JPH0652199B2 - Optical pulse intensity distribution measuring method and apparatus - Google Patents

Description

The present invention relates to an optical pulse intensity distribution capable of measuring the optical intensity distribution of an optical pulse with a resolution not limited to the resolution inherent to a photodetector. The present invention relates to a measuring method and device.

[Conventional technology]

A typical example of the measurement of the light pulse intensity distribution is the measurement of the radiation energy distribution using the conventional scintillation phenomenon.

In this case, the scintillation light emitted from the scintillator in a short time by the action of radiation usually consists of many photons, and each scintillation light is regarded as an optical pulse. Since the intensity of scintillation light, that is, the light pulse intensity, is proportional to the amount of energy given to the scintillator by the action of radiation, the measurement of the light pulse intensity distribution is performed by measuring the radiation energy distribution using a scintillation radiation detector. Has become the basic technology of.

Today, in various fields such as science and engineering and nuclear industry, the technology for measuring the radiation energy distribution is one of the important radiation measurement technologies. Therefore, regarding the measurement technology of the optical pulse intensity distribution, Over the years, many researches and developments have been conducted on a global scale to improve the technology.

Conventionally, in any case, the measurement of the light pulse intensity distribution is performed by a photodetector from a wave height (amplitude) of a magnitude proportional to the light pulse intensity.
Is obtained by amplifying the electric pulse having the above-mentioned value and amplifying the electric pulse to an appropriate size by a proportional amplifier, and measuring the pulse height distribution using a multi-channel pulse height analyzer. This conventional method has the advantage that the light pulse intensity distribution can be measured directly, but the resolution is limited by the inherent resolution of the photodetector.

[Problems to be Solved by the Invention]

As described above, in the conventional measurement of the optical pulse intensity distribution, after the electric pulse obtained from the photodetector is amplified by the proportional amplifier, the pulse height distribution of the pulse is measured by the multi-channel pulse height analyzer. Multichannel pulse height analyzers are generally relatively expensive.

It is not easy to guarantee a high stability of the pulse height of the electric pulse due to the gain fluctuation of the photomultiplier tube, which is the photodetector. To overcome this, the structure of the measuring device is complicated. In addition, the cost becomes higher.

Furthermore, the resolution in measuring the pulse height distribution of the electrical pulse from the photodetector is limited by the intrinsic resolution of the photodetector, and the intrinsic resolution of the photodetector decreases as the light intensity of the optical pulse decreases. Therefore, there is a very serious problem such that it is impossible to measure the light intensity distribution of the light pulse having a low light intensity with high resolution.

The present invention has been made to solve the above problems, and has a nonlinear response characteristic (input (light intensity) and output (electric pulse generation probability)) having a photodetector. The purpose of the present invention is to obtain an optical pulse intensity distribution measuring method and device capable of measuring the optical intensity distribution of an optical pulse having a low optical intensity with high resolution, based on the principle of utilizing a (relationship).

[Means for Solving the Problems]

An optical pulse intensity distribution measuring method according to the present invention attenuates an optical pulse having a constant average count rate at known optically different attenuation rates, and an optical pulse obtained by this optical attenuation is determined according to a nonlinear function. Under the condition of the characteristic, it is converted into electric pulses, the number of these electric pulses is measured, and k pieces of measurement data n ₁ showing the number of electric pulses per constant time, which are obtained for different optical attenuation rates, n ₂ , n ₃ , ...
A set of measurement data consisting of n _k and m components (m ≦
The optical pulse is solved by using a mathematical method to solve a simultaneous equation consisting of the intensities H ₁ , H ₂ , H ₃ ... Hm (unknown) of each component of the optical pulse intensity distribution represented by a histogram with k). Determine the intensity distribution.

Further, the optical pulse intensity distribution measuring device according to the present invention includes a variable optical attenuating means for optically attenuating an optical pulse having a constant average count rate or a plurality of optical attenuating means having different attenuating rates, and the optical attenuating means. Photoelectric conversion means for converting the optical pulse obtained by the above into an electric pulse under the condition of input / output characteristics determined according to a non-linear function, and a measuring means for measuring the number of electric pulses converted and output by the photoelectric conversion means. It is composed of.

