to low light intensity in measurement of scattered light in combination with a photodiode array employed for its high signal to noise ratio, which is beneficial in transmittance measurement. The scattered light may be measured in an angle selective fashion by use of a motorized aperture that is concentrically positioned with respect to the impinging beam axis and moveable along the impinging beam axis. An ellipsoidal mirror collects the scattered light that passes through the motorized aperture and focuses the scattered light towards the charge-coupled device.

Description:
PRIORITY CLAIM 
     The present Utility Application claims priority to and from the Provisional Application of the same Title and Inventors filed on 03-APR-2008 with Application No. 61/042,238 filed Apr. 3, 2008. 
    
    
     FIELD OF INVENTION 
     The present invention relates to methods and apparatus for combined transmittance and scattering measurements of fluid suspended particles for simultaneous determination of refractive index n, extinction coefficient k, particle size and particle density (number of particles per volume). In particular, the present invention relates to methods and apparatus for determination of n, k, particle size and particle density by combined use of a photodiode array detector for transmittance measurement and a charge-coupled device detector for scattering measurement. 
     BACKGROUND OF INVENTION 
     Optical techniques for remotely characterizing fluid suspended particles are receiving increased attention in the industry because they are highly suitable for high quality measurements in a non invasive and quasi real time fashion. Most common are transmittance based measurement techniques, in which light is directed through the fluid and the directly emitting remaining portion of the incident light is used to characterize the suspended particles. Transmittance based measurement techniques are less sensitive to noise especially at short wavelengths in the UV regime but are well suitable to obtain information about particles. However, information about particle sizes and particle distributions, and n and k are difficult to obtain with transmittance measurement alone as is well known in the art. This is mainly due to the strong correlations between n, k, size, and density of particles in the analysis. For example, increasing the particle density has a similar effect, to certain extent, as increasing the particle size to the transmittance spectra. Therefore, there exists a need for an optical measurement technique for fluid suspended particles that is capable of providing information about particle sizes and particle distributions. The present invention addresses this need. 
     Increasing attention has been received lately regarding scattered light measurement techniques to derive information about fluid suspended particles. In combination with well known mathematical algorithms and methods that are preferably computationally implemented, light scattering measurements may require relatively small optical design effort while providing highly accurate measurement results. A low number of lenses, mirrors and optical fibers are employed to direct a broadband spectral light source onto the fluid suspended particles and collect and direct the scattered light towards a detector. Also, the measurement has characteristics that can be computationally analyzed to determine particle size and n and k. One such well known characteristic is a wavelength dependent oscillation of the scattered light. From such oscillations, n and k may be roughly computationally determined. Unfortunately, scattering oscillations decrease with particle size such that at approximately 0.2 μm particle sizes and below, n and k cannot be reliably determined from the scattered light at a fixed scattering angle. Therefore, there exists a need for an optical measurement technique for fluid suspended particles that provides information of n and k of particles also substantially below 0.2 μm size. The present invention also addresses this need. 
     In the prior art, scattered light is detected either by a single stationary or a single moveable detector or a number of stationary detectors. The more scattered light is detected as a function of angle, the more information about the suspended particles may be derived. Of particular interest are variations of the scattered light in relation to the scattering angle. Such variations can be detected in a continuous fashion over an extended scattering angle range. Prior art stationary detector(s) to the contrary provide simultaneous detection of only a fraction of the scattered light near a given scattering angle. Prior art moveable detectors may be continuously moved around the scatter origin but only along a linear path, which amounts also only to a small fraction of the total scattered light within a predetermined measurement range. Also, a moveable detector or a configuration for variable angle detection may require extensive design effort. Therefore, there exists a need for a method and apparatus capable of simultaneously detecting a substantial portion of the total scattered light along a predetermined scattering angle. The present invention also addresses this need. 
