METHOD FOR THE SIGNAL PROCESSING OF A PHOTOSENSOR

Abstract

A method for photosensor signal processing includes carrying out, by measuring a combination of readout channels of a direction e with linearly increasing and linearly decreasing signal strength, a linear coding in at least one e-direction. The linearly increasing and linearly decreasing signal strengths of readout channels of the direction e, which are respectively used for the linear coding, are multiplied by each other. The linear coding satisfies the following edge condition: Q.sub.1(e)=c.sub.1.Math.e.sup.c2+c.sub.3, Q.sub.2(e)=c.sub.4.Math.e.sup.c5+c.sub.6, c.sub.1=const.(0, ), c.sub.4=const.(, 0), c.sub.3, c.sub.6=const.(, ), and 0.5<c.sub.2; c.sub.5<1.5. Q1 denotes the charge of the output channel signal strengths increasing via the e-position, and Q2 denotes the charge of the output channel signal strengths decreasing via the e-position and the coding direction.

Claims

1: A method for photosensor signal processing, the method comprising: carrying out, by measuring a combination of readout channels of a direction e with linearly increasing and linearly decreasing signal strength, a linear coding in at least one e-direction, wherein the linearly increasing and linearly decreasing signal strengths of readout channels of the direction e, which are respectively used for the linear coding, are multiplied by each other, wherein the linear coding satisfies the edge condition:
Q.sub.1(e)=c.sub.1.Math.e.sup.c2+c.sub.3
Q.sub.2(e)=c.sub.4.Math.e.sup.c5+c.sub.6
c.sub.1=const.(0,)
c.sub.4=const.(,0)
c.sub.3,c.sub.6=const.(,)
0.5<c.sub.2; c.sub.5<1.5, wherein Q.sub.1 denotes the charge of the output channel signal strengths increasing via the e-position; and Q.sub.2 denotes the charge of the output channel signal strengths decreasing via the e-position and the coding direction, and wherein the depth of interaction is approximated using: ${}_{\mathrm{light}}^2=\frac{{}_2}{{}_0}-\frac{{}_1^2}{{}_0^2}$ and associated calibration measurements from a first moment of the e-direction and a linear transformation of a second moment of the e-direction.

2: The method according to claim 1, wherein a linear coding in an x-direction is carried out via signals of output channels A and B according to: $x=\frac{Q_A-Q_B}{Q_A+Q_B},$ and wherein signals of output channels A and B are multiplied by each other and/or in which a linear coding in the y-direction is carried out via signals of output channels C and D according to: $y=\frac{Q_C-Q_D}{Q_C+Q_D},$ and wherein the signals of output channels C and D are multiplied by each other.

3: The method according to claim 1, wherein four readout channels with outputs E, F, G, and H are used for the linear coding, each of the four readout channels contributing to the linear coding in an x-direction and a y-direction, wherein a linear coding for the x-direction is carried out via signals according to: x=((Q.sub.F+Q.sub.H)(Q.sub.E+Q.sub.G))/(Q.sub.E+Q.sub.F+Q.sub.G+Q.sub.H), and/or wherein a linear coding in the y-direction is carried out via signals according to: y=((Q.sub.E+Q.sub.F)(Q.sub.G+Q.sub.H))/(Q.sub.E+Q.sub.F+Q.sub.G+Q.sub.H), and wherein signals for the coding of the x-direction according to: (Q.sub.F+Q.sub.H)*(Q.sub.E+Q.sub.G) for the x-direction and signals for the coding of the y-direction (Q.sub.E+Q.sub.F)*(Q.sub.G+Q.sub.H) for the y-direction are multiplied.

4: The method according to claim 1, wherein the moment of the 2nd order is additionally determined by a summing network.

