- Email: [email protected]
A video-based automatic method to measure charges in nuclear track emulsions
314
Nuclear Instruments and Methods in Physics Research A257 (1987) 314-320 North-Holland, Amsterdam
A VIDEO-BASED AUTOMATIC METHOD TO MEASURE CHARGES IN NUCLEAR TRACK EMULSIONS E. GANSSAUGE, Ch. MÜLLER, B. DRESSEL, S. HACKEL, H. KALLIES and W. SCHULZ Department of Physics, Philipps-University, 3550 Marburg/L., FRG Received 23 December 1986 A new method is developed for measuring charges of tracks in nuclear track emulsion. We use an automatic charge measuring device, consisting of a microscope, equipped with a stepping motor-driven stage, a CCD-video camera and a picture analysis system. Special parts of the distribution of local track widths show clear correlation to the charges which can be measured in the range 10 5_ Z <- 26. The precision of one charge unit is achieved by introducing new specific quantities . 1. Introduction The nuclear track emulsion is well known as a very sensitive detector with many excellent properties . But there is a large handicap in using this detector, namely the high manpower necessary for getting reasonable statistics of data. Especially the determination of charges has to be done in an automatic way [2]. We used the great progress in picture analysis with microcomputers to solve this problem. We developed a measuring system which is able to follow a track by itself while analyzing it. We adapted the idea of basic cells [1] and used certain new quantities to achieve a precision of d Z = f 1 . This accuracy is good enough for most experimental applications. It should be noted that this kind of analysis highly depends on the type of emulsion and the processing procedure [3]. This work was done with Ilford G5 emulsion out of a stack exposed to a 56 Fe beam of 2 A GeV at the LBL/Berkeley and processed there.
These requirements are met in our configuration essentially by the units described in the following section (see fig. 1) .
2. The apparatus An automatic measuring device has to fulfil the following requirements : - The stage of the microscope has to be automatically movable by remote-control. - The microscopic picture must be taken by a camera and stored in a computer memory. - The evaluation of the stored data has to be possible in a reasonable time . * This work is based on the "Diplomarbeit" of Ch. Mailer at the experimental High Energy Group of the University of Marburg. 0168-9002/87/$03 .50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Fig. 1. The apparatus, consisting of a microscope, equipped with a stepping motor-driven stage, a CCD video camera and a picture analysis system .
E. Ganssauge et al. / Automatic method to measure charges in emulsions 2.1 . Microscope and camera
512
The microscope (Leitz-Ortholux) is equipped with a stage (Mdrzhäuser, MCC 13) which is movable horizontally by means of stepping motors with a step width of 0.25 lm. The stage is movable in x and y directions, 210 mm and 100 mm respectively with a precision of some microns per 200 mm . For vertical positioning a third stepping motor drives the z-screw of the microscope. All three stepping motors are remote-controlled by a central unit (Märzhäuser, MCC 13-JS) [4], with a joystick or the host processor (DEC, LSI 11/23 +). The CCD-camera (Sony XC 37/47) [5] differs from common cameras of comparable prices by a very high precision of the picture and low lag. These advantages combined with very small dimensions [12 cm x 4.5 cm x 3 cm) and high sensitivity (minimum illlumination: 3 lux) were reasons to choose this camera . We achieved with a 100 X objective a resolution of 0.25 pm x 0.25 Am per pixel, which is good enough for our purpose. 2.2. Picture analysis system (Imaging, IP-512) (61 The picture analysis system consists of an analog processor (AP) and a frame buffer (FB) . As shown in fig. 2, the AP consists of two A/D and D/A converters and of two transformation units LUT. The FB on the other hand contains 256 Kb RAM. The LUT and the FB are controlled by the host, as explained in the following. 2.2.1 . The AP The video signal, digitized in the A/D converter, is transformed in real time passing the LUT. Inside the A/D converter there is attributed to each pixel one of 256 possible grey values (gv) . The LUT transforms each of these gv's into a new LUT value. For this transformation we always programmed the LUT with linear functions. 2.2.2. The FB This fast buffer enables us to manipulate the stored picture. The gv's of the digitized picture are stored with AP
FB
Video !7_Z----_-__"j in !
video out
IoHLUI~ ii i ~/q
LUT
256 KB RAM
Fig. 2. The picture analysis system, consisting of an analog processor (AP) and a frame buffer (FB) . The AP contains A/D and D/A converters and transformation units LUT. The FB contains 256 Kb RAM. Both LUT and FB are controlled by the host .