     Analyzing raw measurement data of transmittance spectra and scattering spectra is well known in the art. There are dispersion models such as Forouhi-Bloomer (U.S. Pat. No. 4,905,170), Cauchy, or others commonly implemented to reduce the number of variables. Other parameters in conjunction with basic formulations to perform calculations based on Beer-Lambert (BL) law are taught for example in Swanson et al, Applied Optics, 38, p. 5887, 1999; Nefedov et al, Applied Optics, 36, p. 1357, 1997, Furthermore, the extinction cross section of a single particle is also known to be calculated from Mie scattering theory as taught, for example in C. F. Boren and D. R. Huffman, “Absorption and Scattering of Light by Small Particles, Wiley, New York, 1983”. Also, single scattering conditions in the transmittance of fluid suspended particles are for example, taught in Swanson et al, Applied Optics, 38, p. 5887, 1999. Also, it has been noticed in experiments that some forward scattered light may also be detected as transmitted light like in Nefedov et al, Applied Optics, 36, p. 1357, 1997. All prior art address some isolated issues relating to analyzing fluid suspended particles, but fail to teach a combination of detector choice and apparatus setup, and fail to teach a relevant analytical solution to address the need for simultaneously determining refractive index, extinction coefficient, particle size and particle density. The present invention also addresses this need. 
     SUMMARY 
     Broadband spectral light is directed towards a target area within a vessel that contains particles suspended in fluid. Particles present at the target scatter a portion of the impinging light in a fashion that highly depends on the particles&#39; size, distribution and refractive index. A portion of the impinging light that is not absorbed or scattered by the suspended particles, propagates directly through the vessel and is detected by a first detector and recorded as transmittance spectrum T. The scattered light is detected by a second detector positioned at a suitable position with respect to the direction of the impinging light and recorded as scattering spectrum or spectra S. The raw transmittance T and scattering S data are then computationally analyzed preferably in a simultaneous iterative fashion to derive refraction index n and extinction coefficient k particle size and particle density. In an alternate approach, n and k and size may also be determined from the S alone. Once n and k are known, the particle size and density may be computed from T alone. 
     In a first embodiment, a photodiode array (PDA) detector was employed as first detector and a charge-coupled device (CCD) detector was employed as second detector. The PDA detector with its high signal to noise ratio and high pixel well depth was best suited for detecting the transmitted light. The CCD detector to the contrary with its high sensitivity to low light intensity provided satisfactory detection of the scattered light which commonly is much lower in intensity compared to the transmitted light. The combination of PDA detector for transmittance measurement and CCD detector for scattering measurement supplemented each other favorably resulting in an increased data output over a wavelength range that would be unobtainable if only a single type detector would be employed. 
     To ensure single scattering while obtaining sufficient signal from particles, the particle density and optical path length of the selected vessel was approximated such that the measured transmittance T after normalization was in the range of 10˜80% for all wavelengths. The path length may be adjusted by vessel size, to get optimized T. On the other hand, the density of particles may be changed by diluting the fluid in which they are suspended. By warranting this well known single scattering, well known physical models including Mie&#39;s scattering theory and Beer-Lambert law computation of n and k, particle size and density was accurately achieved. Due to the broad data made available by combining PDA transmittance detection and CCD scatter detection, initial assumptions and iterative computation could be kept to a minimum resulting in fast and highly accurate results. 
     Further more, angle selective detection of the scattered light may be accomplished by a motored aperture preferably concentrically positioned around the axis of the impinging light. The motored aperture may be axially adjustable with respect to the impinging light axis. The motored aperture may shield all but a predetermined angular portion of the scattered light from reaching a surrounding mirror, which reflects the scattered light towards the second detector. By moving the aperture while light impinges the suspended particles, the scattered light may be detected selectively with respect to its scattering angle. The concentrically arranged motored aperture and surrounding mirror capture a substantial portion of the scattered light. Correlating the position of the motored aperture to the simultaneously detected scattered light provides for a profile of the scattered light with respect to the entire scattering angle range covered by the mirror and the motored aperture. As a favorable result, scattering angle specific intensity of the scattered light may be obtained with high accuracy and utilized as an additional parameter for measurement of n and k, particle size and particle density 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  is a schematic depiction of scatter S and transmittance T of light impinging on particles suspended in fluid. 
         FIG. 2  schematically illustrates a combined PDA transmittance detection and CCD scatter detection. 
         FIG. 3  is a schematic depiction of representative apparatus for backscattering detection. 
         FIG. 4  is a graph of measured versus computationally curve fitted T and S spectra. 
         FIG. 5  is a graph of n and k derived from the measured T and S of  FIG. 4 . 
         FIG. 6  shows a schema of an apparatus including a motored ring aperture for T and S measurements with a single detector. 
         FIG. 7  depicts a schema of the apparatus of  FIG. 6  configured for simultaneous T and S measurements with two detectors. 
         FIG. 8  is a graph of scattering intensities for a 0.5 μm particle size simulated for various scattering angles. 
         FIG. 9  is a graph of scattering intensities for a 0.05 μm particle size simulated for various scattering angles. 
         FIG. 10  is a graph of angle dependent scattering intensities for varying particle sizes at a given wavelength. 
     
