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An optical method for the precise determination of scattering angles in nuclear physics geometries
NUCLEAR
INSTRUMENTS
AND
METHODS
135 (I976) I45-I49;
©
NORTH-HOLLAND
PUBLISHING
CO.
AN O P T I C A L M E T H O D F O R T H E P R E C I S E D E T E R M I N A T I O N OF S C A T T E R I N G A N G L E S IN N U C L E A R P H Y S I C S G E O M E T R I E S A N D R E A S B O C K I S C H , PAUL-J1DRGEN D I C K E R S , W E R N E R K L E I N and A L A N M. K L E I N F E L D
L Phystkalisches Instttut, Universitat zu K6ln, 5 Koln 41, Germany Received 22 J a n u a r y 1976 and m revised f o r m 1 March 1976 In nuclear physics it is often necessary to determine absolute scattering angles with high accuracy. A n optical method IS described here, which allows the determination o f absolute angles with an error < +0.1 °, without reliance on precision machined parts.
1. Introduction
In nuclear physics one is frequently confronted with the problem of determining the absolute value of an angle, as illustrated in fig. 1. The angle (0) is determined by the incident beam direction, its intersection with the target plane (A) and the slit (S), which masks the detector. Quite often it is necessary to determine this angle within the confines of a scattering chamber and at the same time to perform this determination with a precision of better than +0.1 °. Such measurements have generally relied on either the nominal accuracy of some precision machined device (such as ,e.g. a precision rotatable table) and the corresponding alignment of this device with respect to the chamber geometry, or on-line techniques employing nuclear scattering or reactions. The method described below I[the rotating target (RT) method] was devised to avoid this reliance, and can be performed off-line. The experimental arrangement for which this angle determination was intended consisted of several surface barrier detectors mounted every 15 ° from 0 ° to 180 ° and positioned 10-20cm from the target axis. 'The incident ion beam direction was defined primarily by the 2" diam. entrance aperture of a quadrupole ,doublet lens located 3.5 m from the target and a 1.5 m m orifice placed about 7 cm before the target. The resulting maximum possible divergence of the incident
slit
beam direction
| T
large!
Fig. 1. Scheme o f the scattering geometry.
%.~
beam, corresponding to a uniform distribution of the beam intensity over the 2" aperture, was ___0.4° . However, since optimal focussing was found to correspond to the approximate centering of the intensity maximum of the beam in the 2" aperture and since measurements taken at different times were consistent it is believed that the effective divergence was probably of the order of _ 0.1 °.
2. Check measurements
To ascertain the reliability of the RT method, which is described in sect. 4, several additional independent determinations of the angles using more conventional approaches were performed. By first considering these check measurements, better appreciation of the RT method will be obtained. In the first method photographs of the chamber, containing the relevant angle defining components, were taken at a height of 1.5 m above the scattering plane. There were two versions of this technique: one using a well lit chamber and the other using a darkened chamber in which a laser beam, whose direction was defined by the above mentioned apertures, was reflected from a mirror placed in the target plane. The angles were determined from the lengths AC and BC, measured on photographic enlargements. The main limitations were due to the finite laser beam width and possible aberrations in the photographic and enlargement processes. In addition, in this method we were limited by the configuration of the scattering chamber to the angles shown in table 1, where the results of both versions and their averages are listed. Depending on the angle the accuracy is about +0.5 ° . The second type of measurement for which there were also two versions, was based on nuclear scattering kinematics. In version one a measurement of the elastic
146
ANDREAS
BOCKISCH
e t al.
TABLE I Scattering angles determined
Photographs ~
using the three methods
described in the text.
