WO2012153496A1 - 分布解析装置 - Google Patents
分布解析装置 Download PDFInfo
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- WO2012153496A1 WO2012153496A1 PCT/JP2012/002951 JP2012002951W WO2012153496A1 WO 2012153496 A1 WO2012153496 A1 WO 2012153496A1 JP 2012002951 W JP2012002951 W JP 2012002951W WO 2012153496 A1 WO2012153496 A1 WO 2012153496A1
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- distribution
- measurement data
- sensor
- measurement
- field
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- VJZDBRGSBDTGKQ-UHFFFAOYSA-N CC1(C)CC(CO)CCC1 Chemical compound CC1(C)CC(CO)CCC1 VJZDBRGSBDTGKQ-UHFFFAOYSA-N 0.000 description 1
- GDOPTJXRTPNYNR-UHFFFAOYSA-N CC1CCCC1 Chemical compound CC1CCCC1 GDOPTJXRTPNYNR-UHFFFAOYSA-N 0.000 description 1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/02—Measuring direction or magnitude of magnetic fields or magnetic flux
- G01R33/10—Plotting field distribution ; Measuring field distribution
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/0064—Arrangements or instruments for measuring magnetic variables comprising means for performing simulations, e.g. of the magnetic variable to be measured
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/12—Measuring magnetic properties of articles or specimens of solids or fluids
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
- G06F17/13—Differential equations
Definitions
- the present invention relates to a distribution analyzer for analyzing a field having characteristics satisfying the Laplace equation.
- the spatial distribution of magnetic field strength (hereinafter also referred to as magnetic field distribution) is used in various fields such as the location of an abnormal current path inside an electronic component or the inspection of a diseased part of a human body.
- a superconducting quantum interferometer element Superconducting Quantum Interference Device
- a magnetoresistive effect element Magnetic Sensor
- a superconducting quantum interferometer element is also referred to as a “SQUID element”.
- Patent Document 1 proposes a configuration in which a carbon nanotube magnetic probe is used as an MFM probe.
- Patent Document 2 discloses a method for measuring a three-dimensional distribution such as a magnetic field, an electric field, or a temperature field in a three-dimensional space.
- a Laplace equation which is a basic equation of a static magnetic field, is strictly used by using a two-dimensional magnetic field distribution and a two-dimensional magnetic field gradient distribution obtained on a specific measurement surface as boundary conditions.
- a three-dimensional magnetic field distribution in the space around the measurement surface is obtained.
- the magnetic field gradient means a magnetic field gradient in a direction normal to the measurement surface.
- the space around the measurement surface includes both a three-dimensional space above and a three-dimensional space below the measurement surface.
- Patent Document 2 it is possible to image the structure of a magnetic field generation source using measurement data of a magnetic field distribution obtained in a region far from the magnetic field generation source (magnetic field generation source).
- the image showing the structure of the magnetic field generation source can be used, for example, for medical diagnosis or failure analysis of electronic components.
- the spatial resolution in the measurement of the magnetic field distribution depends on the size of the coil or magnetoresistive element used for the SQUID element. By miniaturizing these magnetic field sensors, it is possible to image the magnetic field distribution with higher spatial resolution. However, in practice, there is a limit to the miniaturization of the magnetic field sensor. For example, it is not easy to produce a magnetic field sensor having a size of 100 nm or less. Further, in the miniaturized magnetic field sensor, the electrical signal output from the sensor sensing area is also small, and the SN ratio (signal noise ratio) is low.
- an object of the present invention is to provide a distribution analysis apparatus that can analyze a distribution of a magnetic field or an electric field with high resolution even when a sensor sensitive area is large.
- a distribution analysis apparatus is a distribution analysis apparatus that analyzes a field distribution having characteristics satisfying the Laplace equation, and that moves in a measurement region in which the field distribution is measured.
- an acquisition unit for acquiring measurement data indicating the distribution measured through the sensor sensing area which is an area where the fields are summed and sensed in the area, and a finite number corresponding to the size of the sensor sensing area Using the arithmetic expression obtained by deriving the solution of the Laplace equation using the boundary condition that the integration of the solution of the Laplace equation in the interval is compatible with the measurement data, the resolution is higher than that of the measurement data.
- a calculation unit for calculating analysis data indicating the distribution of the field is a calculation unit for calculating analysis data indicating the distribution of the field.
- the distribution analysis apparatus can calculate analysis data using an arithmetic expression obtained by deriving a solution of the Laplace equation using measurement data as a boundary condition.
- the distribution analyzer can directly calculate the analysis data theoretically by substituting the measurement data directly into the arithmetic expression. Therefore, the distribution analyzer can analyze a magnetic field, an electric field, and the like in a region smaller than the size of the sensor sensitive region even when a large sensor sensitive region is used.
