Variable sampling-time technique for improving count rate performance of scintillation detectors

N U C L E A R I N S T R U M E N T S AND METHODS

158 ( 1 9 7 9 )

459-466 ; ©

N O R T H - H O L L A N D PUBLISHING CO.

VARIABLE SAMPLING-TIME TECHNIQUE FOR IMPROVING COUNT RATE PERFORMANCE OF SCINTILLATION DETECTORS EIICHI TANAKA, NORIMASA NOHARA and HIDEO MURAYAMA

Division of Physics, National Institute of Radiologieal Sciences, Anagawa, Chiba-shi, Japan 260 Received 2 June 1978 A new technique is presented to improve the count rate capability of a scintillation spectrometer or a position sensitive detector with minimum' loss of resolution. The technique is based on the combination of pulse shortening and selective integration in which the integration period is not fixed but shortened by the arrival of the following pulse. Theoretical analysis of the degradation of the statistical component of resolution is made for the proposed system with delay line pulse shortening, and the factor of resolution loss is formulated as a function of the input pulse rate. A new method is also presented for determining the statistical component of resolution separately from the non-statistical system resolution. Preliminary experiments with a NaI(TI) detector have been carried out, the results of which are consistent with the theoretical prediction. However, due to the non-exponential scintillation decay of the NaI(TI) crystal, a simple delay line clipping is not satisfactory, and an RC high-pass filter has been added, which results in further degradation of the statistical resolution.

1. Introduction In many applications of scintillation detectors using relatively slow scintillators such as Nal(TI) crystals, the count rate limitation due to pulse pile-up is often a serious problem. Numerous methods for reducing pulse pile-up have been reported. A commonly used method ~) is to select the relevant events on a fast time scale (in the detector current pulse mode), and to selectively integrate the pulses of interest which meet with experimental requirements such as non-pulse-pileup, pulse-height selection, coincidence or anticoincidence with other detectors, etc. by using a fast gated integrator. However, when the pulse width is relatively long, the pile-up of the detector pulses still limits the maximum count rate available, although several correction methods for spectral distortion due to pile-up have been reported2). Amsel et al. 3) have shown that the detector pulse width can be shortened by passive filters, and Brassard 4) and Vartsky et al. s) have reported the fractional charge collection technique which combines the shortening of detector pulses with the selective integration method. Muehllehner et al. 6) also reported similar techniques for a positron imaging camera. The main disadvantage of this technique is, however, that the information of accumulated charge will be of poorer statistical character resulting from the use of short integration time rather than the full pulse duration. We can assume that the energy resolution of a

scintillation detector is given by the convolution of the two effectsT.8): the statistical resolution which arises from the Poisson statistics associated with the finite number of photoelectrons accumulated on the first dynode of the photomultiplier tube, and the non-statistical system resolution which includes the intrinsic resolution of the scintillation crystal, inhomogeneity of the photocathode of the photomultiplier tube, etc. The fractional charge collection technique apparently affects only the statistical resolution which becomes important at lower radiation energy. On the other hand, position sensitive detectors such as Anger type scintillation cameras 9,j°) are usually designed so that the position signal is not sensitive to the radiation energy, and accordingly the statistical component of the resolution plays a dominant role in the spatial resolution for commonly used energies (100-200 keV), although the other non-statistical effects such as multiple interactions of gamma-rays in the crystal, etc. may cause some additional resolution loss for high energy. Therefore, the use of the fractional charge collection technique in the scintillation camera will result in a considerable degradation of the spatial resolution together with the degradation of the energy resolution to a lesser extent. The present work was originally motivated to develop new scintillation cameras having both a good spatial resolution at low count rate and a good temporal resolution at high count rate with

460

E. TANAKA et al.

minimum loss of the spatial resolution. These cameras will be useful for various high count rate applications in nuclear medicine such as fast dynamic flow study, coded aperture imaging, annihillation coincidence positron imaging, Compton scatter tomography, although the technique is also applicable for spectrometry of low energy radiations at high count rate.

