A new method to measure track density and to differentiate nuclear tracks in CR-39 detectors

Radiation Measurements 34 (2001) 119–122

www.elsevier.com/locate/radmeas

A new method to measure track density and to di!erentiate nuclear tracks in CR-39 detectors D. Palaciosa , F. Palaciosb , L. Saj,o-Bohusa , J. P,alfalvic; ∗ a Universidad

Sim on Bol var, P.O. 89000, Caracas, Venezuela de Oriente, Santiago de Cuba, Cuba c Atomic Energy Research Institute, P.O. B. 49, H-1525 Budapest, Hungary b Universidad

Received 28 August 2000; received in revised form 29 December 2000; accepted 13 March 2001

Abstract An alternative method to count and di!erentiate nuclear tracks in SSNTD is described. The method is based on the analysis of Fraunhofer di!raction pattern of coherent light produced by tracks of an etched SSNT detector. The di!raction pattern was also simulated by applying computational Fourier Optics. The comparison between results obtained by simulation and by the theoretical model gave satisfactory concordance. The proposed method is capable of di!erentiating tracks in CR-39 by their diameter and energies. The diameter resolution ranged between 8% and 25%, while the counting error was less than 15%. The discriminating ability to distinguish genuine etched tracks from defects and background anomalies is demonstrated. The incidence angle did not in9uence signi:cantly the total count and the track parameter measuring capability. Errors due to track c 2001 Elsevier Science Ltd. All rights reserved. overlapping are only signi:cant for track densities higher than 3×105 cm−2 . 

1. Introduction

2. Basic equations

A large number of semiautomatic or automatic methods for counting etched tracks have been developed (Durrani , , 1997; P,alfalvi et al., 1997), but their general use is and IliC limited because of the high cost and the necessity of quali:ed personnel. Such systems use sophisticated software and their complexity increases if di!erent track parameters like diameter or incident angle are to be determined. In spite of new developments in automation of track counting and identi:cation, problems subsist even for very high track density, when great speed in information processing is required. The objective of the present work was to establish a new method to discriminate and count nuclear tracks on passive detectors with low cost and great operation simplicity. At the same time, greater speed in delivery of results is guaranteed, while the track counting and discrimination capabilities remain similar to some of the developed automatic systems.

Assuming that the light density pro:le of a binarised image of a track, considered as a circularly symmetrical object, can be described by

∗ Corresponding author. Tel.: +361-395-9220e1495; Fax: +361-395-9162. E-mail address: [email protected] (J. P,alfalvi).

D(r) = D

for 0 6 r 6

d 2

and D(r) = 0

for

d ¿r; 2

(1)

where D and d are the light density of the track and the track diameter, respectively, and r is the polar coordinate in the track plane. Using the approach of the Bessel function, given by TFuke et al. (1978), the intensity distribution in the Fraunhofer di!raction pattern (FDP) is described by the formula I (R) = A(R)A∗ (R)
  1 3 2 2 = D d + D d cos 2aRd − ; 4 aR3 2

c 2001 Elsevier Science Ltd. All rights reserved. 1350-4487/01/$ - see front matter
PII: S 1 3 5 0 - 4 4 8 7 ( 0 1 ) 0 0 1 3 5 - 4

(2)

120

D. Palacios et al. / Radiation Measurements 34 (2001) 119–122

Fig. 1. Fraunhofer di!raction pattern of a set of tracks (left), from which the radial intensity distribution can be obtained (right) by scanning along radial lines with Np =2 pixels.

where A(R) = FT [D(R)] is the amplitude distribution in the Fourier plane given by the 2-D Fourier transform (FT) of the density pro:le, a = f ;  is the wavelength of illuminating light, f is the focal length of the transform lens used and R is the polar coordinate in the Fourier plane. For an image formed by Nt tracks, Parseval’s theorem (Meyer and Arendt, 1984) can be applied and the equation for the total intensity dispersed by the objects may be expressed as
  Nt   1 3 2 2 D d +D d cos 2aRd − Itot (R) = : i i i i i 4 aR3 2 i=1 (3)

The radial intensity distribution can be measured by scanning the FDP of the object along radial lines. On the left side of Fig. 1 the FDP is shown, while the radial intensity distribution is given on the right side of the same :gure. Applying the FT on the radial intensity distribution we obtain  Nt
 1 2 1 2 FT [Itot (R)R3 ] = Di di (0) + Di di (2adi ) ; 2a 4a i=1 (4)

where FT (1) = 2 (0)

and

FT (cos(!0 t)) = (!0 ):

(5)