315
a 8-bitplanes T
Fig. 3. The structure of the frame buffer FB : The grey values, consisting of 8 bits each, are stored in the registers which are attributed to the x and y coordinates of the picture in 512 x 512 bytes. a transfer rate of 10 Mio. per second (107 Hz). This is possible by means of a special "high-speed video bus" which connects the AP with the FB . In the FB the gv's and the coordinates of the pixels are stored in the way shown in fig. 3. The x and y coordinates in the FB correspond to the x and y coordinates of the picture. It is possible to access directly to these gv's using the host by means of the control registers, and read them out or change them in the FB. The manipulation and evaluation of the FB is the most time-consuming part of the measurement. The reason is that each step has to go via the host and a control register . For visual control the stored data of the FB are transformed back into a video signal by a D/A converter after passing a second LUT. 2.3. The host As main control a Q-bus computer LSI 11/23 + is used . It is linked to the control unit MCC 13 (see sect . 2.1) via a serial interface (RS-232) . The Q-bus installed AP and FB are manipulated by the host through 18 control registers. For data storage the computer is equipped with a main buffer of 1.5 MByte RAM, and some external devices shown in fig. 1. The LSI runs with a multi-user, multitask system RSX 11 M (DEC). The software mainly consists of FORTRAN programs and some ASSEMBLER routines . 3. Charge determination by track-geometry measurements 3.1 . The measurement 3.1 .1. Measuring procedure (1) Centering the track. The camera is aligned in such a way that the lines are parallel to the track (= : x direction) . The gv's of each line of the picture lead to a corresponding "mean grey-value" (mgv). Dark pixels correspond to small gv's. The line with the lowest mgv
E. Ganssauge et al /Automatic method to measure charges :n emulsions
316
contains the core, the center of the track. To position this core into the middle of the picture a possible deviation in the y direction is corrected . The core region is now known in the picture storage, and it is possible to evaluate directly. (2) Focussing the track. To focus the track, the height (z coordinate) is varied till the mgv of the darkest line reaches a minimum. At this position the picture is evaluated (see sect. 3 .2) . As soon as a piece of the track has been evaluated, the stage is moved 75 lAm in the x direction, and the whole procedure starts again (see fig. 4) .
3.1 .2 . Measuring values
By using a 100 x oil objective the field of view is a rectangle of 65,um x 57 Am in the emulsion. We use an FB area of 256 x 220 pixels, which leads to a resolution of 0 .25 lim x 0.26 ,am per pixel . After focusing the track, from the whole picture (see sect . 3 .1 .1) a window of 50 lAm x 12 pm is taken onto a field with dimension Start
determine Y-DEVIAT ION
change 'Y-POSITION
change X-POSITION
no
determine CONTRAST
change Z POSITION
store DATA
n
DATA File
Stop
Fig . 4 . Flow diagram of the measuring procedure .
(200, 50). These values are used for evaluating the picture (see fig . 5) .
3.2 . Evaluation and results 3.2 .1 . Data taking
The initial and final heights of the track are calculated and stored . Since these are relative heights the thickness of the pellicle has to be measured and stored as well. Moreover the absolute values of the mgv's, taken of the brightest and the darkest line in the rectangular window, are stored . (a) Creating a "binary picture" To restrict the amount of data, for each picture point only two possibilities are allowed : it either belongs to the track or it belongs to the background. With this method a kind of shadow of the track will be produced, which can then be examined with less difficulty . A problem in creating a binary picture is the definition of the "limit" g, i.e. the brightest gv of a pixel to be attributed to the track. The value of g clearly has to he between the brightest (he) measured and the darkest (du) measured value . To find the optimum limit, different values were used and the digital pictures compared with the real track (see figs . 6 and 7) . It is essential to avoid dirt in the pellicle and all kinds of background which could be misinterpreted as delta rays . On the other hand, as much of the track core as possible and as many of the real 8-rays as possible should be recorded . Therefore we count from the core (white line in fig. 6) in both +y and -y directions and add the rest, after passing the limit, to the background . By doing so we can be sure that no dirt in the emulsion is counted as long as it is not directly connected with the track . The comparison of figs . 6 and 7 shows the limit g := du + a(he - du) with a = 5/8 being the optimum value. This implies for this method that 8-ray counting is not a proper way to determine charges since there are also 8-rays with no clear connection to the track. (b) Dividing the picture into basic cells (bc) To get the structure of the track in detail we divide the window of 50 tLm length (see above) into 40 sections, so-called "basic cells", of 1 .25 ltm length each . In this way the dimension of a be is larger than a typical 8-ray width and it is thus possible to eliminate those parts of the track, the structure of which does not correspond to the charge . Thus we can avoid wrong mean values . Another reason for introducing bc's was the hope to find correlations between the charge Z of the track-producing particle and certain statistical moments of the basic cell distribution (bcd) [1] . During the evaluation 80 values are stored, 2 of which give the number of pixels belonging to the track in the +y and -y direction respectively .