5: The method according to claim 1, wherein a strict linear coding is carried out.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The present invention will be described in even greater detail below based on the exemplary figures. The invention is not limited to the exemplary embodiments. All features described and/or illustrated herein can be used alone or combined in different combinations in embodiments of the invention. The features and advantages of various embodiments of the present invention will become apparent by reading the following detailed description with reference to the attached drawings which illustrate the following:

[0022] FIG. 1 shows a photosensor having output channels A, B, C, and D in schematic form;

[0023] FIG. 2 shows a photosensor having output channels E, F, G, and H in schematic form;

[0024] FIG. 3 shows a multiplied photocurrent profile of channels A and B plotted against time in seconds;

[0025] FIG. 4 shows a voltage profile of channels E and F plotted against time in seconds;

[0026] FIG. 5 shows typical light distributions measured when using monolithic scintillator crystals with position-resolving photodetectors;

[0027] FIG. 6 shows a 1.sup.st normalized moment, which can be determined with the aid of the position-coded currents according to the prior art;

[0028] FIG. 7 shows a 2.sup.nd normalized moment, which can be determined with the aid of position-coded currents according to the prior art, using a summing circuit;

[0029] FIG. 8 shows a standard deviation, which can be determined according to the prior art from normalized 1.sup.st and 2.sup.nd moments with the aid of formula 7;

[0030] FIG. 9 shows an approximated 2.sup.nd normalized moment, which can be calculated according to an embodiment of the invention from the product of the position-coded currents;

[0031] FIG. 10 shows a linearly-transformed, approximated 2.sup.nd moment according to formula 8; and

[0032] FIG. 11 shows a standard deviation, which is determined, according to an embodiment of the invention, from the normalized 1.sup.st and the linearly-transformed, approximated 2.sup.nd moments with the aid of formula 7.

DETAILED DESCRIPTION

[0033] Embodiments of the invention provide methods for reading out signals of a photosensor which overcome certain disadvantages of prior art and with which the parallax error in the determination of an LOR can be reduced. According to embodiments of the invention, methods are provided that allow the use of scintillation monocrystals for the detection of signals in positron emission tomography, wherein the DOI problem can be avoided by reducing the parallax error in the determination of the LOR. Methods according to embodiments of the invention are suitable for all types of photosensors with monolithic crystals and pixelated crystal arrays which produce a depth of interaction-dependent light distribution and, additionally, respectively contain a spatial coding which should be as linear as possible. The PET detector does not have to be modified in this case. It is therefore also possible to upgrade existing PET and MR/PET systems on the software side with such methods.

[0034] The sensitivity and resolution of photosensors can be improved with methods according to embodiments of the invention, since the depth of interaction is additionally determined. The depth-of-interaction resolution depends upon the x-y resolution of the photosensor. Furthermore, methods according to embodiments of the invention, which are also compatible with MR, are suitable for operating photosensors together with an MRIin particular, with high magnetic fields. The accuracy of small PET rings, or with PET rings that closely adjoin the examination object, can be improved. The space required by the additional electronics for determining the depth of interaction normally associated with the measuring arrangement can be reduced. Space that can usually consume sensitive photosensor surface area can be saved by the unnecessary integration of, for example, resistor networks. The costs for the device can be reduced. Methods according to embodiments of the invention are not to be limited in application to use in PET, but shall generally be capable of being used for scintillation monocrystals and arrays of scintillation crystals which have a light distribution dependent upon a depth of interaction.

[0035] With methods according to the invention, it is now possible to reduce parallax errors in the determination of the LOR'sin particular, in the case of scintillation monocrystals. The sensitivity and resolution of measuring methods and of measuring devices are improved. The use of scintillation monocrystals which are longer in the z-direction is made possible. Methods according to the invention can also be applied to photosensors which are operated together with an MRI device. Especially for devices with smaller tube dimensions, or if the PET ring closely adjoins the examination object, the parallax error is reduced. Space for the associated electronics and costs are saved. Methods according to the invention achieve a level of detail of the z-resolution dependent upon the x-y resolution. This can lead to a very high resolution of the depth of interactionin particular, in the case of high-resolution photosensors, such as LG-SiPM, SeSP, or iSiPM. This results in a more accurate estimate of the 2.sup.nd order moment. Methods according to the invention can be used for all photosensors which are coded spatially, in particular where the coding is as linear as possible, e.g., SiPM, such as LG-SiPM, SeSP and iSIPM, ADP, such as position-sensitive APD, or PMT, such as position-sensitive PMT, and arrays of scintillation crystals having a light distribution dependent upon the depth of interaction.