Input ~

IS"ORTENIOII

DL-I

,

t,

,

JINTEGR'TORI Gate~.~

oL-3Q

[

Oth;rstatus

I

' I

]Clear

I Inhibit

Gate J

1 ½

I REJECTION

_I

!OGIC

l

2. Principle of the variable sampling-time technique The technique described in this paper is a combination of pulse shortening and selective integration in which the period of integration is not fixed but controlled by the arrival of the Following pulse, so that a good compromise is achieved between count rate capability and energy or spatial resolution. The principle of the technique is based on the following fact. Suppose that a detector current pulse is shortened to a unipolar pulse by means of a suitable linear circuit as shown in fig. lb and the shortened pulse is integrated for a certain period ts. The statistical resolution of the integrated signal amplitude is generally degraded as compared to the full integration of the original pulse, but the degree of the degradation is a function of t~ and is made negligibly small by increasing ts. The detailed analysis will be described in the next section. Fig. 2 shows a simplified block diagram indicating the principle of the new technique and a time chart of signal pulses. An input pulse proportional to the detector current is first shortened to a un~polaf pulse. The shortened pulse is delayed by the delay line DL-I, and fed to the gated integrator. The gate signal for the gated integrator is supplied From the clearable univibrator, which is triggered by a delayed (by DL-2) trigger pulse if the fast dis-

Original ~ _ detector ( a ) pulse

Shortened pulse

(b)

Integrated ( c ) ~

signal

.h..... . . . .

v-v

" ~

I' te

Fig. I. Pulse waveforms in the variable sampling-time technique.

input signal ~tc';

- ~ t r ~-

delayed signal

Uni-vibrator I ntegrator Gate signal

I: ~

~i ~ { ~ '~

tw

,,

l~ R

I ~; I.

integ ated

signal

Sample hold gate signa~

I

!

I

~

L

~

', Sampled signal

[

~

:

\

Fig. 2. Simplified block diagram showing the principle of the variable sampling-time technique and a time chart of signal pulses.

criminator and other status are acceptable. The pulse width tw of the univibrator is set to a value sufficiently long as compared to the scintillation decay time constant (typically, 3-4 times the decay constant). The delay time of DL-2 is set so that the integration starts just before the leading edge of the delayed input signal. The trigger pulse is also Fed to the clear input of the univibrator. Thus, the integration is usually performed for a relatively long period to ensure good statistical resolution, but if the following pulse occurs during the above period, the univibrator is cleared and the sample-and-hold circuit is actuated to produce the output signal. Immediately after the sampling, the gated integrator is reset and accepts the second input pulse. The delay time tr Of DL-I is chosen such as to allow the completion of the above actions before the second pulse appears at the input, of the gated integrator. To prevent pulse pile-up distortion in the output, two requirements should be imposed by the pulse pile-up rejection logic. One is that the sampling should be performed only for pulses which are preceded by a certain pulse-free time interval ta. The other is that when the integration period for a pulse is shortened beyond a certain time interval, t~, due to the arrival of the following pulse,