Further, a variable optical attenuating means for optically attenuating an optical pulse having a constant average count rate or a plurality of optical attenuating means having different attenuating rates, and an optical pulse obtained by the optical attenuating means are defined by a non-linear function. A plurality of measuring systems may be provided which include photoelectric conversion means for converting electric pulses under the condition of output characteristics and measuring means for measuring the number of electric pulses converted and output by the photoelectric conversion means.

Further, it is possible to provide counting means for counting the electric pulses output from the variable optical attenuating means corresponding to each measuring system or a plurality of optical attenuating means having different attenuating rates at the same time or simultaneously.

[Action]

In the measuring method of the present invention, an optical pulse having a constant average count rate is attenuated at an optically known attenuation rate, and the optical pulse obtained by this optical attenuation is converted into an electric signal pulse,
The number of these electric pulses is measured, and the light pulse intensity distribution is determined based on a set of measurement data consisting of the number of electric pulses per constant time obtained according to the degree of light attenuation.

Further, in the measuring device of the present invention, when the optical pulse attenuated and output by the optical attenuating means and having a constant average count rate is converted into electric pulses by the photoelectric converting means, the number of electric pulses converted and output by the measuring means is changed. And a set of measurement data, that is, measurement data indicating the number of electric pulses for different light attenuation rates is secured.

Further, when each optical pulse attenuated and output by the plurality of optical attenuating means and having a constant average count rate is converted into an electric pulse by the corresponding photoelectric converting means, each measuring means converts and outputs each electric pulse. The number of pulses is measured by each measurement system, and one set of measurement data is secured.

Further, the counting means counts each electric pulse output from the optical attenuating means corresponding to each measuring system at the same time or multiple times simultaneously, and a set of measurement data is secured.

〔Example〕

FIG. 1 is a block diagram for explaining the configuration of an optical pulse intensity distribution measuring apparatus showing an embodiment of the present invention. Reference numeral 1 is an optical fiber light guide, which is an optical pulse generated from a light source of interest and having a constant average count rate. To the variable optical attenuator 2. The variable optical attenuator 2 attenuates the light intensity of the optical pulse guided to the optical fiber light guide 1 at a desired attenuation rate within a range described later, that is, has various optical attenuation ratios. Reference numeral 3 denotes a photodetector (which also serves as photoelectric conversion means) composed of, for example, a photomultiplier tube, which converts the attenuated light pulse into an electric pulse (output pulse). A proportional amplifier 4 amplifies the electric pulse converted into an electric signal. A wave height analyzer 5 analyzes the wave height of the amplified electric pulse.

6 is a counter which also serves as a measuring means. The optical pulse attenuated and output by the variable optical attenuator 2 is converted into an electric pulse by the photodetector 3, and the number of converted and output electric pulses is measured for each optical attenuation ratio, and the result will be described later. The optical pulse intensity distribution is determined based on the observation equation.

The photodetector 3 composed of a photomultiplier tube has a photomultiplier for each incident light pulse when the absolute value of the light intensity of the incident light pulse is in a limited range with a low intensity region. The probability that one or more photoelectrons are generated in the photocathode of the tube can be determined according to a non-linear function with the light intensity of the incident light pulse as a variable, and in the photocathode, one or more photoelectrons per incident light pulse When photoelectrons are generated, it has a characteristic of always generating an output pulse. Therefore, in this embodiment, when the incident light pulse is optically attenuated and the light intensity of the light pulse is gradually changed within a predetermined range described later, the output pulse from the photomultiplier tube The light intensity distribution of the light pulse is determined based on a series of data obtained by measuring the number of the light pulses per unit time.

The operation of FIG. 1 will be described below with reference to FIGS. 2 to 4.

An optical pulse having a light intensity distribution represented by a certain histogram is transmitted through the optical fiber light guide 1 to the variable optical attenuator 2
Be led to.

Then, the light is optically attenuated and is incident on the photodetector 3, where it is converted into an electric pulse with the occurrence probability determined according to the light intensity. At this time, under the condition that the occurrence probability of the electric pulse is determined according to a certain nonlinear function having the light intensity of the light pulse incident on the photodetector 3 as a variable, it corresponds to each histogram component with respect to the change of the light attenuation ratio. The electric pulse generation probability of the light pulse changes at different rates. The electric pulse output from the photodetector 3 is amplified by the proportional amplifier 4 to an appropriate size and then incident on the wave height analyzer 5. Then, the counter 6 is caused to count the number of electric pulses output from the wave height analyzer 5 per unit time. The intensity of each component of the histogram is unknown based on a set of measurement data consisting of data n ₁ , n ₂ , n ₃ , ..., N _k indicating the number of electric pulses counted for each optical attenuation ratio. A multi-dimensional simultaneous simultaneous equation is defined as The optical pulse intensity distribution is determined by solving this multi-dimensional simultaneous simultaneous equation.

