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Apparatus for real-time measurement of particle size distribution
P o w d e r Technology, 20 (1978} 273 - 284 ~) Elsevier S e q u o i a S.A., Lausanne - - P r i n t e d in t h e N e t h e r l a n d s
Apparatus
for Real-Time Measurement
273
of Particle Size Distribution
J A N U S Z W. S A D O W S K I a n d E E R O B Y C K L I N G
Helsinki Un;-versity o f Technology, D e p a r t m e n t o f Technical Physics, S F - 0 2 1 5 0 Espoo I 5 ( F i n l a n d ) (Received March 20, 1978)
In this paper we describe an apparatus for real-time measurement of particle size distribution. By introducing a fast moving water stream with suspended particles and stroboscopic illumination, a large number of pictures (samples) can be analysed by means of a TV c~mera connected to a computer. In this manner complete particle size distribut i o n is a c h i e v e d w i t h m i n i m a l d e l a y . S a t i s f a c tory results were obtained when the apparatus was tested as an on-line device in a flotation plant, demonstrating the full ability of the system to control the flotation process.
I . INTRODUCTION 1.1 l~lethods for deterrnining particle size distribution Particle size determination has applications in many fields. It can be used in studies of polluted atmospheres and waters, flotation processes, paint industry, cement industry, powder technology, industrial hygiene, etc. A number of different methods have been developed for these applications. Generally, all methods depend on the properties and size of the particles, desired accuracy of the measurement and the environment of the particles. They can be classified into seven groups:
(i) Sieving (2) M e t h o d s employing gravitation (a) sedianentation (b) elutriation (c) centrifugal (3) T h e Coulter Counter ~4) P e x m e a m e t r y
(5) S u r f a c e a r e a m e a s u r e m e n t adsorption
phenomena
-- mainly
(6) Optical (7) Miscellaneous There are several methods in each group, and good descriptions of these methods exist in the literature [1 - 3]. Here, a brief discussion of the optical methods only will be given. T h e t-Lrst o p t i c a l m e t h o d u s e d t o d e t e r m i n e particle size was microscopy. In this method, the individual particles are measured and classified by means of various ocular micrometers, photomicrographs or microprojection. P a r t i c l e t h i c k n e s s is m e a s u r e d b y f o c u s i n g t-urst o n t h e t o p a n d t h e n o n t h e b o t t o m o f the particle and reading the difference on the micrometer drum. The useful particle size range for microscopy, in principle, is limited only by the resolving power of the objective used, and for visual light it is 2 - 100 pro. By use of electron microscopy (TKM or SEM) particles of size 0.001 - 5/zm call be measured. In all kinds of microscopical determinat i o n o f p a r t i c l e s i z e d i s t r i b u t i o n , s a m p l i n g is the most critical and greatest source of errors. For such a time~onsuming method, a proper sample must be chosen to be statistically representative. To improve the efficiency of microscopical investigations, around 1950 some authors [4 - 6] tried to solve the problem of replacing the human operator by an electro~)ptical system. They first developed scanning techniques in microscopy by memus of a scanning slit [4] or scanning spot [5]. At the present time the task is
accomplished b y commercially available automatic picture analysers [7 - 11] connected to a computer. T h e image shearing method, applied in microscopy [12], also decreases the h u m a n involvement in the measurement process, but is not fully automatic. Using such instruments the time needed for determination of particle size
274 d i s t r i b u t i o n f r o m a s a m p l e is r a d i c a l l y r e d u c ed and more samples can be tested in a given t i m e , b u t p r o p e r s a m p l i n g is s t i l l v e r y impo~ant. IAght-scattering methods of particle size determination also use optical phenomena. Usually a ratio of intensities at different a n g l e s a n d f o r d i f f e r e n t w a v e l e n g t h s , as w e l l as a s t a t e o f p o l a r i z a t i o n o f t h e s c a t t e r e d l i g h t , is m e a s u r e d [ 1 3 ] . R e c e n t l y , m u c h a t t e n t i o n has been paid to solving theoretically and in practice the problem of light scattering by a ~ b i t r a r i l y s h a p e d p a r t i c l e s [ 1 4 , 1 5 ] , w h i c h is important especially in remote sensing techniques and other measurements of inaccessible particles. T h e a n a l y s i s o f d i f f r a c t i o n patte_--ns c a n b e a useful technique for particle size measurem e n t , b u t i t is s t i l l d i f f i c u l t t o i n t e r p r e t t h e data for particles of an arbitrary shape [16, 171_ Lately, some new optical methods have been reported_ Jin Wu [18] has developed an optical instrument to measure particle size and velocity. In the apparatus two parallel laser beams, shifted along the direction of par*Acle m o t i o n a n d l a t e r a l l y f r o m t h i s d i r e c tion, are detected by two photo-transistors. It is c l a i m e d t h a t a f t e r e l e c ~ o n i c e x ' a m i n a t i o n o f the dark signal given by moving particles, the size and velocity can be deduced approximately. This method, however, does not give high accuracy of particle size measurement a n d is m o r e c o n v e n i e n t f o r v e l o c i m e t r y . Some authors [19 - 22] have used holography to measure particle size and velocity. A zhree~imensional scanner, for quantitative particle analysis from a real holographic i m a g e , is a l s o c o m m e r c i a l l y a v a i l a b l e [ 8 ] . B u t , because of the time needed for the preparation of the hologram, holography cannot be used for real-time measurement. The method described in the present work is b a s e d o n a f a s t c o m p u t e r a n a l y s i s o f particle images given on a two
2. S T R O B O S C O P I C SYSTEM FOR MEASUREMENT OF PARTICLE SIZE DISTRIBUTION
2.1 Basic idea As mentioned above, the system described in t h i s p a p e r is i n t e n d e d f o r t h e c o n t r o l o f t h e flotation process. The particles, the size of w h i c h is t o b e m e a s u r e d , a r e m i n e r a l s , m a i n l y metal ores. The photomicrograph on Fig. 1 shows their arbitrary and sometimes very complicated shape. In principle, the most exact method for measuring particles of an a r b i t r a r y s h a p e is t h e m i c r o s c o p i c m e a s u r e ment of each individual particle. At present a number of microscopic devices with computer p i c t u r e a~u~ysers e x i s t [7 - 1 1 ] , b u t i t is s t i l l difficult to use them for on-line measurement, because the time needed for the preparation o f s a m p l e s is r e l a t i v e l y l o n g . T o a v o i d t h i s , and many other problems, an apparatus used should meet the follo~-ing requirements. It should ( 1 ) g i v e a l a r g e n u m b e r o f s a m p l e s in a short time for the analyser, (2) make fast analysis of given samples, (3) give an o u t p u t w i t h m i n i m a l d e l a y , easy to read by an operator, (4) w o r k c o n t i n u o u s l y in p l a n t e n v i r o n ment without failure, (5) keep error within estimated limits, (6) be easy to operate, and (7) be easy to change to different applications. To solve requirement no. (1), one has to decrease the time needed for sample preparation. It should be shorter than the time needed by a computer to analyse a single picture. The solution has been found in the following manner: the particles, diluted in water, are r u n n i n g in a l a m i n a r s t r e a m i n f r o n t o f a
"C o
Fig. 1. Copper ore particles.
~ -:j
275 rrAcroscope connected to a TV camera. A short light pulse (0.6 ps) "'captures" them and forms an image on a TV imaging device (twodimensional photodiode array). Since all i n f o r m a t i o n f r o m t h e w h o l e i m a g e a r e a is s t o r e d i n t h e T V c a m e r a s i m u l t a n e o u s l y , i t is sufficient to use only one light pulse to get o n e c o m p l e t e s a m p l e . A f t e r o n e i m a g e is processed, the next one can immediately be taken. In this way the speed limitations are mainly determined by the computer. To test this basic idea, the photographing system, shown schematically in Fig. 2, was built. By means of this system we studied the question: is it possible in practice to capture moving particles with a stroboscopic light? The photographing system consists of a nozzle (I) producing a stream of water with particles, a low power microscope objective (2) connected to the Polaroid camera (3), and a flash lamp unit (4). To get pictures without optical distortion, the stream has to be laminar, without standing waves, and of good optical surfaces. This can be achieved by means of the special nozzle, as described by R u n g e [ 2 3 ] . A s i m i l a r n o z z l e ~vith t h e s h a p e adopted to the use of low viscosity liquids, such as water, has been designed. The results obtained with the help of this system were quite satisfactory. On the series of photographs there were no apparent signs of particle movement, and the resolution and focus were good. Figure 3 shows a series of t h r e e s h o t s d o n e o n o n e P o l a r o i d f ' d m . I t is interesting to see that in a fast stream the particles have no tendency to join together and with sufficient dilution they do not cover each other on the image. Careful study of the photographs gave a wealth of useful information for further design of a prototype, connected with writing a computer program or improving the optics
/
/
/
A
Fig_ 3. Photographs o f m o v i n g particles.
o f t h e s y s t e m . F o r e x a m p l e , f r o m ~he p h o t o s one can estimate an approximate number of quartz particles, which are almost transparent and always have a brighter centre with a dark boundary. The appearance of such cases must be accounted for in the computer programme. I f t h e l i g h t i n t e n s i t y is i n c r e a s e d , s m a l l e r p a r t i c l e s b e c o m e i n v i s i b l e . I f i t is n o t n e c e s sexy to count these, better contrast for :,arger ones can be achieved. Also, in this inexpensive way, other parameters can be tested, such as sensitivity for defocusing, small fluctuations of the stream, application of microscopic contrast techniques -- phase and interference contrast, etc. A large number of such investigations at this first stage allowed us to make optimum decisions on the construction of the prototype. 2.2 Optical system The apparatus for real-time determination of particle size distribution consists mainly of the previous experimental device, With the Polaroid camera replaced by a TV camera and a computer. A schematic diagram of the total s y s t e m is s h o w n i n F i g . 4 . 6
_L
__2
__3
/
/
Fig_ 2. S c h e m a t i c diagram o f the photographic s y s t e m . (1) N o z z l e , ( 2 ) m i c r o s c o p e objective, (3) Polaroid camera, (4) flash lamp.