There is a de:nite correlation between the peaks observable in the spectrum and described by Eq. (4), and the track diameters. The measured spectral frequency is always characteristic of the track diameter distribution. 3. Methodology The Eqs. (3) and (4) form the basic formalism of the track analysis suggested in this work. If ni is the number of tracks with di diameter, Np is the number of image pixels, NT represents the classes of tracks, Ki is the background and Fi is the track form factor, then Eq. (3) changes to the

Fig. 2. Comparison between the theoretical model described by Eq. (2) (continuous curve) and the curve of radial intensity distribution calculated by the developed software (circles).

expression: Itot (R)R3 =

NT Np =2   

Mni di RKi

i=1 R=1



×


 R 1 3 1 + cos 2 di − Fi Np 2

(6)

where M is a proportional constant to be experimentally determined. Eq. (4) can be transformed to the form: FT [Itot (R)R3 ] =

NT 

I0N (0) + IpNii (di );

(7)

i=1

where the parameters are de:ned as follows: I0N the harmonic amplitude of zero order, and IpNi i the secondary harmonic amplitude that de:nes tracks having a diameter of di . To obtain the parameter values in Eqs. (6) and (7) a computer program named “TRACKS” was developed. The program is divided into the following main parts: • Input: image digitalisation of etched nuclear track detectors using a SONY camera (SSS-DC14), a digitiser board (PV-BT878P Prolink) and a PC (Pentium II). • Graphic operations: to enhance the image quality. • Image processing: using :ltration, smoothing, binarisation, FT, etc. operations. • Track parameter identi:cation, data storage and manipulation. It is evidently seen from Eqs. (6) and (7) that a linear relationship exists between IpNii and ni . Once the parameter values are obtained for Eq. (6), the function approximates, satisfactorily, the expected curve (given by Eq. (3)) as seen in Fig. 2. If only track counting and classi:cation by the diameter are required, then it is enough to analyse the images applying the following operations: soften, erode, dilate and :nd edges, others having minor in9uence. In order to study track structure and geometry in more detail, the images are processed by applying also the following operations: median, stretch, edge enhancement, binarisation and inversion. The output of the analysis provides the following track

D. Palacios et al. / Radiation Measurements 34 (2001) 119–122

parameters: major and minor axes, track area, angle of incidence and, for some particular cases, the track length also. The proposed method allows the reading of several :elds of view per second. One of the main advantages of this technique is the intrinsically low dependence on the illumination level and focusing. 4. The following studies have been carried out 1. We have considered also the overlapping tracks, obtaining a correction factor when a relatively high track density image is under scrutiny. This way, the analysis of a detector can be extended to higher track densities of the order of 105 cm−2 , while errors in track density calculations remain around 10% (Fig. 3). 2. It is well known that the FDP depends on the position of etched tracks, i.e. two di!erent patterns are produced for two detectors even if they have the same track density. The in9uence of this e!ect has been studied following the Array theorem (Meyer and Arendt, 1984). Statistical analysis of the results is presented in Table 1, where the precision equals N = NS 100(%) and the accuracy is |(Real − Calculated=Real)|100(%).

121

3. In general, for the determination of track densities, when it is increasing, the method is less precise but more exact, except when the tracks have large diameters, then the accuracy of both parameters decreases. Nevertheless, these results can be considered satisfactory since the errors √ introduced by the track distribution itself are below N . 4. To demonstrate that the proposed method can di!erentiate genuine tracks from defects, di!erent types of marks and rips were simulated in the vision :eld where true tracks existed. Results evidenced minimum in9uence of these defects. This advantage of the method is due to the fact that openings with similar forms and repeated with a certain periodicity are those which contribute more to the intensity distribution and its FT. 5. It was observed that accuracy of counting depends only on the magnitude of the minor axis and the major axis while their orientations have little in9uence. In the FT of the radial intensity, distribution peaks corresponding to major and minor axes of elliptic openings give the possibility of evaluating the incidence angle of the particles. 6. DiTculties caused by tracks truncated by the borders of the vision :eld are not signi:cant. It has been demonstrated that incomplete tracks located in borders contribute very little to FT (if less than 80% of their total area is included in the :eld of view).

5. Results

Fig. 3. Relationship between calculated and simulated track densities, as track density increases, for di!erent track images with diameters ranging between 4 and 16 pixels.

In Fig. 4 a histogram of etched track images are given. The numbered curves (1– 4) correspond to a histogram of one track diameter. This superposition of the four histograms allows the discrimination of track diameter groups with a resolution that ranged between 8% and 25%. This result is in accordance with that reported by Wong and Tommasino (1982). We observed that tracks di!ering by more than two pixels can already be distinguished.