FIG. 2 is a diagram showing the relationship between the output pulse generation probability P of the photodetector 3 and the incident light pulse intensity m shown in FIG. 1, and the vertical axis represents the output pulse generation probability P of the photodetector 3. The horizontal axis represents the incident light pulse intensity m, that is, the average number of photoelectrons generated from the photocathode per pulse of the incident light pulse.

The output pulse generation probability P in this figure is expressed by the following equation (1).

P = 1-exp (-m) (1) As can be seen from this figure, when the incident light pulse intensity m becomes larger than about 5, that is, when m5,
The output pulse generation probability P is actually 1.

If m is smaller than about 0.1, that is, m
In the case of 0.1, the output pulse generation probability P is approximately m
Is equal to

FIG. 3 is a characteristic diagram showing the wave height distribution of the output pulse of the photodetector 3 shown in FIG. 1, where the vertical axis shows the number of output pulses and the horizontal axis shows the output pulse wave height. The wave height distribution A corresponds to the wave height distribution of the output pulse of the photodetector 3 when the average number m of photoelectrons per pulse in the photocathode of the photodetector 3 is about 0.2.

In this figure, A shows the pulse height distribution of the output pulse when the gain is stable, and B shows the pulse height distribution (broken line) of the output pulse when the gain drifts and increases.

When the intensity of the light pulse (incident light pulse intensity m) incident on the high resolution photomultiplier of the photodetector 3 is sufficiently low at about 0.2, the pulse height distribution A of the output pulse corresponds to a single photoelectron. With a distinctive peak P ₁ and a relatively low peak P ₂ corresponding to two photoelectrons. In addition,
As the incident light pulse intensity m becomes higher than 0.2,
The height of the peak P ₂ becomes relatively high, and at the same time, a third peak corresponding to three photoelectrons appears.

The total area surrounded by the wave height distribution A and the horizontal axis represents the number of output pulses from the photodetector 3, but is now sufficiently lower than the wave height value corresponding to the peak P ₁ as the lower limit value of the output pulse wave height. When the value H ₁ is set and the upper limit value is set to a value H ₂ sufficiently higher than the peak value corresponding to the peak P ₂ , the area S obtained by integrating the number of output pulses in the section from the value H ₁ to the value H _{2 is} set.
Is approximately equal to the total area S ₀ . Further, even if the gain of the photodetector 3 changes, this area S is kept substantially constant without being affected by it. Due to this fact, it becomes possible to guarantee the accuracy of the measurement of the optical pulse intensity distribution by the optical pulse intensity distribution measuring method. As described above, the output pulse of the photodetector 3 is amplified to a proper size by the proportional amplifier 4 and applied to the pulse height analyzer 5.
When the two discrimination levels of the wave height analyzer 5 are set so as to correspond to the above-mentioned lower limit value and upper limit value H ₁ and H ₂ , the counting rate n of the output pulse of the wave height analyzer 5 (that is,
The number per unit time) represents the counting rate of the output pulse of the photodetector 3 without being affected by the change in the gain of the photodetector 3 (however, the area S, the total area S ₀ and Only if the relationship is approximately equal).

Then, the counting rate of the output pulse of the wave height analyzer 5 is measured by the counter 6.

Next, from the series of measurement data obtained by measuring the count rate of the electric pulse from the wave height analyzer 5 while changing the optical attenuation ratio of the variable optical attenuator 2 whose attenuation ratio is variable, Information about the intensity distribution is obtained as follows.

The light intensity of the light pulse is in the range from O to Lm (however, L
m is the upper limit of the light intensity), and this is represented by a histogram having m components. Further, the width of each component of the histogram is assumed to be equal, and the intensity Hi (where i = 1, 2, ..., M) of the i-th component per unit time of an optical pulse having a light intensity corresponding to that component. It shall indicate the number (count rate).

