SECTOR OF THE ART
The present invention belongs to the field of detector
physics. It is a device which permits the position of the impact of a gamma ray
within a scintillator crystal to be determined, with a high resolution and an image
reconstruction with very low parallax error. It has applications in medical physics,
detector physics and astrophysics.

STATE OF THE ART
Methods for detecting gamma rays use the effects of radiation
on matter to obtain information on it and be able to characterise the radiation
field. There exist various types of gamma ray detectors characterised by the type
of materials used, standing out among which are those which use scintillating crystals.
Scintillation detectors use crystals (Nal, CsI, BGO, LSO, etc.) or liquids and their
functioning is based on the excitation of the scintillating material which releases
energy emitting photons in the visible energy range and in a quantity proportional
to the energy of the incident gamma ray. These photons can be detected by a detector
very sensitive to individual photons, which transform the light of the scintillator
crystal into an electric signal. Belonging to this group of photodetectors are photomultipliers
(PMT), avalanche photodiodes (APD), solid state photomultipliers (SSPM), visible
light photon counters (VLPC), hybrid photodiodes (HPD), silicon photomultipliers
(SiPM) and silicon photodiodes (PIN photodiodes). The information contained in the
signal provided by the photodetector depends very much on the type of said photodetector.
For example, a normal photomultiplier without spatial resolution only provides information
on the energy of the gamma ray, the interaction instant and its duration. Using
photodetectors with spatial resolution (the term position sensitive photodetector
and photodetector with spatial resolution used in this specification refers at all
times to photodetectors with intrinsic resolution or several photodetectors without
resolution grouped to form a position sensitive photodetector) will, in addition
to the above variables, also be able to determine the position of the impact of
the gamma ray. This latter information is indispensable for capturing gamma ray
images in two or three dimensions for their later analysis in a range of fields
(gamma cameras in astrophysics, gamma cameras in medical physics, PET, SPECT, calorimeters
in the physics of position sensitive particles, radiation monitors and Compton cameras).

The scintillator crystals can be continuous or pixeled.
Most designs of gamma ray detectors use pixeled crystals with a scintillator crystal
size reduced until an acceptable spatial resolution is obtained. This latter method
is very common in detectors used for positron emission tomography (PET).

Independently of their application, scintillator crystals
must always have a finite thickness in order to ensure that a high percentage of
gamma particles interact with the scintillator crystal. Said finite thickness implies
an indetermination in the interaction depth of the gamma ray along it. Not knowing
the interaction position of the gamma ray along the perpendicular of the entrance
window prevents one from distinguishing among possible lines of incidence which
do not have the same angle of incidence or which interact at different depths of
the crystal, which produces a *parallax error* (see figure 1).

In detectors with very thick scintillator crystals, a parallax
error is introduced when just the positions along the directions falling within
the entrance window of the photodetector are determined, since these two directions
are not sufficient for reconstructing the real line of incidence of the gamma ray.
To prevent this, the angle of incidence or the interaction depth must be known.
With current techniques of gamma ray detection it is completely impossible to measure
the angle of incidence in any way, which means that the interaction depth must necessarily
be determined. Nevertheless, there does not so far exist any gamma ray detector
whose resolution at the interaction depth is comparable to its spatial resolution
in the other dimensions, which means that an error is always introduced in the position
of the origin of the gamma ray.

The parallax error becomes more important the greater the
energy of the gamma ray, since thicker scintillator crystals are needed for being
able to record a high percentage of the gamma radiation.