Nuclear elastic
Rotating target method
scattering
Posltlon F
Positron A
44.8 °
44.7°+0.2 °
44.4°4-0.1 °
59.6 °
59 7 ° ± 0 . 2 °
59 3 ° ± 0 . 1 °
44.3°:t:0.3 ° 59.0o 4 - 0 . 2 ~
74.9 ° __
74 7 ° ± 0 . 3 ° __
74 2 ° ± 0 . 1 ° 89.3°±0 1o
74 2 ° 4 - 0 2 °
74.2°4-0 1°
89.2°+0.2 °
89.3°+0.1 °
105.7 °
__
103.4°4-0.3 °
104 0 ° ± 0
2 '~
Average
44.4o+0.1 ' 5 9 . 3 o - l - 0 1°
103.T~+0 2
E s t i m a t e d e r r o r for all a n g l e s a b o u t 0.5 °
scattering of 63 MeV i s o from a thin target composed of a 10/~g/cm 2 layer of carbon, a 10 k~g/cm2 layer of Cu and a 5/~g/cm 2 layer of 2°9Bi. From the pulse height spectra obtained with surface barrier detectors the channel numbers of the elastic peaks Xc, and XB, may be related to the energies of the scattered ions by
aXcu+b aXB,+b
Eofc,(O) - AEc, Eofa,(O) - AEB,
(1)
where a and b are the analyser calibration constants, E 0 the incident beam energy y (0) is the two body kinematic function, AEcu, AEB, represent target and detector dead layer energy losses and effects due to vacuum polarization and screening due to the atomic electrons1). In the present case E 0 = 63 MeV ± 60 keV and AEcu and AEa, were (37+ 10) keV and (20_+ 5) keV respectively. It was also assumed that b = 0. However, since the energy defect of the detector is contained in b and may be appreciable [10(O300 keV2)] this will introduce the major uncertainty in the measurement. Due to the small cross sections for elastic scattering from Cu for angles greater than 60 ° the measurement was performed only for 45 ° and 60 ° and only the 60 ° data were analyzed. Taking the energy and channel positions (_+ 1) uncertainties into account 60.00_+0.3 ° was found. An arrangement was used in the second version which was largely independent of most of the uncertainties of the above method. The elastic scattering of 20 and 25 MeV 160 ions~ from thin layers of Al and Bi vacuum evaporated onto a 10 k t g / c m 2 carbon backing, was measured. Uncertainties in the difference of the incident projectile energies were minimized by holding the tandem terminal voltage fixed and varying the 90 ° analyzing magnet to obtain 1 6 0 3 + and 1604+ ions. Low incident bombarding energies were chosen in
order to obtain appreciable count rates for the elastic scattering from AI. The rapid decrease in the AI elastic cross section prevented the application of the measurement, even at these low energies, to angles greater than 75 °. In this method differences corresponding to the two incident energies are compared. Thus a ratio R may be expressed as R
-- XAI(2)
-- XAI(I)
XB,(2) - XB,(I) lEo(2) - Eo(l)] fa,(0) - ,dEAl
(2)
lEo(2) - Eo(l)] Yn,(0) - ~ E B I ' where the indices 1 and 2 correspond to the 20 and 25 MeV incident energies respectively and AE now corresponds to the differences in the quantities denoted by AE in eq. (l) and therefore have smaller uncertainties. The actual values of AE were very close to zero, i.e. 25 keV. Moreover, since differences are taken R is not affected by the energy zero intercept or calibration. Hence the ratio of channel differences is equal to a function whose only unknown is the angle 0. For the case considered here the sensitivity indicated by the percentage change of the ratio R per degree, was 1.6 for 45 °, 2.2 for 60 ° and 2.6 for 75 °. The channel differences ranged, as a function of 0, from 100 to 240 for A1 and from 330 to 365 for Bi. Up to and including 75 °, intensities were sufficient to determine the peak center of mass to better than _ 0.3 channels. And since the peak shapes for 20 and 25 MeV were identical, R could be determined with a precision of 0.34).5% corresponding to errors in the scattering angles of about 0.2 °. The results of this measurement (shown in table 1) are expected to be quite reliable. The main difficulties are the small intensity and, due to the low energy of the scattered particles, the poor resolution of the AI peak.