Fig. 4. S c h e m a t i c diagram o f t h e s y s t e m f o r real-time d e t e r m i n a t i o n o f particle size d i s t r i b u t i o n . T h e n u m b e r s have the f o l l o w i n g m e a n i n g : (1) nozzle, (2) m i c r o s c o p e objective, (3) T V camera, (4) c o m p u t e r , (5) s t r o b o s c o p e , (6) condenser.
27fi The purpose of the TV camera, in the form o f a t w o - d i m e n s i o n a l p h o t o d i o d e a r r a y , is t o change the optical image of the particles into analog signals for further processing_ The RCA 53232 silicon imaging device, having a 5 3 2 X 3 2 0 e l e m e n t s e n s o r , is u s e d t o p r o d u c e electronic signals from a visual input. The image area of the device has dimensions 7.33 × 9.25 mm, and thus the size of a single i m a g e c e l l is 0 . 0 3 X 0 . 0 3 r a m . B a s e d o n t h e geometry of this device, one can estimate useful magnification, calculate depth of field and check the resolving power. These calculations are necessary, for proper design of the system. I n t h e f l o t a t i o n p r o c e s s i t is u s e f u l t o h a v e information about the particle size distribution within the range 6 - 250 pro. The smaller particles cause most difficulties, because they require higher magnification and better r e s o l u t i o n . I n a r e a l - t i m e s y s t e m t h e r e is n o time for changing the magnification, and the optimal one must be chosen_ In order to simplify these brief design calculations, we will assume an ideal case of square particles. ~'aen a particle covers a part of a single image cell, an analog signal, proportional to the c o v e r e d a r e a , is c r e a t e d . T h e d i s c r i m i n a t i o n leve! of the digitizer (see Section 2.3 for explanations) can be set on a value causing change from 1 into 0 when 50% of the cell a r e a is c o v e r e d . T h u s , a n i m a g e o f t h e s m a l l e s t p a r t i c l e s h o u l d h a v e t h e d i m e n s i o n s d." = 0 . 0 3 / x/2 = 0.02 ram. The size of the smallest p a r t i c l e o f i n t e r e s t is 6 g i n , s o t h e m a g n i f i c a t i o n s h o u l d b e J3 = ~ ' / ~ = 3 . 5 . A n i m a g e o f t h e l a r g e s t p a r t i c l e w i l l h a v e d i m e n s i o n s ¢" = 0.875 ram. The depth of field can be calculated with the help of Fig. 5 (after [24] ). It shows schematically an arbitrary optical system (e.g. lens, objective, etc.) with entrance pupil Z, exit pupil Z', and conjugate object and image p l a n e s ~ a n d ~" r e s p e c t i v e l y . I f o n e c o n s i d e r s p o i n t o b j e c t A i n t h e o b j e c t p l a n e ,w a n d neglects aberrations and diffraction, an image A" i n t h e c o n j u g a t e p l a n e r." w i l l a l s o b e a point. Other point objects located on other p l a n e s (e.g. ~ o r ~ 2 ) p a r a l l e l t o ~ , b u t s o m e d i s t a n c e a p a r t , swill n o t f o r m p o i n t s , b u t s p o t s in the plane ~'. Now, image detectors have u s u a l l y ~ m i t e g r a i n s t r u c t u r e (e.g. e y e , p h o t o graphic emulsion, photodiode array), so there is s o m e l i m i t i n g s p o t , w h i c h is s t i l l d e t e c t e d a s
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Fig. 5_ D e p t h o f field o f an a r b i t r a r y o p t i c a l s y s t e m . See t e x t for e x p l a n a t i o n . a p o i n t . T h e d i a m e t e r o f t h i s b o u n d a r y s p o t is usually equal to a dimension of a single grain. T h e d e p t h o f f i e l d is t h e r e f o r e a m a x i m u m distance between arbitrary planes parallel to ,~, f r o m w h i c h a l l p o i n t o b j e c t s a r e s t i l l d e t e c t ed by a defined detector as points, not spots. First we define front Ap and back At depth o f f i e l d ( s e e F i g . 5}. F r o m t r i g o n o m e t r i c r e l a tions we obtain c~z
--b --Ap
A/o
Ap
--b --÷3 Alo
w h e r e ~ z is e n t r a n c e p u p i l d i a m e t e r a n d b is the distance from the object to the entrance pupii. Inserting a magnification factor/3 = A l ' o / A l o , Al'o = m a x i m u m s p o t s i z e , o n e g e t s --b X p
-
-
I'-~o ÷ 1 For a low power microscope objective an a p e r t u r e a n g l e is s m a l l , a n d o n e c a n w r i t e , with a good approximation, ~z = 2b NA, NA = n s i n u, n --- 1 . T h i s y i e l d s _kp • -~
--b
12 b
I
-X77o i +3
a n d s i m i l a r l y f o r At: b
12 b NAt_ 1 At;
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In this particular case, because of large b and small Al~, with/~ = 3.5 ×, the fractions in the denominators will have a large value, so without introducing large errors (approx.
277 0.01%), one can neglect --1 and +1 in the denominators. Thus Ap = --A t, the negative sign appearing according to the sign rules in optics, and finally A = A t -- Ap -
Alo NA
The numerical value, if Alo = 0.03, 5 = 3.5 X, N A = 0 . 0 5 , is _~ = 0 . 2 m m . Thus, the thickness of the laminar stream should be 0.2 mm to achieve a sharp image of all parLicles w i t h i n t h e e s t i m a t e d size r a n g e . R e l a t i v e e r r o r s d u e t o c h a n g e s in s t r e a m t h i c k n e s s , as w e l l as d e f o c u s i n g e r r o r s , a r e d i f f e r e n t for different sizes. Generally, the relative error can be expressed by a function
B =
$D
NA
-
- 100%
W w h e r e B is the relative error for particles o n the b o u n d a r y of the stream, 5 D is the deviation of the stream thickness, or defocusing related to the object space, a n d IV is the n o m i n a l d i m e n s i o n of the particle. It is obvious that proper determination of the smallest particles is e x t r e m e l y sensitive for defocusing. A thin laminar stream with particles, especially w h e n it has to w o r k c o n t i n u o u s l y i n a n i n d u s t r i a l p l a n t , is m o r e difficult to achieve than a thick one. Too big particles can cause blocking of a nozzle and stopping of the whole system, and therefore p e r i o d i c a l c l e a n i n g is r e q u i r e d . A n i m p r o v e ment could be achieved by diminishing the measurement range, or dividing it into two, one for small particles, with high magnification and very thin stream, and the second with low magnification and thick stream. In this case, however, some presizing of the p a r t i c l e s is n e c e s s a r y . D e c r e a s e o f t h e r a n g e will lead to more satisfactory jet parameters. For example, if the smallest measurable p a r t i c l e is t a k e n t o b e 2 0 p m ( r a n g e 2 0 2 5 0 / L m ) , t h e u s e f u l m a g n i f i c a t i o n is 1 X a n d the depth of field, i.e. permissible stream thickness free of defocusing errors, extends to 0.6 ram. The resolving power of the microscope objective u~l in the system can be calculated from the formula d = k/2 NA. If we have k = 0.45/zm, fromNA = 0 . 0 5 o n e g e t s d = 4 . 5 pro_ T h i s r e s o l u t i o n is m o r e t h a n s u f f i c i e n t . I t is, of course, well known that large depth of field means low resolution, and vice uersa.
The illumination system consists of the stroboscope (5) and the condenser (6). The requirements for the condenser are the following. The numerical aperture of the condenser must match the numerical aperture of the objective used, and it must illuminate t h e c o m p l e t e f i e l d o f v i e w . T h i s is e a s y t o attain by employing a commercially available condenser matched with the objective. The r e q u i r e m e n t f o r t h e s t r o b o s c o p e b u l b is t o produce enough light, sufficient to illuminate the photodiode army. In this system, flashtubes FX-35B or FX-101B from EG & G have been chosen because of their short pulse durat i o n , 0 . 6 # s . I t is u s e f u l t o c a l c u l a t e t h e p o w e r output of the light source. The electrical data of the flashtubes are: pulse duration t = 0.6 ps e n e r g y i n p u t p e r f l a s h Ein = 0 . 0 0 1 3 W s efficiency of tubes E t = 5 - 10 lm per watt arc surface approx. S = 5/16 x 5/64 in 2 = 0.16 mm 2 Thus, one can calculate the light emission for the lower value of the tube efficiency, = E=Et
= 6.5 • 10 -3 lms
candle power, I=--d~ =0.52. 4;r
10 -3 cds
luminance, L-
I
-8.26-
103nts
S and illumination E'h~
of the photodiode
array:
sin2u = 7rTL - -- 1 . 6 7 l x s /32
w h e r e T = 0 . 8 is t h e a s s u m e d t r a n s m i t t a n c e coefficient, sin u = 0.05 and/3 = 3.5 X. In the case of the highest efficiency, the illumination reaches the value E~ax = 6.688 Ix s Saturation exposure p h o t o d i o d e a r r a y is
required
for
the
E~'at = 2 . 6 7 " 1 0 - 3 f c s = 0 . 2 8 7 I x s B y c o m p a r i s o n o f t h e s e v a l u e s i t is c l e a r that the above flashtubes exceed the requirement and can be used in the system, together with filters and an aperture diaphragm, in the whole efficiency range.