E. Ganssauge et al. /Automatic method to measure charges in emulsions
r
317
~65~tm-.
E
501 1 l Fig. 5. The resolution of the buffer is 256X220 pixels of .26 .25X0 gm2 each in an area of 65 Wm X 57 Am. After focusing the track, a 0 window of 50 pm X 12 pm is defined and finally transformed for evaluation onto a field of dimension (200, 50). 3.3. Data analysis
a=4/8
3.3.1 . Principal considerations The distribution of ( x1 ) = (Px/bc) is called bcd (see above; Px := number of pixels). Now we look for the first three moments of the (bcd) and their possible correlation to the charge Z. The following definitions are used : n 1 first moment : X1 ~_ - Y_ x, = x; n 1
a=5/8
a=6/8
second moment : --~ X
Fig. 6. "Binary picture" of a track (Z = 26), taken with "limits" g := du + a(he-du) for different a values.
X2 :=
- third moment : X3
:=
n is the number of bc's .
n
1 1 1
(X)
E(x, - z) 2 ; 1
n
Y(x, - x) 3 . 3
2
Fig. 7 . Monitor picture of the track (Z = 26), to be compared with the "binary picture" of fig. 6.
E. Ganssauge et al. /Automatic method to measure charges in emulsions
318
Figs . 8-10 show the results. None of these moments allow a reasonable determination of Z. Therefore we searched for other qualities of the bcd's. We divide the amount of measured values of { x, ) of 5 pictures (i =1 . . . 200) into k so-called "classes" of equal size . We draw the distribution of the number Nk falling into the class k as a function of k . These histograms (k = 20), shown in fig. 11 as almost smooth curves, show distinct differences for the different charges, at least for higher charge values . (Note the different scales!) A detailed analysis tells us : - All distributions are asymmetric . - With growing charge the distribution becomes wider, therfore the mode, the most frequent value, becomes smaller and - the mode shifts to higher values . - While the left hand side of the distribution allows a clear separation of charges, this is not the case at the right hand side . This most probably results from the background dirt in the emulsion . Therefore it is important to become independent of the right hand side of the distributions. We choose the following parameters : 1) "Mode position" k m (maximum of the bcd) with Nk . >__ Nk; k = 1 . . . kt;n,,j (see fig 12). 2) "Mode" := Nk (k m) (see fig. 13). 3) "LiV" ~_ E%= I Nk : giving the sum of frequencies Nk till a chosen limit 1. Depending on this limit we define three different quantities "LiVl" to "LiV3" (see figs . 14-16) . All these parameters depend, of course, on the division of the classes. We choose the most favourable class width for the purpose of determining the charges 10 <__ Z < 26. From figs . 13-16 we see that the new-defined parameters "Mode" and "LiVl" to "LiV3" are very suitable for that purpose, while the other one, "Mode position" (fig . 12) cannot be used for defining charges.
46-
2
240-
1a0-
120-
Z
60
Fig. 9. Second moment (X2 /Pxz) as a function of Z.
-150-
X3
-200-
-250-
-300-
-350 -1-~ . . 6
i i i-Tr -r7- I-r 7-,--r16 . . 21 26
Z
11
Fig. 10 . Skewness (X3) as a function of Z.
3.3.2. Determination of charges
Fits to the curves are given in the figure captions of figs . 13-16, the favoured class widths are given as well .
X1 /Px +
39-~
+
+
32-
+
25-I
i
18
-r . . . . . . . . . . 16 21 26
6
Px 300- X2 /
11
Z.
Fig. 8. First moment (X1 /Px) as a function of Z.
Fig. 11 . Distribution of the number Nk of basic cells. The histograms, shown as smooth curves, show distinct differences for different charges. (Note the varying scales!)
319
E. Ganssauge et al. / Automatic method to measure charges to emulsions
Fig. 12 . The parameter "Mode position" as function of charge Z.
