Nuclear Instruments and Methods in Physics Research A264 (1988) 523 525 523 North-Holland, Amsterdam

Letter to the Editor

THE APPLICATION OF THE PARTITION N O I S E THEORY

J o h n T H O R N T O N *

Department of Electronic and Electrical Engineering, Uniuersi{v of Surrey, Guildford, Surrey, GU2 5XH, England

Received 16 July 1987 and in revised form 22 August 1987

The operation of the wedge and strip position sensing element in three different types of detector (muhichannel plate device, parallel plate proportional counter and multiwire proportional counter) is examined, it is shown that, unlike the two other detector types, the position resolution of a multiwire proportional counter cannot be affected by partition noise because its wedge and strip works from induced charge rather than collected charge.

Wedge and strips (ws) are position sensing elements for X-ray detectors. They have been used as anodes in multichannel plate devices (MCP) and parallel plate proportional counters (PPPC) and as cathodes in multi- wire proportional counters (MWPC) [1,2]. Fig. 1 shows a ws designed to provide 2-D information. It consists of three electrodes: the wedge, the strip and the Z; the wedge fingers become thicker in the y-direction and the strips become wider in the x-direction.

The action of an MCP during the detection of an X-ray is illustrated in fig. 2. The cloud of electrons emitted from the bot tom of the active channel together with the ws are shielded, from the positive charges remaining in the channel, by a conductive coating on the bottom of the plate. The electric field between the conductor and the ws causes the electrons to accelerate to the ws where they are collected by the ws electrodes. The amplitudes of the signals derived from the elec- trodes are proportional to the charges collected and hence the relative areas of the electrodes beneath the charge cloud's footprint. The tapering of the wedge fingers and the widening of the strips therefore enables position information to be obtained from the relative signal amplitudes, for example, the x coordinate can be obtained from

X = s / ( s + w + z ) , (1)

where s, w and z are the signal amplitudes from the wedge, strip and Z electrodes respectively. Note that X is dimensionless. Normally the charges are measured by charge sensitive preamplifiers, one connected to each electrode.

Partition noise was proposed as a limitation to the

* Previously at Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking, Surrey, Eng- land.

0168-9002/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

y, / I-1 H l

"l I I #

#

S~>Insutating

> X

Channels

Fig. 1. A wedge and strip pattern with three electrodes: the wedge (W), the strip (S) and the Z (Z).

position resolution of the ws when the ws were being employed with MCP [3]. Taking the x-direction and the strip electrode as examples, the argument was as fol- lows. The mean number of electrons collected by the strip electrode, over many events each producing charge Q, will be:

n =LQ/e , (2)

where £ is the fraction of the cloud's footprint 's area covered by the strip electrode and e is the electronic charge. However, the number collected by the strip electrode, during a single event, will be subject to chance. The appropriate statistical distribution is binomial be- cause an electron can be collected in two ways, by the strip electrode or not. The standard deviation of such a distribution is [4]:

o = [ L ( 1 - f s ) Q / e ] °5. (3)

Effectively, f , is the probabili ty that an electron will be collected by the strip electrode and (1 - f ~ ) is the prob- ability that it will not. To find the effect of small

524 J. Thornton /Application of the partition noise theory

MCP PPPC MWPC

X-Ray Ph n

W, o t ° t , /

-V Window 2/.1

-/-.L/. 3(/~)

Induced Eharge Disfribution

Post-Avalanche She[I of Ions

Anode Wire

Window / / / / - - o • -o • - - V 4-++

- - 0

Fig. 2. Schematic diagrams of a multichannel plate device (MCP), a parallel plate proportional counter (PPPC) and a multiwire proportional counter (MWPC), showing the different mechanisms involved in detecting an X-ray in each detector: (1) photoelectric absorption, (2) primary electron diffusion, (3) electron multiplication avalanching and (4) collected charge footprint. Electrons and positive ions are described by dashes and crosses respectively. The relative magnitudes of the electric potentials shown are:

V >> d V > 0.

changes, in the strip signal ampl i tude on the calculated position, X, we can differentiate eq. (1) with respect to s, remember ing that because the electrons which do not land on the strip are collected by the other electrodes, the denomina to r of eq. (1) is a constant , Q. Assuming the signal ampli tudes to be propor t iona l to the numbers of electrons collected and the f luctuat ion in s, ds, to be propor t ional to o, we obtain:

d X = [ L ( 1 - L ) e / Q ] °5, (4)

where d X is the spread in the x coordinate due to par t i t ion noise.