461

VARIABLE SAMPLING-TIME TECHNIQUE

trons reaching the first dynode fluctuates statistically from its mean value given by eq. (1) according to the Poisson law. As a result, the amplitude of the integrated signal will also fluctuate not only at every event but also with time. Supposing the integrated signal is sampled at a time ts(>tc), the 3. Theoretical analysis variance ~(ts) of the sampled signal is given by, 3.1. RESOLUTIONDEGRADATIONDUE TO THE from the principle of the delay line shortening, FRACTIONAL INTEGRATIONWITH PULSESHORTENING Before discussing the performance of the pro- Vs(t~) = e -'/r (1--e-to~T) 2 dt + posed system, we shall consider the relation be0 tween the loss of statistical resolution and the ints N -t/r tegration period, assuming that the scintillation + T e dt decays exponentially. The system resolution is ignored in this section. Amsel et al. 3) have shown = N(I - e -'c/r) (1-e-t°lr+e-ts/r). (3) that an exponentially decaying pulse can be Since the relative standard deviation of the amshortened without producing undershoot by a suitable passive filter or a delay-line clipping circuit. plitude with the full integration of the original We consider here the delay-line method for the pulse is equal to l/x/N, the factor of resolution simplicity of the following analysis, although more loss Rs is given by generalized filters may be similarly applicable. (4) As shown in fig. 3, the delay-line pulse short- R, = x/V'l~S = {1 + [ e - ' s / r / ( l - - e - ' ~ / r ) ] } '1. I / \ / N ening is achieved by subtracting a suitable fraction of the delayed pulse from the original pulse by us- The value of R, is plotted in fig. 4 for tc = 100, 150 ing the partial reflection of the signal at the end and 250 ns assuming T = 250 ns for a NaI(T/) deof a delay line. Effective shortening is obtained tector. We see that Rs decreases with increasing t~ when the fraction is e x p ( - t c / T ) , where t¢ is the and that there is no practical loss of resolution clipping time or the shortened pulse width and T when t~ is sufficiently long. the decay time constant of the scintillation. We shall express the input pulse in terms of the num- 3.2. STATISTICALRESOLUTIONAND COUNT RATE ber of photoelectrons reaching the first dynode of PERFORMANCE OF A SYSTEMBASEDON THE the photomultiplier tube in unit time as follows: VARIABLE SAMPLING-TIMETECHNIQUE

the sampling of the integrated signal for the former pulse should be inhibited. Thus, the pulses followed by a pulse-free time interval longer than tb = t~+t~ can only produce the sampled outputs.

f

tS -- tc

(1)

I = (N/T) e x p ( - t / T ) ,

where N is the total number of photoelectrons of a scintillation event. If the shortened pulse is integrated, the mean integrated signal has a constant value given by: S = N [-1 - e x p ( - t c / T ) ] ,

(2)

We shall consider the statistical resolution of the sampled signal in the system shown in fig. 2 under the following assumptions • the energy spec1.8

Z

after a time t---to. In practice, however, the number of photoelec-

Input

C

;,~TN,

]

o_

t¢

_J"a

14. O

Output

T : 2so ns

\

1 ~6

•

=, O tO I.g n,.

O

K

65 O3 q

\

t c = 100 ns

e~

o

1.2

~

O

7 At = t o / 2

_1

U.

1.0

I 0

I

,

I

I 500

INTEGRATION

Fig. 3. A circuit of the delay-line pulse shortening.

I

I 1000

PERIOD:

ts

(ns)

Fig. 4. Factor of resolution loss in the fractional integration with delay-line pulse shortening.

462

E. TANAKA et al.

trum is mono-energetic, and signal pulses are sampled only when the pre- and post-pulse time intervals are longer than ta and tb, respectively, (ta, tb>tc). The waiting period (the maximum integration period) tw should be set at a value around 3 T - 4 T , but we here assume it to be infinitely long, and that an integrated signal is sampled at a time interval tr before the arrival of the following pulse, where rr is the time required for sampling and resetting of the integrator. To obtain the mean variance of the sampled signal amplitude, we have to consider the effect of all the preceding pulses which have non-zero variance during the integration period for the pulse of interest. First, we shall consider the mean variance of the sampled signal itself neglecting the effect of the preceding pulses. If a signal of interest is sampled at t = t~ the variance is given by ecl. (3). Denoting the post-pulse time interval by t,, we have ts = t l - t r . Since the probability distribution of t, is given by nexp(-ntl), where n is the input pulse rate, the expected variance of the sampled signal is given by Vm =

f:

Vdt,--/r) tl e-"" dtl

b

n e-"" dt l IJtb

= N(I - e -'~/r)

(

l - e -'~/r + ~

e -"~-'mr

)

.