Fig. 15 . "LiV2"(Z). Class width: 7 pixels, 1=4, fitted with straight line Z(LiV2)=(-1/8 .9)(LiV2-262 .0).
Z
Fig. 13 . "Mode"(Z). Class width: 7 pixels fitted with a second order polynomial, leading to 123-Mode(abs .) Z(Mode)=40 .3- 1626 .80.06
\ 1/2
From this there follows the procedure to automatically determine the charge . A value 2 := 21 { Z(Mode) + Z(LiV3)) is calculated .
Fig. 16 . "LiVl"(Z). Class width: 4 pixels, 1=12, fitted with polynomcal of second order: Z(LiVl)=12 .6+1158.0+
140.0 - LiV1 0. 35
1/2
In case Z __ :!5; 16, this value is taken as the actual charge . In case Z > 16, the program calculates Z(LiV2). In case Z(LiV2) 5 21, this value is accepted as being the true charge ; for Z(LiV2) > 21, the last calculation Z(LiVl) is executed and the result taken as the real charge value . In table 1 this procedure is summarized By analyzing the accuracy with which the charge Z can be determined there are two main difficulties to be taken into account. Table 1 Summary of charge calculation -< 16
Fig. 14 . "LiV3"(Z). Class width: 1 pixel, 1=25, fitted with straight line Z(LiV3) = ( -1 /8 .3XLiV3- 232.0).
Z = 1(ZMode + ZL.V2 ZLV2
< 21
> 21
Charge taken Z
ZLiV3) *
ZUV2 ZLiV1
320
E. Ganssauge et al. /Automatic method to measure charges in emulsions
(1) The error of Z depends on the time duration of the measurement, i.e . on the length of the measured track. In the figures shown of the calibration (figs . 13-16) there were 3 mm of track length evaluated for each charge . This guarantees errors clearly smaller than one charge unit . It is possible to speed up the measurement by measuring shorter lengths . A reasonable compromise seems to be measuring about 0.5 mm, which takes about 10 min . (2) It is far more difficult to solve the question how the calibration measurements correspond to the real charges . Obviously the precision of larger Z is higher than that of smaller charges (see figs . 16 and 15). Among these smaller values especially the two Z =16 values do not fit well. It could even be that both belong to charge 15, but it is hard to decide from the underlying track . 3.3.3. Some remarks on unsolved problems The uncertainties in the quantities used for determining charges could be attributed to the following reasons : (1) Height dependence. In contrast to most measurements published [7], we do not make any correction for the height of the track in the emulsion. This is because this parameter is implicitly contained in our method, but it could be that there is still some influence left. (2) Energy dependence . According to Bethe-Bloch the exact determination of charge Z from the ionization is only possible if the velocity of the fragment is known . In our measurements this parameter was not exactly given, the velocity was taken to be constant in all tracks and to be ß = 0 .94 [8] .
sion. New parameters, based on the introduced "basic cells", have been found and the way of measuring them is shown . The comparison of the correlation between certain parameters, called "Mode" and "LiV", and the charge Z of the track-producing particle (see figs . 13-16) shows that the charge determination in between one charge unit is possible . This is precise enough for most tasks in physics.
Acknowledgements We would like to express our thanks to Dr . H .H . Heckman, LBL Berkeley, for providing us with emulsion pellicles and the BEVALAC staff for the excellent exposure. Our thanks also go to Dr. Poppensieker from the GSI Darmstadt. This work was supported by the Bundesminister für Forschung and Technologie under the number 06 MR 158 .
References
[4] [5] [6] [7]
4 . Summary We have shown that it is possible to automatically determine charges 10 <_ Z :5 26 in nuclear track emul-
[8]
R . Ammar, Nuovo Cimento Suppl . 15 (1960) 181 . A . Laschek, Diplomarbeit, F.B . Physik, Marburg (1983) unpublished . W. Barkas, Nuclear Research Emulsion, vol . 1 (Academic Press, New York, 1963) p . 353 . Fa . Lang, Betriebsanleitung MCC13-JS, Hüttenberg (1984). Fa . Sony, Operation Manual XC-37/47, 1st ed ., Japan . Fa. Imaging, Technical Manual IP-512, USA (1983) . S . Behmetz, K. Kristiansson, S. Lindstam and K. Sbderstrbm, and references therein . Cosmic Ray Physics Report LUIP-CR-73-01 (1973) U . Bieschke, Diplomarbeit, F.B . Physik, Marburg (1983) unpublished .
Nuclear Instruments and Methods in Physics Research A257 (1987) 314-320 North-Holland, Amsterdam
A VIDEO-BASED AUTOMATIC METHOD TO MEASURE CHARGES IN NUCLEAR TRACK EMULSIONS E. GANSSAUGE, Ch. MÜLLER, B. DRESSEL, S. HACKEL, H. KALLIES and W. SCHULZ Department of Physics, Philipps-University, 3550 Marburg/L., FRG Received 23 December 1986 A new method is developed for measuring charges of tracks in nuclear track emulsion. We use an automatic charge measuring device, consisting of a microscope, equipped with a stepping motor-driven stage, a CCD-video camera and a picture analysis system. Special parts of the distribution of local track widths show clear correlation to the charges which can be measured in the range 10 5_ Z <- 26. The precision of one charge unit is achieved by introducing new specific quantities . 1. Introduction The nuclear track emulsion is well known as a very sensitive detector with many excellent properties . But there is a large handicap in using this detector, namely the high manpower necessary for getting reasonable statistics of data. Especially the determination of charges has to be done in an automatic way [2]. We used the great progress in picture analysis with microcomputers to solve this problem. We developed a measuring system which is able to follow a track by itself while analyzing it. We adapted the idea of basic cells [1] and used certain new quantities to achieve a precision of d Z = f 1 . This accuracy is good enough for most experimental applications. It should be noted that this kind of analysis highly depends on the type of emulsion and the processing procedure [3]. This work was done with Ilford G5 emulsion out of a stack exposed to a 56 Fe beam of 2 A GeV at the LBL/Berkeley and processed there.
These requirements are met in our configuration essentially by the units described in the following section (see fig. 1) .
2. The apparatus An automatic measuring device has to fulfil the following requirements : - The stage of the microscope has to be automatically movable by remote-control. - The microscopic picture must be taken by a camera and stored in a computer memory. - The evaluation of the stored data has to be possible in a reasonable time . * This work is based on the "Diplomarbeit" of Ch. Mailer at the experimental High Energy Group of the University of Marburg. 0168-9002/87/$03 .50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Fig. 1. The apparatus, consisting of a microscope, equipped with a stepping motor-driven stage, a CCD video camera and a picture analysis system .
E. Ganssauge et al. / Automatic method to measure charges in emulsions 2.1 . Microscope and camera
512
The microscope (Leitz-Ortholux) is equipped with a stage (Mdrzhäuser, MCC 13) which is movable horizontally by means of stepping motors with a step width of 0.25 lm. The stage is movable in x and y directions, 210 mm and 100 mm respectively with a precision of some microns per 200 mm . For vertical positioning a third stepping motor drives the z-screw of the microscope. All three stepping motors are remote-controlled by a central unit (Märzhäuser, MCC 13-JS) [4], with a joystick or the host processor (DEC, LSI 11/23 +). The CCD-camera (Sony XC 37/47) [5] differs from common cameras of comparable prices by a very high precision of the picture and low lag. These advantages combined with very small dimensions [12 cm x 4.5 cm x 3 cm) and high sensitivity (minimum illlumination: 3 lux) were reasons to choose this camera . We achieved with a 100 X objective a resolution of 0.25 pm x 0.25 Am per pixel, which is good enough for our purpose. 2.2. Picture analysis system (Imaging, IP-512) (61 The picture analysis system consists of an analog processor (AP) and a frame buffer (FB) . As shown in fig. 2, the AP consists of two A/D and D/A converters and of two transformation units LUT. The FB on the other hand contains 256 Kb RAM. The LUT and the FB are controlled by the host, as explained in the following. 2.2.1 . The AP The video signal, digitized in the A/D converter, is transformed in real time passing the LUT. Inside the A/D converter there is attributed to each pixel one of 256 possible grey values (gv) . The LUT transforms each of these gv's into a new LUT value. For this transformation we always programmed the LUT with linear functions. 2.2.2. The FB This fast buffer enables us to manipulate the stored picture. The gv's of the digitized picture are stored with AP
FB
Video !7_Z----_-__"j in !
video out
IoHLUI~ ii i ~/q
LUT
256 KB RAM
Fig. 2. The picture analysis system, consisting of an analog processor (AP) and a frame buffer (FB) . The AP contains A/D and D/A converters and transformation units LUT. The FB contains 256 Kb RAM. Both LUT and FB are controlled by the host .