FIG. 4 is a diagram showing the relationship between the light intensity and the probability of occurrence of an output pulse, where the horizontal axis represents the light intensity (the upper limit value Lm of the light intensity),
The vertical axis represents the output pulse generation probability P.

In this figure, m is the intensity of the incident light pulse (however, it indicates the light intensity indicated by the average number of photoelectrons generated in the photocathode per pulse of the incident light pulse), and the light pulse is optically converted by the variable optical attenuator 2. The incident light pulse intensity m corresponding to the upper limit value Lm of the light intensity is attenuated to be 20, 10, 5, 2, 1,
It is a plot of the function values obtained by calculating the output pulse generation probability P based on the above equation (1) for each of 0.5 and 0.2.

As a result, when the optical pulse is optically attenuated by the variable optical attenuator 2 and the optical intensity corresponding to the upper limit value Lm of the optical intensity is, for example, m = 10, an output pulse is generated for the optical intensity of each component of the histogram. The probability can be easily determined from the curve of the incident light pulse intensity value m = 10 shown in FIG.

Therefore, if the output pulse generation probability for the optical pulse corresponding to the i-th component of the histogram is ε _1i , the number of output pulses from the photodetector 3 due to these optical pulses per unit time is Hi · ε _1i . expressed. Therefore, the number n ₁ of output pulses from the photodetector 3 per unit time is
It is a composite of the number of each component of the histogram,
It is expressed by the following equation (2) (observation equation).

n ₁ = H ₁ · ε ₁₁ + H ₂ · ε ₁₂ + ... + H _m · ε _{1 m} (2) Further, the optical pulse is optically attenuated so that the light intensity corresponding to the upper limit Lm of the light intensity is increased. When m = 5, photodetector 3
Letting n ₂ be the number of output pulses per unit time from, the observation equation for the light intensity m = 5 is obtained from the following equation (3).

n ₂ = H ₁ · ε ₂₁ + H ₂ · ε ₂₂ +… + H _m · ε _2m (3) where ε _2i (where i = 1, 2, ..., m) is assigned to each component of the histogram. This is the output pulse generation probability for an optical pulse having a corresponding light intensity, and can be obtained directly from the curve of m = 5 in FIG. 4 or by calculation from the above equation (1).

Similarly, the light intensity corresponding to the upper limit value Lm of the light intensity is set to, for example, m = 4, 3.5, 3 by optically attenuating the light pulse, and the output pulse from the photodetector 3 is set each time. The number of units per unit time was measured to be n _k-2 ,
expressed as n _k-1, n _k, each of the values calculated as the output pulse generation probability for light pulses of the light intensity corresponding to each component of the histogram from the equation (1) when, respectively epsilon _{(k- 2) i} , ε _{(k-1) i} , ε _ki gives the following observation equation.

n _k-2 = H ₁ · ε _{(k-2) 1} + H ₂ · ε _{(k-2) 2} +… + H _m · ε _{(k-2) m} … (4) n _k-1 = H ₁ · Ε _{(k-1) 1} + H ₂ · ε _{(k-1) 2} +… + H _m · ε _{(k-1) m} … (5) _nk = H ₁ · ε _k1 + H ₂ · ε _k2 +… + H _m · ε _km … (6) The above equations (2) to (6) are m unknowns H ₁ , H ₂ …, H m
Construct a multi-dimensional system of equations containing.

Then, the intensity distribution of the optical pulse is determined by calculating the above multi-dimensional simultaneous equations according to the following conditions (a) and (b).

(A) Basic conditions A simultaneous equation must be composed of m or more equalities (observation equations).

(B) of equations constituting the requirements simultaneous equations for each equation are independent, any respect two equations, each unknown count epsilon _ji, epsilon _ki ratio ε _ji / ε _ki ( However, i = 1, 2, ..., M, and j and k represent arbitrary two equalities) must not be constant for all i. That is, the following expression (7) must not hold.

ε _ji ≈C · ε _ki (7) However, C is an arbitrary constant.

For example, the number of unknowns between the equations (2) and (3)
When the relationship of the equation (7) is approximately satisfied, n ₁ ≈approximate between the measured values n ₁ and n ₂ of the number of output pulses.
It is expected that the relationship of C · n ₂ will be established, and the above (2)
Equation (3) becomes substantially the same equation.