278
2.3 I n f o r m a t i o n p r o c e s s i n g
IG]
Processing of the information obtained by t h e o p t i c a l s y s t e m is d o n e i n t h r e e s t e p s : (1) v i d e o p r o c e s s i n g in t h e T V c a m e r a , (2) digitization of electronic signals and adaptation of them for a computer, (3) c o m p u t i n g . A synchronization and control logic system f r o m t h e T V c a m e r a is u s e d t o t r i g g e r t h e flash lamp unit. The end of the vertical blanki n g i n t e r v a l p l u s 1 0 ;Lm d e l a y d e t e r m i n e s t h e beginning of the triggering pulse. In this way, independently of the computer requirement f o r a n e w p i c t u r e t o a n a l y s e , all even ( o r o d d ) lines are illuminated wkh the stroboscopic l i g h t . S i m u l t ~ a e o u s l y ~vith t h e n u m e r i c a l a n a l y s i s , a n o r m a l v i d e o o u t p u t is t a k e n f r o m the camera for monitor control (Fig. 6). T h e m a i n p a r t o f t h e T V c a m e r a is a s i l i c o n imaging device, constructed with a 3-phase, N-channel, vertical frame organization (see Fig. 7). Its image area consists of an array of analog CCD (Charge-Coupled Device) shift registers c:,ntaining 320 parallel vertical c o l u m n s ~f 2 5 6 s e n s i n g c e l l s d r i v e n w i t h t h r e e register -'locks. When vertical register clocks a r e p u b :l svith t h e v o l t a g e w a v e f o r m s , a l i g h t i m a g e f o c u s e d o n t h i s r e g i s t e r is i n t e g r a t e d into a charge pattern of electrons during the normal active TV display time and transferred to the storage area during the vertical blanking interval. The horizontal register receives one line of picture information from the storage area during each horizontal blanking i n t e r v a l , a n d t h e n t h e C C D s i g n a l is e x t r a c t e d by the output circuit. In a normal TV display, t h e e f f e c t i v e n u m b e r o f v e r t i c a l e l e m e n t s is interlaced by alternation of second and third
..
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Fig. 7 . B l o c k d i a g r a m o f t h e i m a g i n g d e v i c e .
register clocks and approximately 482 lines are displayed, but in the particular case of the particle size measurement system, only even ( o r o n l y o d d ) l i n e s a r e u s e d , i.e. 2 4 1 l i n e s . An analog charge pattern formed in the imaging device and representing an image of the particles must be digitized for input to a c o m p u t e r . T h i s is d o n e b y m e a n s o f t h e Camera-to-Computer Adapter Unit (C.C.A.U.). Figure 8 shows a block diagram of the information processing system. Because of the long distance (approx. 20 m) between the camera operation place and the computer r o o m , t h e Line T r a n s c e i v e r U n i t (L_T.U.) h a s to be used to amplify signals leaving the camera. These signals are amplified again just when they enter the C_C.A.U. Digitalization o c c u r s in t h e C o m p a r a t o r , w h e r e c h a r g e p a t t e r n o f e l e c t r o n s is c o m p a r e d w i t h a p r e s e t voltage value. For every clock pulse, if a signal
Fig. 8. Block diagram of the information processing
Fig-6-TVpictureofmovingparticles.
system. The meaning o f t h e a b b r e v i a t i o n s is: LTU - Line Transceiver Unit, SPC - - Serial to Parallel Convertor, r ' - ~ A U - Camera-to-Computer A d a p t e r Unit.
279 from the camera exceeds this value, the c o m p a r a t o r gives o u t p u t s i g n a l 1 , o t h e r w i s e s i g n a l 0 is p r o d u c e d . B y c h a n g i n g Lhe c u t - o f f level during calibration, an optimum value can be estimated to eliminate low energy signals representing particles too small and unwanted in the measurement or noise. To compute results, the PDP-11 16-bit m i n i c o m p u t e r is u s e d . T o b e a c c e p t a b l e t o t h e computer, the output from the camera has to be converted from series to 16-bit parallel s i g n a l . T h i s is d o n e i n t h e S e r i a l - t o - P a r a l l e l C o n v e r t e r . In this m a n n e r e v e r y T V line gives twenty 16-bit words. A part of the digital input received by the c o m p u t e r is s h o w n as a n e x a m p l e i n F i g . 9 . It represents one-third of the field of a single p i c t u T e in X d i r e c t i o n a n d o n e - f i f t h i n Y d i r e c t i o n . I n t h e w h o l e f i e l d t h e r e axe 2 4 1 lines, each line divided into 320 parts. Thus the position of every point in the TV picture is d e t e r m i n e d b y X a n d Y c o o r d i n a t e s . W h e n the computer, analysing point by point every l i n e , m e e t s t h e ~-~rst s i g n a l 0 , i t gives t h e p o s i -
tion (address) of this point to the memory and reserves this place. When a continuum of 0-signals coming from one particle in the first l i n e is e n d e d , t h e c o m p u t e r s t o r e s t h e a d d r e s s . T h e s a m e p r o c e d u r e is r e p e a t e d f o r t h e n e x t particles in the same line. When the next line is s c a n n e d a n d t h e c o m p u t e r g e t s 0 - s i g n a l s f r o m a p a r t i c l e , i t r e a l i z e s i f t h e c o m i n g 0s i g n a l s b e l o n g t o t h e s a m e p a r t i c l e as i n t h e l i n e a b o v e , a n d t h i s is t a k e n i n t o a c c o u n t in constructing the complete particle. In order to avoid problems due to single s i g n a l s 1 i n t h e p i c t u r e , t h e r e is a p r o c e d u r e t o add 0-signals to both ends of a line of zeros. This procedure of adding pixels gives a limitation for the separation of two single particles. If they touch each other at corners, like: ...000 ...000 000..
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280 s e p a r a t i o n o f m i n i m u m 2 c o l u m n s is n e c e s s a r y _ W h e n t h e f i e l d is c o m p l e t e d , a s u m o f a l l the points under one address is calculated to obtain the measurement of a projected surface area. Particles with a transparent "'hole" i n t h e m i d d l e , e.g. q u a r t z p a r t i c l e s , c a n a l s o b e recognized by the programme, and in this case the procedure is as foUows. The upper edge of the particle is processed in the same way as for a "'normal" case. The computer scanning t h e f i r s t l i n e m e e t s F~rst 0 s i g n a l s a n d d e t e r mines the address. If in one of the next lines t h e r e is a n i n t e r r u p t i o n i n t h e c o n t i n u u m o f 0 signals, but with both parts belonging to the s a m e a d d r e s s , i t c a n m e a n t w o cases= ( 1 ) t h e particle has "'~'" shape, or (2) it has a "'hole". The next lines can still contain similar interruption, so the last or the closing line of this p a r t i c u l a r p a r t i c l e is d e c i s i v e . I f i t j o i n s together both arms, the computer counts this particle as a "'quartz"; ~ the "hole" remains o p e n , t h e p a r t i c l e is c o u n t e d a s a " ' n o r m a l " . I n t h e c a s e o f a m o r e c o m p l i c a t e d s h a p e , i t is sufficient for a particle to have only one "'hole" inside to be counted as the "'quartz"_ Particles of "'U'" shape are calculated first as two separate particles, and when the joining line is discovered, they merge together to create one bigger particle under the same address. In thi; manner, particles of different sizes are sel~.ted, separated from the transparent o n e s , a n d t h e n u m b e r o f t h e m is c o u n t e d within different size ranges corresponding to an imaginary mesh. In this way results directly comparable with the sieving technique are attained. After the analysis of one picture, the computer keeps the results in the memory and adds them to results from the next -
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pictures, up to a preset quantity. Common r e s u l t s a r e p r i n t e d o u t i n t h e -way s h o w n a s a n e x a m p l e i n F i g . 1 0 . T h e p n n t - o u t is c o m p o s e d of: (a) general information concerning all particles counted in a series of pictures, and (b) particle size distribution. The general information printed in the heading contains = n u m b e r o f a n a l y s e d pict,~uces, t o t a l n - t u b e r o f counted particles, number of transparent particles, average area, density, number of particles exceeding the measuring range, and t i m e o f t h e c o m p u t a t i o n . T h e s e c o n d p a r t is divided into ten columns in which the foUowi n g i n f o r m a t i o n is i n c o r p o r a t e d ( s e e F i g . 1 0 ) :
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281 V = ( ~ / p ) 3 , w h e r e P is t h e a v e r a g e a r e a f r o m c o l u m n no_ 8. The suitability of this method for industrial p r o c e s s e s h a s bee11 v e r i f i e d i n t h e f l o t a t i o n plant and compared with other methods_ 3. APPLICATIONS AND R E S U L T S
3.1 Applications The stroboscopic system described in this work can be applied in almost all processes where rapid determination of particle size d i s t r i b u t i o n is r e q u i r e d a n d w h e r e i t is p o s sible to form a laminar stream (of air or liquid) with suspended particles. The prototype of the apparatus has been used and tested in a flotation plant. F l o t a t i o n is a p r o c e s s f o r r e m o v i n g a n d concentrating valuable mineral ore from a mixture of ores and waste materials. The flotation process utilizes differences in the surface properties (surface energy or surface tension) to effect separation [25]. Usually, t h e gas p h a s e ( a i r b u b b l e s ) is i n t r o d u c e d i n t o aqueous medium with crushed minerals. The difference in adhesion permits removal of a p a r t i c u l a r m i n e r a l f r o m t h e b u l k as a f r o t h o f d i f f e r e n t c o m p o s i t i o n . F l o t a t i o n is w i d e l y used in the concentration of complex leadzinc--iron and copper-iron sulphide ores, non-sulphides such as mineral phosphates, potassium ores, fluorite and barite, cleaning of coal and in many other fields. Extensive treatments of the flotation process can be found in the literature [26 - 28]. The optimization of particle size in the flotation process has to take into consideration different conflicting requirements. For instance, for reasons of economy and minimum use of energy, larger particles are p r e f e r r e d i n f l o t a t i o n , b u t t h i s r e s u l t s i n a less purified product and higher losses via large a n d h e a v y p a r t i c l e s . A l s o , f l o a t a b i l i t y as a function of particle size has a maximum, w h i c h is s l i g h t l y d e p e n d e n t o n t h e i n d i v i d u a l case.
