extending laser diffraction for particle shape characterization_ technical aspects and application

1、? . Powder Technology 118 2001 180–187www.elsevier.comrlocaterpowtecExtending laser diffraction for particle shape characterization: technical aspects and applicationZhenhua Ma), Henk G. Merkus, Brian ScarlettParticle Te

2、chnology Group, Faculty of Applied Sciences, Delft UniÕersity of Technology, Julianalaan 136, Delft 2628 BL, NetherlandsAbstractExtending the laser diffraction technique to measurement of both particle size and shap

3、e is quite an interesting topic, especially for on-line process control and monitoring. It is possible as the scattering pattern of particles contains both types of information. This article describes the application of

4、a novel sensor with two-dimensional pixel arrays for obtaining particle shape information. The fluctuating scattered light intensities in the azimuthal directions are transformed via cross-correlation into Particle Angle

5、 Spectra, which reflect the shape information. Possibilities for improvement of this information by using single-sweep analysis, small numbers of particles in the measurement zone, principal component analysis and Fourie

6、r analysis are discussed. Its potential for application is demonstrated by monitoring the shape change of cubic crystals during attrition. q 2001 Elsevier Science B.V. All rights reserved.Keywords: Laser diffraction; Par

7、ticle shape; On-line measurement1. IntroductionParticle shape is a very important characteristic of particulate matter, as is particle size. Both shape and size are directly related to the product quality and have consid

8、- erable effect on many processes. Therefore, on-line shape measurement, together with particle sizing, can play an important role in control of particulate production pro- cesses. Particle shape characterization is norm

9、ally done by w x sensing and analyzing particle images 1,2 . In these im- ages, the particle contour lines are usually either com- pressed by using shape factors, such as fractal dimension or aspect ratio, or they are tr

10、ansformed by Fourier analysis into a set of Fourier coefficients to reflect particle shape information. Until now, most of these image analysis methods are based on off-line analysis and are time-con- suming. Therefore,

11、it is difficult to adapt them for on-line process control. At present, laser diffraction is a very popular technique for measurement of particle size distributions. It has the advantage of being a fast, non-intrusive and

12、 reproducible technique and it is being used in a large variety of particu- w x late processes 3 . In a normal laser diffraction measure- ment, a parallel laser beam illuminates a collection of) Corresponding author. Fax

13、: q 31-15-278-4452. ? . E-mail address: z.ma@tnw.tudelft.nl Z. Ma .dispersed particles; the resulting scattering pattern, to- gether with the remainders of the laser beam, is collected and focussed by a lens to its back

14、focal plane. Here, normally a series of detector elements is placed to record the diffraction pattern and the extinctionrobscuration of the incoming beam. In absence of these detectors, of course the light wavelets furth

15、er propagate and arrive at the image plane. Here, they overlap and interfere to form an inverted image of the particles collective. Thus, the lens forms two distinct patterns of interest. One is the Fourier ? . transform

16、 on the back focal plane, conjugate to the plane of the source, i.e., the diffraction pattern. The other one is the image of the object, formed at the plane conjugate to the object plane. Both patterns contain the same i

17、nforma- w x tion 4 . An alternative way for obtaining particle shape information is, therefore, to directly sense the scattering pattern from the particles. In the present laser diffraction instruments, the particle size

18、 information is obtained by assuming spherical particles. In view of the advantages of this technique, its extension to particle shape measurement has become quite an interesting topic, especially for on-line process con

19、trol and monitoring. For measuring particle shape, both effective sensing and analyzing the scattering pattern are required. When particle size is significantly larger than the inci- dent wavelength or its refractive ind

20、ex is significantly different from the surrounding medium, most of the light is0032-5910r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. ? . PII: S0032-5910 01 00309-6( ) Z. Ma et al.rPowder Tec

21、hnology 118 2001 180–187 182sensor was used, the Fuga 15d, with 512=512 pixels and a 7.3=7.3 mm2 sensor area. It is manufactured by C-CAM Technologies, Belgium. The ArD converter of the device is set to cover four decade

22、s of light intensity, which is sufficient to cover the dynamic range of scattering pattern in most cases. The maximum pixel readout speed is 4 MHz; the speed for reading out full frames depends on the performance of PC.

