GB2500592A - Multi-threshold algorithm for analyzing out of focus particles and droplets - Google Patents

Abstract

A methodology is presented that enables efficient acquisition of sufficient particle/droplet information (e.g. diameter and aspect ratio) from images of in and out of focus droplets. The newly developed multi-threshold algorithm is successfully implemented in the automatic particle/droplet image analysis (PDIA) system. It employs continuous thresholds until the local background level to process each particle/droplet in the images, rather than only two thresholds implemented in the dual threshold methods (which are widely used in the commercial software). It uses a curve matching method to compare the results with the calibrated data, to acquire the particle/droplet size, aspect ratio and the distance from the focal plane, which provides a possibility to get the three-dimensional position of the particles/droplets from the two-dimensional images. The multi-threshold method significantly increases the depth of field (DoF) of small particles with diameter smaller than 50µm, and it performs more efficiently than the dual threshold methods. The multi-threshold method is also capable of generating the aspect ratios of particles/droplets more accurately than the dual threshold methods.

Description

1. Introduction

Photography is the process of forming visible images directly or indirectly by the action of light or other forms of radiation onlo sensitive surfaces. Recently the image proccssing tcehnique has hccn widely adopted in analyzing spray drops and solid particles because it offers several imporlant advantages over alternative particle sizing techniques such as Phase Doppler Anemometry (PDA). Among these advantages are the simplicity and relative inexpensiveness of photographic apparatus, flexibility, and the capability of detecting and analyzing non-spherical particles. The aspect ratio of non-spherical particles plays an important part in the study of respiratory tract deposition of inhaled pharmaceutical aerosols. The interception of the tip of a particle with an airway wafl should be taken into account in the study of the inhalation of particles. Accordingly, previous researchers have previously noted that high aspect ratio drug particles are easily delivered to the peripheral lung. However these particles exhibit aerodynamic properties that reduce their deposition in the upper airways as compared to mass equivalent spherical particles, interception is expected to increase their deposition in smaller peripheral airways.

Here a previously developed digital image analysis technique capable of sizing partieks of arbitrary shape and size and with wide dynamic range accounting for out of focus effects is refined. The fundamental principles of the technique and a description of the calibration procedure in which the image processing routine was vcrilied with calibration data of known particle sizes were described in Kashdan et al.. The measurement performance of the particle/droplet image analysis (PDIA) system has been assessed initially in terms of individual object diameters (1)). The aim of this experimental investigalion was Lu assess the rohusiness and accuracy oF Lhe Lechnique and to improve it by using localized and dynamic thresholding. The accuracy of the threshold meihod determines the precision of pariicle/droplei characlers in PDIA, and here Lhree threshold methodologies are evaluated. Two existing methods (named dual threshold meihods) are hased on the work from Yule ci al. and Kashdan ci a]., which are common'y used in commercial particle/droplet analysis software. However, dual threshold methods cannot detect excessively defocused particles, which is explained in section 2.2.

Generally, smaller pariicles have a viable smaller depth oF field than larger ones. in order to detect more small particles (D<5ORm) from a certain set of images, a larger measurable depth of field is preferred in the image process. The newly developed methodology, named the mulLi-threshold meihod increases the acceptable depth of field oF pariides especially for the small ones compared to the dual threshold method. it enables more smafl particles Lobe deLecLable in PDIA.

Section 3 explains the layout of the measurement system. Section 4 makes a first step to describe the calibration procedure for PDIA with CCD camera and diode laser system by using calibraLion circles (Paiterson globes and circles), From which the usage of software, comparison of different threshold methodologies and depth of field (Dofl determinaiion are sLudied. Here, the Dof is delined as ihe disLance range along Lhe opticai axis within which the particle is considered to exist. in order to test the applicability of PDIA, a population of glass spheres of known size characteristics were analyzed using the diode laser system. Detailed discussion of the results generated by different threshold methods will he presented in section 5.

I

2. Principle of the DPIA program 2.1 General Experimental Principle Kashdan et al. shows a composite image matrix of the Patterson Globes calibration cirdes with increasing diameter and al increasing defocus distance. ()hviousy the out-ol-focus particles look larger than they really are and become bigger hut fainter with the increase in the defocus dislance unifi Ihey disperse mb Ihe background. Ii indicates Ihat the basic problem to bc solved concerning imagc processing algorithms is light diffraction at the particle image boundary: the grayscale varies continuously and the appropriate value of the lhreshold grayscale should he determined. A detailed comparison of different thrcshold methods is discussed in scction 2.2. In mcasuring a group of particles dispersed in three dimensional space, the two dimensional image captured by the camera syslcrn probably contains imagcs of off-focused particles, overlapping particles and particles touching the image boundary, which can cause a measurement error. For accurale measurement, Ihe images of the oil-locus particles should he sized correcily.