(5) The factor of resolution loss R,, of the sampled signal itself is then given by

Rm

= x/V~/S = ( nT e-(tb-'~)/_~ "~I/x/N \1 + 1--+nT T ~ ) "

pulses on a sampled signal at the input pulse rate n is given by Vp --

V2(t I --tr) n e -nil dt I

n

e - ' t ' dt 1

I dtb

b

-- N(1 - e -'~/r) n T e -'°/r

I + ~

e

.

(9) The factor of resolution loss, Rp, due to the preceding pulses is then given by

x/Vp/S['nTe-t"/T[ " Ro =

1/4N

-

Li

(,

nT

)]~ "

+

(10) The overall factor of resolution loss is g =

(11)

The values of R, R m and Rp are plotted as a function of the input pulse rate in fig. 5 for typical parameters. In the above discussion, we have assumed a mono-energetic pulse-height distribution. However, if the distribution is not mono-energetic and the pulses of interest have a higher pulse-height by a factor of k as compared to the mean pulseheight of the distribution, eq. (11) should be replaced by 2 )- . R' = .,,/( ' RT~ v + Rp/k (12) Finally, we shall consider the count rate performance of the system. The sampled signal is usually held for a certain period th for energy analysis or position computation. Since the minimum pulse

(6) 2-0

Next, we shall consider the effect of the preceding pulses. The variance of the charge accumulated in a time interval t = 0 - q due to a preceding pulse having occurred at a time t = - r 2 is shown to be I/1 (t2) = N e - t 2 / T ( 1 - - e - t ~ / T ) (1 + e - i s / T ) . (7) Since a pulse of interest is only sampled when the pre-pulse interval, fi, is longer than t,, the mean total variance of all the pulses having occurred before a time t = - t ~ is given by

t/)

tc

ou) " Z 1.5 o

: 100 ns

/

t a : 200 ns t b - t r : 200 ns T 2s

~

2 ~

ffu

n VI(t2)

~ 0-S O I 50k

dt 2

= NnT e -t°/r (1 - e -tdr) (1 +e-'S/r).

100k

500k INPUT

(8)

Then, the mean variance of the effect of preceding

-

~ 1.0

O,O

V2(/s) =

-

PULSE

1M RATE

t

i 5M

(cps)

Fig. 5. Factor of resolution loss as a function of input pulse rate in the variable sampling-time technique. Rm: resolution loss due to the fractional integration, Rp: resolutiort loss due to the effect of preceding pulses, R: overall resolution loss.

463

VARIABLE S A M P L I N G - T I M E TECHNIQUE

interval of the sampled signals is equal to tb, when th tb, it may cause additional counting loss due to the non-paralyzable dead-time, th--tb. It should be noted, however, that an integrated signal maintains its amplitude during the waiting period tw, unless the following pulse occurs in this period. Then, if th <(t, +t~), the above function acts as a kind of buffer memory, and we can expect a much better count rate capability than expected f~om a simple combination of the paralyzable and non-paralyzable dead-times.

On the other hand, if we measure the charge accumulated in t = ts-oo, the variance will be given by replacing t2 and ts in eq. (7) by ts and ~ , respectively, as follows: ~ - (t~) = N(I - e -'=/r) e -'s/r.

Note that ~ _ ( q ) does not include the system variance because the mean amplitude of the signal in the time interval t = t s - ~ is zero. From eqs. (14)-(16), we have Vs- (t~) = Vs(t~) - ~,(oo).

where Vo is the system variance. The total variance in the full integration is given by putting q--, ~ in eq. (14): ~(oo) = N ( 1 - e - ' ° / r ) 2 + I%.

01

L-

LI _ _ _

(15)

---t

Fig. 6. Illustration of the variances of the signals integrated during three different periods.