For this reason, there exist different approaches for producing
a detector that provide information on the interaction depth. One of them is the
*phoswich* method *("Depth of* interaction *detector block for high
resolution positron emission tomography", Nutt Ronald, Andreaco Mark S., Casey Michael
E, Williams Charles W.,* US-Patent: US6288399, *"PET detector capable
of providing depth directional information", Yamamoto Seiichi,* JP Patent:
JP2000056023, see also "*A GSO depth of interaction* detector
*for PET", Yamamoto S., Ishibishi H.,* IEEE Transactions on Nuclear Science,
Vol. 45 No. 3 1998, *"Depth identification accuracy of* a three
*layer Phoswich PET detector module", Seldel J., Vaquero J.J., Siegel S., Gandler
W.R.; Green M.V.,* IEEE Transactions on Nuclear Science, Vol. 46 No. 3 1999),
in which different scintillator crystals are simultaneously used which are distinguished
in the time length of the scintillation signal. This difference is then used for
reconstructing the interaction depth. Another possibility is to introduce absorbent
layers between different layers of pixeled scintillators *("Means for measuring
the* depth interaction *of gamma-rays* in *scintillation crystals in*
order to *improve the spatial resolution of positron imaging systems", Thompson
Christopher,* US Patent: US5122667, "*A depth encoded PET detector",
Bartazkos P., Thompson C.J.,* IEEE Transactions on Nuclear Science, Vol. 38
No. 2 1991). The absorbent layers reduce the scintillation light by a specific
amount, from which the interaction depth can later on be deduced. In both cases,
the resolution at the interaction depth is moderate and is limited to values equal
to the dimension of the scintillation crystals and is therefore quantised. One method
(light-sharing) ("*An LSO Scintillator Array for a PET detector Module with depth
of interaction measurement", Huber J.S., Moses W.W., Andreaco M.S., Patterson O.,*
IEEE Transactions on Nuclear Science, Vol. 48 No. 3 2001, *"Depth of interaction
system in nuclear imaging", Chang Wei, Ordonez Caesar, Matthews Kenneth,*
US Patent: US6459085) which provides a measure of the unquantised interaction
depth is the use of additional photodetectors and the determination of that parameter
starting from the sharing out of the scintillation light between the two photodetectors.

There also exist detectors *("Depth-of-interaction normalisation
of signals for improved positioning, and energy resolution in scintillation camera",
Gagnon Daniel,* US-Patent: US5576546, *"Depth-of-interaction and other
high order moments filtering* for *improved detection in thick scintillation
crystals;" Dililippo Frank P., Gagnon Daniel,* US Patent: US5813983; "*A
depth-encoding Anger detector using scintillating fibers," Matthews Kenneth L.,
Lenoard Scott M., Ordonez Caesar E., Perysk Dennis E., Chang Wei,*
IEEE Transactions on Nuclear Science, Vol. 48 No. 4 2001) which use the width
of the distribution of the scintillation light for determining the interaction depth,
exploiting the fact that the scintillation light is distributed isotropically which
gives rise to different densities of light at different points of the scintillator.
As a result a distribution of scintillation light is obtained whose width permits
the interaction depth of the gamma ray to be deduced.

There are two methods known for determining the width.
The first is to calculate the standard deviation following the detection of the
quantity of light in different places using several photodetectors. These signals
are later digitised and the standard deviation is calculated starting from them
by means of specific software. Given that the photodetectors used so far are normally
of a dimension comparable to the actual width of the scintillation light, the variation
in standard deviation with depth is very small, which does not allow the depth to
be determined with precision. Also, a large number of electronic channels are needed
along with a considerable computational effort for doing this. The second method
avoids these problems by using optical fibres *(wavelength shifting fibres)*
which guide the light from the scintillator crystal towards an additional position
sensitive photodetector. With the aid of this additional photodetector and establishing
a detection threshold in the fibre, the width of the scintillation light distribution
can be estimated. Nevertheless, the light trapped in these fibres has very little
intensity, thereby it displays major statistical fluctuations which in turn prevents
any measurement of the interaction depth with precision.

Other ideas not classified in the above paragraphs can
be consulted in the following references: *"Scintillation detector* for
*three-dimensionally measuring the gamma-ray absorption position and* a
*position CT apparatus utilizing the Scintillation detector," Shimtzu Keiji, Omura
Tomohide, Uchida Hiroshi, Yamashita Takaji,* US Patent: US4823016, "Gamma
*ray imaging detector with three dimensional event posi tioning and method of
calculation", Knoll Glenn F., Engdahl John C., Rogers William* L, US Patent:
US6124595, *"Development of a depth of interaction detector for gamma-rays",
Liu H., Omura T., Wanalabe M., Yamashi ta T,* Nuclear Instruments & Methods
in Physics Research, Section A. Vol. 459 2001.