PRECISE
DETERMINATION
OF SCATTERING
3. Rotating target method
ANGLES
147
of the needle about the axis was less than ___0.2 mm. It should be emphasized that it is not essential that the target axis be precisely perpendicular to the scattering plane. The axis was rotated with an angular frequency of ~0.65 Hz using an electronically regulated motor that was coupled through a flexible drive to a reducer which was fixed to the target axis. Since the mirror rotated with angular frequency ~ 0 . 6 5 H z the spectrally reflected laser beam rotated with angular frequency ,-,1.3 Hz. As the laser beam spot moved across the slits (composed of 0.1 m m thick Ni foil whose beam exposed edges were electrolytically polished) a pulse was produced in the transistors. The LSTs were Valvo type BPX 25, having 1.5/~s rise times. Positioning of the transistors whose actual sensitive area is ,-~ 1 m m 2, could in principle lead to systematic errors. However, these transistors come with a light collecting lens of ~ 3 m m diam. which largely eliminates errors from this source, as confirmed by actual measurement as a function of lateral LST position. The timing signals were obtained by processing the LST outputs through an amplifier, Schmitt trigger and RS flip-flop combination. The RS outputs were then used to gate a 1 M H z counter. A block diagram of the relevant circuit elements is shown in fig. 3. The determination of 0 ° for either of the two laser beam directions was accomplished using the arrangements shown in fig. 2. Before impinging on the mirrortarget the incident beam passed through a 1 m m slit. In the 0 ° mirror position the beam was reflected by the beam splitter into the LST at Co or C'0. The autocollimation of the 1 m m slit limits the spread in the 0 ° position of the mirror to <0.05 °. The agreement between results obtained for both beam directions confirms this accuracy.
Of the methods discussed above version 2 of the second kind, is the one which appears to be most accurate in practical applications, being capable without special effort of about _ 0.2 ° precision. Its major drawback is the on-line requirement. The RT method which we will now discuss can be used off-line with similar or possibly greater accuracy. Referring to fig. 2 it is seen that the RT method employs a laser beam, reflected by a rotating mirror located in the target plane (T). The reflected light lS detected by light sensitive transistors (LST) placed behind the slits at C. The angle between two detectors is determined from the relation AO= 2ogAT, where co is the angular frequency of the mirror and At the time needed for the reflected beam to traverse the distance between transistors. Details of the method and results of the measurements will now be discussed. Measurements were performed for two different geometries. In the first, the laser (He-Ne, 1.0 mW) was positioned before the quadrupole lens aperture (A), so that the laser light followed the actual beam direction. In the second configuration (indicated by the dashed lines) the laser was positioned 1.5 m behind the target (at F) and hence the laser beam direction was antiparallel to the normal beam direction. Use of both geometries provided an excellent check of the symmetry of our arrangement. The laser beam was allowed to impinge on a mirror located at the target position and rotating with the target axis. The mirror, which was surface silvered and optically flat, was placed on the target holder so that the target holder axis and mirror surface coincided. The eccentricity of the target axis was checked with a telescope, by following the movement of a needle positioned on the target axis as it rotated about this axis. The observed wobble _ 60 ° LST
quadrupole
beam splitter
T /
beam splitter
,
, lens
f
8
.
mlrror m
R~
ol~ target pos. C 0 ° LST 3 5m
: :
.
.
.
.
.
.
.
<~--
faraday cup
[:7 Col
D
Fig. 2 A r r a n g e m e n t for the r o t a t i n g t a r g e t m e a s u r e m e n t S. s a m e sht as m fig. I, B, B ' d i a p h r a g m s w i t h a h o l e d i a m e t e r o f 1 m m .
148
A N D R E A S B O C K I S C H et aL
. . . . . .
BPX25
91k_~J ;k_.L~l_.~015
L
,.-J,
: I I I
"m ..... ~oo
:~
""
r
="
" ~
I "
5V
.....
BPX25
"91
~_220
;/x,l ! (" nI I =1_ I:i
I
k
/
,
l
9V.-~
li220
i
~ - ~ ;
015
SN 741
Y ~)
~°~
/2SN7t,O0
All ttonsLstors BSX 38 A
Fig. 3. Block diagram o f the electronics.
Since the angle determined is directly proportional to the angular frequency 09, the measurement accuracy will depend upon the integral value as well as the constancy of 09 over an entire period of rotation. The integral value of o9 was quite easy to determine, It is simply obtained from the time, at a given angle, for one complete rotation of the mirror. The results of a typical measurement are shown in fig. 4 and demonstrate the relative constancy of the integral value of 09 ( 0 . 6 5 0 H z _ 0 . 0 5 % ) and the statistical nature of the fluctuations. Constancy of 09 as a function of angle, 09(0), was checked uncoupling the target axis and drive and then freely rotating the axis. Any lnhomogenities
in 09(0) should therefore be shifted to new angles. Within the measurement accuracy, the obtained values of 0 were independent of this procedure. 4. Measurement procedure and checks Actual measurements were performed by obtaining the start signal from the LST located at 0 and the stop signal from the 0 ° L S T . This procedure was proceeded
90 °
t-
sec
9 680
"-5 6 •
• 9 670
D
10
15
20
ms
.
• •
0050
•
oil
(b)
.
i'5°
It)
JE:
¢-
0*
. . . . . . .
Jgger
threshold
i 9.660
,
,
,
,
I
,
,
,
i
[
i
,
,
,
I
i
1o
a
i
t
f
20 number
Fig. 4. Results o f a measurement series (20 measurements) o f the period o f rotation,
,
,
2
,
,
t.
,
,
,
i
i
6 8 ms
i
i
0
i
2
i
i
t, ms
Fig. 5. LST output signals; (a) untnggered, (b) and (c) triggered by the counter gate signal.
PRECISE DETERMINATION
and followed by measurements of o~ and was repeated about 20 times at each angle. Much of the uncertainty in the method is related to the complex LST output pulse form. The intrinsic response of the LST itself (1.5 ps rise time) does not contribute to this uncertainty. Rather, diffraction of the laser beam by the 1 mm collimating slits, the finite width of the angle defining slits and the intensity profile of the beam itself are the most important problems. A typical output pulse, which demonstrates the seriousness of the diffraction effects is shown in fig. 5a. Separation of secondary maxima (about 4 ms) agrees well with the simple diffraction (d sin ( 0 ) = 2 ) estimate using 2 = 6328 A, d - 1 mm and a distance between the 1 mm collimator and LST of ~50 cm. With 0 ~ 0 . 6 5 Hz typical pulse widths (fwhm) are about 10 ms, corresponding to an angular width of ,~0.5 °. In order to determine the time difference corresponding to the primary maxima of the pulses it was necessary to correct each angle for the time difference between the gate signal and the maximum. For each angle this time difference was determined by measuring the LST output using a storage scope triggered by the RS flip-flop output. The 45 ° case is shown in fig. 5b where it is seen that the trigger thereshold is rather high (0.6~.8 mV). In applying this correction it was assumed that the central maximum corresponds to the same relative position of the laser pulse maximum and the center of the slit at each angle. Reproducibility was monitored by determining this correction at various times during the measurement, for different I_,STs and for both laser positions. To insure that the error due to the finite width of the angle defining slits is minimized, these slits were
OF S C A T T E R I N G
ANGLES
149
dosed down, with the exception of 0 °, to the widths between 0.1 and 0.5 mm. It is clear that if the slit width is of the same order as the beam profile width considerable averaging of the pulse form will result. This as seen from the pulse forms in fig. 5c seems to be the case for several angles and has to do with a combination of slightly varying slit widths and different distances from the target. The latter are proportional to the separation of the diffraction maxima. Hence the factors contributing the most to the pulse form width are the intrinsic laser profile plus the effects of diffraction. In all, we concluded that the maximum of the pulse form could be determined to better than +0.5 ms which corresponds to about _ 0.02 °. 5. Discussion of the results
The final results including time intervals, angles and errors for each laser position and the average of the two have been arranged in table 1. As this table demonstrates, the RT method is more accurate than the other methods mentioned above and can, in addition, be used off-line. Aside from automatization at various steps in the procedure improvements are to be sought in the axial drive for the rotating mirror. This can be achieved by coupling a syncronized motor directly to the axis. Fluctuations in the angular frequency of less than 0.1% should be achievable. The other factor which limits the accuracy is the finite beam profile and the attendent uncertainty in the timing signal. Appreciable improvements either through laser construction or a smaller wavelength source are not expected. Improvements should therefore be sought in the determination of the peak maximum, primarily through a more detailed analysis of the pulse form.
INSTRUMENTS
AND
METHODS
135 (I976) I45-I49;
©
NORTH-HOLLAND
PUBLISHING
CO.
AN O P T I C A L M E T H O D F O R T H E P R E C I S E D E T E R M I N A T I O N OF S C A T T E R I N G A N G L E S IN N U C L E A R P H Y S I C S G E O M E T R I E S A N D R E A S B O C K I S C H , PAUL-J1DRGEN D I C K E R S , W E R N E R K L E I N and A L A N M. K L E I N F E L D
L Phystkalisches Instttut, Universitat zu K6ln, 5 Koln 41, Germany Received 22 J a n u a r y 1976 and m revised f o r m 1 March 1976 In nuclear physics it is often necessary to determine absolute scattering angles with high accuracy. A n optical method IS described here, which allows the determination o f absolute angles with an error < +0.1 °, without reliance on precision machined parts.
1. Introduction
In nuclear physics one is frequently confronted with the problem of determining the absolute value of an angle, as illustrated in fig. 1. The angle (0) is determined by the incident beam direction, its intersection with the target plane (A) and the slit (S), which masks the detector. Quite often it is necessary to determine this angle within the confines of a scattering chamber and at the same time to perform this determination with a precision of better than +0.1 °. Such measurements have generally relied on either the nominal accuracy of some precision machined device (such as ,e.g. a precision rotatable table) and the corresponding alignment of this device with respect to the chamber geometry, or on-line techniques employing nuclear scattering or reactions. The method described below I[the rotating target (RT) method] was devised to avoid this reliance, and can be performed off-line. The experimental arrangement for which this angle determination was intended consisted of several surface barrier detectors mounted every 15 ° from 0 ° to 180 ° and positioned 10-20cm from the target axis. 'The incident ion beam direction was defined primarily by the 2" diam. entrance aperture of a quadrupole ,doublet lens located 3.5 m from the target and a 1.5 m m orifice placed about 7 cm before the target. The resulting maximum possible divergence of the incident
slit
beam direction
| T
large!
Fig. 1. Scheme o f the scattering geometry.
%.~
beam, corresponding to a uniform distribution of the beam intensity over the 2" aperture, was ___0.4° . However, since optimal focussing was found to correspond to the approximate centering of the intensity maximum of the beam in the 2" aperture and since measurements taken at different times were consistent it is believed that the effective divergence was probably of the order of _ 0.1 °.
2. Check measurements
To ascertain the reliability of the RT method, which is described in sect. 4, several additional independent determinations of the angles using more conventional approaches were performed. By first considering these check measurements, better appreciation of the RT method will be obtained. In the first method photographs of the chamber, containing the relevant angle defining components, were taken at a height of 1.5 m above the scattering plane. There were two versions of this technique: one using a well lit chamber and the other using a darkened chamber in which a laser beam, whose direction was defined by the above mentioned apertures, was reflected from a mirror placed in the target plane. The angles were determined from the lengths AC and BC, measured on photographic enlargements. The main limitations were due to the finite laser beam width and possible aberrations in the photographic and enlargement processes. In addition, in this method we were limited by the configuration of the scattering chamber to the angles shown in table 1, where the results of both versions and their averages are listed. Depending on the angle the accuracy is about +0.5 ° . The second type of measurement for which there were also two versions, was based on nuclear scattering kinematics. In version one a measurement of the elastic
146
ANDREAS
BOCKISCH
e t al.
TABLE I Scattering angles determined
Photographs ~
using the three methods
described in the text.
Nuclear elastic
Rotating target method
scattering
Posltlon F
Positron A
44.8 °
44.7°+0.2 °
44.4°4-0.1 °
59.6 °
59 7 ° ± 0 . 2 °
59 3 ° ± 0 . 1 °
44.3°:t:0.3 ° 59.0o 4 - 0 . 2 ~
74.9 ° __
74 7 ° ± 0 . 3 ° __
74 2 ° ± 0 . 1 ° 89.3°±0 1o
74 2 ° 4 - 0 2 °
74.2°4-0 1°
89.2°+0.2 °
89.3°+0.1 °
105.7 °
__
103.4°4-0.3 °
104 0 ° ± 0
2 '~
Average
44.4o+0.1 ' 5 9 . 3 o - l - 0 1°
103.T~+0 2
E s t i m a t e d e r r o r for all a n g l e s a b o u t 0.5 °
scattering of 63 MeV i s o from a thin target composed of a 10/~g/cm 2 layer of carbon, a 10 k~g/cm2 layer of Cu and a 5/~g/cm 2 layer of 2°9Bi. From the pulse height spectra obtained with surface barrier detectors the channel numbers of the elastic peaks Xc, and XB, may be related to the energies of the scattered ions by
aXcu+b aXB,+b
Eofc,(O) - AEc, Eofa,(O) - AEB,
(1)
where a and b are the analyser calibration constants, E 0 the incident beam energy y (0) is the two body kinematic function, AEcu, AEB, represent target and detector dead layer energy losses and effects due to vacuum polarization and screening due to the atomic electrons1). In the present case E 0 = 63 MeV ± 60 keV and AEcu and AEa, were (37+ 10) keV and (20_+ 5) keV respectively. It was also assumed that b = 0. However, since the energy defect of the detector is contained in b and may be appreciable [10(O300 keV2)] this will introduce the major uncertainty in the measurement. Due to the small cross sections for elastic scattering from Cu for angles greater than 60 ° the measurement was performed only for 45 ° and 60 ° and only the 60 ° data were analyzed. Taking the energy and channel positions (_+ 1) uncertainties into account 60.00_+0.3 ° was found. An arrangement was used in the second version which was largely independent of most of the uncertainties of the above method. The elastic scattering of 20 and 25 MeV 160 ions~ from thin layers of Al and Bi vacuum evaporated onto a 10 k t g / c m 2 carbon backing, was measured. Uncertainties in the difference of the incident projectile energies were minimized by holding the tandem terminal voltage fixed and varying the 90 ° analyzing magnet to obtain 1 6 0 3 + and 1604+ ions. Low incident bombarding energies were chosen in
order to obtain appreciable count rates for the elastic scattering from AI. The rapid decrease in the AI elastic cross section prevented the application of the measurement, even at these low energies, to angles greater than 75 °. In this method differences corresponding to the two incident energies are compared. Thus a ratio R may be expressed as R
-- XAI(2)
-- XAI(I)
XB,(2) - XB,(I) lEo(2) - Eo(l)] fa,(0) - ,dEAl
(2)
lEo(2) - Eo(l)] Yn,(0) - ~ E B I ' where the indices 1 and 2 correspond to the 20 and 25 MeV incident energies respectively and AE now corresponds to the differences in the quantities denoted by AE in eq. (l) and therefore have smaller uncertainties. The actual values of AE were very close to zero, i.e. 25 keV. Moreover, since differences are taken R is not affected by the energy zero intercept or calibration. Hence the ratio of channel differences is equal to a function whose only unknown is the angle 0. For the case considered here the sensitivity indicated by the percentage change of the ratio R per degree, was 1.6 for 45 °, 2.2 for 60 ° and 2.6 for 75 °. The channel differences ranged, as a function of 0, from 100 to 240 for A1 and from 330 to 365 for Bi. Up to and including 75 °, intensities were sufficient to determine the peak center of mass to better than _ 0.3 channels. And since the peak shapes for 20 and 25 MeV were identical, R could be determined with a precision of 0.34).5% corresponding to errors in the scattering angles of about 0.2 °. The results of this measurement (shown in table 1) are expected to be quite reliable. The main difficulties are the small intensity and, due to the low energy of the scattered particles, the poor resolution of the AI peak.
PRECISE
DETERMINATION
OF SCATTERING
3. Rotating target method
ANGLES
147
of the needle about the axis was less than ___0.2 mm. It should be emphasized that it is not essential that the target axis be precisely perpendicular to the scattering plane. The axis was rotated with an angular frequency of ~0.65 Hz using an electronically regulated motor that was coupled through a flexible drive to a reducer which was fixed to the target axis. Since the mirror rotated with angular frequency ~ 0 . 6 5 H z the spectrally reflected laser beam rotated with angular frequency ,-,1.3 Hz. As the laser beam spot moved across the slits (composed of 0.1 m m thick Ni foil whose beam exposed edges were electrolytically polished) a pulse was produced in the transistors. The LSTs were Valvo type BPX 25, having 1.5/~s rise times. Positioning of the transistors whose actual sensitive area is ,-~ 1 m m 2, could in principle lead to systematic errors. However, these transistors come with a light collecting lens of ~ 3 m m diam. which largely eliminates errors from this source, as confirmed by actual measurement as a function of lateral LST position. The timing signals were obtained by processing the LST outputs through an amplifier, Schmitt trigger and RS flip-flop combination. The RS outputs were then used to gate a 1 M H z counter. A block diagram of the relevant circuit elements is shown in fig. 3. The determination of 0 ° for either of the two laser beam directions was accomplished using the arrangements shown in fig. 2. Before impinging on the mirrortarget the incident beam passed through a 1 m m slit. In the 0 ° mirror position the beam was reflected by the beam splitter into the LST at Co or C'0. The autocollimation of the 1 m m slit limits the spread in the 0 ° position of the mirror to <0.05 °. The agreement between results obtained for both beam directions confirms this accuracy.
Of the methods discussed above version 2 of the second kind, is the one which appears to be most accurate in practical applications, being capable without special effort of about _ 0.2 ° precision. Its major drawback is the on-line requirement. The RT method which we will now discuss can be used off-line with similar or possibly greater accuracy. Referring to fig. 2 it is seen that the RT method employs a laser beam, reflected by a rotating mirror located in the target plane (T). The reflected light lS detected by light sensitive transistors (LST) placed behind the slits at C. The angle between two detectors is determined from the relation AO= 2ogAT, where co is the angular frequency of the mirror and At the time needed for the reflected beam to traverse the distance between transistors. Details of the method and results of the measurements will now be discussed. Measurements were performed for two different geometries. In the first, the laser (He-Ne, 1.0 mW) was positioned before the quadrupole lens aperture (A), so that the laser light followed the actual beam direction. In the second configuration (indicated by the dashed lines) the laser was positioned 1.5 m behind the target (at F) and hence the laser beam direction was antiparallel to the normal beam direction. Use of both geometries provided an excellent check of the symmetry of our arrangement. The laser beam was allowed to impinge on a mirror located at the target position and rotating with the target axis. The mirror, which was surface silvered and optically flat, was placed on the target holder so that the target holder axis and mirror surface coincided. The eccentricity of the target axis was checked with a telescope, by following the movement of a needle positioned on the target axis as it rotated about this axis. The observed wobble _ 60 ° LST
quadrupole
beam splitter
T /
beam splitter
,
, lens
f
8
.
mlrror m
R~
ol~ target pos. C 0 ° LST 3 5m
: :
.
.
.
.
.
.
.
<~--
faraday cup
[:7 Col
D
Fig. 2 A r r a n g e m e n t for the r o t a t i n g t a r g e t m e a s u r e m e n t S. s a m e sht as m fig. I, B, B ' d i a p h r a g m s w i t h a h o l e d i a m e t e r o f 1 m m .
148
A N D R E A S B O C K I S C H et aL
. . . . . .
BPX25
91k_~J ;k_.L~l_.~015
L
,.-J,
: I I I
"m ..... ~oo
:~
""
r
="
" ~
I "
5V
.....
BPX25
"91
~_220
;/x,l ! (" nI I =1_ I:i
I
k
/
,
l
9V.-~
li220
i
~ - ~ ;
015
SN 741
Y ~)
~°~
/2SN7t,O0
All ttonsLstors BSX 38 A
Fig. 3. Block diagram o f the electronics.
Since the angle determined is directly proportional to the angular frequency 09, the measurement accuracy will depend upon the integral value as well as the constancy of 09 over an entire period of rotation. The integral value of o9 was quite easy to determine, It is simply obtained from the time, at a given angle, for one complete rotation of the mirror. The results of a typical measurement are shown in fig. 4 and demonstrate the relative constancy of the integral value of 09 ( 0 . 6 5 0 H z _ 0 . 0 5 % ) and the statistical nature of the fluctuations. Constancy of 09 as a function of angle, 09(0), was checked uncoupling the target axis and drive and then freely rotating the axis. Any lnhomogenities
in 09(0) should therefore be shifted to new angles. Within the measurement accuracy, the obtained values of 0 were independent of this procedure. 4. Measurement procedure and checks Actual measurements were performed by obtaining the start signal from the LST located at 0 and the stop signal from the 0 ° L S T . This procedure was proceeded
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Fig. 4. Results o f a measurement series (20 measurements) o f the period o f rotation,
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Fig. 5. LST output signals; (a) untnggered, (b) and (c) triggered by the counter gate signal.
PRECISE DETERMINATION
and followed by measurements of o~ and was repeated about 20 times at each angle. Much of the uncertainty in the method is related to the complex LST output pulse form. The intrinsic response of the LST itself (1.5 ps rise time) does not contribute to this uncertainty. Rather, diffraction of the laser beam by the 1 mm collimating slits, the finite width of the angle defining slits and the intensity profile of the beam itself are the most important problems. A typical output pulse, which demonstrates the seriousness of the diffraction effects is shown in fig. 5a. Separation of secondary maxima (about 4 ms) agrees well with the simple diffraction (d sin ( 0 ) = 2 ) estimate using 2 = 6328 A, d - 1 mm and a distance between the 1 mm collimator and LST of ~50 cm. With 0 ~ 0 . 6 5 Hz typical pulse widths (fwhm) are about 10 ms, corresponding to an angular width of ,~0.5 °. In order to determine the time difference corresponding to the primary maxima of the pulses it was necessary to correct each angle for the time difference between the gate signal and the maximum. For each angle this time difference was determined by measuring the LST output using a storage scope triggered by the RS flip-flop output. The 45 ° case is shown in fig. 5b where it is seen that the trigger thereshold is rather high (0.6~.8 mV). In applying this correction it was assumed that the central maximum corresponds to the same relative position of the laser pulse maximum and the center of the slit at each angle. Reproducibility was monitored by determining this correction at various times during the measurement, for different I_,STs and for both laser positions. To insure that the error due to the finite width of the angle defining slits is minimized, these slits were
OF S C A T T E R I N G
ANGLES
149
dosed down, with the exception of 0 °, to the widths between 0.1 and 0.5 mm. It is clear that if the slit width is of the same order as the beam profile width considerable averaging of the pulse form will result. This as seen from the pulse forms in fig. 5c seems to be the case for several angles and has to do with a combination of slightly varying slit widths and different distances from the target. The latter are proportional to the separation of the diffraction maxima. Hence the factors contributing the most to the pulse form width are the intrinsic laser profile plus the effects of diffraction. In all, we concluded that the maximum of the pulse form could be determined to better than +0.5 ms which corresponds to about _ 0.02 °. 5. Discussion of the results
The final results including time intervals, angles and errors for each laser position and the average of the two have been arranged in table 1. As this table demonstrates, the RT method is more accurate than the other methods mentioned above and can, in addition, be used off-line. Aside from automatization at various steps in the procedure improvements are to be sought in the axial drive for the rotating mirror. This can be achieved by coupling a syncronized motor directly to the axis. Fluctuations in the angular frequency of less than 0.1% should be achievable. The other factor which limits the accuracy is the finite beam profile and the attendent uncertainty in the timing signal. Appreciable improvements either through laser construction or a smaller wavelength source are not expected. Improvements should therefore be sought in the determination of the peak maximum, primarily through a more detailed analysis of the pulse form.