(17)

Eq. (16) or (17) indicates that ~_(t~) Is a direct measure of the increase in statistical variance due to the fractional integration. The statistical component, V~(~), of the variance in the full integration is given by Vs(oO ) = N ( 1 - - e - t o ~ T )

3.3. STATISTICAL COMPONENT OF THE RESOLUTION Since a scintillation detector has the non-statistical system resolution as described in section 1, the factor of statistical resolution loss due to the fractional integration can not be determined directly from the measurement of the amplitude variance unless the fraction of the statistical component in the total (observed) variance has been determined. In this section, we shall describe a unique method to determine the statistical component experimentally. Suppose again an exponential scintillation pulse is shortened by a delay line with a clipping time tc, as shown in fig. 6. Since the charge accumulated in a time interval t = 0 - t ~ ( > t c ) has the statistical variance given by eq. (3), the total variance can be written as ~(t~) = N ( I - - e -to~T) ( I - e - t c / r + e - t s l r ) + Vo, (14)

(16)

2 = ( 1 - - e -'dr) Vs-(0),

(18)

where 9 - ( 0 ) is the extrapolated value of Vs_(q) at ts = 0. The total number N of photoelectrons accumulated is also estimated from the following relation: g = Fs- (0)/(1 --e-'°/r). (19) 4. Preliminary experiments with a NaI(TI) detector 4.1. SHORTENINGOF NaI(TI) PULSES The theoretical analysis described in section 3 is based on the assumption that the light intensity of a scintillator is expressed by a single exponential function. Unfortunately, however, this assumption does not hold for NaI(TI) crystals. Numerous investigations have been reported on the scintillation decay of the NaI(TI) crystalstl-~3), and the marked property is the existence of a flat portion of about 100 ns followed by an exponential decay with a time-constant of about 250 ns. Thus, the following experiments have been carried out to examine the effectiveness of the delay-line pulseshortening and to check the validity of the theoretical analysis. A system similar to the one shown in fig. 2 was constructed except for the pulse pile-up rejection circuits. In addition, a variable time delay unit was inserted in the trigger input of the univibrator to allow the delayed integration for the measurement of F~_ (ts). The detector was a NaI(TI) crystal of 3.8 cm diameter by 3.8 cm height coupled to a 5.1 cm diameter photomultiplier tube (HT.V R329). The detector pulses were amplified and shortened by the delay-line clipping circuit shown in fig. 3.

464

E. TANAKA et al.

Fig. 7. Photographs of pulse waveforms. The time-scale is 200 ns/div. (A) Original input pulse. (B) Delayed and shortened pulse. (C) Integrated signal (integration period is 1000 ns). (a) Pulse from the pulse generator. (b) NaI(TI) detector pulse for 57Co. (O NaI(TI) detector pulse for 57Co with the decay correction filter shown in fig. 8.

The clipping time was lOOns. The shortened pulses were delayed about 260 ns by a delay line (420.0 impedance) and fed to a gated integrator. The gated integrator and sample-and-hold circuit were designed in our laboratory. The sampled signals (500 ns width) were fed to a 4k channel pulseheight analyzer through a suitable pulse-shaping network. Prior to the experiments, our electronic system was tested using a pulser which generates exponential pulses having 30 ns rise-time and adjustable decay time constant. The pulser was triggered by a commercial random pulse generator (BNC Corp. DB-2). It was confirmed that our system works well beyond 500 kcps. The pulse waveforms are shown in fig. 7a, in which the input pulses, the delayed and shortened pulses and the integrated signals are demonstrated. Fig. 7b shows similar waveforms of the detector pulses obtained with a 57Co y-ray source (122 keV). We can see that the shortened pulses have a tail beyond 150 ns, and the integrated signals are rising until about 400 ns. This is apparent-lk

ly due to the peculiar decay property of the NaI(TI) crystal. To improve this, a simple RC high-pass filter was added as shown in fig. 8. The waveforms with this decay correction were quite satisfactory as shown in fig. 7c. The amplitudes of the sampled signals for the full energy peak were constant within +_2% for the integration period from 150 to 1200 ns. 4.2. STATISTICAL RESOLUTIONS