Moreover, the acquisition electronics forms an essential
part of any gamma ray detector. Its function is to convert the electric signals
provided by all the photodetectors into digital information accessible by computer,
which permits reconstruction of the images. To achieve this, the signals from the
photodetectors have to be digitised and used for calculating the information required
such as energy, position and depth of interaction. It is also possible to calculate
these same parameters of interest analogically and before digitisation, which drastically
reduces the number of electronic channels needed and consequently the cost and noise
of the electronics. For that end, different networks of resistances are used, both
one and two dimensional, such as Anger logic, the proportional resistance network
or a combination of both, the hybrid resistance network ("Simple Charge Division
Readouts for Imaging Scintillator Arrays using a Multi-Channel PMT", S. Siegel,
R.W. Silverman, Y. Shao, S.R. Cherry, IEEE Trans. Nucl. Sci. Vol. 43, No. 3,
June 1996). These circuits consist of a chain or matrix of resistances acting
as load dividers and connected to the photodetectors (or the different outputs in
the case of a position sensitive photodetector) and they instantaneously provide
the interaction point (centroid) and the energy of the gamma ray. On account of
its simplicity and low cost it is the method most used for the time being, though
no network provides information on the depth of interaction in its original design.
In the present invention modifications are proposed for the different networks of
resistances which also permit measurement of the second moment of the scintillation
light distribution with the same networks of resistances without losing energy and
the centroid.

The desirable thing is for the electronics to carry out
the processing very quickly, since the time used for the conversion contributes
to the dead time of the entire detector, which means that fast electronics allows
greater detection efficiency. It is also preferable to have electronics with the
minimum possible components since each component increases the cost of the whole
electronics and introduces a statistical error (electronic noise) which adds on
to the noise caused by the rest of the components. In general, electronic designs
which analogically calculate the parameters of interest (such as the networks of
resistances mentioned above) comply well with these two requirements but they normally
introduce systematic errors, while electronic designs which digitise the signals
before calculating the parameters are normally much slower and complicated, but
they permit systematic errors to be avoided in a better way.

With the present invention, the aim is to develop a gamma
ray detector with high resolution in the interaction depth and which we are going
to describe in the following section.

DESCRIPTION OF THE INVENTION
Brief description
This invention describes a design of gamma ray detector
characterised in that its structural elements are as follows: a continuous scintillator
crystal, a position sensitive photodetector and associated electronics intended
to calculate, in addition to the gamma ray energy and the position of its interaction
in the crystal, the interaction depth in said crystal from the standard deviation
of the scintillation light distribution.

Said gamma ray detector provides information on the three-dimensional
position of the interaction point of the gamma ray inside the continuous scintillator
crystal. Said information may be obtained electronically, in analog form and therefore
instantaneous, from the different moments of the scintillation light distribution.

Also described is a way of implementing said invention
by means of specific electronics characterised by analogically calculating the 1^{st}
moment of the distribution and simultaneously the 2^{nd} moment of the distribution
without affecting the calculation of the 1^{st} moment of the distribution.
In order to calculate the 2^{nd} moment a voltage adder is used in the interconnection
points of the resistances as shown in figure 4. The standard deviation starting
from the 2^{nd} moment is carried out by means of specific software.

Detailed description
The object of the invention is a gamma ray detector characterised
in that its structural elements are as follows: a continuous scintillator crystal,
a photodetector (photomultipliers (PMT), avalanche photodiodes (APD), solid state
photomultipliers (SSPM), visible light photon counters (VLPC), hybrid photodiodes
(HPD), silicon photomultipliers (SiPM) and silicon photodiodes (PIN photodiodes))
sensitive to position and associated electronics permitting, in addition to the
energy of the gamma ray and the positions of its interaction in the crystal, also
the depth of interaction therein to be calculated from the standard deviation of
the distribution of the scintillation light.

A diagram of the present invention can be seen in figure
3:

- 1) Continuous scintillator crystal
- 3) photodetector sensitive to the light from the scintillator crystal and to
position
- 5) electronics board permitting the interaction depth to be determined, 2) being
optical grease and 4) being the entrance window of the photomultiplier.

There do not exist any gamma ray detectors based on continuous
crystals and a single position sensitive photodetector which provide information
on the interaction depth of the gamma rays in the crystal.

The gamma ray detector with interaction depth coding provides
the three-dimensional position of the impact of the gamma ray inside the continuous
scintillator crystal instead of the two-dimensional position of normal gamma ray
detectors.

The scintillation light generated by the impact of the
gamma ray is distributed isotropically within the scintillation crystal, provided
it is continuous, and, by two-dimensional projection, it causes a characteristic
distribution in the entrance window of the position sensitive photodetector, where
the point with the highest density of light is the projection of the impact position.
Moving away from the plane of the entrance window of that point, the density of
the light decreases. This decrease contains information on the depth of interaction,
given that the light distribution becomes wider to the degree that the interaction
point moves away from the entrance window (see figures 1 and 2). From the statistical
point of view, this corresponds to an increase in standard deviation, which in turn
corresponds to the 2^{nd} moment of the distribution with respect to the
mean.

For the present invention to be able to use the scintillation
light distribution it is essential to use continuous crystals, since cuts in the
crystal or reflecting layers destroy the distribution. It is also necessary to use
segmented photodetectors, with the dimension of the segments being considerably
less than the width of the light distribution, in order to take samples of the distribution.

The distribution of the light in the entrance window of
the photodetector is made up of intervals of extension corresponding to the dimensions
of the same photodetector segments and will then be converted into electric signals.
This set of measurements can be used for the complete reconstruction of the light
distribution by means of adjustments or for the determination of characteristic
properties of the distribution (e.g., 1^{st} moment, 2^{nd} moment
and area). The 1^{st} moment is normally calculated with one of the possible
networks of resistances mentioned earlier (Anger logic, proportional resistance
network or their combination) and it is extracted from the network of resistances
in the form of currents linearly coded with the position of the centroid of the
two-dimensional projection, while the 2^{nd} moment is weighted up with
the distance between two elements of the detector and, together with the 1^{st}
moment, permits the reconstruction of the standard deviation following its digitisation.
Said standard deviation is automatically coded with the interaction depth of the
gamma ray.

In the case of position sensitive avalanche photodiodes
("Evaluation of a Position Sensitive Avalanche Photodiode for PET", K..C. Burr,
A. Ivan, J. LeBlanc, S. Zelakiewicz, D.L. McDaniel, C. L. Kim, A. Ganin, K.S. Shah,
R. Grazioso, R. Farrrell, J. Glodo, IEEE Transaction on Nuclear Science, Vol.
40, No. 4 August 2003), the photodiode contains a resistive layer which permits
currents linearly coded in position to be extracted at the four ends of the photodiode.
In this way, no coupled resistance network is required, since the resistive layer
replaces it and permits the calculation of the centroids starting from the four
currents extracted at the ends. Nevertheless, the position sensitive avalanche photodiodes
do not permit the computation of the 2^{nd} moment in their current form
and require modification equivalent to that required for the network of resistances
in order to permit measurement of the interaction depth.

Current theories on obtaining the interaction depth are
normally based on physical effects such as absorption of the scintillation light,
*light-sharing,* the extension of the scintillation light projection by means
of using optical fibres *(wavelength shifting fibres)* and additional detectors
or *phoswich* technology. The problems with these techniques, in all cases
are that not only are the resolutions moderate at the interaction depth but also
they are complicated and costly detectors to build and their electronics is complex.

The determination of the interaction depth in the present
invention permits correction of the two-dimensional position in the plane of the
entrance window determined by extraction of the centroid, since the centroid is
only an approximation to the real position and it depends on the distance from the
plane of the window of the photodetector to the position of the impact of the gamma
ray within the scintillator crystal.

Therefore, the determination of the interaction depth makes
it possible to reduce the parallax error and it will also improve the spatial resolution
of the gamma ray detector by means of a later correction using specific software.
This correction is possible because the dependence of the centroid with the interaction
depth can be parametrised analytically and, therefore, permits its compensation
once the interaction depth is known. For this form of constructive improvement,
the use of continuous scintillator crystals with large dimensions is unavoidable.
Owing to the segmented crystal design of the majority of gamma ray detectors providing
an estimate of the interaction depth, the same information does not allow any improvement
in the spatial resolution of the detector, since the distribution of the light is
destroyed in exchange for a better *light-yield.*

Obtaining the interaction depth with less error will allow
a more efficient reduction in the parallax error.

The gamma ray detector forming the object of the invention,
which provides information on the three-dimensional position of the interaction
point of the gamma ray inside the continuous scintillator crystal, is essentially
characterised in that the stated information is obtained electronically, in analog
form and therefore instantaneous, on the basis of the different moments of the scintillation
light distribution, detected with any position sensitive photodetector or array
of photodetectors.

The information on the interaction depth is obtained from
the standard deviation of the scintillation light distribution, a characteristic
of the scintillation light in detectors with continuous scintillation crystals.
Instead of multiple photodetectors, the proposed detector can use a single position
sensitive photodetector, with the size of the elements comprising it being less
than the typical width of the scintillation light distribution, which means that
a variation in the width causes an appreciable variation in the set of electric
signals from the single position sensitive photodetector.

Therefore, the detector proposed in this invention (see
figure 3) determines the two-dimensional position of the impact of the gamma ray
in the plane of the entrance window of the single position sensitive photodetector
and also the interaction depth of the gamma ray within the scintillator crystal,
with a single photodetector without any need to use additional detectors or scintillator
crystals.

An additional object of the present invention is a modification
to existing networks of resistances characterised by analogically computing the
1^{st} moment of the distribution which permits a simultaneous calculation
of the 2^{nd} moment of the distribution without affecting the computation
of the 1^{st} moment of the distribution. For the case of position sensitive
avalanche photodiodes, the modification is such that it uses the involved resistive
layer of these devices.

To calculate the 2^{nd} moment, in all cases a
voltage adder is used at the interconnection points of the resistances as shown
in figure 4. For the avalanche photodiodes electrical contacts would be connected
to the resistive layer of the PSAPD (see figure 5) in such way that the distance
between them is the same for each pair of contiguous contacts. These contacts supply
the signal for the adder. The number of such contacts is limited only by their size
and the size of the PSAPD. The calculation of the standard deviation starting from
the 2^{nd} moment is carried out by means of specific software.

That light distribution is converted into a current distribution
by a position sensitive photodetector and is analogically pre-processed by a network
of resistances directly connected to the outputs from the same photodetector which
simultaneously and without interference extracts the first and second moment of
that distribution.

In the present invention, the information on the 2^{nd}
moment of the light distribution, weighted with the distance between the elements
of the detector, is obtained from a network of resistances (Anger network, proportional
resistance network of mixture of them) modified with an analog adder.

The gamma ray detector that is proposed uses electronics
consisting of one of the possible modified networks of resistances which simultaneously
calculates the centroid corresponding to the 1^{st} moment of the distribution
of the scintillation light and which will be obtained in the usual way by an Anger,
proportional, or hybrid resistance network, and the 2^{nd} moment of the
scintillation light distribution which arrives at the entrance window of the position
sensitive photodetector (see figure 2). The 2^{nd} moment is an excellent
estimation of the interaction depth, with a resolution being obtained that is comparable
to the resolution of the centroid, since it permits the calculation of the standard
deviation of the light distribution.

The reading of the signals from the segmented photodetectors
is done in the present invention by means of a network of equal resistances connected
together (see figure 4) or, in the case of PSAPDs, with their resistive layer (see
figure 5). The currents injected in the inputs of the network are divided according
to the sharing of the resistances and depending on the position of the injection
point within that network. Next, the different fractions of each connection point
are superposed for being read at the two ends of the network (*J*_{1}
and *J*_{r} in figure 4). The superposition of the fractions
of the currents computes the centroid of the distribution of the light detected
by the photodetector. That information is, together with the area of the distribution,
the only information exploited in existing Anger detectors. In the case of PSAPDs,
the signal is established in the same way with the sole difference that the resistive
layer of the PSAPDs acts like a two-dimensional network of resistances that is continuous
instead of being discrete. The resistances which are seen by a current injected
in any point of the PSAPD with respect to the four outputs are proportional to the
distances between the injection point and the outputs.

Nevertheless, the same currents injected by the photodetector
into the network or the resistive layer cause potentials at the connection points
of the network of resistances, which are square coded with the position of the point
in that network. These voltages can be used for measuring properties of the distribution
as well as their 1^{st} moment and without destroying it, on condition that
the measurement of the voltages does not affect the currents produced by them.

The superposition of all the voltages at the different
connection points of the network of resistances corresponds to the 2^{nd}
moment of the light distribution. This sum will be used in this invention for calculating
the standard deviation of the light distribution. Although each one of the injected
currents causes voltages at all injection points of the network of resistances,
this fact does not destroy the square coding of the sum of the voltage, instead
it results solely in a multiplying factor independent of the position of the injected
current. The sum of the voltages can be extended to any number of anode segments,
provided the adder circuit is working correctly.