[0036] In the following, the invention is described in its general form, without this being interpreted restrictively.

[0037] A detector concept for PET measurements is provided in which each individual detector has at least one scintillation monocrystal and at least one photosensor which is positioned on one side of the scintillation crystal. The photosensor is preferably mounted on the x-y plane of the scintillation monocrystalparticularly preferably on the side of the scintillation monocrystal facing away from the center of the detector ring. In another embodiment, the photosensor may be mounted on a side of the scintillation monocrystal that is not on the x-y planefor example, on the x-z or y-z plane. This, however, has the disadvantage that, for photo sensors that are mounted on the x-z or y-z plane, scanner sensitivity losses arise. If the sensor is located on the side facing the center, additional Compton effects arise.

[0038] Multiple scintillation monocrystals can also be coupled to one or more photosensors.

[0039] The use of the scintillation monocrystal has the advantage that the sensitivity of the monocrystal to pixelated scintillation crystals can be maximized. In the case of pixelated scintillation crystals, the efficiency of the scintillation monocrystals is significantly reduced, e.g., to only 71% or 59% with a crystal pixel size of 0.8 mm0.8 mm or 0.5 mm0.5 mm of a pixelated crystal array. The scintillation monocrystal may, for example, consistbut not restrictivelyof LSO, LYSO, BGO, GSO, BaF.sub.2, or NaI:Tl (thallium-doped sodium iodide). The materials are known to the person skilled in the art. The ratio of the z-dimension of the scintillation monocrystal to its dimension in the x-direction of less than or equal to 1 leads to good results in the case of a square cross-section for x-y. The best results are obtained with a ratio of 0.25. Optionally, the ratio can also be smaller. The length of the scintillation monocrystal thereby achieved is more likely determined by practical circumstances, such as the diameter of the PET ring or the costs associated with large monocrystals. The dimensioning of the scintillation monocrystal in the z-direction depends upon the desired sensitivity to be achieved. Achieving the large dimension of the scintillation monocrystal in the z-direction is a result of the readout of the photosensor according to the invention described below, which enables such dimensioning in which minimization of DOI errors occurs.

[0040] The method can also be used when using specially produced scintillation crystal arrays. The requirement in this case is that the crystal arrays be constructed in such a way that a light distribution over the sensor surface is produced as a function of the depth of interaction. A recently published method is to mount a light guide for light distribution on the surface facing away from the sensor. Scintillation light is reflected there and distributed to several pixels as a function of the depth of interaction in the pixel [18]. Another known method in this respect is superposing 2 or more crystal arrays, which are offset from one another, so that a top crystal distributes light to severaltypically, 4underlying crystals. Based upon the width, it can thus be decided in which crystal array layer the scintillation event took place [19], [20].

[0041] Any photosensor which includes a spatial coding can be used with the method according to the invention.

[0042] One photosensor or several small photosensors that are assembled to form a larger photosensor can be mounted on a scintillation monocrystal. These photosensors can be glued onto the scintillation monocrystal. If several small photosensors are assembled, they are considered a single photosensor within the meaning of the invention if they are mounted together on one side of the scintillation monocrystal. The adhesive used for this purpose should be transparent. Furthermore, a layer of a light distributor may be located between the scintillation monocrystal and the photosensor if the light intensity is too bundled. An arrangement is also possible in which more than one photosensor is mounted on the monocrystal. For example, a stack along the z-axis can be provided, in which photosensors and scintillation monocrystals alternate. This is particularly expedient when scintillation monocrystals are used in which the light distribution in certain crystal regions cannot be differentiated to such an extent, and a division of the scintillation monocrystal into several layers with a respective sensor is expedient. In another embodiment, photosensors may also be mounted on the sides of the scintillation monocrystal that are not on the x-y plane of the scintillation monocrystal. One, two, or more, e.g., 3, photosensors can be mounted on different sides. In this case, photosensors can be mounted on two opposite sides of the scintillation monocrystal or on adjoining sides of the scintillation monocrystal which are in the x-z or y-z direction. Any sub-combination is conceivable. The variant in which photosensors are mounted on opposite sides has the advantage that the accuracy is thus increased when a measurement signal is received. However, the advantage of the embodiment according to the invention of the method and of the device is precisely that the signals have to be read out only on one side of the scintillation monocrystal. This corresponds to an embodiment with a single photosensor. In this way, the method and device according to the invention also become cost-effective.

[0043] The photosensor is designed according to the invention in such a way that, in the x-direction and/or in the y-direction, it allows a linear coding of the currents with respect to the position of the corresponding pixel. For this purpose, the sensor chip can be designed in different ways, inter alia, with the coding possibilities mentioned in the prior art, which, for example, can be realized with a resistor network.

[0044] A linear coding of the signals or the currents in the x-direction and the y-direction then respectively results in linearly increasing and linearly decreasing signal strengths for the output channels, which signal strengths are respectively multiplied by each other, according to the invention, for the x-direction and/or for the y-direction.

[0045] According to the invention, any combination of readout channels with linearly increasing and decreasing signal strengths for which the linearly increasing and linearly decreasing signals are multiplied by each other can be used for the linear coding. The direction in which the signal strengths increase or decrease linearly can deviate from the x- and y-direction of the photosensor. In this case, a direction of the linearly increasing and decreasing signal strengths is denoted by e.

[0046] In a generally preferred case, the readout channels are exclusively situated on the x-axis or the y-axis of the photosensor.

[0047] In one embodiment, as can be seen from FIG. 1, output channels A and B are available for the x-direction, and output channels C and D are available for the y-direction, which provide a linearly-coded signal of the light distribution.

[0048] The x-position is calculated from the currents Q of the channels A and B according to formula 1:

[00002]$\begin{array}{cc}x=\frac{Q_A-Q_B}{Q_A+Q_B}& \left(\mathrm{Formula}.Math..Math.1\right)\end{array}$

[0049] The y-position is calculated from the currents Q of the channels C and D according to formula 2:

[00003]$\begin{array}{cc}x=\frac{Q_A-Q_B}{Q_A+Q_B}& \left(\mathrm{Formula}.Math..Math.1\right)\\ \mathrm{and}& \\ y=\frac{Q_C-Q_D}{Q_C+Q_D}& \left(\mathrm{Formula}.Math..Math.2\right)\end{array}$

[0050] In this case, the x-y position is calculated from the detected currents Q of the channels A through D. Thus, the x- and y-positions result from the formulae:

[00004]$\begin{array}{cc}y=\frac{Q_C-Q_D}{Q_C+Q_D}& \left(\mathrm{Formula}.Math..Math.2\right)\end{array}$

[0051] In this embodiment, the signals of channels A and B for the x-direction and C and D for the y-direction are multiplied by each other.

[0052] In an embodiment of the invention in which four readout channels contribute to the linear coding, viz., any combination of readout channels to the linearly increasing and decreasing signal strengths or, in a special case, linearly increasing and decreasing signal strengths in the x- and/or y-direction, the signal strengths for the x- and/or y-position can be described by the formulae 3 and 4.

X=((Q.sub.F+Q.sub.H)(Q.sub.E+Q.sub.G))/(Q.sub.E+Q.sub.F+Q.sub.G+Q.sub.H)(Formula 3)

y=((Q.sub.E+Q.sub.F)(Q.sub.G+Q.sub.H))/(Q.sub.E+Q.sub.F+Q.sub.G+Q.sub.H)(Formula 4)

[0053] In this embodiment, resistor networks or resistive layers may be used. In doing so, the currents that result in the signals can, for example, be distributed to the corners of the photosensor. For clarification purposes, a photosensor with the corners E, F, G, and H is shown in FIG. 2.