23、For Pentium 166, the frame speed is 5 framesrs. This speed is large enough for particle sizing. For shape measurement, a higher frame speed is required, since particles are moving in the measurement cell and their projec

24、tion should be stable during the measurement of one frame. Due to the flexible pixel address function of this sensor, the required frame speed can be obtained by selecting a suitable lower number of pixels. Of course, th

25、e pixel number should still be large enough to deliver suffi- cient resolution. In our current measurement cell used, a speed of 300 framesrs is high enough to take particle movement into account; accordingly, the number

26、 of pixels ? . comes out at about 4000 with Pentium 166 . For the application of size andror shape measurement, the pixels can be grouped to form a simulated detector array with certain geometry in order to improve the s

27、ignal-to-noise ratio of the signals. For the shape case, a wedge type of detector geometry was used, the inner and outer bound- aries of which were chosen in relation to the range of particle sizes present. For the gener

28、al case, it can be concluded that the high dynamic range and flexible pixel readout enable this device to be applied as a robust and flexible on-line sensor for both particle size and shape. As the inherent relationship

29、between signal and light intensity is different for the pixels, each pixel must be calibrated in order to be useful in laser diffraction, espe- cially for particle sizing. This can be done by taking the w x sensor respon

30、se at the given different light intensities 9 . Based on this CMOS detector, a new measuring system ? . was built see Fig. 2 . The optical setup uses a reverse Fourier system and consists of a 1.25-mW He–Ne laser of ? 0.

31、6328 mm wavelength, a Fourier lens with a focal length . ? f , the effective focal distance distance between detector . and sample cell d of which is selected depending on the particle size of the sample, and a narrow fl

32、ow cell of 2 mm path length, all aligned on an optical bench. The detector isFig. 2. Instrumentation setup.positioned at the focal plane to record the diffraction pattern images. These images are then processed by the co

33、mputer. In addition to the above equipment, we used a CCD camera for monitoring of particle images during attrition ? . see Section 5 .3. Signal processingThe general signal-processing procedure is envisaged to be as fol

34、lows. The scattering pattern images of particles are measured in a number of sweeps at a certain resolution per image frame. After locating the scattering center, the calibrated values of these pixels are grouped into a

35、wedge-type detection area and thereby averaged to imitate the azimuthal signals of the wedge-type detector. In order to characterize the average particle shape infor- mation, a set of time-averaged correlation values bet

36、ween w x pairs of wedges was calculated as follows 6,10 :N 1r s r , 3 ? . Ý m i,iqm N is1where the cross-correlation coefficient r is: i, jNs L ym L ym ? . ? . Ý i,s i j,s j ss1 r s . 4 ? . i, j N N s s 2 2 L y

37、m L ym ? . ? . Ý Ý ) i,s i j,s j ss1 ss1These correlation coefficients represent the degree of correlation of signal fluctuations between two wedges: they are zero if the fluctuations are not correlated and one

38、 if they are completely related. As the correlation matrix in ? . Eq. 4 is symmetric, the r values also show symmetry. m Therefore, normally, the values in the range of 0–1808 of correlation angle are used to plot a corr

39、elation graph, called the Particle Angle Spectrum, which characterizes the shape information. Fig. 3 gives a simulated result for three different shapes of particle projection: circle, square and ellipse. In practice, th

40、is correlation graph, however, appears to be rather sensitive to the number of particles in the mea- surement zone. An increasing number of particles is detri- mental to the shape information. The best information, there

41、fore, can be obtained by allowing only one or a few particles to be present at the same time in the measurement zone. This can be done by decreasing the concentration or the beam diameter. Of course, one has to ascertain