Unt i l recently the electronic noise, f rom the pre- amplifiers, prevented the invest igation of the smaller par t i t ion noise, however, experiments have now taken place with low capaci tance ws which enabled the elec- t ronic noise to be reduced. The initial experiments, to test the presence of par t i t ion noise, used specially desig- ned ws and a capacitively coupled probe to simulate the act ion within detectors. No charge was collected by the ws electrodes, charges were induced as the p robe was sent voltage pulses. Par t i t ion noise was found not to affect posi t ion resolution. It was proposed that it would not affect any type of detector using a ws - including the MCP [5]. Fur ther experiments, wi th M C P and ws, have now determined that par t i t ion noise does cont r ib- ute in an MCP system [6]!

Before applying the par t i t ion noise theory it is neces- sary to unders tand how the ws works in the detector being used. The action of detect ing an X-ray in a PPPC is i l lustrated in fig. 2 [7,8]. A series of clouds of elec-

trons are collected by the ws and a trail of ions are left in the avalanche region to migrate to the ca thode grid. The signal ampl i tudes do not reach their max imum unti l all the ions have been collected by the cathode, however, the final signal ampl i tudes f rom the electrodes will be p ropor t iona l to the numbers of electrons they collect. Par t i t ion noise will apply because these numbers will be subject to chance - a b inomial dis t r ibut ion again.

The act ion of detect ing an X-ray in a M W P C is i l lustrated in fig. 2 [7,8]. A n induced surface charge d is t r ibut ion appears on the ws after the electron avalanche, the magni tude of the induced charge in- creases as the ions, p roduced in the avalanche, migrate away from the anode wire. The shape of this surface charge d is t r ibut ion is not subject to chance but is con- trolled by an electric field produced by the effective charge at the centre of the expanding shell of ions. In a symmetr ic M W P C the field is expected to be that of an electric tripole [8]. The signals from the ws are processed and a coordinate de te rmined soon after the avalanche, typically within 0.01 ms. The ions collected by the ws arrive much later, typically after 0.1 ms. Part i t ion noise is therefore not expected to limit the posi t ion resolution of the M W P C because, like the probe experiment, the signal ampl i tudes are dependen t on induced charges and not collected electrons. Similar behaviour is ex- pected from a single-wire propor t iona l counter (SWPC) and ws based detector.

In the M W P C the coordinates of the centre of the ion shell is subject to chance, even if ava lanching occurs

J. Thornton / Application of the partition noise theory 525

on the same spot on the anode wire. However, these var iat ions are small compared to par t i t ion noise; the respective posi t ion resolut ion limits, expressed in uni ts of length, being: d ( e / Q ) °'5 and L ( e / Q ) °'5 respec- tively, where d is the size of the the ion shell (typically 1 or 0.1 m m depending on the direction) and L is the length of the ws (typically > 100 mm).

The inherent l imitat ions to posi t ion resolut ion of the ws are impor tan t to designers of X-ray detectors. The controversy over the appl icat ion of the par t i t ion noise theory is becoming more impor tan t with the emergence of low self-capacitance ws technology. This a t t empt to explain the basic physics in the opera t ion of the ws in MCP, PPPC, M W P C and SWPC, should therefore prove useful.

Acknowledgements

The author is grateful to the staff of MSSL and in

part icular: J.S. Lapington, H.E. Schwarz, I.M. Mason and J.L. Cu lhane for useful discussions.

References

[1] O.H.W. Siegmund, S. Clothier, J. Thornton, J. Lemen, R. Harper, I.M. Mason and J.L. Culhane, IEEE Trans. Nucl. Sci. NS-30 (1983) 503.

[2] H.E. Schwarz and I.M. Mason, Nature 309 (1984) 532. [3] C. Martin, P. Jelinsky, M. Lampton, R.F. Malina and H.O.

Anger, Rev. Sci. Instr. 52 (1981) 1067. [4] A.M. Mood, F.A. Graybill and D.C. Boes, Introduction to

the Theory of Statistics, 3rd ed. (McGraw-Hill, New York, 1974).

[5] H.E. Schwarz, Nucl. Instr. and Meth. A238 (1985) 124. [6] J.S. Lapington, A.D. Smith, D.M. Walton and H.E.

Schwarz, IEEE Trans. Nucl. Sci. NS-34 (1987) 431. [7] Rice-Evans, Spark, Streamer, Proportional and Drift

Chambers (Richelieu, London, 1973). [8] J.G. Thornton, Ph.D. Thesis, University of London (1986).