    
    
     DETAILED DESCRIPTION 
     Referring to  FIG. 1 , light  10  impinging on fluid  12  may pass directly through without being scattered or absorbed by particles  14  suspended in the fluid  12 . This directly through transmitted light  18  may be detected and compared to the impinging light  10  to determine the transmittance T. A portion of the impinging light  10  interacts with the particles  14 , in which it is absorbed or scattered at scattering angle θ. The scattering angle θ is between 0 and 180 degrees. When scattering angle is close to 180 degrees the scattered light is referred to as backscattering. The optical path length  20  is the distance within which the impinging light  10  interacts with suspended particles  14 . Single scattering occurs when the scattered light  16  emerges from the fluid without interacting again with another particle  14 . Multiple scattered light  21  occurs when initially scattered light  19  interacts again with a particle  17  before emerging again from the fluid  12 . A portion of the scattered light  16 ,  21  may be captured and measured. The larger the portion of the angle resolved scattered light that is measured, the more accurate and detailed the scatter measurement may be. Single scattered light  16  and multiple scattered light  21  are not easily distinguishable in the measurement. To avoid ambiguous interpretation of the scatter measurement, it is desirable to minimize multiple scattered light  21 . The fluid  12  is confined by the vessel  44  within the pass length  20 . 
     In the present invention, multiple scattered light  21  is substantially avoided by selecting the optical path length  20  in conjunction with an approximated density of the suspended particles  14  such that at least 10% of the impinging light  10  is detected as transmitted light  18 . 
     Referring to  FIG. 2 , a particle characterization system  30  in general may include a broadband light source  32 , a light delivering component  34 , a vessel  44  to hold fluid  12 , a first and second light collection component  36 ,  40  and first and second detectors  38 ,  42 . The vessel may be made of fused silica, glass or any other optically transparent material for the desired measurement wavelength range with preferably a cylindrical or better spherical curvature at least within the penetration area of the impinging light  10 , transmitted light  18  and scattered light  16 . 
     The impinging light  10  may be polarized or un-polarized light. For that purpose, a well known polarizer (not shown in  FIG. 2 ) may be used to create polarized light from un-polarized light source  32 . The polarizer may be rotated mechanically or electrically dependent on polarizer type and design. In this case, Eq. 3 should be changed accordingly and is well known in the art. 
     The fluid  12  is preferably chosen to substantially and statically suspend the particles  14  at least during the measurement process. The first detector  38  may be specifically configured for transmittance measurement preferably utilizing a well known PDA sensor including well known CMOS and NMOS sensors that are advantageous with their large dynamic range and high signal-to-noise ratio for detecting high intensity light. 
     The second detector  42  may be specifically configured for scatter measurement utilizing a well known CCD (including back-thinned) imaging sensor that is naturally integrating the receiving light over time and is more sensitive and better for low intensity light detection. Scattered light  16  may amount to about 0.001% or less of the impinging light  10 , whereas transmitted light  18  amounts at least to 10% of the impinging light  10 , which is five orders of magnitude higher than the scattered light  16 . Due to this large difference between scattered light  16  and transmitted light  18 , selection and configuration of sensors  38 ,  42  and collection systems  36 ,  40  is important to retrieve raw S and T data that can be unambiguously analyzed. 
     Nevertheless, the present invention may include embodiments in which both detectors  38 ,  42  utilize CCD sensors. A CCD sensor may be adjusted with shutter speed and other well known means to the intensity of the transmitted light  18 . Using the same type of sensors for both S and T may greatly reduce design effort of a combined S and T measurements apparatus as will be explained further below. 