In the present case of the improved detector for gamma
rays with interaction depth coding, the sum carried out analogically signifies an
instantaneous calculation of the 2^{nd} moment and, therefore, it only requires
a small additional processing following its digitisation. Also, the determination
of the second moment in analog mode implies just a few supplementary electronic
devices since the square coding is established automatically by the network of resistances
or the resistive layer and the sum is performed with operational amplifiers. Therefore,
the modification of the possible networks of resistances or of the PSAPD gives rise
to insignificant costs.

Finally, the currents exiting from the ends of the networks
of resistances of from the PSAPD and the sum of the voltages at the interconnection
points are digitised in the usual way and processed by software. In particular,
the difference between the square of the 1^{st} moment and of the 2^{nd}
moment with the aim of determining the standard deviation has to be done by means
of specific software after their digitisation. Similarly, the reconstruction of
the interaction depth will be done starting from the standard deviation by means
of specific software.

Owing to the fact that the information on the interaction
depth will be obtained from the standard deviation of the light distribution according
to claim 1 and using improved interanodic networks according to claim 2, the information
obtained on the interaction depth will be continuous. In other words, the information
will not be quantised by the way it is obtained as in the *phoswich* method
or using absorbent layers between different crystals.

Neither scintillator crystals nor additional photodetectors
are needed for obtaining this information. There does not currently exist any detector
which provides information on interaction depth without using additional photodetectors
or crystals.

A particular object of the present invention is the use
of the device described above in producing a positron emission tomography camera
and in the production of a gamma camera, which permits the parallax error to be
considerably reduced.

An additional object of the present invention is the use
of the device described above in producing a detector for particle physics and astrophysics,
which permits the parallax error to be considerably reduced. The gamma ray detector
that has been described can be used for any situation in which the detection of
gamma rays (particles) needs to be known with greatest possible exactitude. In particle
physics, the energies of gamma rays cover a broad range of values. The parallax
error will be greater for higher energies in gamma ray detectors that use scintillators,
since their thickness has to be sufficiently large for guaranteeing a reasonable
efficiency. Particularly in research, detectors with excellent resolution are required,
a condition that is met by the gamma ray detector presented here, since it drastically
reduces the parallax error and permits the correction of the centroids using the
depth of interaction.

Another type of gamma ray detector is the Compton camera.
Its functioning principle consists of inducing Compton scattering within a target
in the form of a semiconductor block. This semiconductor is in turn a detector which
records the position of the scattering along with the energy transferred to the
target. The scattered gamma ray is recorded in a total absorption detector. This
detector has to completely absorb the scattered gamma ray and measure its remaining
energy along with the position of the absorption, and it normally uses scintillators
in combination with photodetectors. Owing to *Doppler Broadening,* the Compton
camera achieves an acceptable resolution only for gamma ray energies comparable
to 511 keV or more in positron emission tomography, which means that the absorption
detector requires very thick scintillator crystals which suffer from parallax error.
Also, while scattering detectors (semiconductors) can be very small in size, absorption
detectors have to cover a large angle. The gamma ray detector presented here meets
all these requirements of the absorption detectors, and can therefore be used in
Compton cameras.

