International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 7.1, p. 627

## Section 7.1.6.2.1. Localization of the detected photon

U. W. Arndtb

#### 7.1.6.2.1. Localization of the detected photon

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There are several methods of deriving the position of the detected photon that are applicable to both linear and area detectors.

• (1) The charge produced in the avalanche can be collected on a resistive anode. In the case of linear detectors, the central wire can be given a low or a very high resistance. The latter type is most commonly made from a quartz fibre coated with carbon. The emerging pulse is detected at both ends of the wire (Borkowski & Kopp, 1968; Gabriel & Dupont, 1972). Area detectors with a resistive disc anode must have at least three read-out electrodes (Stümpel, Sanford & Goddard, 1973). With low-resistance electrodes, the position of the event can be computed by analogue circuits from the relative pulse amplitudes (Fig. 7.1.6.4a) ; a preferred method with high-resistance anodes is to measure the rise times of the output pulses that are determined by the time constant formed by the input capacity of the pulse amplifier at each output and the resistance of the path from the detection point to the output electrode (Fig. 7.1.6.4b).

 Figure 7.1.6.4 | top | pdf |Read-out methods for gas-filled LPSD's. (a) Charge division with low-resistance anode wire. (b) Rise-time method with high-resistance anode. (c) Delay-line read-out. (d) Amplifier-per-wire method. From Mochiki (1984); courtesy of K. Mochiki.
• (2) The anode or cathode can be constructed in the form of two or more interleaved resistive electrodes insulated from each other. Provided that the charge distribution covers at least one unit of the pattern, positional information can be derived by relative pulse height or by timing methods. Examples of this type of read-out are the linear backgammon (jeu de jacquet) counter together with its two-dimensional variant (Allemand & Thomas, 1976), the wedge-and-strip anode developed by Anger and his collaborators (Anger, 1966; Martin, Jelinsky, Lampton, Malina & Anger, 1981), and its polar coordinate analogue (Knibbeler, Hellings, Maaskamp, Ottewanger & Brongersma, 1987), for two-dimensional read-out. The method seems capable of a higher spatial resolution than any other (Schwarz & Lapington, 1985).

• (3) The anode or cathode can be made from a number of sections connected to a tapped delay line (Fig. 7.1.6.4c). Positional information is derived from the time delay of the pulse relative to the arrival of an undelayed prompt pulse. Linear PSD's (LPSD's) with delay-line read out are usually made straight, but variants have been produced in the form of circular arcs (Wölfel, 1983; Ballon, Comparat & Pouxe, 1983).

Area detectors of this type require two parallel planes of parallel wires with the wires in the two planes at right angles to one another placed on either side of the anode, which also consists of parallel wires. The prompt pulse in such a detector, the multiwire proportional chamber (MWPC), is usually taken from the anode (Fig. 7.1.6.5 ). In counters without a drift space, the electron avalanche always ends up on one anode wire, and there is then a pseudo-quantization in the position measurement made at right angles to the direction of the anode wires. In drift-space detectors with a narrow anode-wire spacing, the avalanche lands on more than one wire and some interpolation is possible. In the direction parallel to the anode wires, there is never any quantization and the resolution can be better than the cathode wire spacing: Although pulses are induced on several wires, the centroid of the delayed group of pulses can be measured with precision. Delay-line read-out LPSD's have reached the highest resolution in the hands of Radeka and his group (Smith, 1984). MWPC's of this type have been used for several years (Xuong, Freer, Hamlin, Neilsen & Vernon, 1978; Bordas, Koch, Clout, Dorrington, Boulin & Gabriel, 1980; Baru, Proviz, Savinov, Sidorov, Khabakhshev, Shuvalov & Yakovlev, 1978; Anisimov, Zanevskii, Ivanov, Morchan, Peshekhonov, Chan Dyk Tkhan, Chan Khyo Dao, Cheremukhina & Chernenko, 1986). They have a relatively low maximum count rate (< 105 s−1) determined by the space charge due to earlier events and by the fact that position digitization takes of the order 1 µs. Limitations in the closeness of practicable wire spacing leads to a pixel size of the order of 1 mm.

 Figure 7.1.6.5 | top | pdf |Three-plane MWPC. Note the pseudo-quantization due to charge collection on one anode wire. The cathode wires may either be connected to a tapped delay line as in Fig. 7.1.6.4(c) or to individual amplifiers as in Fig. 7.1.6.4(d) (courtesy of A. R. Faruqi).
• (4) A faster read out is possible with MWPC's in which the positional information is derived from the centroid in amplitude of the group of induced cathode pulses (Fig. 7.1.6.4d). Individual amplifiers of carefully equalized gain are required for each individual wire or at least for small groups of adjacent wires (Pernot, Kahn, Fourme, Leboucher, Million, Santiard & Charpak, 1982). Counting rates in excess of 106 s−1 are then possible.

### References

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