     Referring to  FIG. 3  and in accordance with a first embodiment of the invention, a system  100  for detection of backscattered light  16  as shown in  FIG. 1 , was configured with a CCD spectrometer, for example USB4000™  142 , and a probe  111  all commercially available from Ocean Optics Inc. The scatter probe  111  featured a central collection fiber  140  with 200 μm in diameter and a numerical aperture of 0.22, within which backscattered light  16  was captured while the probe  111  was immersed in the fluid  12 . Six illumination fibers  134  also having a 200 μm diameter surrounded the central collection fiber  140 . 
     Broadband light provided by the white light source  132  was passed via fiber  133  to the probe  111 . The captured scattered light  16  was guided via fiber  144  to the spectrometer  142  for measurement. The captured scattered light  16  was passed through a 25 μm wide slit at the entrance of the spectrometer  142 . 
     In the first embodiment, fluid  12  including the suspended particles  14  was transferred into two vessels  44  of 0.5 mm and 0.2 mm optical path length for measurements of their respective transmittance spectra. The transmitted light  18  was measured with an Agilent 8453™ transmittance measurement spectrometer. The transmittance spectrometer was configured with a 50 μm slit. Polystyrene Latex (PSL) particles with 0.5 μm from Duke Scientific™ were diluted in DI water to provide the suspended particles  14 . The S measurement was performed by use of the configuration described above in reference to  FIG. 3 . Measurements of T and S are depicted in  FIG. 4 . Curves  402 ,  404  are the measured normalized transmittance intensities with the 0.2 mm and 0.5 mm vessels  44  over a wavelength range of 190 nm and 1000 nm. 
     The curve  405  illustrates the intensity of the backscattered light  16  captured at near 180 degree scatter angle θ. The S measurement becomes increasingly noisy with smaller wavelength, making its interpretation increasingly ambiguous. T measurement to the contrary has very low noise across the entire measurement spectrum but only significant intensity oscillations in the small wavelength range substantially below 380 nm. The S measurement to the contrary had substantial intensity oscillations along the entire measurement spectrum with increasing noise towards the UV spectrum. By using a well known back-thinned CCD detector with much better UV sensitivity, the S measurement may be extended to smaller wavelengths. The graph clearly shows the favorable combination of T and S measurements and their particular intensity oscillations to derive high content raw measurement data that is highly suitable for non-ambiguous interpretation and accurate analysis. 
     During analysis of the measurement data, multiple transmittance spectra with different particle densities and/or different optical path lengths  20  and scattering spectra with different scattering angles θ are preferably analyzed together. The particle intrinsic properties such as n, k and diameter are set as the same in the calculations for different spectra. Well known dispersion models such as Forouhi-Bloomer, Cauchy, or others are implemented to reduce the number of variables. The analysis is started with an initial assumption for parameters including size, density and dispersion of the particles  14 . Other parameters in conjunction with the following basic formulations are also applied to perform the calculations based on the below Equations (1) and (2). From Beer-Lambert (BL) law we have
 
 T (λ)= I   t (λ)/ I   o (λ)=exp[−τ(λ)]=exp[− NC   ext ( n,k,d,λ ) L]   (1)
 
Where I t  is the transmitted intensity for particles in liquid, I o  is the transmitted intensity for pure liquid with the same vessel but without particles, N is density of particles  14  in liquid fluid  12  (number of particles per volume), C ext  (n, k, d, A) is the extinction cross section of a single particle  14  calculated from Mie scattering theory which is a function of n, k, wavelength, and diameter of the particle  14 , and L is the optical path length  20  in the liquid in transmittance measurement.
 
