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Rate dependent image distortions in proportional counters
Nuclear Instruments and Methods in Physics Research A 348 (1994) 232-236 North-Holland
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH Section A
Rate dependent image distortions in proportional counters M.W. T r o w a,,, A.C. B e n t o b, A. Smith a a Department of Space and Climate Physics, University College London, Mullard Space Science Laboratory, Holmbury St Mary, Dorking, Surrey, RH5 6NT, UK b Department of Physics, Uniuersity of Coimbra, P-3000 Coimbra, Portugal
The positional linearity of imaging proportional counters is affected by the intensity distribution of the incident radiation. A mechanism for this effect is described, in which drifting positive ions in the gas produce a distorting electric field which perturbs the trajectories of the primary electrons. In certain cases, the phenomenon causes an apparent improvement of the position resolution. We demonstrate the effect in a detector filled with a xenon-argon-CO 2 mixture. The images obtained are compared with the results of a simulation. If quantitative predictions for a particular detector are required, accurate values of the absolute detector gain, ion mobility and electron drift velocity are needed.
1. Rate dependent effects in proportional counters Position sensitive p r o p o r t i o n a l c o u n t e r s are used in a variety of applications for d e t e c t i o n of X U V a n d X-ray p h o t o n s a n d o t h e r radiation. T h e dynamic r a n g e of these detectors has previously b e e n limited by the position r e a d o u t electronics, b u t several r e c e n t r e a d o u t designs are capable of functioning at the m a x i m u m rate of the counter. Hell et al. [1] observed image distortions at rates of 15 to 30 M H z / c m z of M o - K r a d i a t i o n in a n M W P C having a 9 m m drift gap. T h e gas used was A r + 1% C O 2 at 4 a n d 8 bar. D m i t r i e v a n d F r u m k i n [2] have described their experiences of these effects. They used a similar c h a m b e r with a drift gap of 10 mm, a n d f o u n d m e a s u r a b l e distortions at rates of a few tens of kHz. T h e i r d e t e c t o r was filled with A r + 18% C O 2 at a p r e s s u r e of 1 atm. T h e distortions h a d the following characteristics, not all of which were observed simultaneously: distortion of b e a m profiles, d e c r e a s e of a p p a r e n t b e a m width, a p p a r e n t i m p r o v e m e n t of the position resolution, separate profiles moving closer together, and smearing of profiles n e a r intense illumination. T h e s e distortions occurred in conjunction with a c o u n t - r a t e d e p e n d e n t c h a n g e of the gas gain. In a r e a d o u t system w h o s e lower level discriminator is set n e a r the low energy tail of the usual pulse height distribution, this is a c c o m p a n i e d by a loss in counting efficiency. B o t h effects are d u e to the electric field
* Corresponding author.
c o n t r i b u t i o n of the positive ions p r o d u c e d in the avalanches. T h e general principles of ion i n d u c e d gain d e p r e s s i o n were outlined by H e n d r i c k s [3] a n d f u r t h e r t r e a t m e n t s can be f o u n d in refs. [4-8].
2. Distortion mechanism I m m e d i a t e l y following a n electron avalanche in a p r o p o r t i o n a l counter, t h a t is, after all the electrons have r e a c h e d t h e a n o d e wire, a cloud of positively ionised gas atoms or molecules begins to drift toward the c a t h o d e [9]. T h e resulting distribution of ions can b e calculated if the electric field in the d e t e c t o r is known. In the special case of a coaxial d e t e c t o r in which avalanches are distributed uniformly a r o u n d t h e a n o d e wires, a c o n s t a n t c o u n t i n g rate p r o d u c e s a uniform density of ions. T h e charge density p for a c o u n t rate n is given by: nq~ o p = IzVC, w h e r e q is the avalanche charge, V is the a n o d e voltage and C is the capacitance p e r wire p e r unit length, p~ is the ion mobility, a n d e 0 is t h e permittivity of free space. This expression can also b e applied n e a r the a n o d e s of o t h e r types of detector. W h e n a d e t e c t o r is illuminated by a n a r r o w b e a m or point, a s h e e t of ions will b e p r o d u c e d in the drift regions. This charge g e n e r a t e s an electric field which has a c o m p o n e n t p e r p e n d i c u l a r to the p l a n e of the sheet. Primary electrons are a t t r a c t e d to this region of ion density as they drift toward the a n o d e (see Fig. 1).
