82
but the ratio of picoseconds/cm does not (Figu
As far as linearity of time vs. axial path, the re
excellent (Figure 64), but the counting efficie
epm/uCi decreases by about 10% toward the ¢
the rod for reasons not entirely understood, bu’
likely related to absorptive, reflective and couplin
losses, the sum of which is not constant as the se
tion occurs throughout the rod. This variation
ciency ig inconvenient but unavoidable, since
mately, its equivalent will be met sooneror later
study concerning the human body, where the de:
efficiency will vary because of the unequal thicl
encountered throughout the length and width
body.
From this point on we will not consider displ:
{
Fic. 62.—Orthogonal projections and perspective trace of
skew path of light ray in cylindrical rod.
Nof(c) is the number of photoelectrons released
therefrom;
f(rir2) is a function of the rise and decay time of
the fluor;
f(r) is the effect of the dispersion in the total
electron transit time in the phototube and
of the fraction of each pulse utilized; and
f(Z) is the effeet of the dispersion of the light
photons traveling through the rod.
tems but consider instead that, once one identif
distribution of scintillation in the reds surroundi
body, one must consider which experimental para
contribute most to information concerning distri
of the radioactivity in the body. This problem
folding is essentially stated by the Fredholm eq
of the first kind or by its equivalent matrix eq
which, in the presence of experimental error, vie
proximate solutions of what are considered “il:
2"x2' PILOT B
with Al
It is possible to explain some of the experimental results
150-
PSEC/CM ROD
obtained if we recall the analysis of Potter® on the
conduction of light through optical fibers. In a eylindrical or square rod of length Z, the length of either a skew
or meridional ray1s proportional to Z/cos @, 6 being the
angle between the ray and the axis or a line parallel to
it. A meridional raywill stay in the same plane, whereas
square of their transit time measured in units of the
transit time of the axial ray.“ If one trips the circuits
with a smaller and smaller fraction of the pulse, one
selects predominantly the rays traveling the shortest
paths; hence the time per unit axial distance decreases,
but the spatial resolution (W1,;2) remains unchanged.
Hence, if one shifts a collimated point souree along the
rod, the number of cm per channel of the TAC* remains
insensitive to the fraction r of the pulse that is utilized,
* Time-amplitude converter.
140-
130-
120-7
CALC.FWHM-CM ROD
a skewray (Figure 62) will, in general, spiral down the
rod keeping, however, the angle 6 = constant and the
path length equal to 1,/cos @. These relationships obtain
irrespective of the magnitude of the cross section.
Since the rays emitted along the larger @’s will arrive
later, and the emissionis isotropic, it can be shown that
the instantaneous flux density will decrease as the
mylar reflector
l60-
ZERO POT. SET.
Fic. 63—Top, transit time per axial unit distan
bottom, spatial resolution as a function of fraction ©
utilized.
DOL
Alb bday
ot