Table 1 Uncertainty in track density calculations Diameter (
m)

Diameter (pixels)

Number of tracks simulated

Number of tracks calculated (NS ± N )

Error precision= accuracy (%)

Real track density (cm−2 )

Calculated track density (cm−2 ) (S ±  )

Error precision= accuracy (%)

9.4 9.4 9.4 9.6 9.6 9.6 10.0 10.0 10.0

4 4 4 10 10 10 16 16 16

10 500 2000 7 80 330 5 35 130

11.0 526.0 1976.0 8.0 89.0 297.0 6.0 37.0 99.0

5.0=10.0 3.4=5.2 7.8=1.2 7.5=14.2 6.7=11.2 15.4=10.0 15.0=20.0 8.9=5.7 15.1=23.8

2:8 × 103 1:39 × 105 5:56 × 105 1:20 × 104 1:33 × 105 5:50 × 105 1:95 × 104 1:36 × 105 5:05 × 105

(3.01 ±0:13) × 103 (1.44 ±0:05) × 105 (5.49 ±0:43) × 105 (1.43 ±0:09) × 104 (1.47 ±0:09) × 105 (4.95 ±0:76) × 105 (2.47 ±0:33) × 104 (1.44 ±0:1) × 105 (3.91 ±0:6) × 105

4.3=7.5 3.5=3.6 7.8=1.3 6.2=19.1 6.1=10.5 15.4=0.1 13.3=26.6 6.9=5.9 15.3=22.6

± ± ± ± ± ± ± ± ±

0.5 18.0 154 0.6 6.0 46 0.9 3.3 15.0

122

D. Palacios et al. / Radiation Measurements 34 (2001) 119–122

Fig. 4. Simulated track density distributions. For each classes of circular tracks, 50 tracks were considered. The diameter classes of 4 (curve 1), 9 (curve 2), 14 (curve 3) and 20 (curve 4) pixels were de:ned.

Fig. 6. Track diameter distributions obtained from track images on CR-39 detectors perpendicularly irradiated with di!erent particles with the same energy (18 Mev): particles of 7 Li and 16 O (curve 1); particles of 7 Li and 12 C (curve 2).

peak appears at the diameter corresponding to particles of 7 Li with 18 MeV. 7. Conclusions We presented an alternative method to analyse SSNT detectors taking advantage of the Fourier Optics, in particular the analysis of Fraunhofer di!raction pattern. Our results could well be compared in quality with other current methods as a whole, moreover, the proposed method possesses bene:ts converting it into a potential and attractive new tool for quanti:cation and di!erentiation of nuclear tracks. Particularly, this method is advantageous when detectors with high track density are analysed. Fig. 5. Track diameter distributions obtained from track images on CR-39 detectors perpendicularly irradiated with particles of 7 Li in di!erent combinations of energy: 13 Mev 7 Li (curve 1); 17 Mev 7 Li and 13 Mev 7 Li (curve 2); 18 Mev 7 Li and 13 Mev 7 Li (curve 3).

6. Experimental part To evaluate experimentally the discrimination possibilities, CR-39 detectors were irradiated as described by Saj,o-Bohus et al. (1996) with di!erent ions having the same or di!erent energies. The produced images of the etched tracks were analysed and the results are given in Figs. 5 and 6. Results su!er from large errors (10%) because of the low particle 9uence and track loss due to the etching process. However, the results shown in Fig. 5 suggest that tracks with diameter equal to 3 pixels correspond to particles of 7 Li with 13 MeV, while tracks with diameters of 7 and 9 pixels correspond to energies of 17 and 18 MeV, respectively. This result is corroborated in Fig. 6, where a

References , , R., 1997. Radon Measurement by Etched Track Durrani, S.A., IliC Detectors: Applications in Radiation Protection, Earth Sciences and the Environment. World Scienti:c, Singapore. Meyer, J.R., Arendt, M.D., 1984. Introduction to Classical and Modern Optics. Prentice-Hall, Englewood Cli!s, NJ. P,alfalvi, J., EFordFog, I., Sz,asz, K., Saj,o-Bohus, L., 1997. A new generation image analyzer for evaluation SSNT detectors. Radiat. Meas. 28, 849–852. Saj,o-Bohus, L., Birattari, Rozlosnik, N., Gadioli, E., P,alfalvi, J., Greaves, E., 1996. Identi:cation of heavy ions and nuclear reaction fragments by means of latent tracks in passive detectors CR-39. Acta Phys. Hung. Series, Heavy Ion Phys. 3, 135–139. Hungarian Academy Press, Budapest. TFuke, B., Seger, G., Acchatz, M., Seelen, W.V., 1978. Fourier optical approach to the extraction of morphological parameters from the di!raction pattern of biological cells. Appl. Opt. 17, 2754–2761. Wong, C.F., Tommasino, L., 1982. Energy discrimination of alpha particles by electrochemical etching of track detectors. Nucl. Tracks 6, 17–24.