0168-9002/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0 1 6 8 - 9 0 0 2 ( 9 4 ) 0 0 1 1 4 - M
M.W. Trow et aL / NucL Instr. and Meth. in Phys. Res. A 348 (1994) 232-236
.• ,+/f
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++++
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/ +++
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Fig. 1. Longitudinal cross section of a proportional counter showing an anode wire and two cathode planes. Radiation with the intensity distribution shown enters through the upper cathode, and the resulting avalanches produce an ion distribution mainly in the regions marked with +. Electron trajectories - of photons absorbed nearby are attracted to the ion-filled region, and the recorded image is distorted. The amount of lateral drift will depend on the density of ions in the sheet, the location of the primary ionisation, and the drift velocity of the electrons. At any point in the electron's path, the direction of drift is that of the gradient of the total electric field, and the drift velocity is a complex function of the field strength. This function is usually highly dependent on the proportions of the gas mixture. The magnitude of the perturbing field of the ion sheet decreases with distance. Therefore, photons absorbed close to the ion sheet will drift more than those absorbed further away. In addition, the perturbing field is weaker near the edges of the ion distribution, i.e. near the cathodes or between the wires in a MWPC, than in the centre of the drift volume. An electron whose trajectory which begins at the upper cathode will drift more than an electron absorbed close to the anode wire, because the latter experiences sideways drift for a shorter time. Since the sites of initial ionisation occur at a range of depths in the gas, it can be expected that a distribution of lateral drifts will be observed for a particular initial perpendicular distance from the ion sheet.
3. Practical consequences
Each point in an image will produce its own positive ion sheet, which can affect the electron trajectories in all other parts of the detector. The trajectories of the ions will also be modified by the distribution of ions, although the magnitude of this effect will be smaller due to the ion's lower mobilities. The result will be that bright regions in any image will attract one another, and the degree of attraction will be a function of the
233
count rate. Certain regions in the recorded image will increase in intensity, and others parts may decrease. The overall number of counts in the image is unchanged, unless a greater number of pulses fall below the readout system's lower level discriminator due to gain-related changes in the pulse height distribution. In a flat field, or rectangular image, the centre of attraction will be the centre of the field. There will be an enhancement of intensity near the centre of the image, and a decrease at the edges. Distortions in images of a number of small, bright points, separated by regions of low intensity, will appear largely as motion of the points towards their common centre. However, since the shifts depend on the depth of photon absorption, the profiles of the points will become skewed. If the size of the features is less than the position resolution of the system, the skew of the distorted profiles can result in a worsening of the measured resolution. Medium sized features, with scale lengths a few times larger than the position bin width, can be affected in the opposite way. If there are no features nearby that can significantly affect the centroid of the feature, and the intensity of the feature is sufficient to cause distortions, the profile will remain symmetrical but will decrease in width (self-focusing). The measured position resolution will therefore appear to improve. In many systems, the position resolution is limited by the gas, and the point spread function is over-sampled by the readout electronics. Position resolution measurements are very often made with test images consisting of small points separated by large regions of zero intensity. Under these conditions, one can obtain an anomalous improvement of the resolution with higher count rate, without any measurable change of the centroid of the points.
4. Tests with a position sensitive proportional counter
To determine the effect of counting rate on a test image, we illuminated a position sensitive detector through a mask mounted against its window. Table 1 describes the detector used for these tests. Identical detectors were flown in the Yohkoh Bragg Crystal Spectrometer [10], which is used to study the soft X-ray emission of solar flares, and their performance has been described elsewhere [11,12]. The mask was a 0.9 mm thick sheet of aluminium with a slit and pinholes. The slit was perpendicular to the axis of the anode wires, and the holes were arranged along a line parallel to the anodes at various distances from the slit: 5, 4, 3, 2, and 1 mm on one side and 1.5, 2.5, 3.5, 4.5 and 5.5 mm on the other. Each hole had an area of 0.79 mm 2 (diameter 0.5 mm), and I. GASEOUS DETECTORS
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M.I~E Trow et al. / N u c l . Instr. and Meth. in Phys. Res. A 348 (1994) 232-236
Table 1 Properties of the position sensitive proportional counter Internal cross section (D × W) Active area (L × W) Body material Window Readout Gas fill (permanently sealed)
20 mm× 48 mm x 2 sections 89 mm × 44 mm × 2 sections stainless steel 125 ~m Be backgammon [13,14] type (1-D charge division) 47.5% Xe, 47.5% Ar, 5%
Pressure Typical anode voltage Anode (diameter, material) Number of anodes (per section) Anode spacing Anode distance to cathode (readout) Anode distance to cathode (window)
approximately 2 mm, so this parallax did not affect the m e a s u r e d position of the hole profiles. C h a r g e sensitive preamplifiers ( A m p t e k A250) conn e c t e d to a n o d e s a n d r e a d o u t c a t h o d e s were used to obtain signals for each event, a n d the pulses were r o u t e d to commercial shaping amplifiers. T h e height of each pulse was d e t e r m i n e d by 12 bit A D C s and the data acquired by a computer, which calculated the position of each event by dividing the induced charge signal from one of the c a t h o d e ' s " w e d g e s " by the sum of the charge on b o t h wedges [11]. W e o b t a i n e d a n u m b e r of images of the mask at a n o d e voltages of 1480, 1510 and 1540 V a n d c o u n t rates from 100 Hz to 2 kHz. T h e central slit was obscured at the lowest gain. A typical s e q u e n c e of images is shown in Fig. 2. T h e s e plots show the profiles of the pinholes moving towards the central region, a n d b e c o m i n g m e r g e d together. A " t a i l " can be seen on the side of the o u t e r profiles. T h e i n n e r pinholes are affected first, but the whole image is affected at the higher rates. T h e contrast in the image is poor at higher rates. E a c h image was analysed in turn by a peak finding a n d fitting program. This was able to fit a G a u s s i a n to each pinhole image if it was distinct from its neighbour. T h e total width of the image (the difference between the centroids of the two peaks at e i t h e r edge of the group) was d e t e r m i n e d , a n d is plotted against c o u n t rate in Fig 3. T h e data consists of images t a k e n at 1480 V with the slit closed and with the slit open. T h e width at the lowest rate (300 Hz) was t a k e n to be 1.0, a n d the o t h e r widths are relative to this.