     BL law has assumed single scattering in the transmittance, which is the case when −ln T is smaller than 4. 
     The scattered light  16 , S(λ, θ), can also be collected in the measurement, which is connected to the complex scattering amplitude function, s(λ, n, k, d, θ), in Mie calculation,
 
 S (λ,θ)= Is (λ,θ)/ Io (λ)= B*|s (λ,n,k,d,θ)| 2   +A *exp(− C*λ )  (2)
 
Where θ is the scattering angle, which is defined to be 0 at forward scattering and 180 at backward scattering direction, Io(λ) is the normalization spectrum collected either directly from the source or from a flat surface that gives a uniform reflectance, such as quartz, Is (λ, θ) is the scattered light collected at angle θ. This measurement is relative. A, B, C are adjustable parameters. A*exp(−C*λ) is used to account for the diffuse scattering, and s(λ, n, k, d, θ) is the complex scattering amplitude function given by Mie calculation. Clearly, the measured S (λ, θ) is still relative and cannot be used to determine the absolute number or density of particles. For un-polarized light and spherical particles,
 
| s ( λ,n,k,d,θ )| 2 =[λ/(2π)] 2 *0.5(| S 1| 2   +|S 2| 2 )  (3)
 
     Where S 1  and S 2  are the amplitude functions for the two orthogonally polarized E vectors as are well known in the art. 
     Here again single scattering is assumed, which means the light that is collected is only scattered once by the particles  14 . 
     When A=0 and B=1, one can run simulations and see the angular and wavelength dependence of the scattering from free particles  14 . 
     In most experiments, some forward-scattered light  16  is also recorded as transmitted light  18 . Therefore, C ext  (n, k, d, λ) in Eq. 1 should be replaced by
 
 C   ext ( n,k,d,λ )−2π           | s ( λ,n,k,d,θ )| 2  sin θ dθ 

     The integral is from 0 to the maximum collection angle in T. 
     The calculated spectrum fitted to the measured spectrum example are superimposed in  FIG. 4  represented by spectra  401  and  403 . The fitted backscattering spectrum is depicted by  406 . In  FIG. 5 , extracted n is illustrated by curve  502  and extracted k is shown by curve  504 . 
     In the above example, the determined parameters are listed in below Table 1: 
     
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Diameter 
                 n@589 
                   
               
               
                 Parameters 
                 (μm) 
                 nm 
                 Density (×10 9 /ml) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Calculated 
                 0.49 
                 1.59 
                 2.6 (0.2 mm vessel), 
               
               
                 (from measurements) 
                   
                   
                 2.3 (0.5 mm vessel) 
               
               
                 Nominal (from vender) 
                 0.50 
                 1.59 
                 2.5 
               
               
                   
               
             
          
         
       
     