Overlapping particles can be processed assuming the particles are spherical, which will he explained in section 4.7. This image process algorithm rejects particles touching the edge of the image field-of-view since the amount of particle out of field-of-view cannot he estimated. Another important consideration is the acceptable depth of field (DoF) critenon. The DoF varies with the particle sites; larger parbicles have a large acceptabk depth of field. When the same DoF criterion is imposed on polydispersed particles contained within a linite measuring vothme, a number of smaller drops may he considered out of DoF and eliminated from the counting throughout the image processing.

To restore the missing small particles remaining outside the DoF or to avoid losing larger parlides, Ihe number ol' the parlides within the DoF region should he mulliplied by weighting factors corresponding to each size group. A quantitative determination of DoF is given during the calihraLion procedure in section 4. II' a parlide remains oulside the acceptable depth of ficid around thc focal point, thc particle should not be countcd.

2.2 Particle/droplet identification Figure 1(i) shows a schematic representation of a lypical in-focus droplel positioned at the centre of the plane of best tbeus, and the corresponding idealized intensity profile across the object centre is illustrated in Figure 1(a). Ibis schematic clearly shows that the contrasi heiween the particle shadow and the background is very sharp is thus Ihe droplet diameter (D) is relatively easy to measure.

If the droplel is located at some displacemeni from the focal plane of the objective lens, the resulting shadow image becomes deflicused. As illustrated by Figure I (ii) and Figure 1(h), defocused parlicles no longer have the sharp conirasi as observed in Figure 1(i) and there exists a continuous graduation of intensity between the dark object centre and the light image background. I'he region between the background threshold and the inner dark region of Figure 1(ü) is termed the parlicle halo' and typically has a conslani inlensily gradient. Dual threshold methods and multi-threshold method are implemented to analyze the defocused particles.

Dual threshold methods The total area of the partide halo' (AR) as shown in Figure 1 (ii) , expressed here as the number of pixels increases with increasing defocused dislance and is used lo extraci the true object diameter. The PDIA uses this intbrmation as a means of determining the localion of a particle or droplel relalive Lu the plane oF hesi focus, which is robust and commonly used in commercial particle/droplet analysis.

In order to define Lhe accurale parlide si/c, (be low-er (JL) and higher threshold (JH) limits are defined in dual thrcshold methods, as shown in Figure 1(b). Ihe particle interior is extracted by the low-er lhreshold (Tfl, which is Ihe tolal pixel counL wiih ihe intensity weaker than the lowcr threshold (J<Ju). Thc halo area (AH) is dcfined as the total pixel with the intensity betwcen lowcr threshold and higher threshold (I,cJ<I,,). Total area (Ar) of the whole out of focus particle is the sum of the particle interior area (AL) and Lhe halo area (AI=AL +AL). There are two main dual threshold methods presenied here Lu determine I, and I: Method 1 (Kashdan et al.): ft and H are the functions of background intensity ([background) of Lhe whole image with a difference oF 0.117, cakulated from Eq. (1) and (2).

H = 0.85 X ftackg round (I L'JI -0.117 (2) Method 2 (Yule et al.): L and H are the thnctions of the background intensity (1i,a,*g,-ou,,) and minimum intensity (I,,,j,,), calculated from Eq. (3) and (4).

= 0.64 >< ( background -men) + mEn (3)

H = 0. I 5 X ( background -ruin) + ft (4)

Yule et al. stated that the exact coefficients (0.64 and 0.15) chosen for Eq. (3) and (4) are arbitrary and not critical provided that the same values arc used for both calibration process and the actual particle size measurements. From the above equations, both dual threshold methods rely on the background intensily. The following calibration procedure (section 4.2) will detail how background intensities affect PDTA results.

However, neither of Ihe dual threshold methods is capable of analyzing excessively defocused particles as shown in Figure 1(iii), since the particle interior can not he detected by the lower threshold. Method I sets Ihe dilTerence heiween higher and low thmsholds as a constant (0.117, Eq. 2), which can only deal with the particles with better locus than thai shown in Figure!(iii). Although the difference between higher and low thmsholds set in Method 2 is the function of background, a similar rcstriction of detecting far more defocused particle occurs during PDIA process. This limitation is fundamental to dual threshold methods.