Assuming that the optimum solutions for i n d i v i d u a l c a s e s a r e k n o w n , t h e n e x t s t e p is t o keep the particle size distribution within the optimum limits. This cannot be done without the aid of a sufficiently accurate measurement of the actual particle size distribution. Present flotation plants usually have sizing devices -screens and classifiers -- which give an indication of particle size, but the need of an on-
l i n e , r e a l - t i m e c o n t r o l s y s t e m is s t r o n g l y f e l t in process development.
3.2 Comparison o f results by d i f f e r e n t methods The apparatus described in this paper has been tested and calibrated by direct comparison with two sieving machines: the Tyler RoTap sieve shaker [29] and the Alpine air-jet sieve [30 - 32]. The Alpine covers the size range 20 - 200 pm while the Ro-Tap covers 74 - 294 pro. The stroboscopic analyser s y s t e m ( t h e A n a l y s e r ) gives r e s u l t s a f t e r t h e analysis of 600 pictures per measurement in the 26 - 208 pm size range. The lower size range of the Analyser can be compared with the Alpine, while the upper range can be compared with the Ro-Tap technique. There is a n o v e r l a p c o m m o n f o r a l l t h r e e m e t h o d s i n the range 74 - 200 pro. Measurements o f sLx d i f f e r e n t b u l k compositions in the flotation process were carried out during several days. Some results from three consecutive days are collected in Table 1. The values in the table are percentages of particles from a defined sample, passed through the corresponding mesh. The particle size distribution of one sample was measured by means of the three mentioned techniques. Direct comparison of the results o b t a i n e d is m o r e c l e a r l y v i s i b l e i n t h e f o r m o f a graph, like the one on Fig. 11 showing the results of measurement no. 8 (Table 1). Graphs of the other measurements look rather similar, always having the same kind of differences between the curves. T h e R o - T a p t e c h n i q u e gives r e s u l t s v e r y close to those obtained by the Analyser, but o n e m u s t r e m e m b e r t h a t t h e r e is a g r e a t v a r i a tion in the size of openings in the Ro-Tap sieves, permitted in the standard for the sieve [33]. The deviations from the nominal size increase with the decrease of the opening size and have the values: f o r m e s h 2 9 4 a n d 2 0 8 $zm, b e l o w 1 % , for mesh 147 and 104 pro, below 2%, for mesh 74 Urn, about 4%. The results attained by the Alpine method and the Analyser always differ in the lower size range (20 - 80 ~m) by about 10 - 15%. The differences seem to be of a systematic character, showing good reproducibility in the series of measurements. In all cases, the differences have similar tendencies:
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Fig. 11. Particle size dL~h'ibutlon from o n e sample measured b y three differe i t m e t h o d s ; ~ - - Alpine, o - - Ro-Tap, n - - Analyse~. (a) t h e p e r c e n t a g e o f p a r t i c l e s w h i c h p a s s e d t h e d e f i n e d m e s h is s m a l l e r f o r t h e A n a l y s e r than for the Alpine in the lower size range (20 - 90 pm), ( b ) t h e s a m e p e r c e n t a g e is s l i g h t l y l a r g e r f o r the Analyser in the upper size range (90 210 urn)The shift of the lower part of the Analyser curve (Fig. 11) to the direction of the larger p a r t i c l e s i z e is t c b e e x p e c t e d d u e t o s e v e r a l r e a s o n s . O n e is d i s c u s s e d a b o v e , t h e d e f o c u s ing effect (see Section 2.2), spreading the image of a particle and causing a rise in the n u m b e r o f l a r g e r p a r t i c l e s c o u n t e d . A l s o , L~t order to get sufficient illumination of the photodiode array, the aperture diaphragm of the condenser has to he kept open. When the a m o u n t o f l i g h t is i n c r e a s e d , s o m e o f t h e smallest particles become invisible for the system, which obviously affects the results. However, the shift of the curve remains constant for different particle size distributions and thus can easily be compensated for.
4. CONCLUSION The above compar£son of the new stroboscopic analyser for particle size distribution measurement, with two traditional sieving techniques, shows the full usability and many advantages of the analyser. Because of the very short response time and good reproduci b i l i t y o f r e s u l t s , as c o m p a r e d w i t h o t h e r t e c h -
niques, the system can fulfil the lack of online devices for measurement of particle size distribution in many technological processes. Further development of the system should include the foUowing aspects. First, improvement of the o~Cical system should give better contrast and visibility of smaller particles, without changing the nozzle parameters. Application of different microscopical contrast techniques should give satisfactory results. Secondly, shorter computing times would allow analysis of more samples, thus giving the real statistical picture of the p a r t i c l e s i z e d i s t l i b u t i o n m o r e r a p i d l y . T h i s is easily accomplished by designing, specifically for this purpose, a simple computer with fast logic. And thirdly, more sophisticated software, suitable also for other applications, should include quantitative measurements of particle size, shape and edge texture, allowing recognition of different materials and structuras_
ACKNO~.¥LEDGE,%IENTS
The authors to Outokumpu this article and :of tests in the F i g . 11).
wish to express their gratitude Oy for permission to publish for making use of the results flotation plant (Table 1 and
REFERENCES
1 R. D. Cadle, Particle Size D e t e r m i n a t i o n , Interscience, New York, 1955. 2 R. R. Irani and C. F. Callis, Particle Size: Measurement, I n t e r p r e t a t i o n and Application, Wiley, New York, 1963_ 3 T. Allen, Particle Size Measurement, C h a p m a n a n d Hall, L o n d o n , 1975. 4 H. S. Wolff, Nature, 165 (1951) 967. 5 J. Z. Young a n d F. Roberts, Nature, 167 ( 1 9 5 1 ) 231; 169 (1952) 963. 6 W. H. %Valton, Nature, 169 (1952) 518. 7 Spatial Data Systems Inc., Goleta~ Cal. Manufacturer o f the EyeCom. 8 0 p t r o n i e I n t e r n a t i o n a l Inc., C h e l r ~ f o r d , Mass. Manufacturer o f the S-3000 Specscan, S-3400 P h o t o m a t i o n Mark IV a n d H-9000 Holoscan. 9 Ernst Leitz Wetzlar G m b H , Wetzlar, W. G e r m a n y . Manufacturer o f t h e L e i t z - ~ S . M . , Leitz-T.A.S. and Classimat. 10 D . J . Berry and T. Kelly, Particulate Matter, Mar. 1973, pp. 49 - 53. 11 J. E. J o h n s t o n and L. J. Rosen, Powder Technol., 14 (1976) 195 201_ -
284 12 Coulter Electronics Ltd., Harpenden, Herts., England. Manufacturer of the Timbrell]Coulter Shearicon. 1 3 J . P. K r a t o h v i l , A m . C h e m . , 3 6 ( 5 ) ( 1 9 6 4 ) L155R. 1 4 B. H. J . M c K e l l a r , A p p l . O p t . , 1 5 ( 1 9 7 6 ) 2 4 6 4 . 1 5 P. C h ~ l e k , J . O p t . S o c . A m . , 6 7 ( 1 9 7 7 ) 1 3 4 8 . 16 R. Davies, Am. Lab., 6 (1974) 73. 17 A . L. ~ V e r t h e i m e r a n d W. L . W i l c o c k , , k p p l . O p t . , 15 ( 1 9 7 6 ) 1 6 1 6 . 18 Jin Wu, AppL Opt., 16 (1977) 596. 1 9 B . J . T h o m p s o n , J . H . W a r d a n d W. R . Z i n k y , Appl. Opt., 6 (1967) 519. 20 R. Hickling, J. Opt. Soc. Am., 59 (1969) 1334. 2 1 J . D . T r o H n g e r , R . A . B e l z a n d J . E. O ' H a r e , P r o g . Astronaut. Aeronaut., 34 (1972) 249. 22 H. R o y e r , O p t . C o m m u n . , 20 ( 1 9 7 7 ) 7 3 . 2 3 P. K . R u n g e a n d R . R o s e n b e r g , I E E E J- Q u a n t u m Electron., QE-8 (Dec. 1972) 910.
24 R. J6~wicki, Optyka Instrurnentalna, WNT, %Varsaw, 1 9 7 0 . 25 Encyclopedia Americana, Int. Edn., Vol. 11, Americana Corp., New York, 1974. 26 A.M. Gaudin, Eng. Min. J., 141 (10) (1940) 43 - 44. 27 V . A . G l e m b o t s k i i , V. J. K l a s s e n a n d J. N. Plaksin, Flotation, Primary Sources, New York, 1972. 28 A. M. G a u d i n , F l o t a t i o n , McGraw-Hill, N e w York, 1957. 29 K . T . W h i t b y , Syrup. o n Particle Size M e a su r e m e n t , AST~I Spec. T e c h . Publ., ( 2 3 4 ) ( 1 9 5 8 ) 3. 3 0 O. E. B r o w : l , (3. S. B o b r o w s k i a n d G . E. K o v a l l , ASTM Spec. Tech. Publ., (473) (1970) 82 - 97. 31 V . M . M a l h o t r a a n d N. G. Z o l d n e r s , A S T M Spec. Tech. Publ., (473) (1970) 98 - 105. 3 2 T . M. J o n e s , P r o c . Sc, c. A n a l . C h e m . , 7 ( 9 ) ( 1 9 7 0 ) 159 - 163. 3 3 H. ~V. D a e s c h n e r , E. E. S e i b e r t a n d E. D. P e t e r s , ASTAI Spec. T e c h . Publ., ( 2 3 4 ) ( 1 9 5 8 ) 26 - 47.