315
a 8-bitplanes T
Fig. 3. The structure of the frame buffer FB : The grey values, consisting of 8 bits each, are stored in the registers which are attributed to the x and y coordinates of the picture in 512 x 512 bytes. a transfer rate of 10 Mio. per second (107 Hz). This is possible by means of a special "high-speed video bus" which connects the AP with the FB . In the FB the gv's and the coordinates of the pixels are stored in the way shown in fig. 3. The x and y coordinates in the FB correspond to the x and y coordinates of the picture. It is possible to access directly to these gv's using the host by means of the control registers, and read them out or change them in the FB. The manipulation and evaluation of the FB is the most time-consuming part of the measurement. The reason is that each step has to go via the host and a control register . For visual control the stored data of the FB are transformed back into a video signal by a D/A converter after passing a second LUT. 2.3. The host As main control a Q-bus computer LSI 11/23 + is used . It is linked to the control unit MCC 13 (see sect . 2.1) via a serial interface (RS-232) . The Q-bus installed AP and FB are manipulated by the host through 18 control registers. For data storage the computer is equipped with a main buffer of 1.5 MByte RAM, and some external devices shown in fig. 1. The LSI runs with a multi-user, multitask system RSX 11 M (DEC). The software mainly consists of FORTRAN programs and some ASSEMBLER routines . 3. Charge determination by track-geometry measurements 3.1 . The measurement 3.1 .1. Measuring procedure (1) Centering the track. The camera is aligned in such a way that the lines are parallel to the track (= : x direction) . The gv's of each line of the picture lead to a corresponding "mean grey-value" (mgv). Dark pixels correspond to small gv's. The line with the lowest mgv
E. Ganssauge et al /Automatic method to measure charges :n emulsions
316
contains the core, the center of the track. To position this core into the middle of the picture a possible deviation in the y direction is corrected . The core region is now known in the picture storage, and it is possible to evaluate directly. (2) Focussing the track. To focus the track, the height (z coordinate) is varied till the mgv of the darkest line reaches a minimum. At this position the picture is evaluated (see sect. 3 .2) . As soon as a piece of the track has been evaluated, the stage is moved 75 lAm in the x direction, and the whole procedure starts again (see fig. 4) .
3.1 .2 . Measuring values
By using a 100 x oil objective the field of view is a rectangle of 65,um x 57 Am in the emulsion. We use an FB area of 256 x 220 pixels, which leads to a resolution of 0 .25 lim x 0.26 ,am per pixel . After focusing the track, from the whole picture (see sect . 3 .1 .1) a window of 50 lAm x 12 pm is taken onto a field with dimension Start
determine Y-DEVIAT ION
change 'Y-POSITION
change X-POSITION
no
determine CONTRAST
change Z POSITION
store DATA
n
DATA File
Stop
Fig . 4 . Flow diagram of the measuring procedure .
(200, 50). These values are used for evaluating the picture (see fig . 5) .
3.2 . Evaluation and results 3.2 .1 . Data taking
The initial and final heights of the track are calculated and stored . Since these are relative heights the thickness of the pellicle has to be measured and stored as well. Moreover the absolute values of the mgv's, taken of the brightest and the darkest line in the rectangular window, are stored . (a) Creating a "binary picture" To restrict the amount of data, for each picture point only two possibilities are allowed : it either belongs to the track or it belongs to the background. With this method a kind of shadow of the track will be produced, which can then be examined with less difficulty . A problem in creating a binary picture is the definition of the "limit" g, i.e. the brightest gv of a pixel to be attributed to the track. The value of g clearly has to he between the brightest (he) measured and the darkest (du) measured value . To find the optimum limit, different values were used and the digital pictures compared with the real track (see figs . 6 and 7) . It is essential to avoid dirt in the pellicle and all kinds of background which could be misinterpreted as delta rays . On the other hand, as much of the track core as possible and as many of the real 8-rays as possible should be recorded . Therefore we count from the core (white line in fig. 6) in both +y and -y directions and add the rest, after passing the limit, to the background . By doing so we can be sure that no dirt in the emulsion is counted as long as it is not directly connected with the track . The comparison of figs . 6 and 7 shows the limit g := du + a(he - du) with a = 5/8 being the optimum value. This implies for this method that 8-ray counting is not a proper way to determine charges since there are also 8-rays with no clear connection to the track. (b) Dividing the picture into basic cells (bc) To get the structure of the track in detail we divide the window of 50 tLm length (see above) into 40 sections, so-called "basic cells", of 1 .25 ltm length each . In this way the dimension of a be is larger than a typical 8-ray width and it is thus possible to eliminate those parts of the track, the structure of which does not correspond to the charge . Thus we can avoid wrong mean values . Another reason for introducing bc's was the hope to find correlations between the charge Z of the track-producing particle and certain statistical moments of the basic cell distribution (bcd) [1] . During the evaluation 80 values are stored, 2 of which give the number of pixels belonging to the track in the +y and -y direction respectively .