CO
2
1.2 atm 1480 V 15 ~m, P t - W 2 16 mm 3.2 mm 16.8 mm
the slit, of width 0.5 mm, h a d an area of 6 m m 2 (accounting for the effect of the window s u p p o r t structure). T h e length of the slit was such that only o n e a n o d e was illuminated. T h e slit was positioned halfway along the length of the detector, a n d the holes were positioned 3 m m perpendicularly from the active anode. A n N b target X-ray source with an a p e r t u r e of 3 m m d i a m e t e r was positioned 127 cm from the c e n t r e of the detector. R a d i a t i o n e n t e r e d the d e t e c t o r normally t h r o u g h the slit, b u t at an angle of 0.22 ° to the n o r m a l t h r o u g h the f u r t h e s t hole. However, the m e a n absorption d e p t h for N b - L X-rays in this particular gas is
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Fig. 2. Images of a slit and pinholes at increasing rates, showing distortion of the image and loss of contrast. 2.2 keV X-rays, anode at 1510 V. Rates (per second) of 500 (top), 1000, 1500 and 2000 (bottom).
235
M.W. Trow et al. / N u c l . Instr. and Meth. in Phys. Res. A 348 (1994) 232-236 1.00
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Fig. 3. Total width (difference of centroids of the features at the edge of the test pattern) vs. count rate. Two data sets were analysed, both with anode at 1480 V, with central bright slit and without. All data were scaled so that the width of the lowest rate image is 1. The actual separation of the features was 10.5 ram.
T h e contrast, defined here as the ratio of the maxim u m of a peak to the average of the m i n i m a on e i t h e r side, was r e t u r n e d by the fitting procedure. This definition is not m e a n i n g f u l for the extreme peaks, as its value d e p e n d s on the spacing of the f e a t u r e s a n d the intrinsic position resolution. Fig. 4 shows the contrast as a function of c o u n t rate for the first n o n - e x t r e m e p e a k in the image, which relates to a p i n h o l e 4.5 m m from the slit centre. Again, the data is for 1480 V with slit o p e n a n d with slit closed.
5. Results of a s i m u l a t i o n
A n u m e r i c a l model of the image distortion effect was d e v e l o p e d by the authors. T h e two-dimensional form of t h e a n o d e field was first d e t e r m i n e d using a finite e l e m e n t m e t h o d . This was t h e n used to c o m p u t e the distribution of a sheet of ions at unit c o u n t rate, using a particle following algorithm. W e a s s u m e d t h a t all avalanches were uniformly
distributed in azimuth angle a r o u n d the wire. A large n u m b e r ( ~ 1000) of equal angle i n c r e m e n t s were selected, and for each angle the trajectory of the ion in the a n o d e field was d e t e r m i n e d . T h e volume of the-detector was divided into r e c t a n g u l a r elements, a n d the ion density c o m p u t e d by accumulating for each elem e n t the n u m b e r of tracks which passed t h r o u g h the element, weighted by the time t a k e n to cross the element. F o r simplicity, we a s s u m e d t h a t the ions did not interact with one a n o t h e r , and t h a t diffusion was negligible. T h e resulting density array was stored for later use. For an arbitrary c o u n t rate, the densities were scaled appropriately. E l e c t r o n trajectories were calculated by c o m p u t i n g the field c o n t r i b u t i o n of a single thin ion sheet at various points in the detector, a n d following the history of a test electron. W e assumed that the test particle did not p r o d u c e any ions, so t h a t the only interaction was b e t w e e n a single electron and the sheet of ions. In addition, we a p p r o x i m a t e d the electron drift velocity function with a simple linear relationship, t h a t is, we defined a c o n s t a n t electron mobility. A t any point in the detector, the electric field of the ion s h e e t was f o u n d by s u m m i n g the c o n t r i b u t i o n s from each of the r e c t a n g u l a r e l e m e n t s in the ion density grid. C o m b i n i n g this with the a n o d e field gave the total field, a n d h e n c e the electron drift velocity. T h e test electron was t h e n m o v e d an a p p r o p r i a t e distance, and the field calculation r e p e a t e d at its new location, until the electron r e a c h e d t h e anode. T h e calculations were r e p e a t e d for positions similar to those used in the test mask, and for a r a n g e of c o u n t rates. T h e results are s u m m a r i s e d in Fig. 5.