     An apparatus  600  for combined angle selective scattering measurement and transmittance measurement with a single T and S detector in accordance with a second embodiment of the invention is depicted in  FIG. 6 . In apparatus  600 , the impinging light beam  10  is concentrically surrounded by a motored aperture  609 ,  611 . The first and second aperture segments  609  and  611  may be combined and/or independently moved along the axis  610 A. Movement of the aperture segments  609 ,  611  offsets their respective aperture edges  607 ,  605  providing a cylindrical opening that is concentric with respect to the impinging light beam  10  and the vessel  44 . The cylindrical opening has a varying height that may be remotely controlled via the motored aperture segments  609 ,  611 . Scattered light  16  may propagate only through the variable opening in a predetermined scattering angle, θ, its range, Δθ. 
     The scattered light  10  passing through the cylindrical opening impinges on an ellipsoidal mirror  603 , in the following preferred configuration. The ellipsoidal mirror  603  is positioned such that its first focal point coincides with the focal point of the impinging light beam  10  and the vessel  44 . At the second focal point of the ellipsoidal mirror  603 , an optical receiver  601  in the form of an optical fiber end may be placed to receive the scattered light  16  and to direct it further towards a sensor. Alternatively an optical element(s) such as a lens or mirror may be appropriately placed in order to collect light from the second focal point, as may be well appreciated by anyone skilled in the art. The combination of the concentrically arranged mirror  603  and the concentrically arranged aperture segments  609 ,  611  allows all of the light  16  scattered in a predetermined angle θ and predetermined range Δθ around the axis  610 A to be substantially collected for measurement. 
     The optical receiver or collecting components  601  is preferably positioned on and aligned with the optical axis  610 A. A selectively removable door  613  may be opened such that transmitted light  18  may be directly captured by the light receiver  601  while the moveable apertures  609 ,  611  are closed. As a favorable result, T and S may be measured with a single spectrometer in well known optical communication with the light receptacle  601 . Such single spectrometer may preferably be a CCD detector. 
     An apparatus  700  for combined angle selective scattering measurement and transmittance measurement with a separate T and S detector, in accordance with a third embodiment of the invention, is depicted in  FIG. 7 . Apparatus  700  is similar to apparatus  600  except that it is configured for independent and/or simultaneous S and T measurements. Instead of the removable door  613 , a redirecting mirror  736  may direct the transmitted light  18  away from the optical axis  710 A and out of the path of the scattered light  16 . A second light receiver  738  that may also be an optical fiber end or collection components may receive the transmitted light  18 , simultaneously with the first light receiver, receiving the scattered light  16 . The second light receiver  738  may be in well known optical communication with an intensity sensor  38 , preferably configured as PDA sensor. This transmittance sensor  38  operates in conjunction with a scattering sensor  42  as explained under  FIG. 2 . The scattering sensor is in well known optical communication with the first optical receiver  701 . A focusing mirror  715  may be positioned in the impinging light  10  path between the light source  732  and the vessel  44  such that the light source  732  may be placed out of the optical axis  710 A giving room for structural components that guide and move the aperture segments  709 ,  711 . 
     Ellipsoidal mirrors  603  and  703  are preferred since they provide refocusing of the scattered light  16  in a single step, which results in minimal deterioration of the scattered light  16 . Nevertheless, the scope of second and third embodiment may include other curved mirrors such as parabolic, and/or toroidal mirrors. 
     Capturing the scattered light  16 , in a substantially circumferentially continuous fashion, is accomplished by the combination of cylindrical aperture  609 ,  611 ,  709 ,  711  and mirrors  603 ,  703  that are circumferentially positioned with respect to the impinging light beam  10 . This, in combination with angle selective scattering measurement accomplished by the motored aperture segments  609 ,  611 ,  709 , and  711 , provides maximum signal intensity and signal to noise ratio of the scattered and captured light. Moreover and also due to the motored aperture segments  609 ,  611 ,  709 , and  711 , scatter angle resolution can be selected independently, which may additionally contribute to measurement accuracy as may be well appreciated by anyone skilled in the art. 
     Simulation results of angular dependent scattering are depicted in  FIGS. 8-10 . In  FIG. 8 , curves  802 ,  804 ,  806  and  808  illustrate, in an arbitrary unit, the scattering intensities for 0.5 μm PSL suspended in DI water at scattering angles θ of 45, 90, 135 and 180 degrees respectively. In  FIG. 9 , curves  902 ,  904 ,  906  and  908  depict the simulated intensities, also in an arbitrary unit, for 0.05 μm PSL suspended in DI water at scatter angles θ of 45, 90, 135 and 180 degree respectively. It is noted that scattering intensities are higher at shorter wavelength. In  FIG. 10 , the curves  1002 ,  1004 ,  1006  and  1008  show simulated scattering intensities of 1.0, 0.5, 0.1 and 0.05 μm PSL particles at 400 nm wavelength. 
     Accordingly, the scope of the invention described in the Figures and Specification above is set forth by the following claims and their legal equivalent: