O4
4
J
|
DISTRIBUTION f (x) COMPUTED
USING ONLY READINGS OVER
50 \— tHE BODY
(c) the position of the peaks in the eomp
|
™
7
_
50
cro
CONCLUSIONS
l
\fo
From the above, we nowdrawthe followi
sional conclusions:
(a) For the distribution f(z) considered hei
I
KE
'
o
=
2
oO
=
a
I
possible to obtain fairly accurate «
§
'
(+3 %) of total activity, net (integrated
in a certain interval Az and of the shap
if all the parameters involved in the prob.
as collimation, ete., are properly chosen
text above). This is true even if statistic
in g(x’) and K(z,x#’) are of the order of 5
to
WwW
>
E
a
—_
tu
Yr
\
I
\
1
1
l
|
_
I
\
1
1
\—_
!
(b The FWHMI of the kernel K(z,z’) does |
to influence the calculation of the total
instead it seems to affect the shape of f(z
net (integrated) activity in subintervals
practice, it is imposstble to recogni:
changes in the shapeof f(z) that are sepe
distances less than the FWHMandto «
i
I
\
60
Fic. 80-—Distribution {(z) computed using only readings
over the body,
I’. Tests on the Iterative Technique
In order to establish whether the iterative technique
reported elsewhere®? could lead to more accurate results
in the case of the distribution f(2) considered here and
in the case of the experimental parameters described
above, a program of calculations was undertaken for
FWHAI = 8.5 em and hk = 1 em. Theiteration was
stopped when f(x) became negative somewhere within
the interval (a,b), or when the error corresponding to
g(x’) reached the level of the expected error. The results
were deemed unsatisfactory inasmuch as
(a) the approximations were not converging;
(b) the amplitudes varied more than in the true
knowndistribution f(2)—in other words, oscillations in the solution were not betng dampened;
|
|
I
DISTRIBUTION f (x) COMPUTED
USING READINGS EXTENDING —BEYOND THE BODY
r
I
RELATIVE AMOUNT OF ACTIVITY
tained by taking readings beyond the interval (a,b) of
the actual distribution, and by requiring f(x) to vanish
outside this interval. The results for f(z} obtained with
and without readings beyond the actual distribution are
plotted respectively in Figures 80 and 81. These figures
showa clear improvement, of the shape of f(z) in the interval 0-14 em when additional values of g(z)' are used.
60
REAL DISTRIBUTION ——|
I
|
{
|
!
|
|
|
{
20t—
——= —_— =
Le
|
REAL DISTRIBUTION
i
°
= 40
ne
|
|
ae
F
=
ul
>
e
were erroneous since they were related
those apparent in g(x’); some of those
g(x’) were due to statistical error.
In conclusion, the results were consistent with
ments made elsewhere as to the experimental c
suitable for the success of iterative techniques.
I
|
|
J
0
10
20
Fig. 81—Distribution f(z)
tending beyond-the body.
30
40
50
computed using read