E. Ganssauge et al. /Automatic method to measure charges in emulsions
r
317
~65~tm-.
E
501 1 l Fig. 5. The resolution of the buffer is 256X220 pixels of .26 .25X0 gm2 each in an area of 65 Wm X 57 Am. After focusing the track, a 0 window of 50 pm X 12 pm is defined and finally transformed for evaluation onto a field of dimension (200, 50). 3.3. Data analysis
a=4/8
3.3.1 . Principal considerations The distribution of ( x1 ) = (Px/bc) is called bcd (see above; Px := number of pixels). Now we look for the first three moments of the (bcd) and their possible correlation to the charge Z. The following definitions are used : n 1 first moment : X1 ~_ - Y_ x, = x; n 1
a=5/8
a=6/8
second moment : --~ X
Fig. 6. "Binary picture" of a track (Z = 26), taken with "limits" g := du + a(he-du) for different a values.
X2 :=
- third moment : X3
:=
n is the number of bc's .
n
1 1 1
(X)
E(x, - z) 2 ; 1
n
Y(x, - x) 3 . 3
2
Fig. 7 . Monitor picture of the track (Z = 26), to be compared with the "binary picture" of fig. 6.
E. Ganssauge et al. /Automatic method to measure charges in emulsions
318
Figs . 8-10 show the results. None of these moments allow a reasonable determination of Z. Therefore we searched for other qualities of the bcd's. We divide the amount of measured values of { x, ) of 5 pictures (i =1 . . . 200) into k so-called "classes" of equal size . We draw the distribution of the number Nk falling into the class k as a function of k . These histograms (k = 20), shown in fig. 11 as almost smooth curves, show distinct differences for the different charges, at least for higher charge values . (Note the different scales!) A detailed analysis tells us : - All distributions are asymmetric . - With growing charge the distribution becomes wider, therfore the mode, the most frequent value, becomes smaller and - the mode shifts to higher values . - While the left hand side of the distribution allows a clear separation of charges, this is not the case at the right hand side . This most probably results from the background dirt in the emulsion . Therefore it is important to become independent of the right hand side of the distributions. We choose the following parameters : 1) "Mode position" k m (maximum of the bcd) with Nk . >__ Nk; k = 1 . . . kt;n,,j (see fig 12). 2) "Mode" := Nk (k m) (see fig. 13). 3) "LiV" ~_ E%= I Nk : giving the sum of frequencies Nk till a chosen limit 1. Depending on this limit we define three different quantities "LiVl" to "LiV3" (see figs . 14-16) . All these parameters depend, of course, on the division of the classes. We choose the most favourable class width for the purpose of determining the charges 10 <__ Z < 26. From figs . 13-16 we see that the new-defined parameters "Mode" and "LiVl" to "LiV3" are very suitable for that purpose, while the other one, "Mode position" (fig . 12) cannot be used for defining charges.
46-
2
240-
1a0-
120-
Z
60
Fig. 9. Second moment (X2 /Pxz) as a function of Z.
-150-
X3
-200-
-250-
-300-
-350 -1-~ . . 6
i i i-Tr -r7- I-r 7-,--r16 . . 21 26
Z
11
Fig. 10 . Skewness (X3) as a function of Z.
3.3.2. Determination of charges
Fits to the curves are given in the figure captions of figs . 13-16, the favoured class widths are given as well .
X1 /Px +
39-~
+
+
32-
+
25-I
i
18
-r . . . . . . . . . . 16 21 26
6
Px 300- X2 /
11
Z.
Fig. 8. First moment (X1 /Px) as a function of Z.
Fig. 11 . Distribution of the number Nk of basic cells. The histograms, shown as smooth curves, show distinct differences for different charges. (Note the varying scales!)
319
E. Ganssauge et al. / Automatic method to measure charges to emulsions
Fig. 12 . The parameter "Mode position" as function of charge Z.