6. D i s c u s s i o n
T h e m o d e l l e d results are well a p p r o x i m a t e d by a family of exponential functions describing the position modelled ,
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Fig. 4. Contrast index vs. count rate; anode at 1480 V. This is the contrast (defined in text) of a feature 4.5 mm from the centre of the test pattern.
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Fig. 5. Summary of model results, showing the position shift vs. actual position for a series of count rates, as marked. I. GASEOUS DETECTORS
236
M.W. Trow et al./Nucl. Instr. and Meth. in Phys. Res. A 348 (1994) 232-236
shift as a function of distance from the central bright region: shift = A e x p ( - x / d ) , w h e r e A is a p a r a m e t e r d e p e n d i n g on the c o u n t rate, x is the distance of the test p e a k from the bright region a n d d is a scale length p a r a m e t e r . W e find t h a t d = 8.3 m m best describes the m o d e l results. It is clear that the m o d e l l e d shifts are not large e n o u g h to account for the distortions seen in practice. In addition, the exponential law followed by t h e model was not c o n f i r m e d in the experiment. T h e f o r m e r suggests that some physical p a r a m e t e r s used in the model are incorrect, a n d the latter t h a t the m o d e l was not sufficiently r e p r e s e n t a t i v e of the e x p e r i m e n t a l situation. T h e physical p a r a m e t e r s t h a t seem most likely to affect the size of the shifts are those which affect the total n u m b e r of ions in the drift region, namely the ion mobility and the gain. In the absence of any values in the literature, we took the ion mobility to b e t h a t of x e n o n in its own gas. T h e gain was estimated as 1.5 x 104 at 1480 V, which may b e s o m e w h a t lower t h a n t h e true value due to ballistic deficit in the shaping amplifiers. In compiling the m o d e l results, we a s s u m e d t h a t t h e smaller images would not influence o n e a n o t h e r comp a r e d with the bright slit, a n d so we calculated the position shift for each separately. T h e a s s u m p t i o n was shown to b e invalid by t h e data o b t a i n e d with t h e slit closed, w h e r e the pinhole images were seen to b u n c h t o g e t h e r such t h a t t h e i n n e r pair (closest to the slit position) m o v e d away from o n e a n o t h e r .
7. Conclusion W e have d e m o n s t r a t e d rate d e p e n d e n t image distortions in a o n e - d i m e n s i o n a l position sensitive p r o p o r tional counter. Whilst this c o u n t e r was not i n t e n d e d for use in high rate applications, it did allow us to study the effect at m o d e r a t e rates a n d with conventional e q u i p m e n t . In particular, the "slow" gas mixture a n d large drift volumes, c o m b i n e d with the relatively d e e p drift region, c o n t r i b u t e d to the m a g n i t u d e of this phenomenon. If o n e wishes to avoid this type of behaviour, the gas mixture a n d geometry must b e chosen accordingly, so
as to minimise the density of ions in the d e t e c t o r volume. Predictive models of the effect require as a starting point a good description of the electric field everyw h e r e in the detector, a n d a p p r o p r i a t e values for the electron drift velocity a n d ion mobility. If complex images are to b e studied at high rate a n d high positional accuracy, the models should be configured with those types of images in mind.
Acknowledgements T h e a u t h o r s would like to t h a n k colleagues at t h e i r institutes for their s u p p o r t a n d e n c o u r a g e m e n t , a n d for m a n y stimulating discussions.
References [1] E. Hell, H.J. Besch, k Brabetz, P. Kuhn and A.H. Walenta, Nucl. Instr. and Meth. A 269 (1988) 404. [2] G.D. Dmitriev and I.B. Frumkin, Nucl. Instr. and Meth. A 295 (1990) 384. [3] R.W. Hendricks, Rev. Sci. Instr. 40 (1969) 1216. [4] H. Sipila and V. Vanha-Honko, Nucl. Instr. and Meth. 153 (1978) 461. [5] H. Sipila and V. Vanha-Honko, J. Bergqvist, Nucl. Instr. and Meth. 176 (1980) 381. [6] E. Mathieson, Nucl. Instr. and Meth. 249 (1986) 420. [7] G.C. Smith and E. Mathieson, IEEE Trans. Nucl. Sci. NS-34 (1987) 410. [8] E. Mathieson and G.C. Smith, Nucl. Instr. and Meth. A 316 (1992) 246. [9] F. Sauli, Principles of operation of multiwire proportional and drift chambers, CERN Report 77-09 (1977). [10] J . k Culhane, E. Hiei, G.A. Doschek, A.M. Cruise, Y. Ogawara, Y. Uchida, R.D. Bentley, C.M. Brown, J. Lang, T. Watanabe, J.A. Bowles, R.D. Deslattes, U. Feldman, A. Fludra, P. Guttridge, A. Henins, J. Lapington, J. Magraw, J.T. Mariska, J. Payne, K.J.H. Phillips, P. Sheather, K. Slater, K. Tanaka, E. Towndrow, M.W. Trow and A. Yamaguchi, Solar Phys. 136 (1991) 89. [11] M.W. Trow, J.S. Lapington and R.D. Bentley, Nucl. Instr. and Meth. A 310 (1991) 344. [12] M.W. Trow, ESA SP-356 (1992) 383. [13] R. Allemand and G. Thomas, Nucl. Instr. and Meth. 131 (1976) 141. [14] B.P. Duval, J. Barth, R.D. Deslattes, A. Henins and G.G. Luther, Nucl. Instr. and Meth. 222 (1984) 274.