Multi-threshold methods Analysis of the far more defocused particle as shown in Figure 1 (iii) is the main issue br the dual threshold methods, especially for the small particles which are easily out of focus within a small dcfocused distance. Maximum dcfocus distances of small and large particks differ greatly, which causes highly non-unilbrm control volume weighting factors to bc applied to diffcrent size classes to reconstruct true particle size distributions.

This in turn makes dual threshold methods overly sensitive to the error prone measurements of the smaller objects recorded. The proposed solution is simply to use multiple thresholds, in the aptly named multi-threshold method.

PDTA works best when using the particle thcal background levd to determine the particle information rather than the global image background intensity, it is difficult with dual threshold methods and an additional algorithm is required to find the local background level. However, sincc the multi-threshold method cmploys continuous thresholds until the local background level to process each particle in the images, it

naturally uses a local background intensity.

As shown in Figure 1(e), a typical defocused particle could he delecied Irom the I 0th threshold till the local background intensity of the particle. however, the excessively defocused particle is delectahle From the 7gth threshold Lill us local background inlensily as shown in Figure Iffi. This shows the multi-threshold method is capable of analysing Lhe parlicles wiLh a wider range of defocused disiance than the dual threshold method, which is crucial in small particle analysis. Quantitative comparisons of dual threshold methods and the multi-threshold method are presented in section 4.

2.3 Weighting factor for correction of the particle/droplet size PDF The PDIA algorithm rejects particles louching the edge of the image field-of-view since the amount of particle out of field-of-view cannot be estimated. This results in a statistical correclion as the larger particles have more possihililies to touch the boundaries of the images. This weighting factor defined as: 1 WH i-n = (W-D)(H-D1) (5) Here n is the weighing faclcr for the particles with a mean diameter of D1, and W and Hare the width and height of the image field of view respectively.

3. Conceptual experimental design Experiment layoui of (be PDIA syslem is simple and slraighlforward compared Lo ihe other partiele/dropict analysis methods, which is shown in Figure 2. Field of view (FoV) of the measurement area is delermined by Lhe focal length of Lhe lens, Ihe site of Ihe charge coupled device (CCD) of the camcra and the distance between camcras CCD and lens. Delerminalion of the acceplable deplh of field (DoF) of PDIA system is detailed in section 4.

Before real spray analysis, calibration of the PDIA system is required with the calibration circles of known sizes. Patterson globes and circles were used to calibrate the particles wiLh diameter of I S,.tm-450Rm wilbin the field of view of 2.Ommx 1.6mm. Tn ordcr calibrate the system at thc different defocused distancc and with various illuminalion intensilies, ihe experimeni rig for the calibration is built up as shown in Figure 2. The minus sign in defocused distance (DF) indicates thc test circles near the diffuser and the laser. As introduced in section 2.2, background intensity is important for PDTA. Therefore neuiral density fillers with Lransmission of 13.7%, 23.5%, 51.2% and 69.3% are implemented to changc the illumination intensitics and find how the

background intensity affect the results.

In order to test Ihe applicability of the PDIA algoriihm, we analyie moving glass sphercs dispersed in a water tank by thc stirrcr and discussions of the results arc prcsented in secLion 5. The glass spheres are provided by Jencons-Plus wiLh diameter range of 70-A 10pm and T 00 -200 jim. The experiment layout of thc glass sphere analysis is similar to the calibration setup as shown in Figure 2, where here the gTass spheres are dispersed in a Iransparenl glass of waler.

4. Calibration with diode laser The fundamental principles of the technique and a description of the calibration procedure in which the image processing routine was verified with calibration data of known particle sizes were described in Ihe previous works 0! olher researchers. The experimental setup is illustrated in section 3.

S

4.1 Determination of acceptable depth of field with dual threshold method The literature has revealed thai there exisLs numerous definitions of the depth of field (Dof) with dual threshold methods and it is necessary to clarify how this should he interpreted in the present study. First the variations of characters for some calibration circles with different diameters (D) as a function of dctbcus distance (DI-) arc presented.

Figure 3 shows, by using dual threshold method for l4SRm, 110pm, 74Rm, 37Rm and l8pm calibration circles, how-total area (AT) varies with defocus distance (DF) from their in-focused size (A1f0,4). The larger particles have a wider DoF and more magnification with increasing defocus distance. For instance for the l4Spim calibration circle, it could he magnified up to 2.5 times of that at the thcal plane, while only 1.2 times for the I circle.

In a further study of halo area variation, the ratios between halo area and total area (A H/A T) at different defocused distance have been plotted in Figure 4. At the same defocused distance, the ratio generated by the threshold method of Yule is more than that generated hy Ka.shdan. Under the threshold method of Yule and with increasing the defocus disiance, A11/A increases up to 0.9 for the larger circles (D>l8pim) and 0.6 for the one of 1 8Rm. However, hy the method of Kashdan method, A11/A1-increases only up to 0.8 of the larger circles (D>lSp.m) and only around 0.4 for the l8pm one. A11/A-,-indicates how dclocuscd each particle is from the local plane and is a signilicant parameter in real particle sizing. Within the same depth of field, the method of Yule provides more variations in A11/A than Kashdan, which generates a calibration database with a wider dynamic range and hence more accurate subsequent real spray analysis.

In Kashdan ci al., ihe acceptable Dof is relaied Lu the position where halo area reaches a peak as the function of defocus distance. however, from Figure 4, this method does not work in ihis study since there is no pealc value in the halo area vanalion, which is mainly caused by the different optical sct-up. Thercforc, an alternative way is presented here.

The particle interior area defined in Figure I (ii) decreases with increasing deFocus distance until it vanishes in the background. the position whcrc thc particle interior is minimum is considered here as a parameter relating to acceptable DoF, which is defined as the criiical position D0F*.

l'he variations of lower arca (A,) as a function of defocus distance for 145pm, 1 l0tm, 74pm, 37p.m and l8pm calibration circles by dual threshold methods are shown in Figure 5. AL/AT decreases continuously with increasing the defocus distance br each calibraiion circle as expected. The two endpoints of each curve indicatc where the particle intcrior disappears. Therefore, Ihe crilical D0F* should be delined as ihe posilion where lowest AjAr is. From the figures, D0F* locates within -S<DiD<S under thc method of Yule and -1OcDF/Dc10 under the method of Kashdan, which indicates D0F* is a function of D. Similar lo the method ol' Kashdan, in Ihis siudy, the accepiable DoF is deFined as 70% of the critical position (D0F*), which is shown in Figure 6. It indicates a linear relationship heiween accepiable DoF and pariicle sites for both dual lhreshold methods.

Since thc slope of the linear variations of the acceptable DoF determined by the method of Yule is slightly less than that generated by the method of Kashdan, the method of Yule requires slightly less wcighing of thc actual particle diameters measured.

4.2 Determination of real particle/droplet characters from the calibration process by dual threshold methods The aim of Ihe above calibralion process is lo provide a dalahase in order lo analyze the unknown droplet/particle characters from a set of images (e.g. rca] droplet/particle diameler and its defocus distance from the focal plane). Two main paramelers in the determination of real particle/droplet characters are the ratio of halo area and total area (A H/A) and the calibration circle diameters (or area).

Within the acceptable depth of field as shown in Figure 6, the varialions of AT with A,1/A1-fir 145pm, I 10pm, 74pm, 37pm and lSpm calibration circles by the dual threshold methods are shown in Figure 7, where A18 is total pixel area of the lSpm calibration circle at focal plane. Therefore, for an unknown particle with its A11/A j-and A1-provided, the real diameter (or could be easily interpolated from the calibration database. The method of Yule is better fir the larger particles (D>! 8pm) than the method of Kashdan, as the changes at different defocused positions are more measurable.

However, for the small particles (D=ISpm), ihe method of Kashdan provides wider oul of tbcus degree (0.25< A11/A1<0.7) than the method of Yule (0.35< A11/A1-<0.68), which makes the smaller parlicles more detectable by the method of Kashdan.

As introduced in section 2.2, background intensity is important fir PDIA. Similar to Figure 7, Figure 8 shows how AT varies under two different illumination intensities (lbackerounaO.7 and 1.0). Background inlcnsilics has less influence on AT varialions by Ihe method of Yule (1987) than the method of Kashdan for 145pm, 74pm and 37pm calibration circles. However, the method of Kashdan extended the AH/AT range at higher illumination intensity (Jj,rrou,,j=! .0). Especially for the I 8pm calibration circles, it increased ihe range from 0.36-0.68 10 0.254).68, which makes Ihe circle more delectahie at near focus positions.

Discussion: Dual threshold methods it is difficult to tell from this calibration experiment which dual threshold mcthod is helter. The method of Kashdan has more possihilily k)r detecting wider range (0.25< AH/A]<0.7) of defocused particles, the method of Yule provides less changes of the depth of field for each particle size and less sensitive to the background intensity varialions, which gives more similar prohahilily br detecting diftereni site particles within the field of view. No matter which method is used, the real application must employ the calibration function produced from the same threshold method. Although dual threshold meihods are robust and simple Lo he implemented in commercial software, it still requires correct coefficients chosen in for Eq. (1) (4) each application, it should be noliced Ihal Ihe meihod of Yule will he used to compare with Ihe perlormance ol ihe multi-threshold method in the following content. As stated in section 2.2, excessively defocused particles cannot he analyzed by dual threshold methods. Therefore, the multi-threshold meihod is introduced in seeLion 4.3 and seclion 4.4, which is a general ihreshold methodology, does not require any coefficients and is capable in most particle/droplet analysis applicaLion wiLhout any need to define the coefficients required br dual threshold methods.

4.3 Determination of acceptable depth of field with multi-threshold method Differeni from the dual ihreshold methods, the multi-threshold method generales an area variation curve against each threshold level tbr the particle at a certain detbeused position Irom the local plane. Compared to only Iwo area values provided by the dual threshold methods for detecting one particle, the multi-threshold method generates much more inlormalion which gives more possibilities lo accurately analyze particle characteristics.

Figure 9 shows the variations against each intensity threshold br!45Rm and I calibration circles from the focal plane to thc defocused position of DF/D=1, 2, 3, 4 and 5 (DE: defocused distance; D: circle diameter). For the in-focused large circles (D=225pim), the variation grows rapidly at the beginning ol intensity increase from 0.1 to 0.2 and slows down from 0.4 to the cnd. Howevcr, for thc ISRm circlc at focal plane, it approaches linearly variation. It indicates that the smaller particles are more sensitive to the intensity chosen to threshold, which is similar to the dual threshold methods. There is a little change in the variation curves at different defocused distance for thc small circles (D=i 8pm, and it is very difficult to bind DF accurately. However, br the D=225pm circle, it shows that the variation curves change from convex to lincar and to concave with increasing the defocused distance. This shape' information can he exploited to estimated particle size and axial delocused position.

Figure 10 shows area variations at different intensity thresholds for the 11 ORm calibration circle at different delocused position. From the ligure, D0F* locates within - 15<DFID<15 for thc 110pm calibration circle under multi-threshold method. Each calibration circle (D=145ptm, 74pim, 37Rm and I8pm) has similar data points as the 1 l0tm circle, from which it generates the database for measuring real droplet sizes and defocused position from the focal plane.

Similar Lo ihe dual threshold method, ihe acceptahle Dof is delined as 70% of Ihe critical position (D0F*) in multi-threshold method. It also generates a linear approach to the accepLable depLh of held against particle sizes, shown previously in Figure 6. Most importantly it increases the DoF for the small particle size (D<5ORm) up to 1.5 times than Ihat calculated hy dual Lhreshold methods.

4.4 Determination of real particle/droplet characters from the calibration proccss by multi-threshold methods The dual lhreshold methods use AHIAT as a parameter to measure the particle defocused degree. The multi-threshold method takes the curve shape' as a detbcused degree parameler. For a random parlicle detected in the real world, a curve is generaled hy the multi-threshold method and compared to all the curves from calibration database like the ones shown in Figure 10 to find the closest shape' in each size group of the calibration circles. Then real particle sizes and detbcus positions may he simply interpolated from the calibration database.

4.5 Curve matching method comparisons Several curve matching parameters are reviewed by Efrat et al. and include Fréchet distance, discrete Dynamic lime Warping (DIW) and continuous Dynamic Time Warping. The Fréchet distance is defined as the maximum leash length' over the parameLer heiween two curves. The maximum value can usually cause an error, where a small change from the input can misrepresent the parameter. A sum or average based process can smooLh such disiortions, which is named as Dynamic Time Warping method.

As citcd in Efrat et al, discrete DIW is widely uscd in spccd signal recognition signature tracking and for multivariate time series. Continuous DTW is introduced by Serra and Berthod lo maich sub-pixel contours, and ii is explored by Munich and Perona to measure the similarity of signatures.

Four curve matching meihods (Frdchet distance, discrete DTW, continuous DTW and standard deviation method) were tested for two glass spheres of diameter 4.5jim and 88pm at diflërent defocused position. The siandard deviation meihod (STM) finds the curvc with the mininmm standard deviations betwccn two curves. lie errors generated by each method are based on the differences between the calculated particle diameter by PDIA and the real diameter. Continuous DTW generales the leasi error especially br the smaller particle (D=4.5Rm), while the other methods work similarly for the larger particle (D= 88 jim) and produce more error for the smaller particle (D=4. 5 jim). Therefore an average based conlinuous DTW method is implemenled in this sludy.

4.6 Analysis on the aspect ratio of the calibration circles The aspect ratio of each particle image profile was defined lo he the maximum chord divided by the maximum width normal to the chord. This is consistent with the definitions of aspect ratio for ellipses (maximum diameter divided by minimum diameter).

Sphericily (S) is defined as the perimeter (P) divided by the circumference of a circle with the same area (A), calculated by Fq. (6).

P

= 2V (6) The multi-threshold method defines the aspect ralio (or sphericily) of a particle as a mean of the aspect ratios (or spherieities) of the detected shapes at each threshold. Figure 11 shows how-the aspect ralios and sphericities vary at differeni defocused dislance for the calibration circles by the dual threshold and multi-threshold methods. The calculated aspeci ratio of the large circle (D=l45pm) went up to 2 at DFID= ± 8 by the mulli-threshold method, while ii reached 2 al closer defocused dislance of DF/D=±7 by Ihe dual threshold. The dual threshold method over-predicted the aspect ratio of the small cirde (D=i 8Rm) as a mean of 1-3 even al local plane, whereas the multi-threshold mcthod produccd bcttcr approach for thc small circlc. Shapc variations of thc sphcricitics of the large circle (D= I 45Rm) were delecied out of the range of -8<DF/D<8 by Ihe multi-thrcshold mcthod and out of thc rangc of -5<DFID<5 by thc dual thrcshold method. l'hc dual threshold method under-predicted the sphericities of the small circle (D=l8pm) as a mean of O.98even al the plane of focus. The deviations of the aspeci ratios and sphericiLy arc causcd by thc blur around thc particic edges due to thc non-uniformity of thc diffuscd laser light, and with increasing defocused distance the non-uniformity effects enhance the errors due Lo the wide illumination area of the diffused and slightly non-uniform laser light.

Discussion: Mit/ti-threshold method Compared to thc dual threshold methods, thc multi-threshold method incrcascs thc acceptable DoF from -7<DFID<7 to -IO.5cDFIDc1O.5. It makes the smaller particle (Dc! 8pm) more delectable. However, aspect ratios and sphericities of the particles provide another criterion in the determination of particle sizes accurately. The multi-Lhreshold method allows the reasonable measurement of aspect ratios and sphericities within -8cDF/D<8 for thc large circlc (D=145pm) and -lO<DF/D<lO for thc small circlc (D=l8pm). Whereas the dual threshold method can only process them for the large circle (D=145pm) within at narrower DoF of -5<DF/D<5 accurately and proccss them with notable errors for the small circle (D=l8pm). It provides a possibility to reduce the variations of the DoF due to the particle site groups in the PDIA, which makes the large particles could he measured wiLhin smaller DoF and vice versa. In general, Ihe circles with diameter of l8jim-45Ojim has been calibrated from the above procedure using Patierson globes and circles, within Ihe 2.OOmmxi.6Omm field of view. In order Lo Lest the applicability and the accuracy of the multi-threshold, glass spheres were analyzed wilh PDIA system and comparisons are made Lo the resulis of the dual Lhreshold method and FDA in section 5.

4.7 Overlapping particles the PDIA system separates overlapping circular particles using the sphericity to reconstitute the form of a particle, provided that the particles are essentially circular.

Figure 12 shows the procedure how the multi-threshold method deals with overlapping particles. The background intensity of the image is 0.427, 109 thresholds were used to generate particle information for each threshold. At the lower intensity threshold such as the 22ad threshold, only the overlap part of the two particles could be detected as a black spot shown in Figure 12 ®. This overlapping part will be deleted at a lower intensity threshold and will be compensated in the following threshold procedure. At middle intensity threshold (e.g. 56th threshold as shown in Figure 12 ©), two individual particles could be detected and their area information is recorded with the corresponding threshold.

At higher intensity threshold (e.g. 97rh threshold as shown in Figure 12 ©), two overlapping particles could be separated according to their sphericities and their fully circular areas are recorded. Therefore, the intersecting area will he counted twice at higher intensity threshold for two overlapping particle.

Two tests were undertaken to find how accurately the PDIA dealt with overlapping particles: to compare the PDIA results of the overlapping particles and the separated particles. As shown in Figure 13, two seLs @1 particles with different overlapping IracLions are analyzed. There is less overlapping area fraction of particle 1 and 2 (Figure 13a) than that ol particle 3 and 4(Figure 13h). The individual particles (Figure 13c and Figure 13d) are crcatcd by separating the overlapping particles (Figure 13a and Figurc 13b) and the overlapping parts are compensated by Lheir symmeirically non-overlapping parts.

Fig 13e shows the PDIA results of the overlapping particles and individual particles by the multi-threshold method. For the particle 1, 2 and 3, the comparison indicates little changes between ihe results of PDIA in overlapping parLicles and the original individual particles. ihere is a mean crror of l.S6% ± 0.2% betwccn the calculatcd diamcters of the overlapping particles and the original individual particles. The deviation is due to its non-symmeiry and the error due to the compensaLion procedure of Lhe overlapping pan. The comparison indicates that PDIA is capable of analyzing the ovcrlapping particles reasonably.

5. Glass sphere measurements 5.1 Measurement In order to test the applicability and the accuracy of the PDIA system, two sets of glass sphercs with diffcrcnt diametcr groups (7ORm-A iüm and lOORm-20011m) were analyzed by the PDIA. The exposure time, texp is usually defined as the time required for aparLicle to move a small Iraction ol us own diamelerhy Eq. (7), < (7) where K,; is a constant with a value of 0.1. is the diameter of thc smallest particle to he measured, and 17,, is the particle velocity. Thus for 1OOjtm particle travels with a velocily of I Om/sec, an exposure lime of I sec is required, however, br a 5pm particle travels with a velocity of 2Omlsec, an exposure time of 25nsec is required.

Glass spheres were dispersed by the slirrer in the Iransparent waler tank at a mean particic absolute vclocity of 0.lm/s, particlc images wcrc taken with 2ps of camcra exposure Lime and 1 ps of laser pulse duration. For Lhe sake of finding whal enhancement thc multi-threshold mcthod providcs, thc performance is comparcd to thc dual thrcshold method in analyzing the glass spheres with diameter 70pm -1 10pm and 100pm -200pm.

5.2 Class sphere results analysis 70!um-l 10pm and 100pm-200pm moving glass spheres are analyzed by the dual threshold method and the multi-threshold method. The number based distribution analyzed from 1000 parlicle images are compared with the FDA data and shown in Figure 14. For the 70pm-i I Opm glass spheres, the plot of the number frequency of the parlicles with sphericities (S) larger than 0.97 have Ihe hesi approach to Ihe FDA resulls.

It proves that PDA removes non-spherical particles during the process. However, the peak particle number frequency of the 7Opm-l 10pm glass spheres generated by dual threshold method is 0.24 aL Ihe parlicle diameter of 7Opm, which is clearly differeni from the results of the other two methods. Similarly, for the I 00pm-200pm glass spheres, the outcome of the dual threshold method differs much from the results of the other two melhods. Furthermore, as show-n in Figure 15, the multi-lhreshold method produced closer results on the volume based distributions to the results of PDA than the dual threshold resulLs. The significanl devialions of the resulls of the dual threshold melhod from those of multi-threshold and FDA are due to the insufficient particles detected by the dual thrcshold method in 1000 images. The multi-threshold mcthod found 197S and 890 particles among the 70pm-i 10pm and I OOpm-200Rm glass spheres respectively, while the dual threshold method only detected 345 and 99 particle (on average) for each glass sphere group. Compared to the particle numbers found by the multi-threshold mcthod (1045 for thc 7ORm 11 0m glass sphcrcs and 406 for thc 1 00tm-200pm glass spheres) with the sphericities larger than 0.97, the dual threshold method can only detect 71 and 7 among thc 70tm-110pm and 1 OOpm-200pm glass sphcrcs respectivcly, which is not sufficient to generate statistics. As described in section 2.2, extremely defocused particles are not detected by Ihe dual threshold method, and this is fundamental to the mcthod. In addition, dual thrcshold mcthod will lose particlcs at darkcr background due to the coefficients of Eq. (3) Eq. (4). For instance, at background intensity of 0.5, the higher and lower threshold are 0.4 and 0.3 calculated From Eq. (3) and Eq. (4), which barely dctccts particles with corresponding grayscaics.

In order to find whether the motion of a particle alTects its aspect ratio, two moving glass spheres and two quiescent glass spheres (Figure 16a) with same diamctcr (D=92Rrn) were analyzed. The moving defocused glass spheres were obtained from the images of the dispersed 7Opm-i 10pm glass spheres by the stirrer at the mean particle absolute velocity of 0. lmIs. The moving glass sphere 1 and quiescent glass sphere 3 are at DFID=4. 13, while the moving glass sphere 2 and quiescent glass sphere 4 are at DF/D=0.75. Figure 16b and Figure l6c show the deviations of the aspect ratios and sphericities acquired by the multi-threshold method at each threshold for the glass spheres. The aspect ratios and sphericities of thc defoeused moving glass sphcrcs vary much more from the mean aspect ratio than those of the near focused and the quiescent glass spheres. The light relleetion and refraction Irom the moving glass spheres caused asymmeiry imaging of (be defocused particles, and it leads lo ihe differences of ihe results between the two different states of the glass spheres, which does not greatly influence Ihe results of the near focused or the quiescent particles.

Figure 17 shows the comparisons of the aspect ratios and sphericities acquired by the dual lhreshold and the mulli-lhreshold method br (be 70pm-I 10pm and i00pm-200p.tm glass spheres. the multi-threshold method produces a more reasonable measurement since the peak of the aspect ratios (and spherieities) approach 1. The dual threshold method over-predicted the aspeel ratios since Ihe peak frequency is generated al ihe aspect ratio of 2 and it under-predicted the peak spherieity to 0.97 of the 7ORml 10pm glass spheres and 0.95 of the lOOpm-200j.tm glass spheres. Because only two thresholds are implemenled for the dual lhreshold method, the aspect ratios of moving particles are susceptible to error.

6. Conclusion

A newly developed multi-threshold algorithm was successfully implemented in an aulemalic particle/droplet image analysis (PDIA) syslem. It is able 10 process a large amount of images with simple user inputs.,from which the information on particle halo area, total area and dislance from plane of focus may be obtained. The varialions of halo area and total area for 270pm, 225pm, 145pm, 110pm, 74pm, 37Rm and ISpm calibration circles have been studied under existing dual threshold methods and the new multi-lhreshold method, from which acceplable depth of field (or each particle size has been defined, and acceptable DoF varies linearly with the particle size. the multi-threshold method increases the depth of field (DOF) for small particles (Dc50p.m).

Accurate determination of the aspect ratios and sphcrieities of the calibration circles provides another criterion in PDIA, which can reduce Ihe DoF variations of different particle size groups. Determination of real particle/droplet characters from the calibration data has been implemented into PDTA, which was tested with moving glass spheres.

During the analysis of the 7Opm-l 10pm and lOOpm-200pm glass spheres, thc multi-Lhresho]d method performed more efliciently than dual lhreshold method. The dual threshold method can only detect 1 1%-29% of the particles found by the multi-threshold method, which indicates the results produced by the multi-threshold method for PDIA is more robust and reliable. The multi-threshold method is also capable of generating Ihe aspect ratios and sphcricities of thc particles morc accurately than dual threshold method.

REFERENCE

Kashdan, J. T., Shrimpton, J. S., Whybrew, A., 2003. Two-Phase Flow Characierisation by Automated Digital image Analysis, Part 1: lUndamental Principles and Calibration of the Technique. Part. Part. Syst. Charact. 20, 387-397.

Yule, A. J., Chigier, N.A., Cox, N.W., 1978. Measurement of Particle Sizes in Sprays by the Automated Analysis of Spark Photographs. Pail. Size Anal. lieyden Press, pp. 61 -73.

Efrat, A., Fan, Q.F., Venkatasubramanian, S., 2007. Curve matching, time warping, and light fields: New algorithms for computing similarity between curves. .Iournal qf Mathematical Imaging and Vision, 27, 203-216.

Serra, B., Berthod, M., 1994. Suhpixel contour matching using continuous dynamic programming. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.202-207.

Munich, M.E. Perona, P., 2003. Visual identification by signature tracking, IEEE Transactions PAMI, Vol. 25, No. 2, pp. 200-217. fl

Claims (3)

1. Claims 1. A muhi-threshokl image process algorithm to analyze out of focus particles and droplets. It employs continuous thresholds until the local background level to process each particle/droplet in the images.
2. 2. A multi-threshold image process algorithm according to claim I, uses a curve matching method to compare the results with the calibrated data, to acquire the particle/droplet size, aspect ratio and the distance from the focal plane,
3. 3. A multi-threshold image process algorithm according to claim 2, provides a possibility to get the three-dimensional position of the particles/droplets from the two-dimensional images.