DESCRIPTION OF THE FIGURES

- Figure 1: Explanation of parallax error: very thick scintillator (1); entrance
window for photodetector (2); spatial directions defined by the centroid (3) and
(4) ; of the gamma ray (5) ; line of real incidence of the gamma ray (8); other
possible lines of incidence (7), (9); perpendicular of the entrance windows (12);
parallax error (10); angle of incidence (6); interaction depth (11).
- Figure 2: Illustration of the distributions of the scintillation light for two
different interaction depths and the position of the detector elements (in one dimension
only, for reasons of clarity). Two different light distributions (1) and (2) with
their corresponding widths (&sgr;1) and (&sgr;2) and their corresponding centroids
c1 and c2; light-guides (3), segmented photodetector (4); modified Anger logic (5).
- Figure 3: Assembly diagram of the gamma ray detector with interaction depth
coding: continuous scintillator crystal (1); optical grease layer (2); segmented
photodetector (3), entrance window for photodetector (4); electronic board (5).
- Figure 4: Diagram of the interanodic network of resistances: currents injected
by the photodetector: Ji ; components of the network of resistances:
*R*_{rd}
; voltages at the interconnection points of the resistances *U*_{i}
*.*
- Figure 5: Implementation of measuring the second moment of the light distribution
for position sensitive avalanche photodiodes. A PSAPD is used which determines the
centroids of the light distribution in a known way starting from the output signals
A, B, ..., E. Since the PSAPD has a resistive layer which carries out the linear
coding of the currents extracted at the ends, the voltage that is generated along
the resistive layer of PSAPD caused by the currents will be square coded, always
provided the distances &dgr; between the points 1, 2, 3, 4, 5 (or more) where
the voltages are measured are the same between contiguous points. The voltages will
then be summed with an adder the same as that which would be used with resistance
networks. Optionally, power amplifiers can be used for the measurement points of
the voltages (1,2, ..., 5) in order to improve the result if the input impedance
of the adder is too low for ensuring that the information from the centroids will
not be destroyed.
- Figure 6: Example of embodiment of the invention for a position sensitive photomultiplier
of the multi-anode type with two-dimensional proportional resistance network and
one-dimensional adder.
- Figure 7: Example of embodiment of the invention for a position sensitive photomultiplier
of the crossed wire anodes or crossed plate anodes type with one-dimensional proportional
resistance network and one-dimensional adder.
- Figure 8: Example of embodiment of the invention for a position sensitive photomultiplier
of the multi-anode type with two-dimensional proportional resistance network and
two-dimensional adder.
- Figure 9: Example of embodiment of the invention for a position sensitive photomultiplier
of the multi-anode type with Anger resistance network and one-dimensional adder.

EXAMPLES OF EMBODIMENT OF THE INVENTION
Example 1: Gamma ray detector with interaction depth coding
for photomultipliers of the multi-anode type with two-dimensional proportional resistance
network and one-dimensional adder (Figure 6)
The mechanical assembly of the example is shown in figure
3. The detector will consist of a scintillator crystal, necessarily continuous and
very thick. This crystal is coupled on its polished side by means of optical grease
of intermediate refractive index to the entrance window of the photomultiplier.
The remaining sides of the scintillator crystal not coupled to the photomultiplier
are painted black (absorbent) to prevent the destruction of the shape of the scintillation
light distribution due to reflections of the light at the edges.

In the anodes of the photomultiplier, known as pads, currents
are injected proportional to the quantity of the fraction of scintillation light
in that zone of the entrance window. Said pads are separately connected to the connection
points of the resistances of the two-dimensional interanodic network (see figure
6). The two centroids are formed in a different way. First the centroid for the
"y" direction is formed by means of resistance chains Rd1. These currents are weighted
with the "y" position and are then collected by means of two resistance chains Rd2
which form the centroid for the "x" direction. Finally, they reach the outputs J1,
..., J4, where they are digitised in order to determine the two-dimensional position
of the impact.

Simultaneously, the currents weighted with the "x" position
produce voltages at the connection points of the networks formed by the resistances
Rd2, square coded with the position of the same point within the network of resistances.
The voltages are amplified by means of voltage monitors (Ub) in order to prevent
overly high current extractions from the network of resistances. Nevertheless, these
amplifiers are not strictly necessary for the functioning of the circuit and they
only serve to improve the measurement. Next, these voltages are added with equal
weight by means of an adder formed from the resistances Rs1 and Rs2 and an operational
amplifier Us, which at its output provides the 2^{nd} moment of the light
distribution. Following the digitisation it can be used for calculating the standard
deviation of the light distribution, using a simple arithmetic formula which relates
the voltages measured with their corresponding currents, depending solely on the
value of the resistance Rd2 and on the number of anodes of the photomultiplier.

It is sufficient to determine the standard deviation of
the light distribution along one direction only, since the distribution of the scintillation
light is approximately symmetric to the rotation with respect to any axis running
through the position of impact of the gamma ray. Nevertheless, the 2^{nd}
moment of the distribution will be determined twice, each of the two at one end
of the two-dimensional resistance network (see figure 6). Although this is not strictly
necessary, it leads to an improvement in the resolution due to calculation of the
mean of the two measurements of the interaction depth, owing to the fact that its
determination is not equally efficient for the entire plane of the entrance window.