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH Section A
Rate dependent image distortions in proportional counters M.W. T r o w a,,, A.C. B e n t o b, A. Smith a a Department of Space and Climate Physics, University College London, Mullard Space Science Laboratory, Holmbury St Mary, Dorking, Surrey, RH5 6NT, UK b Department of Physics, Uniuersity of Coimbra, P-3000 Coimbra, Portugal
The positional linearity of imaging proportional counters is affected by the intensity distribution of the incident radiation. A mechanism for this effect is described, in which drifting positive ions in the gas produce a distorting electric field which perturbs the trajectories of the primary electrons. In certain cases, the phenomenon causes an apparent improvement of the position resolution. We demonstrate the effect in a detector filled with a xenon-argon-CO 2 mixture. The images obtained are compared with the results of a simulation. If quantitative predictions for a particular detector are required, accurate values of the absolute detector gain, ion mobility and electron drift velocity are needed.
1. Rate dependent effects in proportional counters Position sensitive p r o p o r t i o n a l c o u n t e r s are used in a variety of applications for d e t e c t i o n of X U V a n d X-ray p h o t o n s a n d o t h e r radiation. T h e dynamic r a n g e of these detectors has previously b e e n limited by the position r e a d o u t electronics, b u t several r e c e n t r e a d o u t designs are capable of functioning at the m a x i m u m rate of the counter. Hell et al. [1] observed image distortions at rates of 15 to 30 M H z / c m z of M o - K r a d i a t i o n in a n M W P C having a 9 m m drift gap. T h e gas used was A r + 1% C O 2 at 4 a n d 8 bar. D m i t r i e v a n d F r u m k i n [2] have described their experiences of these effects. They used a similar c h a m b e r with a drift gap of 10 mm, a n d f o u n d m e a s u r a b l e distortions at rates of a few tens of kHz. T h e i r d e t e c t o r was filled with A r + 18% C O 2 at a p r e s s u r e of 1 atm. T h e distortions h a d the following characteristics, not all of which were observed simultaneously: distortion of b e a m profiles, d e c r e a s e of a p p a r e n t b e a m width, a p p a r e n t i m p r o v e m e n t of the position resolution, separate profiles moving closer together, and smearing of profiles n e a r intense illumination. T h e s e distortions occurred in conjunction with a c o u n t - r a t e d e p e n d e n t c h a n g e of the gas gain. In a r e a d o u t system w h o s e lower level discriminator is set n e a r the low energy tail of the usual pulse height distribution, this is a c c o m p a n i e d by a loss in counting efficiency. B o t h effects are d u e to the electric field
* Corresponding author.
c o n t r i b u t i o n of the positive ions p r o d u c e d in the avalanches. T h e general principles of ion i n d u c e d gain d e p r e s s i o n were outlined by H e n d r i c k s [3] a n d f u r t h e r t r e a t m e n t s can be f o u n d in refs. [4-8].
2. Distortion mechanism I m m e d i a t e l y following a n electron avalanche in a p r o p o r t i o n a l counter, t h a t is, after all the electrons have r e a c h e d t h e a n o d e wire, a cloud of positively ionised gas atoms or molecules begins to drift toward the c a t h o d e [9]. T h e resulting distribution of ions can b e calculated if the electric field in the d e t e c t o r is known. In the special case of a coaxial d e t e c t o r in which avalanches are distributed uniformly a r o u n d t h e a n o d e wires, a c o n s t a n t c o u n t i n g rate p r o d u c e s a uniform density of ions. T h e charge density p for a c o u n t rate n is given by: nq~ o p = IzVC, w h e r e q is the avalanche charge, V is the a n o d e voltage and C is the capacitance p e r wire p e r unit length, p~ is the ion mobility, a n d e 0 is t h e permittivity of free space. This expression can also b e applied n e a r the a n o d e s of o t h e r types of detector. W h e n a d e t e c t o r is illuminated by a n a r r o w b e a m or point, a s h e e t of ions will b e p r o d u c e d in the drift regions. This charge g e n e r a t e s an electric field which has a c o m p o n e n t p e r p e n d i c u l a r to the p l a n e of the sheet. Primary electrons are a t t r a c t e d to this region of ion density as they drift toward the a n o d e (see Fig. 1).