Apparatus
for Real-Time Measurement
273
of Particle Size Distribution
J A N U S Z W. S A D O W S K I a n d E E R O B Y C K L I N G
Helsinki Un;-versity o f Technology, D e p a r t m e n t o f Technical Physics, S F - 0 2 1 5 0 Espoo I 5 ( F i n l a n d ) (Received March 20, 1978)
In this paper we describe an apparatus for real-time measurement of particle size distribution. By introducing a fast moving water stream with suspended particles and stroboscopic illumination, a large number of pictures (samples) can be analysed by means of a TV c~mera connected to a computer. In this manner complete particle size distribut i o n is a c h i e v e d w i t h m i n i m a l d e l a y . S a t i s f a c tory results were obtained when the apparatus was tested as an on-line device in a flotation plant, demonstrating the full ability of the system to control the flotation process.
I . INTRODUCTION 1.1 l~lethods for deterrnining particle size distribution Particle size determination has applications in many fields. It can be used in studies of polluted atmospheres and waters, flotation processes, paint industry, cement industry, powder technology, industrial hygiene, etc. A number of different methods have been developed for these applications. Generally, all methods depend on the properties and size of the particles, desired accuracy of the measurement and the environment of the particles. They can be classified into seven groups:
(i) Sieving (2) M e t h o d s employing gravitation (a) sedianentation (b) elutriation (c) centrifugal (3) T h e Coulter Counter ~4) P e x m e a m e t r y
(5) S u r f a c e a r e a m e a s u r e m e n t adsorption
phenomena
-- mainly
(6) Optical (7) Miscellaneous There are several methods in each group, and good descriptions of these methods exist in the literature [1 - 3]. Here, a brief discussion of the optical methods only will be given. T h e t-Lrst o p t i c a l m e t h o d u s e d t o d e t e r m i n e particle size was microscopy. In this method, the individual particles are measured and classified by means of various ocular micrometers, photomicrographs or microprojection. P a r t i c l e t h i c k n e s s is m e a s u r e d b y f o c u s i n g t-urst o n t h e t o p a n d t h e n o n t h e b o t t o m o f the particle and reading the difference on the micrometer drum. The useful particle size range for microscopy, in principle, is limited only by the resolving power of the objective used, and for visual light it is 2 - 100 pro. By use of electron microscopy (TKM or SEM) particles of size 0.001 - 5/zm call be measured. In all kinds of microscopical determinat i o n o f p a r t i c l e s i z e d i s t r i b u t i o n , s a m p l i n g is the most critical and greatest source of errors. For such a time~onsuming method, a proper sample must be chosen to be statistically representative. To improve the efficiency of microscopical investigations, around 1950 some authors [4 - 6] tried to solve the problem of replacing the human operator by an electro~)ptical system. They first developed scanning techniques in microscopy by memus of a scanning slit [4] or scanning spot [5]. At the present time the task is
accomplished b y commercially available automatic picture analysers [7 - 11] connected to a computer. T h e image shearing method, applied in microscopy [12], also decreases the h u m a n involvement in the measurement process, but is not fully automatic. Using such instruments the time needed for determination of particle size
274 d i s t r i b u t i o n f r o m a s a m p l e is r a d i c a l l y r e d u c ed and more samples can be tested in a given t i m e , b u t p r o p e r s a m p l i n g is s t i l l v e r y impo~ant. IAght-scattering methods of particle size determination also use optical phenomena. Usually a ratio of intensities at different a n g l e s a n d f o r d i f f e r e n t w a v e l e n g t h s , as w e l l as a s t a t e o f p o l a r i z a t i o n o f t h e s c a t t e r e d l i g h t , is m e a s u r e d [ 1 3 ] . R e c e n t l y , m u c h a t t e n t i o n has been paid to solving theoretically and in practice the problem of light scattering by a ~ b i t r a r i l y s h a p e d p a r t i c l e s [ 1 4 , 1 5 ] , w h i c h is important especially in remote sensing techniques and other measurements of inaccessible particles. T h e a n a l y s i s o f d i f f r a c t i o n patte_--ns c a n b e a useful technique for particle size measurem e n t , b u t i t is s t i l l d i f f i c u l t t o i n t e r p r e t t h e data for particles of an arbitrary shape [16, 171_ Lately, some new optical methods have been reported_ Jin Wu [18] has developed an optical instrument to measure particle size and velocity. In the apparatus two parallel laser beams, shifted along the direction of par*Acle m o t i o n a n d l a t e r a l l y f r o m t h i s d i r e c tion, are detected by two photo-transistors. It is c l a i m e d t h a t a f t e r e l e c ~ o n i c e x ' a m i n a t i o n o f the dark signal given by moving particles, the size and velocity can be deduced approximately. This method, however, does not give high accuracy of particle size measurement a n d is m o r e c o n v e n i e n t f o r v e l o c i m e t r y . Some authors [19 - 22] have used holography to measure particle size and velocity. A zhree~imensional scanner, for quantitative particle analysis from a real holographic i m a g e , is a l s o c o m m e r c i a l l y a v a i l a b l e [ 8 ] . B u t , because of the time needed for the preparation of the hologram, holography cannot be used for real-time measurement. The method described in the present work is b a s e d o n a f a s t c o m p u t e r a n a l y s i s o f particle images given on a two
2. S T R O B O S C O P I C SYSTEM FOR MEASUREMENT OF PARTICLE SIZE DISTRIBUTION
2.1 Basic idea As mentioned above, the system described in t h i s p a p e r is i n t e n d e d f o r t h e c o n t r o l o f t h e flotation process. The particles, the size of w h i c h is t o b e m e a s u r e d , a r e m i n e r a l s , m a i n l y metal ores. The photomicrograph on Fig. 1 shows their arbitrary and sometimes very complicated shape. In principle, the most exact method for measuring particles of an a r b i t r a r y s h a p e is t h e m i c r o s c o p i c m e a s u r e ment of each individual particle. At present a number of microscopic devices with computer p i c t u r e a~u~ysers e x i s t [7 - 1 1 ] , b u t i t is s t i l l difficult to use them for on-line measurement, because the time needed for the preparation o f s a m p l e s is r e l a t i v e l y l o n g . T o a v o i d t h i s , and many other problems, an apparatus used should meet the follo~-ing requirements. It should ( 1 ) g i v e a l a r g e n u m b e r o f s a m p l e s in a short time for the analyser, (2) make fast analysis of given samples, (3) give an o u t p u t w i t h m i n i m a l d e l a y , easy to read by an operator, (4) w o r k c o n t i n u o u s l y in p l a n t e n v i r o n ment without failure, (5) keep error within estimated limits, (6) be easy to operate, and (7) be easy to change to different applications. To solve requirement no. (1), one has to decrease the time needed for sample preparation. It should be shorter than the time needed by a computer to analyse a single picture. The solution has been found in the following manner: the particles, diluted in water, are r u n n i n g in a l a m i n a r s t r e a m i n f r o n t o f a
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Fig. 1. Copper ore particles.
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275 rrAcroscope connected to a TV camera. A short light pulse (0.6 ps) "'captures" them and forms an image on a TV imaging device (twodimensional photodiode array). Since all i n f o r m a t i o n f r o m t h e w h o l e i m a g e a r e a is s t o r e d i n t h e T V c a m e r a s i m u l t a n e o u s l y , i t is sufficient to use only one light pulse to get o n e c o m p l e t e s a m p l e . A f t e r o n e i m a g e is processed, the next one can immediately be taken. In this way the speed limitations are mainly determined by the computer. To test this basic idea, the photographing system, shown schematically in Fig. 2, was built. By means of this system we studied the question: is it possible in practice to capture moving particles with a stroboscopic light? The photographing system consists of a nozzle (I) producing a stream of water with particles, a low power microscope objective (2) connected to the Polaroid camera (3), and a flash lamp unit (4). To get pictures without optical distortion, the stream has to be laminar, without standing waves, and of good optical surfaces. This can be achieved by means of the special nozzle, as described by R u n g e [ 2 3 ] . A s i m i l a r n o z z l e ~vith t h e s h a p e adopted to the use of low viscosity liquids, such as water, has been designed. The results obtained with the help of this system were quite satisfactory. On the series of photographs there were no apparent signs of particle movement, and the resolution and focus were good. Figure 3 shows a series of t h r e e s h o t s d o n e o n o n e P o l a r o i d f ' d m . I t is interesting to see that in a fast stream the particles have no tendency to join together and with sufficient dilution they do not cover each other on the image. Careful study of the photographs gave a wealth of useful information for further design of a prototype, connected with writing a computer program or improving the optics
/
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Fig_ 3. Photographs o f m o v i n g particles.
o f t h e s y s t e m . F o r e x a m p l e , f r o m ~he p h o t o s one can estimate an approximate number of quartz particles, which are almost transparent and always have a brighter centre with a dark boundary. The appearance of such cases must be accounted for in the computer programme. I f t h e l i g h t i n t e n s i t y is i n c r e a s e d , s m a l l e r p a r t i c l e s b e c o m e i n v i s i b l e . I f i t is n o t n e c e s sexy to count these, better contrast for :,arger ones can be achieved. Also, in this inexpensive way, other parameters can be tested, such as sensitivity for defocusing, small fluctuations of the stream, application of microscopic contrast techniques -- phase and interference contrast, etc. A large number of such investigations at this first stage allowed us to make optimum decisions on the construction of the prototype. 2.2 Optical system The apparatus for real-time determination of particle size distribution consists mainly of the previous experimental device, With the Polaroid camera replaced by a TV camera and a computer. A schematic diagram of the total s y s t e m is s h o w n i n F i g . 4 . 6
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Fig_ 2. S c h e m a t i c diagram o f the photographic s y s t e m . (1) N o z z l e , ( 2 ) m i c r o s c o p e objective, (3) Polaroid camera, (4) flash lamp.
Fig. 4. S c h e m a t i c diagram o f t h e s y s t e m f o r real-time d e t e r m i n a t i o n o f particle size d i s t r i b u t i o n . T h e n u m b e r s have the f o l l o w i n g m e a n i n g : (1) nozzle, (2) m i c r o s c o p e objective, (3) T V camera, (4) c o m p u t e r , (5) s t r o b o s c o p e , (6) condenser.
27fi The purpose of the TV camera, in the form o f a t w o - d i m e n s i o n a l p h o t o d i o d e a r r a y , is t o change the optical image of the particles into analog signals for further processing_ The RCA 53232 silicon imaging device, having a 5 3 2 X 3 2 0 e l e m e n t s e n s o r , is u s e d t o p r o d u c e electronic signals from a visual input. The image area of the device has dimensions 7.33 × 9.25 mm, and thus the size of a single i m a g e c e l l is 0 . 0 3 X 0 . 0 3 r a m . B a s e d o n t h e geometry of this device, one can estimate useful magnification, calculate depth of field and check the resolving power. These calculations are necessary, for proper design of the system. I n t h e f l o t a t i o n p r o c e s s i t is u s e f u l t o h a v e information about the particle size distribution within the range 6 - 250 pro. The smaller particles cause most difficulties, because they require higher magnification and better r e s o l u t i o n . I n a r e a l - t i m e s y s t e m t h e r e is n o time for changing the magnification, and the optimal one must be chosen_ In order to simplify these brief design calculations, we will assume an ideal case of square particles. ~'aen a particle covers a part of a single image cell, an analog signal, proportional to the c o v e r e d a r e a , is c r e a t e d . T h e d i s c r i m i n a t i o n leve! of the digitizer (see Section 2.3 for explanations) can be set on a value causing change from 1 into 0 when 50% of the cell a r e a is c o v e r e d . T h u s , a n i m a g e o f t h e s m a l l e s t p a r t i c l e s h o u l d h a v e t h e d i m e n s i o n s d." = 0 . 0 3 / x/2 = 0.02 ram. The size of the smallest p a r t i c l e o f i n t e r e s t is 6 g i n , s o t h e m a g n i f i c a t i o n s h o u l d b e J3 = ~ ' / ~ = 3 . 5 . A n i m a g e o f t h e l a r g e s t p a r t i c l e w i l l h a v e d i m e n s i o n s ¢" = 0.875 ram. The depth of field can be calculated with the help of Fig. 5 (after [24] ). It shows schematically an arbitrary optical system (e.g. lens, objective, etc.) with entrance pupil Z, exit pupil Z', and conjugate object and image p l a n e s ~ a n d ~" r e s p e c t i v e l y . I f o n e c o n s i d e r s p o i n t o b j e c t A i n t h e o b j e c t p l a n e ,w a n d neglects aberrations and diffraction, an image A" i n t h e c o n j u g a t e p l a n e r." w i l l a l s o b e a point. Other point objects located on other p l a n e s (e.g. ~ o r ~ 2 ) p a r a l l e l t o ~ , b u t s o m e d i s t a n c e a p a r t , swill n o t f o r m p o i n t s , b u t s p o t s in the plane ~'. Now, image detectors have u s u a l l y ~ m i t e g r a i n s t r u c t u r e (e.g. e y e , p h o t o graphic emulsion, photodiode array), so there is s o m e l i m i t i n g s p o t , w h i c h is s t i l l d e t e c t e d a s
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Fig. 5_ D e p t h o f field o f an a r b i t r a r y o p t i c a l s y s t e m . See t e x t for e x p l a n a t i o n . a p o i n t . T h e d i a m e t e r o f t h i s b o u n d a r y s p o t is usually equal to a dimension of a single grain. T h e d e p t h o f f i e l d is t h e r e f o r e a m a x i m u m distance between arbitrary planes parallel to ,~, f r o m w h i c h a l l p o i n t o b j e c t s a r e s t i l l d e t e c t ed by a defined detector as points, not spots. First we define front Ap and back At depth o f f i e l d ( s e e F i g . 5}. F r o m t r i g o n o m e t r i c r e l a tions we obtain c~z
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-
-
I'-~o ÷ 1 For a low power microscope objective an a p e r t u r e a n g l e is s m a l l , a n d o n e c a n w r i t e , with a good approximation, ~z = 2b NA, NA = n s i n u, n --- 1 . T h i s y i e l d s _kp • -~
--b
12 b
I
-X77o i +3
a n d s i m i l a r l y f o r At: b
12 b NAt_ 1 At;
I
In this particular case, because of large b and small Al~, with/~ = 3.5 ×, the fractions in the denominators will have a large value, so without introducing large errors (approx.
277 0.01%), one can neglect --1 and +1 in the denominators. Thus Ap = --A t, the negative sign appearing according to the sign rules in optics, and finally A = A t -- Ap -
Alo NA
The numerical value, if Alo = 0.03, 5 = 3.5 X, N A = 0 . 0 5 , is _~ = 0 . 2 m m . Thus, the thickness of the laminar stream should be 0.2 mm to achieve a sharp image of all parLicles w i t h i n t h e e s t i m a t e d size r a n g e . R e l a t i v e e r r o r s d u e t o c h a n g e s in s t r e a m t h i c k n e s s , as w e l l as d e f o c u s i n g e r r o r s , a r e d i f f e r e n t for different sizes. Generally, the relative error can be expressed by a function
B =
$D
NA
-
- 100%
W w h e r e B is the relative error for particles o n the b o u n d a r y of the stream, 5 D is the deviation of the stream thickness, or defocusing related to the object space, a n d IV is the n o m i n a l d i m e n s i o n of the particle. It is obvious that proper determination of the smallest particles is e x t r e m e l y sensitive for defocusing. A thin laminar stream with particles, especially w h e n it has to w o r k c o n t i n u o u s l y i n a n i n d u s t r i a l p l a n t , is m o r e difficult to achieve than a thick one. Too big particles can cause blocking of a nozzle and stopping of the whole system, and therefore p e r i o d i c a l c l e a n i n g is r e q u i r e d . A n i m p r o v e ment could be achieved by diminishing the measurement range, or dividing it into two, one for small particles, with high magnification and very thin stream, and the second with low magnification and thick stream. In this case, however, some presizing of the p a r t i c l e s is n e c e s s a r y . D e c r e a s e o f t h e r a n g e will lead to more satisfactory jet parameters. For example, if the smallest measurable p a r t i c l e is t a k e n t o b e 2 0 p m ( r a n g e 2 0 2 5 0 / L m ) , t h e u s e f u l m a g n i f i c a t i o n is 1 X a n d the depth of field, i.e. permissible stream thickness free of defocusing errors, extends to 0.6 ram. The resolving power of the microscope objective u~l in the system can be calculated from the formula d = k/2 NA. If we have k = 0.45/zm, fromNA = 0 . 0 5 o n e g e t s d = 4 . 5 pro_ T h i s r e s o l u t i o n is m o r e t h a n s u f f i c i e n t . I t is, of course, well known that large depth of field means low resolution, and vice uersa.
The illumination system consists of the stroboscope (5) and the condenser (6). The requirements for the condenser are the following. The numerical aperture of the condenser must match the numerical aperture of the objective used, and it must illuminate t h e c o m p l e t e f i e l d o f v i e w . T h i s is e a s y t o attain by employing a commercially available condenser matched with the objective. The r e q u i r e m e n t f o r t h e s t r o b o s c o p e b u l b is t o produce enough light, sufficient to illuminate the photodiode army. In this system, flashtubes FX-35B or FX-101B from EG & G have been chosen because of their short pulse durat i o n , 0 . 6 # s . I t is u s e f u l t o c a l c u l a t e t h e p o w e r output of the light source. The electrical data of the flashtubes are: pulse duration t = 0.6 ps e n e r g y i n p u t p e r f l a s h Ein = 0 . 0 0 1 3 W s efficiency of tubes E t = 5 - 10 lm per watt arc surface approx. S = 5/16 x 5/64 in 2 = 0.16 mm 2 Thus, one can calculate the light emission for the lower value of the tube efficiency, = E=Et
= 6.5 • 10 -3 lms
candle power, I=--d~ =0.52. 4;r
10 -3 cds
luminance, L-
I
-8.26-
103nts
S and illumination E'h~
of the photodiode
array:
sin2u = 7rTL - -- 1 . 6 7 l x s /32
w h e r e T = 0 . 8 is t h e a s s u m e d t r a n s m i t t a n c e coefficient, sin u = 0.05 and/3 = 3.5 X. In the case of the highest efficiency, the illumination reaches the value E~ax = 6.688 Ix s Saturation exposure p h o t o d i o d e a r r a y is
required
for
the
E~'at = 2 . 6 7 " 1 0 - 3 f c s = 0 . 2 8 7 I x s B y c o m p a r i s o n o f t h e s e v a l u e s i t is c l e a r that the above flashtubes exceed the requirement and can be used in the system, together with filters and an aperture diaphragm, in the whole efficiency range.
278
2.3 I n f o r m a t i o n p r o c e s s i n g
IG]
Processing of the information obtained by t h e o p t i c a l s y s t e m is d o n e i n t h r e e s t e p s : (1) v i d e o p r o c e s s i n g in t h e T V c a m e r a , (2) digitization of electronic signals and adaptation of them for a computer, (3) c o m p u t i n g . A synchronization and control logic system f r o m t h e T V c a m e r a is u s e d t o t r i g g e r t h e flash lamp unit. The end of the vertical blanki n g i n t e r v a l p l u s 1 0 ;Lm d e l a y d e t e r m i n e s t h e beginning of the triggering pulse. In this way, independently of the computer requirement f o r a n e w p i c t u r e t o a n a l y s e , all even ( o r o d d ) lines are illuminated wkh the stroboscopic l i g h t . S i m u l t ~ a e o u s l y ~vith t h e n u m e r i c a l a n a l y s i s , a n o r m a l v i d e o o u t p u t is t a k e n f r o m the camera for monitor control (Fig. 6). T h e m a i n p a r t o f t h e T V c a m e r a is a s i l i c o n imaging device, constructed with a 3-phase, N-channel, vertical frame organization (see Fig. 7). Its image area consists of an array of analog CCD (Charge-Coupled Device) shift registers c:,ntaining 320 parallel vertical c o l u m n s ~f 2 5 6 s e n s i n g c e l l s d r i v e n w i t h t h r e e register -'locks. When vertical register clocks a r e p u b :l svith t h e v o l t a g e w a v e f o r m s , a l i g h t i m a g e f o c u s e d o n t h i s r e g i s t e r is i n t e g r a t e d into a charge pattern of electrons during the normal active TV display time and transferred to the storage area during the vertical blanking interval. The horizontal register receives one line of picture information from the storage area during each horizontal blanking i n t e r v a l , a n d t h e n t h e C C D s i g n a l is e x t r a c t e d by the output circuit. In a normal TV display, t h e e f f e c t i v e n u m b e r o f v e r t i c a l e l e m e n t s is interlaced by alternation of second and third
..
]
IG2
rr
CIRCUz:
eHll
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"vs* 0 ~,s2 0
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Fig. 7 . B l o c k d i a g r a m o f t h e i m a g i n g d e v i c e .
register clocks and approximately 482 lines are displayed, but in the particular case of the particle size measurement system, only even ( o r o n l y o d d ) l i n e s a r e u s e d , i.e. 2 4 1 l i n e s . An analog charge pattern formed in the imaging device and representing an image of the particles must be digitized for input to a c o m p u t e r . T h i s is d o n e b y m e a n s o f t h e Camera-to-Computer Adapter Unit (C.C.A.U.). Figure 8 shows a block diagram of the information processing system. Because of the long distance (approx. 20 m) between the camera operation place and the computer r o o m , t h e Line T r a n s c e i v e r U n i t (L_T.U.) h a s to be used to amplify signals leaving the camera. These signals are amplified again just when they enter the C_C.A.U. Digitalization o c c u r s in t h e C o m p a r a t o r , w h e r e c h a r g e p a t t e r n o f e l e c t r o n s is c o m p a r e d w i t h a p r e s e t voltage value. For every clock pulse, if a signal
Fig. 8. Block diagram of the information processing
Fig-6-TVpictureofmovingparticles.
system. The meaning o f t h e a b b r e v i a t i o n s is: LTU - Line Transceiver Unit, SPC - - Serial to Parallel Convertor, r ' - ~ A U - Camera-to-Computer A d a p t e r Unit.
279 from the camera exceeds this value, the c o m p a r a t o r gives o u t p u t s i g n a l 1 , o t h e r w i s e s i g n a l 0 is p r o d u c e d . B y c h a n g i n g Lhe c u t - o f f level during calibration, an optimum value can be estimated to eliminate low energy signals representing particles too small and unwanted in the measurement or noise. To compute results, the PDP-11 16-bit m i n i c o m p u t e r is u s e d . T o b e a c c e p t a b l e t o t h e computer, the output from the camera has to be converted from series to 16-bit parallel s i g n a l . T h i s is d o n e i n t h e S e r i a l - t o - P a r a l l e l C o n v e r t e r . In this m a n n e r e v e r y T V line gives twenty 16-bit words. A part of the digital input received by the c o m p u t e r is s h o w n as a n e x a m p l e i n F i g . 9 . It represents one-third of the field of a single p i c t u T e in X d i r e c t i o n a n d o n e - f i f t h i n Y d i r e c t i o n . I n t h e w h o l e f i e l d t h e r e axe 2 4 1 lines, each line divided into 320 parts. Thus the position of every point in the TV picture is d e t e r m i n e d b y X a n d Y c o o r d i n a t e s . W h e n the computer, analysing point by point every l i n e , m e e t s t h e ~-~rst s i g n a l 0 , i t gives t h e p o s i -
tion (address) of this point to the memory and reserves this place. When a continuum of 0-signals coming from one particle in the first l i n e is e n d e d , t h e c o m p u t e r s t o r e s t h e a d d r e s s . T h e s a m e p r o c e d u r e is r e p e a t e d f o r t h e n e x t particles in the same line. When the next line is s c a n n e d a n d t h e c o m p u t e r g e t s 0 - s i g n a l s f r o m a p a r t i c l e , i t r e a l i z e s i f t h e c o m i n g 0s i g n a l s b e l o n g t o t h e s a m e p a r t i c l e as i n t h e l i n e a b o v e , a n d t h i s is t a k e n i n t o a c c o u n t in constructing the complete particle. In order to avoid problems due to single s i g n a l s 1 i n t h e p i c t u r e , t h e r e is a p r o c e d u r e t o add 0-signals to both ends of a line of zeros. This procedure of adding pixels gives a limitation for the separation of two single particles. If they touch each other at corners, like: ...000 ...000 000..
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280 s e p a r a t i o n o f m i n i m u m 2 c o l u m n s is n e c e s s a r y _ W h e n t h e f i e l d is c o m p l e t e d , a s u m o f a l l the points under one address is calculated to obtain the measurement of a projected surface area. Particles with a transparent "'hole" i n t h e m i d d l e , e.g. q u a r t z p a r t i c l e s , c a n a l s o b e recognized by the programme, and in this case the procedure is as foUows. The upper edge of the particle is processed in the same way as for a "'normal" case. The computer scanning t h e f i r s t l i n e m e e t s F~rst 0 s i g n a l s a n d d e t e r mines the address. If in one of the next lines t h e r e is a n i n t e r r u p t i o n i n t h e c o n t i n u u m o f 0 signals, but with both parts belonging to the s a m e a d d r e s s , i t c a n m e a n t w o cases= ( 1 ) t h e particle has "'~'" shape, or (2) it has a "'hole". The next lines can still contain similar interruption, so the last or the closing line of this p a r t i c u l a r p a r t i c l e is d e c i s i v e . I f i t j o i n s together both arms, the computer counts this particle as a "'quartz"; ~ the "hole" remains o p e n , t h e p a r t i c l e is c o u n t e d a s a " ' n o r m a l " . I n t h e c a s e o f a m o r e c o m p l i c a t e d s h a p e , i t is sufficient for a particle to have only one "'hole" inside to be counted as the "'quartz"_ Particles of "'U'" shape are calculated first as two separate particles, and when the joining line is discovered, they merge together to create one bigger particle under the same address. In thi; manner, particles of different sizes are sel~.ted, separated from the transparent o n e s , a n d t h e n u m b e r o f t h e m is c o u n t e d within different size ranges corresponding to an imaginary mesh. In this way results directly comparable with the sieving technique are attained. After the analysis of one picture, the computer keeps the results in the memory and adds them to results from the next -
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(2) m e s h n u m b e r , (3) percentage of particles which did not pass the corresponding sieve, (4) percentage of particles which pass the sieve, (5) standard deviation, (6) number of particles, (7) percentage of "quartz" particles, (8) average projected area, (9) average volume, and (10) number of particles after subtraction of the "'quartz" particles. Columns no. 3 and 4 do not include the "'quartz" particles. The mathematical model for the calculations has been chosen to be the sLmplest and the fastest, having in mind ability to analyse a large number of pictures i n a s h o r t t i m e . T h u s , p a r t i c l e a r e a is b a s e d o n the sum of the covered elements in the photodiode array, and an average projected area w i t h i n t h e c o r r e s p o n d i n g o p e n i n g is p r i n t e d i n column no. 8. The average equivalent volume ( c o l u m n n o . 9 ) is c a l c u l a t e d u s i n g t h e f o r m u l a
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pictures, up to a preset quantity. Common r e s u l t s a r e p r i n t e d o u t i n t h e -way s h o w n a s a n e x a m p l e i n F i g . 1 0 . T h e p n n t - o u t is c o m p o s e d of: (a) general information concerning all particles counted in a series of pictures, and (b) particle size distribution. The general information printed in the heading contains = n u m b e r o f a n a l y s e d pict,~uces, t o t a l n - t u b e r o f counted particles, number of transparent particles, average area, density, number of particles exceeding the measuring range, and t i m e o f t h e c o m p u t a t i o n . T h e s e c o n d p a r t is divided into ten columns in which the foUowi n g i n f o r m a t i o n is i n c o r p o r a t e d ( s e e F i g . 1 0 ) :
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281 V = ( ~ / p ) 3 , w h e r e P is t h e a v e r a g e a r e a f r o m c o l u m n no_ 8. The suitability of this method for industrial p r o c e s s e s h a s bee11 v e r i f i e d i n t h e f l o t a t i o n plant and compared with other methods_ 3. APPLICATIONS AND R E S U L T S
3.1 Applications The stroboscopic system described in this work can be applied in almost all processes where rapid determination of particle size d i s t r i b u t i o n is r e q u i r e d a n d w h e r e i t is p o s sible to form a laminar stream (of air or liquid) with suspended particles. The prototype of the apparatus has been used and tested in a flotation plant. F l o t a t i o n is a p r o c e s s f o r r e m o v i n g a n d concentrating valuable mineral ore from a mixture of ores and waste materials. The flotation process utilizes differences in the surface properties (surface energy or surface tension) to effect separation [25]. Usually, t h e gas p h a s e ( a i r b u b b l e s ) is i n t r o d u c e d i n t o aqueous medium with crushed minerals. The difference in adhesion permits removal of a p a r t i c u l a r m i n e r a l f r o m t h e b u l k as a f r o t h o f d i f f e r e n t c o m p o s i t i o n . F l o t a t i o n is w i d e l y used in the concentration of complex leadzinc--iron and copper-iron sulphide ores, non-sulphides such as mineral phosphates, potassium ores, fluorite and barite, cleaning of coal and in many other fields. Extensive treatments of the flotation process can be found in the literature [26 - 28]. The optimization of particle size in the flotation process has to take into consideration different conflicting requirements. For instance, for reasons of economy and minimum use of energy, larger particles are p r e f e r r e d i n f l o t a t i o n , b u t t h i s r e s u l t s i n a less purified product and higher losses via large a n d h e a v y p a r t i c l e s . A l s o , f l o a t a b i l i t y as a function of particle size has a maximum, w h i c h is s l i g h t l y d e p e n d e n t o n t h e i n d i v i d u a l case.