Experiments were performed to check eq. (17) for the NaI(TI) crystal irradiated with 24'Am ),-rays (59.5 keY). The values of Vs(ts) and V~_ (t~) were determined from the full width at half-maximum (fwhm) of the full energy peak as a function of ts. For the measurements of Vs_ (t 0, a small fraction of the integrator gate signal was superimposed to the signal pulse so that the sampled signal had a finite amplitude acceptable to the pulse-height analyzer, and the start of the integration was delayed with a fixed integration period of 1200 ns. The fast discriminator was set at the lower limit of the full energy peak. Fig. 9 shows the results obtained without the decay correction filter. In the figure, the measured variances are expressed as a relative value defined by the square of the ratio of fwhm to the mean amplitude of full integration (t~ = 1200 ns), that is: (

Fig. 8. Circuit of the delay line pulse shortening with the decay correction filter for the NaI(TI) detector.

fwhm )2 2.352 (variance) = N 2 ( I _e-t.¢/T) 2 amplitude of full integration

(20)

465

VARIABLE SAMPLING-TIME TECHNIQUE \

0.1

this energy or 4.9 photoelectrons per keV of photon energy. The results obtained with the RC filter for decay correction are shown in fig. 10. In this case, eq. (171 does not hold, because eq. (17) is deduced for a simple delay-line shortening. Instead, the values of ~(ts)-V~(1200) are on another exponential curve (broken line in fig. 10), which is larger than V~_(ts) obtained without the RC filter (fig. 9) by a factor of about 2.0. This implies that the use of the RC filter amplifies the resolution loss by a factor of vJ2.0 = 1.4. The factors of resolution loss obtained from the above experimental results are shown in fig. 11. The solid line shows the theoretical curve given by eq. (4) with t c = 1 0 0 n s and T = 2 2 7 n s , while the broken line shows the curve given by

tl.

2

~

0.01

0.001

I

WITHOUTRCFILTER

R~ = {1 + 21-e-'~/r/(1-e-'~zr)]} -a,

(21)

in which the amplification of resolution loss due to the RC filter is taken into account. The deviation of the data without the RC filter from the 0

500

ts Fig. the and riod

0.1

1000

I ns)

9. Variance of the NaI(TI)detector for 24JAm. ~s(ts) is variance of fractional integration in the period of O - t s , Vs_tts) is the variance of delayed integration in the peof t s - t s + 1200 ns.

It was confirmed that the resolution at the full integration was equal to that obtained with the conventional mode of pulse-height spectrometry. In fig. 9, the values of ~ ( t s ) - ~ - ( t s ) are also plotted. It can be seen that ~ ( t s ) - ~ _ (t~) is almost independent of q, which implies the validity of eq. (17). From fig. 9, the value of ~_(0) was estimated as 0.053 in terms of the quantity defined by eq. (20). In this estimation, we took the extrapolated value of the curve V~_(ts) at t~ = 25 ns because the integration gate was opened about 25 ns before the effective leading edge of the input signal to ensure the complete integration of the rising part of the signal. The decay time constant was also estimated to be 227 ns from the slope of the curve of ~_ (t~). Using these values in eqs. (18) and (19), we estimated that our detector has an overall resolution of 18.2% in fwhm which is composed of the statistical resolution of 13.7% and the system resolution of 11.9% for 59.5 keV. The total number of photoelectrons, N, is 292 for

o Z

O Z

LL U0 IH 0

2 ¢_

~

~s(ts)-V-~(12°°)

I

0.01

\ -r U.

°°

w z 0.001

WITHRCFILTER

N~ .t

w ,,J

w

,,

p,

I , ,

500

ts

,,

I

I

o00

,

( nsl

Fig. 10. Variance of the NaI(TI) detector for 241 Am with the decay correction filter shown in fig. 8. Vs(ts) is the variance of fractional integration in the period of 0 - t s, and Vs -(ts) is the variance of delayed integration in the period of ts - ts + 1200 ns.

466

F.. TANAKA et al.