0168-9002/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0 1 6 8 - 9 0 0 2 ( 9 4 ) 0 0 1 1 4 - M
M.W. Trow et aL / NucL Instr. and Meth. in Phys. Res. A 348 (1994) 232-236
.• ,+/f
Beamprofile
++++
A
~._
Cathode(window)
/ +++
| +++ +++
Anodewire
÷++
Cathode(readout)
_
~
Image i
A
Fig. 1. Longitudinal cross section of a proportional counter showing an anode wire and two cathode planes. Radiation with the intensity distribution shown enters through the upper cathode, and the resulting avalanches produce an ion distribution mainly in the regions marked with +. Electron trajectories - of photons absorbed nearby are attracted to the ion-filled region, and the recorded image is distorted. The amount of lateral drift will depend on the density of ions in the sheet, the location of the primary ionisation, and the drift velocity of the electrons. At any point in the electron's path, the direction of drift is that of the gradient of the total electric field, and the drift velocity is a complex function of the field strength. This function is usually highly dependent on the proportions of the gas mixture. The magnitude of the perturbing field of the ion sheet decreases with distance. Therefore, photons absorbed close to the ion sheet will drift more than those absorbed further away. In addition, the perturbing field is weaker near the edges of the ion distribution, i.e. near the cathodes or between the wires in a MWPC, than in the centre of the drift volume. An electron whose trajectory which begins at the upper cathode will drift more than an electron absorbed close to the anode wire, because the latter experiences sideways drift for a shorter time. Since the sites of initial ionisation occur at a range of depths in the gas, it can be expected that a distribution of lateral drifts will be observed for a particular initial perpendicular distance from the ion sheet.
3. Practical consequences
Each point in an image will produce its own positive ion sheet, which can affect the electron trajectories in all other parts of the detector. The trajectories of the ions will also be modified by the distribution of ions, although the magnitude of this effect will be smaller due to the ion's lower mobilities. The result will be that bright regions in any image will attract one another, and the degree of attraction will be a function of the
233
count rate. Certain regions in the recorded image will increase in intensity, and others parts may decrease. The overall number of counts in the image is unchanged, unless a greater number of pulses fall below the readout system's lower level discriminator due to gain-related changes in the pulse height distribution. In a flat field, or rectangular image, the centre of attraction will be the centre of the field. There will be an enhancement of intensity near the centre of the image, and a decrease at the edges. Distortions in images of a number of small, bright points, separated by regions of low intensity, will appear largely as motion of the points towards their common centre. However, since the shifts depend on the depth of photon absorption, the profiles of the points will become skewed. If the size of the features is less than the position resolution of the system, the skew of the distorted profiles can result in a worsening of the measured resolution. Medium sized features, with scale lengths a few times larger than the position bin width, can be affected in the opposite way. If there are no features nearby that can significantly affect the centroid of the feature, and the intensity of the feature is sufficient to cause distortions, the profile will remain symmetrical but will decrease in width (self-focusing). The measured position resolution will therefore appear to improve. In many systems, the position resolution is limited by the gas, and the point spread function is over-sampled by the readout electronics. Position resolution measurements are very often made with test images consisting of small points separated by large regions of zero intensity. Under these conditions, one can obtain an anomalous improvement of the resolution with higher count rate, without any measurable change of the centroid of the points.
4. Tests with a position sensitive proportional counter
To determine the effect of counting rate on a test image, we illuminated a position sensitive detector through a mask mounted against its window. Table 1 describes the detector used for these tests. Identical detectors were flown in the Yohkoh Bragg Crystal Spectrometer [10], which is used to study the soft X-ray emission of solar flares, and their performance has been described elsewhere [11,12]. The mask was a 0.9 mm thick sheet of aluminium with a slit and pinholes. The slit was perpendicular to the axis of the anode wires, and the holes were arranged along a line parallel to the anodes at various distances from the slit: 5, 4, 3, 2, and 1 mm on one side and 1.5, 2.5, 3.5, 4.5 and 5.5 mm on the other. Each hole had an area of 0.79 mm 2 (diameter 0.5 mm), and I. GASEOUS DETECTORS