[0054] The total energy of a scintillation event is calculated as follows:

Econst..Math.(Q.sub.A+Q.sub.B+Q.sub.C+Q.sub.D)(Formula 5)

or

E=const.*(Q.sub.E+Q.sub.F+Q.sub.G+Q.sub.H)(Formula 6)

[0055] Formula 5 or 6 calculates the energy or the moment of 0.sup.th order .sub.0 and the position along x and/or y the moment of 1.sup.st order .sub.1 of the sampled light distribution.

[0056] The standard deviation of the light distribution .sub.light, which contains the DOI information, is calculated using the 2.sup.nd moment .sub.2 according to the following formula:

[00005]$\begin{array}{cc}{}_{\mathrm{light}}^2=\frac{{}_2}{{}_0}-\frac{{}_1^2}{{}_0^2}& \left(\mathrm{Formula}.Math..Math.7\right)\end{array}$

[0057] The 2.sup.nd order moment is determined according to the prior art by a summing network which generates a signal which is quadratically coded in the position x or y.

[0058] According to the invention, the output signals obtained by output channels A and B and/or C and D are multiplied by each other if the spatial coding takes place according to formulae 1 and/or 2.

[0059] If the spatial coding takes place according to formulae 3 and 4, a value very similar to the moment of the 2.sup.nd order is obtained by the following multiplication:

(Q.sub.F+Q.sub.H)*(Q.sub.E+Q.sub.G) for the x-direction(Formula 8)

and/or

(Q.sub.E+Q.sub.F)*(Q.sub.G+Q.sub.H) for the y-direction(Formula 9)

[0060] Because the signals Q.sub.A, Q.sub.B, Q.sub.C, Q.sub.D, Q.sub.F, Q.sub.H, Q.sub.E, Q.sub.G, and Q.sub.1, Q.sub.2 from the formulae 1, 2, 3, 4, 5, 6, 8, 9 and the below-described formula 11 are linearly coded with the position of the current-supplying pixel, the products (Q.sub.F+Q.sub.H)*(Q.sub.E+Q.sub.G), (Q.sub.E+Q.sub.F)*(Q.sub.G+Q.sub.H), Q.sub.A*Q.sub.B, Q.sub.C*Q.sub.D, and Q.sub.1*Q.sub.2 must be coded quadratically with the position of the current-supplying pixel. In the case of currents in only a single pixel, i.e., all currents in the other pixels disappear, a precise square coding results, which is shown in FIG. 3 and which is identical, as shown in FIG. 4, to the signal from a summing circuit, up to a global, linear transformation. In this case, the linear transformation can result in signals in other units, without impairing the functionality of the method. In the case of currents of several pixels, such as are produced by typical scintillator light distributions, additional mixed terms result, which, however, do not interfere with the functionality of the method. This can be demonstrated most easily by simulations, as can be seen in the figures.

[0061] Since a signal which is very similar to the moment of the 2.sup.nd order results with the multiplication, the standard deviation of the light distribution can be calculated with this obtained approximated 2.sup.nd order moment. For this purpose, before using formula 7, a general linear transformation of the approximated 2.sup.nd moment must be performed: by way of example, the equation of formula 10 can be used for this purpose,

.sub.2=(+.sub.2)(Formula 10),

where .sub.2 is the moment that is approximated using the product and subsequently normalized. The constants and are to be determined with the aid of a calibration measurement. With the aid of .sub.2, the standard deviation can be determined, which, as described above and generally known, is a function of the depth of interaction. This is illustrated by way of example in FIGS. 8 and 11. The functions for calculating the depth of interaction from the standard deviation are to be determined from suitable calibration measurements. The methods are known to the person skilled in the art.

[0062] The multiplication can be performed for both embodiments for a direction x or y, or for both directions x and y.

[0063] If both directions are used for the estimation of the moment of the 2.sup.nd order, it can be more accurately approximated.

[0064] According to the invention, the DOI problems described above are solved, and information on the depth of the signal along the z-direction of the scintillation monocrystal or of the crystal array with a light distribution of the used sensor chip that depends upon the depth of interaction is obtained. The aims presented are all achieved.

[0065] The method can be carried out with all photosensors that include a spatial coding, wherein this is to correspond to a linear coding if possible.

[0066] In this case, the output signal of a channel or a combination of channels must change in a manner as linearly increasing as possible with the x- or y- or e-position, while the output signal of another channel or a combination of channels changes in manner as linearly decreasing as possible with the x- or y- or e-position. The direction e is any direction, which can also be composed of x- and y-direction vectors. Direction vectors which result solely from signals of the x-direction or the y-direction are special cases of signals of the e-direction. A linear coding within the meaning of the invention is understood to be any coding which corresponds to formula 11. Q.sub.1 is the charge of the output channels increasing via the e-position, and Q.sub.2 is the charge of the output channels decreasing via the e-position. The parameter e denotes the coding direction, i.e., x or y or a combination thereof.

Q.sub.1(e)=c.sub.1.Math.e.sup.c2+c.sub.3

Q.sub.2(e)=c.sub.4.Math.e.sup.c5+c.sub.6

c.sub.1=const.(0,)

c.sub.4=const.(,0)

c.sub.3,c.sub.6=const.(,)

0.5<c.sub.2; c.sub.5<1.5(Formula 11)

[0067] Formula 11 takes into account that embodiments that do not satisfy the requirements of strict linearity can still be suitable for realizing the teaching according to the invention. Ideally, the linear coding is strictly linear.

[0068] In addition, it is possible for a sensor chip to have a linear coding in more than one e-directionfor example, e.sub.1, e.sub.2, e.sub.3, etc. In this case, the moment of 2.sup.nd order is respectively approximated by multiplying the corresponding increasing and decreasing signal strengths along the coding direction. The more coding directions that are present, the better the 2.sup.nd order moment can be approximated. A special case is the sensor chips described above, which contain two coding directions, where e.sub.1 corresponds to the x- and e.sub.2 corresponds to the y-direction. In this case, a linear coding is present in at least one e-direction.

[0069] In an advantageous embodiment of the invention, the moment of the 2.sup.nd order is determined with a resistor network, in addition to the multiplication of the output signals according to the method according to the invention. The depth of interaction can in this case be determined even more accurately.

[0070] Current photosensors are SiPM-based sensors, such as LG-SiPM, SeSP and iSiPM, ADP-based sensors, such as position-sensitive APD's, or PMT-based sensors, such as position-sensitive PMT's. The method can also be used in sensors which are developed in the future and have a spatial coding along the x- and y-direction as linear as possible.

[0071] FIG. 1 shows in schematic form a photosensor with outputs A, B, C, and D, wherein outputs A and B are on the y-axis, and outputs C and D are on the x-axis. The x-axis and the y-axis are denoted by the arrows.

[0072] FIG. 2 shows in schematic form a photosensor having a resistor network or a resistive layer distributing the charges to the corners, wherein the output channels E, F, G, and H for the charge to be read out are positioned in the corners of the photosensor. The arrows denote the x-axis and the y-axis.

[0073] FIG. 3 shows a curve in which the multiplication of the photocurrents in [A.sup.2] of two readout channels A and B increasing and decreasing linearly with the x- or y- or e-direction is plotted against the time in [s].

[0074] FIG. 4 shows a curve in which the voltage in [V] of the channel J for the embodiment that uses a summing network to determine the moment of the 2.sup.nd order is plotted against the time in [s].

[0075] The comparison of FIGS. 3 and 4 shows that, for the multiplication according to the invention of the signal strength linearly increasing and linearly decreasing for the x-direction, results are obtained that are equivalent to the determination of the moment of the 2.sup.nd order by means of a summing network.