Monte Carlo simulations have been conducted in order to
check the correct functioning of the described method, both for the distribution
of the scintillation light for a crystal and a typical detector, and for the electronic
circuit. As a result of a simulation for a supposed detector in positron emission
tomography (consisting of a continuous crystal of Lutetium OxyorthoSilicate and
a large area position sensitive photomultiplier), a resolution at the interaction
depth of 2.3 ± 0.5 mm was obtained for specific interactions.

Example 2: Gamma ray detector with interaction depth coding
for photomultipliers of the crossed wire anodes or crossed plate anodes type with
one-dimensional proportional resistance network and one-dimensional adder (Figure
7)
The mechanical assembly of the detector is the same as
in the previous case (see figure 3). Owing to the different shape of the anodes
(crossed wire anodes or crossed plate anodes), the network of resistances is of
another type. Two identical interanode networks are used that are entirely independent
of each other, each for one group of anodes corresponding to one spatial direction
(see figure 6).

The currents of the photomultiplier are injected in the
two networks of resistances in the inputs. The resistances referred to as "Rd" in
figure 6 calculate the centroids of the light distribution along the two space directions.
The operational amplifiers "Ub" in figure 6 are used as voltage monitors and the
resistances "Rs1" and "Rs2", together with the operational amplifiers "Us", form
the adder circuit. In this example too, the amplifiers "Ub" are not strictly necessary
for the functioning of the circuit and they only serve to improve the measurement.
The position of the interaction of the gamma ray within the scintillator crystal
will be able to be deduced from the currents "J1" to "J4" and the depth of interaction
from the square sum voltages (see figure 7).

The functioning principle of the network is analogous to
the previous example. The outputs from the photomultiplier for one spatial direction
are connected to the inputs known as "Anode Wire" (see figure 7). The first and
second moments are formed in the same way by means of sharing and superposition
of the injected currents.

Again, two samples of the standard deviation are taken
in order to minimise measurement error, with the mean of the two measurements being
evaluated. A resolution at the interaction depth of 2.5 ± 0.5 mm was obtained
for specific interactions by means of simulation.

Example 3: Gamma ray detector with interaction depth coding
for photomultipliers of the multi-anode type with one-dimensional proportional resistance
network and two-dimensional adder (Figure 8)
The mechanical assembly of the detector is the same as
in the previous cases (see figures 4 and 5). In the anodes of the photomultiplier,
known as pads (1...64), currents are injected proportional to the quantity of the
fraction of scintillation light in that zone of the entrance window. Said pads are
separately connected to the connection points of the resistances of the two-dimensional
interanodic network referred to as R-Net (1.. 64) and power amplifiers in order
to prevent overly high "Ub" current extractions (se figure 8). The centroids are
determined using the currents J1...J4 as in the example of embodiment 1. As in the
previous examples, the amplifiers are optional for improving the measurement and
are not strictly necessary for the correct functioning of the adder. The voltages
of the points R-Net (1...64) are added with the circuit formed from the "Us" amplifiers
and the "Rs" resistances thereby establishing the square sum signal which is proportional
to the second moment. Given that with this network more measurements are made of
the voltage coded in width of the light distribution, the measurement error will
therefore be less.

Example 4: Gamma ray detector with interaction depth coding
for photomultipliers of the multi-anode type with Anger resistance network and two-dimensional
adder (Figure 9)
The mechanical assembly of the detector is the same as
in the previous cases (see figures 4 and 5) but in this example of embodiment the
Anger network of resistances is used. In order to measure the centroids, the resistances
"Ra" and "Rc" are adjusted in such way that a linear coding is obtained of the currents
measured at points "A" and "C". In the same way, the resistances "Rb" and "Rd" are
adjusted in such way that a linear coding is obtained of the currents measured at
points "B" and "D" ("Part A" in Figure 9). This method of determination is used
in commercial gamma cameras. As in the proportional resistance network described
earlier, the linear coding of the currents causes a square coding of the voltages
at the connection points of the segment of the anodes ("Anode Pads") which once
again can be used to measure the second moment. For that reason, these voltages
are summed with the circuit formed by the amplifier "Us" and the resistances "Rs"
("Part B" in Figure 9) establishing the square sum signal which is proportional
to the second moment. Voltage monitors "Ub" can optionally be used for improving
the measurement as in the above examples. Given that with this network more measurements
are made of the voltage coded in width of the light distribution, the measurement
error will therefore be less.