The light pulse is optically attenuated so that the light intensity corresponding to the upper limit value Lm of the light intensity is, for example, m = 0.5 or m = 0.2.
In the case of, the output pulse generation probability of the photodetector 3 with respect to the light pulse corresponding to each component of the histogram showing the light pulse intensity distribution is as follows: the incident light pulse intensity m shown in FIG. Determined from the curve with m = 0.2,
Since each of these curves is approximately represented by a straight line passing through the origin, the observation equations for these two cases satisfy the relation of the above equation (7), so that they are almost the same equations. .

That is, when the light pulse is optically attenuated so that the incident light pulse intensity m corresponding to the upper limit value Lm of the light intensity is about 0.5 or less, the value of the incident light pulse intensity m is Irrespective of, the observation equation is actually the same.

On the other hand, when the optical pulse is attenuated so that the incident light pulse intensity value m corresponding to the upper limit value Lm of the light intensity is about 20 or more, it is expected from the curve of the incident light pulse intensity m of 20 shown in FIG. As described above, the output pulse generation probability of the photodetector 3 is 1 (probability 100%) for most optical pulses, and the observation equations for these cases are almost the same.

Therefore, in order to obtain an observation equation that satisfies the above condition (b), the optical pulse is optically attenuated and the upper limit value Lm of the light intensity is set.
It is necessary to create an observation equation so that the incident light pulse intensity value m corresponding to is in the range of 0.5 to 20. Then, the intensity distribution of the desired light pulse is obtained by calculating the above observation equation.

In the above embodiment, one photodetector 3 is used to optically attenuate a light pulse to various extents, and the number of output pulses is observed from the photodetector 3 to obtain an observation equation. Although the case of creating the photodetector has been described, as the number of photodetectors 3 is increased, each photodetector 3 (each photodetector 3 is different and the incident light pulse intensity m is 0.5 to 2).
The output pulse number measuring system consisting of the proportional amplifier 4, the wave height analyzer 5, and the coefficient unit 6 corresponding to (the optical attenuation ratio is adjusted so as to have various values different from each other within the range of 0) are independently provided. By providing and using the optical fiber light guide 1 and the like, it is possible to create the required number of observation equations in one measurement.

In addition, when multiple photodetectors 3 are used, one observation equation can be created from the measurement of the output pulses from each photodetector 3, and the output pulse of multiple photodetectors 3 can be created. An observation equation can be created by performing coincidence counting (or multiple coincidence counting). The pulse generation probability in this case is given by the product of the pulse generation probabilities of each photodetector 3.

In this way, a relatively large number of observation equations can be created by performing coincidence counting (or multiple coincidence counting) of the output pulses of the plurality of photodetectors 3.

For example, when three photodetectors A, B, and C are used, in addition to the three observation equations for the output pulse of each photodetector 3, two photodetectors AB, AC, and BC are detected. It is possible to create three observation equations for coincidence counting of the detector 3 and one observation equation for triple coincidence counting of the three photodetectors 3 of ABC. That is, since a total of 7 observation equations can be created from one measurement, an optical pulse intensity distribution represented by a 7-component histogram can be obtained.

Similarly, if four photodetectors A, B, C, and D are used, 15 observation equations including those involved in multiple coincidence can be obtained from one measurement. , The optical pulse intensity distribution represented by the histogram of 15 components can be obtained.

〔The invention's effect〕

As described above, the optical pulse intensity distribution measuring method according to the present invention attenuates an optical pulse having a constant average count rate with a known attenuation rate that is optically different, and nonlinearly converts the optical pulse obtained by this optical attenuation. Converted into electric pulses under the condition of input / output characteristics determined according to a function, measured the number of these electric pulses, and obtained k for each different optical attenuation rate, indicating the number of electric pulses per constant time. Measurement data n ₁ , n ₂ , n ₃ , ..., N _k of one set, and the intensity H of each component of the optical pulse intensity distribution represented by a histogram having m components (m ≦ k) ₁ , H ₂ , H ₃ ...
The optical pulse intensity distribution is calculated and determined by solving a simultaneous equation composed of H _m (unknown number) using a mathematical method, so that the light intensity distribution that is not affected by the resolution of the photodetection mechanism can be measured. .