234
M.I~E Trow et al. / N u c l . Instr. and Meth. in Phys. Res. A 348 (1994) 232-236
Table 1 Properties of the position sensitive proportional counter Internal cross section (D × W) Active area (L × W) Body material Window Readout Gas fill (permanently sealed)
20 mm× 48 mm x 2 sections 89 mm × 44 mm × 2 sections stainless steel 125 ~m Be backgammon [13,14] type (1-D charge division) 47.5% Xe, 47.5% Ar, 5%
Pressure Typical anode voltage Anode (diameter, material) Number of anodes (per section) Anode spacing Anode distance to cathode (readout) Anode distance to cathode (window)
approximately 2 mm, so this parallax did not affect the m e a s u r e d position of the hole profiles. C h a r g e sensitive preamplifiers ( A m p t e k A250) conn e c t e d to a n o d e s a n d r e a d o u t c a t h o d e s were used to obtain signals for each event, a n d the pulses were r o u t e d to commercial shaping amplifiers. T h e height of each pulse was d e t e r m i n e d by 12 bit A D C s and the data acquired by a computer, which calculated the position of each event by dividing the induced charge signal from one of the c a t h o d e ' s " w e d g e s " by the sum of the charge on b o t h wedges [11]. W e o b t a i n e d a n u m b e r of images of the mask at a n o d e voltages of 1480, 1510 and 1540 V a n d c o u n t rates from 100 Hz to 2 kHz. T h e central slit was obscured at the lowest gain. A typical s e q u e n c e of images is shown in Fig. 2. T h e s e plots show the profiles of the pinholes moving towards the central region, a n d b e c o m i n g m e r g e d together. A " t a i l " can be seen on the side of the o u t e r profiles. T h e i n n e r pinholes are affected first, but the whole image is affected at the higher rates. T h e contrast in the image is poor at higher rates. E a c h image was analysed in turn by a peak finding a n d fitting program. This was able to fit a G a u s s i a n to each pinhole image if it was distinct from its neighbour. T h e total width of the image (the difference between the centroids of the two peaks at e i t h e r edge of the group) was d e t e r m i n e d , a n d is plotted against c o u n t rate in Fig 3. T h e data consists of images t a k e n at 1480 V with the slit closed and with the slit open. T h e width at the lowest rate (300 Hz) was t a k e n to be 1.0, a n d the o t h e r widths are relative to this.
CO
2
1.2 atm 1480 V 15 ~m, P t - W 2 16 mm 3.2 mm 16.8 mm
the slit, of width 0.5 mm, h a d an area of 6 m m 2 (accounting for the effect of the window s u p p o r t structure). T h e length of the slit was such that only o n e a n o d e was illuminated. T h e slit was positioned halfway along the length of the detector, a n d the holes were positioned 3 m m perpendicularly from the active anode. A n N b target X-ray source with an a p e r t u r e of 3 m m d i a m e t e r was positioned 127 cm from the c e n t r e of the detector. R a d i a t i o n e n t e r e d the d e t e c t o r normally t h r o u g h the slit, b u t at an angle of 0.22 ° to the n o r m a l t h r o u g h the f u r t h e s t hole. However, the m e a n absorption d e p t h for N b - L X-rays in this particular gas is
1 5 1 0 V, with =l;t
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• (~,,,,) r:~e,,.z73 i ~
2000
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~
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Fig. 2. Images of a slit and pinholes at increasing rates, showing distortion of the image and loss of contrast. 2.2 keV X-rays, anode at 1510 V. Rates (per second) of 500 (top), 1000, 1500 and 2000 (bottom).
235
M.W. Trow et al. / N u c l . Instr. and Meth. in Phys. Res. A 348 (1994) 232-236 1.00
-~;
..........................................
-
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-
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-
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o
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0.60
0.50
.......
,
.........
1000
i
.........
,
.........
2000 3000 Count Rate
,
, .....
4000
5000
Fig. 3. Total width (difference of centroids of the features at the edge of the test pattern) vs. count rate. Two data sets were analysed, both with anode at 1480 V, with central bright slit and without. All data were scaled so that the width of the lowest rate image is 1. The actual separation of the features was 10.5 ram.
T h e contrast, defined here as the ratio of the maxim u m of a peak to the average of the m i n i m a on e i t h e r side, was r e t u r n e d by the fitting procedure. This definition is not m e a n i n g f u l for the extreme peaks, as its value d e p e n d s on the spacing of the f e a t u r e s a n d the intrinsic position resolution. Fig. 4 shows the contrast as a function of c o u n t rate for the first n o n - e x t r e m e p e a k in the image, which relates to a p i n h o l e 4.5 m m from the slit centre. Again, the data is for 1480 V with slit o p e n a n d with slit closed.