(/)

ore, 2.0

~

Z O B I--

¢n

UJ

WITH RC FILTER WITHOUT RC FILTER

%

3 O

• ~'

~'

1.5

nIL O

2 ~ It-

1.0

I

I

--

INTEGRATION PERIOD :

.--.h -

! 000

500

ts

(nsl

Fig. 1 I. Factor of resolution loss due to the fractional integration. Solid line: theoretical curve given by eq. (4). Broken line: theoretical curve given by eq. (21) in which the effect of decay correction filter is taken into account.

theoretical curve for short integration periods ( < 4 0 0 ns) is considered to be caused by the fact that the effective number of photoelectrons decreases with the shortening of ts more rapidly than assumed because of the 100 ns plateau in the scintillation decay. Experiments were also made for 57Co y-rays. Since the full energy peak of 122 keV y-rays (85.4%) was disturbed by accompanying ),-rays of 136 keV (10.8%), the contributions of the latter on the pulse-height distributions were removed prior to the analysis. The overall resolution was 13.8%, the statistical resolution was 9.6%, and the system resolution was 9.9% in fwhm. The number of photoelectrons was 4.8 electrons per keV of photon energy. The characteristics of resolution loss due to the shortening of integration period were quite similar to those for 241Am y-rays. 5. Conclusion and discussion The theoretical analysis and the preliminary experiments predict the possibility of developing a new NaI(TI) spectrometer or gamma-camera accepting an input pulse rate beyond 1 Mcps without any resolution loss at low input pulse rate. In the present technique, the sampling time is controlled by each following pulse, but a simpler method will be feasible in which the integration period is controlled only by the average input pulse rate. The theoretical formulations have been made for the delay-line shortening, but these may be applicable for any other pulse shortening techniques

with some modifications. Furthermore, due to the lack of a sharp rise in the NaI(TI) scintillation pulses, a correction filter is required in the pulse shortening circuit to obtain a better count rate performance, but it will result in additional resolution loss. The use of excessive pulse shortening, however, may be limited by the temperature dependence 14) of the decay property of the NaI(TI) crystals. The change in the decay time constant may result in the base-line shift following the shortened pulses, which will not only affect the sampled signal amplitude but also cause pulse pile-up. Therefore, if the operating temperature of the detector is allowed to vary significantly, then a certain means of compensation must be incorporated in the pulse shortening circuit to keep the base-line shift as small as possible. This work was partly supported by a grant from the Ministry of Health and Welfare, Japan. The authors would like to thank Drs. Y. Umegaki, T. Hashizume and T. A. Iinuma for their kind encouragements and Messrs. T. Tomitani and M. Yamamoto for helpful discussions. References 1) H. S. Katzenstein, IEEE Trans. Nucl. Sci. NS-13 (1966) 527. 2) S. L. Blatt, J. Mahieux and D. Kohler, Nucl. Instr. and Meth. 60 (19681 221. 3) G. Amsel, R. Bosshard and C. Zajde, Nucl. Instr. and Meth. 71 (19691 1. 4) C. Brassard, Nucl. Instr. and Meth. 94 (1971) 301. 5) D. Vartsky, B. J. Thomas and V. Prestwich, Nucl. Instr. and Meth. 145 (19771 321. 6) G. Muehllehner, M. P. Buchin and J. H. Dudek, IEEE Trans. Nucl. Sci. NS-23 (19761 528. 7) j. R. Prescott, Nucl. Instr. and Meth. 22 (19631 256. 8) p. Onno and R. Bell, Nucl. Instr. and Meth. 17 (1962) 149. 9) H. O. Anger, Radioisotope cameras, instrumentation in nuclear medicine, vol. 1 (ed. G. J. Hine; Academic Press, New York, 19671. 10) E. Tanaka, T. Hiramoto and N. Nohara, J. Nucl. Med. 11 (19701 542. tl) F. J. Lynch, IEEE Trans. Nucl. Sci. NS-13 (1966) 140. t2) R. B. Owen, Nucleonics 17, no. 9 (1959) 92. 13) W. R. Wall and K. I. Roulston, IEEE Trans. Nucl. Sci. NS-15 (1968) 153. t4) E. J. Scheid, E. A. Kamykowski and F. R. Swanson, IEEE Trans. Nucl. Sci. NS-24 (1977) 168.