Further, the optical pulse intensity distribution measuring device according to the present invention comprises an optical attenuating means for optically attenuating an optical pulse having a constant average count rate, and an input / output in which the optical pulse obtained by the optical attenuating means is determined according to a non-linear function. Since the photoelectric conversion means for converting into an electric panel under the condition of characteristics and the measuring means for measuring the number of electric pulses converted and output by the photoelectric conversion means are constituted, the measured light pulse intensity distribution The resolution is not limited by the inherent resolution of the photodetector, and can be obtained as the magnitude of the number of each component of the histogram representing the intensity distribution. That is, in the conventional optical pulse intensity distribution measuring method based on pulse wave height measurement, the resolution is limited by the inherent resolution of the photodetector, so that, for example, the incident light intensity of the optical pulse is m = 1.
In the case of about 00 or less, it is impossible in principle to obtain a resolution better than 10%, whereas by using the multi-component histogram of the present invention, a resolution better than 10% can be obtained. The light intensity distribution can be measured with an inexpensive device.

In addition, an optical attenuating means for optically attenuating an optical pulse having a constant average count rate, and a photoelectric converting means for converting the optical pulse obtained by the optical attenuating means into an electric pulse under the condition of input / output characteristics determined according to a non-linear function. Since a plurality of measuring systems each including a converting means and a measuring means for measuring the number of electric pulses converted and output by the photoelectric converting means are provided, it is possible to efficiently measure a necessary number of observation methods by one measurement. Can be created.

Furthermore, since the counting means for counting the electric pulses output from the optical attenuating means corresponding to each measuring system simultaneously or in multiplex is provided, a relatively large number of observation equations can be created even with a small number of photodetection mechanisms. And so on.

[Brief description of drawings]

FIG. 1 is a block diagram for explaining the configuration of an optical pulse intensity distribution measuring apparatus showing an embodiment of the present invention, and FIG. 2 is an output pulse generation probability and incident optical pulse intensity of the photodetector shown in FIG. FIG. 3 is a characteristic diagram showing the pulse height distribution of the output pulse of the photodetector shown in FIG. 1, and FIG. 4 is a diagram showing the relation between light intensity and output pulse generation probability. . In the figure, 1 is an optical fiber light guide, 2 is a variable optical attenuator, 3 is a photodetector, 4 is a proportional amplifier, 5 is a wave height analyzer,
6 is a counter.

Claims (4)

[Claims] 1. An optical pulse having a constant average count rate is attenuated at known optically different attenuation rates, and the optical pulse obtained by this optical attenuation is electrically converted under a condition of an input / output characteristic determined according to a non-linear function. Converted into pulses, the number of these electric pulses is measured, and k measurement data n indicating the number of electric pulses per constant time, which are obtained for different optical attenuation rates, are obtained.
Intensity H ₁ , H ₂ of each component of the optical pulse intensity distribution represented by a histogram having a set of measurement data consisting of ₁ , n ₂ , n ₃ , ..., N _k and m components (m ≦ k) H ₃ , ...
An optical pulse intensity distribution measuring method, characterized in that the optical pulse intensity distribution is determined by solving a simultaneous equation composed of H _m (unknown number) and a mathematical method. 2. A variable optical attenuating means for optically attenuating an optical pulse having a constant average count rate, or a plurality of optical attenuating means having different attenuating rates, and an optical pulse obtained by the optical attenuating means according to a non-linear function. A photoelectric conversion means for converting into an electric pulse under a condition of a defined input / output characteristic, and a measuring means for measuring the number of electric pulses converted and output by the photoelectric conversion means. An optical pulse intensity distribution measuring device used in the method of item 1. 3. A variable optical attenuating means for optically attenuating an optical pulse having a constant average count rate or a plurality of optical attenuating means having different attenuating rates, and an optical pulse obtained by the optical attenuating means according to a non-linear function. A plurality of measurement systems are provided, each of which includes a photoelectric conversion unit that converts an electric pulse under the condition of a specified input / output characteristic and a measurement unit that measures the number of electric pulses converted and output by the photoelectric conversion unit. An optical pulse intensity distribution measuring device for use in the method according to claim 1. 4. A counting means for counting simultaneously or multiple simultaneously each electric pulse outputted from a variable optical attenuating means corresponding to each measuring system or a plurality of optical attenuating means having different attenuation factors. The optical pulse intensity distribution measuring device according to claim (3).