[0076] FIG. 5 shows typical light distributions, measured when using monolithic scintillation crystals with position-resolving photodetectors, when the photoconversion takes place at different depths of interaction t=0.1, t=0.2, t=0.3, and t=0.4 of any units ([a.u.]) in the monolithic scintillation crystal. Axis of abscissas: x-position along the sensor surface [a.u.], axis of ordinates: signal intensity [a.u.].

[0077] FIG. 6 shows, for various depths of interaction t=0.1, t=0.2, t=0.3, and t=0.4 [a.u.], the 1.sup.st normalized moment, which can be determined according to the prior art with the aid of the position-coded currents. Axis of abscissas: actual photoconversion position x along the sensor surface, axis of ordinates: measured photoconversion position (Anger position) [a.u.].

[0078] FIG. 7 shows, for various depths of interaction t=0.1, t=0.2, t=0.3, and t=0.4 [a.u.], the 2.sup.nd normalized moment, which can be determined according to the prior art with the aid of the position-coded currents using a summing circuit. Axis of abscissas: actual photoconversion position x along the sensor surface, axis of ordinates: measured 2.sup.nd moment [a.u.].

[0079] FIG. 8 shows, for various depths of interaction t=0.1, t=0.2, t=0.3, and t=0.4 [a.u.], the standard deviation, which can be determined according to the prior art from the normalized 1.sup.st and 2.sup.nd moments with the aid of formula 7. Axis of abscissas: actual photoconversion position x along the sensor surface, axis of ordinates: measured standard deviation [a.u.].

[0080] FIG. 9 shows, for various depths of interaction t=0.1, t=0.2, t=0.3, and t=0.4 [a.u.], the approximated 2.sup.nd normalized moment, which can be calculated according to the invention from the product of the position-coded currents. Axis of abscissas: actual photoconversion position x along the sensor surface, axis of ordinates: approximated 2.sup.nd normalized moment (normalized product of the two signals) [a.u.].

[0081] FIG. 10 shows, for various depths of interaction t=0.1, t=0.2, t=0.3, and t=0.4 [a.u.], the linearly-transformed, approximated 2.sup.nd normalized moment according to formula 8. Axis of abscissas: actual photoconversion position x along the sensor surface, axis of ordinates: linearly-transformed, approximated 2.sup.nd normalized moment (scaled, measured, normalized product of the two signals) [a.u.].

[0082] FIG. 11 shows, for various depths of interaction t=0.1, t=0.2, t=0.3, and t=0.4 [a.u.], the standard deviation, which can be determined according to the invention from the normalized 1.sup.st and the linearly-transformed, approximated 2.sup.nd moment with the aid of formula 7. Axis of abscissas: actual photoconversion position x along the sensor surface, axis of ordinates: measured, approximated standard deviation [a.u.].

[0083] While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive. It will be understood that changes and modifications may be made by those of ordinary skill within the scope of the following claims. In particular, the present invention covers further embodiments with any combination of features from different embodiments described above and below.

[0084] The terms used in the claims should be construed to have the broadest reasonable interpretation consistent with the foregoing description. For example, the use of the article a or the in introducing an element should not be interpreted as being exclusive of a plurality of elements. Likewise, the recitation of or should be interpreted as being inclusive, such that the recitation of A or B is not exclusive of A and B, unless it is clear from the context or the foregoing description that only one of A and B is intended. Further, the recitation of at least one of A, B and C should be interpreted as one or more of a group of elements consisting of A, B and C, and should not be interpreted as requiring at least one of each of the listed elements A, B and C, regardless of whether A, B and C are related as categories or otherwise. Moreover, the recitation of A, B and/or C or at least one of A, B or C should be interpreted as including any singular entity from the listed elements, e.g., A, any subset from the listed elements, e.g., A and B, or the entire list of elements A, B and C.

REFERENCES

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