5. Results of a s i m u l a t i o n
A n u m e r i c a l model of the image distortion effect was d e v e l o p e d by the authors. T h e two-dimensional form of t h e a n o d e field was first d e t e r m i n e d using a finite e l e m e n t m e t h o d . This was t h e n used to c o m p u t e the distribution of a sheet of ions at unit c o u n t rate, using a particle following algorithm. W e a s s u m e d t h a t all avalanches were uniformly
distributed in azimuth angle a r o u n d the wire. A large n u m b e r ( ~ 1000) of equal angle i n c r e m e n t s were selected, and for each angle the trajectory of the ion in the a n o d e field was d e t e r m i n e d . T h e volume of the-detector was divided into r e c t a n g u l a r elements, a n d the ion density c o m p u t e d by accumulating for each elem e n t the n u m b e r of tracks which passed t h r o u g h the element, weighted by the time t a k e n to cross the element. F o r simplicity, we a s s u m e d t h a t the ions did not interact with one a n o t h e r , and t h a t diffusion was negligible. T h e resulting density array was stored for later use. For an arbitrary c o u n t rate, the densities were scaled appropriately. E l e c t r o n trajectories were calculated by c o m p u t i n g the field c o n t r i b u t i o n of a single thin ion sheet at various points in the detector, a n d following the history of a test electron. W e assumed that the test particle did not p r o d u c e any ions, so t h a t the only interaction was b e t w e e n a single electron and the sheet of ions. In addition, we a p p r o x i m a t e d the electron drift velocity function with a simple linear relationship, t h a t is, we defined a c o n s t a n t electron mobility. A t any point in the detector, the electric field of the ion s h e e t was f o u n d by s u m m i n g the c o n t r i b u t i o n s from each of the r e c t a n g u l a r e l e m e n t s in the ion density grid. C o m b i n i n g this with the a n o d e field gave the total field, a n d h e n c e the electron drift velocity. T h e test electron was t h e n m o v e d an a p p r o p r i a t e distance, and the field calculation r e p e a t e d at its new location, until the electron r e a c h e d t h e anode. T h e calculations were r e p e a t e d for positions similar to those used in the test mask, and for a r a n g e of c o u n t rates. T h e results are s u m m a r i s e d in Fig. 5.
6. D i s c u s s i o n
T h e m o d e l l e d results are well a p p r o x i m a t e d by a family of exponential functions describing the position modelled ,
1.000 8
~
....
i . . . . . . . . .
6b ~
, . . . . . . . . .
I . . . . . . . . .
-
,
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.
.
,
,
, . . . . . . . . .
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-
.
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!
~
5000 3000 2000
c 4
1500
'~
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lOOO 800 500
g
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\x
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2000 3000 Count Rate
4000
5000
Fig. 4. Contrast index vs. count rate; anode at 1480 V. This is the contrast (defined in text) of a feature 4.5 mm from the centre of the test pattern.
0.010
300
0.001
i
0
,
,
,
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,
,
4 from
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mm
Fig. 5. Summary of model results, showing the position shift vs. actual position for a series of count rates, as marked. I. GASEOUS DETECTORS
236
M.W. Trow et al./Nucl. Instr. and Meth. in Phys. Res. A 348 (1994) 232-236
shift as a function of distance from the central bright region: shift = A e x p ( - x / d ) , w h e r e A is a p a r a m e t e r d e p e n d i n g on the c o u n t rate, x is the distance of the test p e a k from the bright region a n d d is a scale length p a r a m e t e r . W e find t h a t d = 8.3 m m best describes the m o d e l results. It is clear that the m o d e l l e d shifts are not large e n o u g h to account for the distortions seen in practice. In addition, the exponential law followed by t h e model was not c o n f i r m e d in the experiment. T h e f o r m e r suggests that some physical p a r a m e t e r s used in the model are incorrect, a n d the latter t h a t the m o d e l was not sufficiently r e p r e s e n t a t i v e of the e x p e r i m e n t a l situation. T h e physical p a r a m e t e r s t h a t seem most likely to affect the size of the shifts are those which affect the total n u m b e r of ions in the drift region, namely the ion mobility and the gain. In the absence of any values in the literature, we took the ion mobility to b e t h a t of x e n o n in its own gas. T h e gain was estimated as 1.5 x 104 at 1480 V, which may b e s o m e w h a t lower t h a n t h e true value due to ballistic deficit in the shaping amplifiers. In compiling the m o d e l results, we a s s u m e d t h a t t h e smaller images would not influence o n e a n o t h e r comp a r e d with the bright slit, a n d so we calculated the position shift for each separately. T h e a s s u m p t i o n was shown to b e invalid by t h e data o b t a i n e d with t h e slit closed, w h e r e the pinhole images were seen to b u n c h t o g e t h e r such t h a t t h e i n n e r pair (closest to the slit position) m o v e d away from o n e a n o t h e r .
7. Conclusion W e have d e m o n s t r a t e d rate d e p e n d e n t image distortions in a o n e - d i m e n s i o n a l position sensitive p r o p o r tional counter. Whilst this c o u n t e r was not i n t e n d e d for use in high rate applications, it did allow us to study the effect at m o d e r a t e rates a n d with conventional e q u i p m e n t . In particular, the "slow" gas mixture a n d large drift volumes, c o m b i n e d with the relatively d e e p drift region, c o n t r i b u t e d to the m a g n i t u d e of this phenomenon. If o n e wishes to avoid this type of behaviour, the gas mixture a n d geometry must b e chosen accordingly, so
as to minimise the density of ions in the d e t e c t o r volume. Predictive models of the effect require as a starting point a good description of the electric field everyw h e r e in the detector, a n d a p p r o p r i a t e values for the electron drift velocity a n d ion mobility. If complex images are to b e studied at high rate a n d high positional accuracy, the models should be configured with those types of images in mind.
Acknowledgements T h e a u t h o r s would like to t h a n k colleagues at t h e i r institutes for their s u p p o r t a n d e n c o u r a g e m e n t , a n d for m a n y stimulating discussions.
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