Fig. 15 . "LiV2"(Z). Class width: 7 pixels, 1=4, fitted with straight line Z(LiV2)=(-1/8 .9)(LiV2-262 .0).
Z
Fig. 13 . "Mode"(Z). Class width: 7 pixels fitted with a second order polynomial, leading to 123-Mode(abs .) Z(Mode)=40 .3- 1626 .80.06
\ 1/2
From this there follows the procedure to automatically determine the charge . A value 2 := 21 { Z(Mode) + Z(LiV3)) is calculated .
Fig. 16 . "LiVl"(Z). Class width: 4 pixels, 1=12, fitted with polynomcal of second order: Z(LiVl)=12 .6+1158.0+
140.0 - LiV1 0. 35
1/2
In case Z __ :!5; 16, this value is taken as the actual charge . In case Z > 16, the program calculates Z(LiV2). In case Z(LiV2) 5 21, this value is accepted as being the true charge ; for Z(LiV2) > 21, the last calculation Z(LiVl) is executed and the result taken as the real charge value . In table 1 this procedure is summarized By analyzing the accuracy with which the charge Z can be determined there are two main difficulties to be taken into account. Table 1 Summary of charge calculation -< 16
Fig. 14 . "LiV3"(Z). Class width: 1 pixel, 1=25, fitted with straight line Z(LiV3) = ( -1 /8 .3XLiV3- 232.0).
Z = 1(ZMode + ZL.V2 ZLV2
< 21
> 21
Charge taken Z
ZLiV3) *
ZUV2 ZLiV1
320
E. Ganssauge et al. /Automatic method to measure charges in emulsions
(1) The error of Z depends on the time duration of the measurement, i.e . on the length of the measured track. In the figures shown of the calibration (figs . 13-16) there were 3 mm of track length evaluated for each charge . This guarantees errors clearly smaller than one charge unit . It is possible to speed up the measurement by measuring shorter lengths . A reasonable compromise seems to be measuring about 0.5 mm, which takes about 10 min . (2) It is far more difficult to solve the question how the calibration measurements correspond to the real charges . Obviously the precision of larger Z is higher than that of smaller charges (see figs . 16 and 15). Among these smaller values especially the two Z =16 values do not fit well. It could even be that both belong to charge 15, but it is hard to decide from the underlying track . 3.3.3. Some remarks on unsolved problems The uncertainties in the quantities used for determining charges could be attributed to the following reasons : (1) Height dependence. In contrast to most measurements published [7], we do not make any correction for the height of the track in the emulsion. This is because this parameter is implicitly contained in our method, but it could be that there is still some influence left. (2) Energy dependence . According to Bethe-Bloch the exact determination of charge Z from the ionization is only possible if the velocity of the fragment is known . In our measurements this parameter was not exactly given, the velocity was taken to be constant in all tracks and to be ß = 0 .94 [8] .
sion. New parameters, based on the introduced "basic cells", have been found and the way of measuring them is shown . The comparison of the correlation between certain parameters, called "Mode" and "LiV", and the charge Z of the track-producing particle (see figs . 13-16) shows that the charge determination in between one charge unit is possible . This is precise enough for most tasks in physics.
Acknowledgements We would like to express our thanks to Dr . H .H . Heckman, LBL Berkeley, for providing us with emulsion pellicles and the BEVALAC staff for the excellent exposure. Our thanks also go to Dr. Poppensieker from the GSI Darmstadt. This work was supported by the Bundesminister für Forschung and Technologie under the number 06 MR 158 .
References
[4] [5] [6] [7]
4 . Summary We have shown that it is possible to automatically determine charges 10 <_ Z :5 26 in nuclear track emul-
[8]
R . Ammar, Nuovo Cimento Suppl . 15 (1960) 181 . A . Laschek, Diplomarbeit, F.B . Physik, Marburg (1983) unpublished . W. Barkas, Nuclear Research Emulsion, vol . 1 (Academic Press, New York, 1963) p . 353 . Fa . Lang, Betriebsanleitung MCC13-JS, Hüttenberg (1984). Fa . Sony, Operation Manual XC-37/47, 1st ed ., Japan . Fa. Imaging, Technical Manual IP-512, USA (1983) . S . Behmetz, K. Kristiansson, S. Lindstam and K. Sbderstrbm, and references therein . Cosmic Ray Physics Report LUIP-CR-73-01 (1973) U . Bieschke, Diplomarbeit, F.B . Physik, Marburg (1983) unpublished .