Assuming that the optimum solutions for i n d i v i d u a l c a s e s a r e k n o w n , t h e n e x t s t e p is t o keep the particle size distribution within the optimum limits. This cannot be done without the aid of a sufficiently accurate measurement of the actual particle size distribution. Present flotation plants usually have sizing devices -screens and classifiers -- which give an indication of particle size, but the need of an on-
l i n e , r e a l - t i m e c o n t r o l s y s t e m is s t r o n g l y f e l t in process development.
3.2 Comparison o f results by d i f f e r e n t methods The apparatus described in this paper has been tested and calibrated by direct comparison with two sieving machines: the Tyler RoTap sieve shaker [29] and the Alpine air-jet sieve [30 - 32]. The Alpine covers the size range 20 - 200 pm while the Ro-Tap covers 74 - 294 pro. The stroboscopic analyser s y s t e m ( t h e A n a l y s e r ) gives r e s u l t s a f t e r t h e analysis of 600 pictures per measurement in the 26 - 208 pm size range. The lower size range of the Analyser can be compared with the Alpine, while the upper range can be compared with the Ro-Tap technique. There is a n o v e r l a p c o m m o n f o r a l l t h r e e m e t h o d s i n the range 74 - 200 pro. Measurements o f sLx d i f f e r e n t b u l k compositions in the flotation process were carried out during several days. Some results from three consecutive days are collected in Table 1. The values in the table are percentages of particles from a defined sample, passed through the corresponding mesh. The particle size distribution of one sample was measured by means of the three mentioned techniques. Direct comparison of the results o b t a i n e d is m o r e c l e a r l y v i s i b l e i n t h e f o r m o f a graph, like the one on Fig. 11 showing the results of measurement no. 8 (Table 1). Graphs of the other measurements look rather similar, always having the same kind of differences between the curves. T h e R o - T a p t e c h n i q u e gives r e s u l t s v e r y close to those obtained by the Analyser, but o n e m u s t r e m e m b e r t h a t t h e r e is a g r e a t v a r i a tion in the size of openings in the Ro-Tap sieves, permitted in the standard for the sieve [33]. The deviations from the nominal size increase with the decrease of the opening size and have the values: f o r m e s h 2 9 4 a n d 2 0 8 $zm, b e l o w 1 % , for mesh 147 and 104 pro, below 2%, for mesh 74 Urn, about 4%. The results attained by the Alpine method and the Analyser always differ in the lower size range (20 - 80 ~m) by about 10 - 15%. The differences seem to be of a systematic character, showing good reproducibility in the series of measurements. In all cases, the differences have similar tendencies:
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Fig. 11. Particle size dL~h'ibutlon from o n e sample measured b y three differe i t m e t h o d s ; ~ - - Alpine, o - - Ro-Tap, n - - Analyse~. (a) t h e p e r c e n t a g e o f p a r t i c l e s w h i c h p a s s e d t h e d e f i n e d m e s h is s m a l l e r f o r t h e A n a l y s e r than for the Alpine in the lower size range (20 - 90 pm), ( b ) t h e s a m e p e r c e n t a g e is s l i g h t l y l a r g e r f o r the Analyser in the upper size range (90 210 urn)The shift of the lower part of the Analyser curve (Fig. 11) to the direction of the larger p a r t i c l e s i z e is t c b e e x p e c t e d d u e t o s e v e r a l r e a s o n s . O n e is d i s c u s s e d a b o v e , t h e d e f o c u s ing effect (see Section 2.2), spreading the image of a particle and causing a rise in the n u m b e r o f l a r g e r p a r t i c l e s c o u n t e d . A l s o , L~t order to get sufficient illumination of the photodiode array, the aperture diaphragm of the condenser has to he kept open. When the a m o u n t o f l i g h t is i n c r e a s e d , s o m e o f t h e smallest particles become invisible for the system, which obviously affects the results. However, the shift of the curve remains constant for different particle size distributions and thus can easily be compensated for.
4. CONCLUSION The above compar£son of the new stroboscopic analyser for particle size distribution measurement, with two traditional sieving techniques, shows the full usability and many advantages of the analyser. Because of the very short response time and good reproduci b i l i t y o f r e s u l t s , as c o m p a r e d w i t h o t h e r t e c h -
niques, the system can fulfil the lack of online devices for measurement of particle size distribution in many technological processes. Further development of the system should include the foUowing aspects. First, improvement of the o~Cical system should give better contrast and visibility of smaller particles, without changing the nozzle parameters. Application of different microscopical contrast techniques should give satisfactory results. Secondly, shorter computing times would allow analysis of more samples, thus giving the real statistical picture of the p a r t i c l e s i z e d i s t l i b u t i o n m o r e r a p i d l y . T h i s is easily accomplished by designing, specifically for this purpose, a simple computer with fast logic. And thirdly, more sophisticated software, suitable also for other applications, should include quantitative measurements of particle size, shape and edge texture, allowing recognition of different materials and structuras_
ACKNO~.¥LEDGE,%IENTS
The authors to Outokumpu this article and :of tests in the F i g . 11).
wish to express their gratitude Oy for permission to publish for making use of the results flotation plant (Table 1 and
REFERENCES
1 R. D. Cadle, Particle Size D e t e r m i n a t i o n , Interscience, New York, 1955. 2 R. R. Irani and C. F. Callis, Particle Size: Measurement, I n t e r p r e t a t i o n and Application, Wiley, New York, 1963_ 3 T. Allen, Particle Size Measurement, C h a p m a n a n d Hall, L o n d o n , 1975. 4 H. S. Wolff, Nature, 165 (1951) 967. 5 J. Z. Young a n d F. Roberts, Nature, 167 ( 1 9 5 1 ) 231; 169 (1952) 963. 6 W. H. %Valton, Nature, 169 (1952) 518. 7 Spatial Data Systems Inc., Goleta~ Cal. Manufacturer o f the EyeCom. 8 0 p t r o n i e I n t e r n a t i o n a l Inc., C h e l r ~ f o r d , Mass. Manufacturer o f the S-3000 Specscan, S-3400 P h o t o m a t i o n Mark IV a n d H-9000 Holoscan. 9 Ernst Leitz Wetzlar G m b H , Wetzlar, W. G e r m a n y . Manufacturer o f t h e L e i t z - ~ S . M . , Leitz-T.A.S. and Classimat. 10 D . J . Berry and T. Kelly, Particulate Matter, Mar. 1973, pp. 49 - 53. 11 J. E. J o h n s t o n and L. J. Rosen, Powder Technol., 14 (1976) 195 201_ -
284 12 Coulter Electronics Ltd., Harpenden, Herts., England. Manufacturer of the Timbrell]Coulter Shearicon. 1 3 J . P. K r a t o h v i l , A m . C h e m . , 3 6 ( 5 ) ( 1 9 6 4 ) L155R. 1 4 B. H. J . M c K e l l a r , A p p l . O p t . , 1 5 ( 1 9 7 6 ) 2 4 6 4 . 1 5 P. C h ~ l e k , J . O p t . S o c . A m . , 6 7 ( 1 9 7 7 ) 1 3 4 8 . 16 R. Davies, Am. Lab., 6 (1974) 73. 17 A . L. ~ V e r t h e i m e r a n d W. L . W i l c o c k , , k p p l . O p t . , 15 ( 1 9 7 6 ) 1 6 1 6 . 18 Jin Wu, AppL Opt., 16 (1977) 596. 1 9 B . J . T h o m p s o n , J . H . W a r d a n d W. R . Z i n k y , Appl. Opt., 6 (1967) 519. 20 R. Hickling, J. Opt. Soc. Am., 59 (1969) 1334. 2 1 J . D . T r o H n g e r , R . A . B e l z a n d J . E. O ' H a r e , P r o g . Astronaut. Aeronaut., 34 (1972) 249. 22 H. R o y e r , O p t . C o m m u n . , 20 ( 1 9 7 7 ) 7 3 . 2 3 P. K . R u n g e a n d R . R o s e n b e r g , I E E E J- Q u a n t u m Electron., QE-8 (Dec. 1972) 910.
24 R. J6~wicki, Optyka Instrurnentalna, WNT, %Varsaw, 1 9 7 0 . 25 Encyclopedia Americana, Int. Edn., Vol. 11, Americana Corp., New York, 1974. 26 A.M. Gaudin, Eng. Min. J., 141 (10) (1940) 43 - 44. 27 V . A . G l e m b o t s k i i , V. J. K l a s s e n a n d J. N. Plaksin, Flotation, Primary Sources, New York, 1972. 28 A. M. G a u d i n , F l o t a t i o n , McGraw-Hill, N e w York, 1957. 29 K . T . W h i t b y , Syrup. o n Particle Size M e a su r e m e n t , AST~I Spec. T e c h . Publ., ( 2 3 4 ) ( 1 9 5 8 ) 3. 3 0 O. E. B r o w : l , (3. S. B o b r o w s k i a n d G . E. K o v a l l , ASTM Spec. Tech. Publ., (473) (1970) 82 - 97. 31 V . M . M a l h o t r a a n d N. G. Z o l d n e r s , A S T M Spec. Tech. Publ., (473) (1970) 98 - 105. 3 2 T . M. J o n e s , P r o c . Sc, c. A n a l . C h e m . , 7 ( 9 ) ( 1 9 7 0 ) 159 - 163. 3 3 H. ~V. D a e s c h n e r , E. E. S e i b e r t a n d E. D. P e t e r s , ASTAI Spec. T e c h . Publ., ( 2 3 4 ) ( 1 9 5 8 ) 26 - 47.