- the acquisition unit may acquire the measurement data indicating the field distribution which is a magnetic field, an electric field, or a temperature field
- the calculation unit may calculate the analysis data indicating the field distribution.
- the distribution analyzer to analyze the spatial distribution of magnetic fields and the like with high resolution.
- the spatial distribution of the analyzed magnetic field or the like can be used in various fields such as failure analysis of electronic components, medical diagnosis, or corrosion inspection of reinforcing bars inside concrete.
- the acquisition unit acquires the measurement data indicating the distribution of the field measured through the sensor sensing region that intersects a measurement surface that is a plane perpendicular to the Z direction that is a predetermined direction
- the calculation unit uses, as the boundary condition, that the integral of the solution of the Laplace equation in the finite section corresponding to the size in the Z direction of the sensor sensitive area matches the measurement data.
- the analysis data may be calculated using the arithmetic expression obtained by deriving a solution.
- the distribution analysis apparatus can calculate analysis data that more accurately indicates the spatial distribution of the magnetic field, the electric field, and the like on the measurement surface even when a large sensor sensitive area in the Z direction is used.
- z represents the coordinate value of the Z-direction
- k x represents the wave number of the X-direction
- the wave number k y is the Y-direction
- ⁇ x indicates the size of the sensor sensitive area in the X direction
- ⁇ z indicates the size of the sensor sensitive area in the Z direction
- ⁇ m (x, y, z) is the coordinate in the Z direction.
- f (x, y) is the measurement data when z of ⁇ m (x, y, z) is 0, and g (x, y) is A function obtained by substituting 0 into z of a function obtained by differentiating ⁇ m (x, y, z) by z, Represents a function after Fourier transform of f (x, y) in the X direction and the Y direction, Indicates a function after Fourier transform of g (x, y) in the X direction and the Y direction, May be used as the arithmetic expression to calculate the analysis data.
- the distribution analyzer can calculate the analysis data using the arithmetic expression. That is, the distribution analysis apparatus can acquire data when the size of the sensor sensitive area is infinitely small using the sensor sensitive area of a finite size by this arithmetic expression.
- the acquisition unit may acquire the measurement data indicating the distribution measured through the sensor sensing area that rotates about a straight line parallel to a predetermined Z direction.
- a three-dimensional space is expressed in cylindrical coordinates using z indicating the coordinate value in the Z direction, ⁇ indicating the declination, and p indicating the radius, and k is the direction of the radius.
- ⁇ z indicates the size of the sensor sensitive area in the Z direction
- g me (p, ⁇ , z) indicates the measurement data when the coordinate value in the Z direction is z
- f m (k, ⁇ ) is g me (p, ⁇ , z ) g me when z of is 0
- p, ⁇ , z) indicates the function of the Fourier transform for the P direction
- g m shown (k, ⁇ ) is g me (p, ⁇ , z ) function after the Fourier transform for the P direction of the function obtained by the substituting 0 to z of the function obtained by differentiating z
- the calculation unit May be used as the arithmetic expression to calculate the analysis data.
- the distribution analyzer can analyze the spatial distribution of a magnetic field or the like that is much smaller than the size of the sensor sensitive area from the measurement data indicating the distribution measured through the sensor sensitive area of a finite size.
- the acquisition unit may acquire the measurement data including the value obtained by multiplying the field value sensed in the sensor sensing region by a window function and the value multiplied by the window function.
- the distribution analysis apparatus can acquire measurement data indicating an appropriate distribution locally through a large sensor sensing area.
- the acquisition unit multiplies the value by the window function depending on a distance from a predetermined position to the sensor sensing area, and the measurement data including the value multiplied by the window function. You may get it.
- the distribution analysis apparatus can acquire measurement data indicating an appropriate distribution in a desired region.
- the distribution analyzer further includes a measurement unit that measures the distribution of the field via the sensor sensing area, and the acquisition unit acquires the measurement data indicating the distribution measured by the measurement unit. May be.
- the distribution analyzer can analyze the measurement data obtained by the measurement with high resolution.
- the distribution analysis apparatus may further include an image processing unit that generates an image indicating the distribution indicated by the analysis data calculated by the calculation unit.
- the distribution of the magnetic field or electric field is analyzed with high resolution.
- FIG. 1 is a diagram showing an overview of the distribution analysis apparatus according to the first embodiment.
- FIG. 2 is a diagram illustrating an aspect when the sensor according to the first embodiment is used.
- FIG. 3 is a diagram showing a state when the sensor according to Embodiment 1 is used from the side.
- FIG. 4 is a diagram illustrating a sensor sensing area of the sensor according to the first embodiment.
- FIG. 5 is a diagram showing a state when the sensor according to the first embodiment is used from above.
- FIG. 6 is a diagram illustrating an aspect when the sensor according to Embodiment 1 measures different measurement surfaces.
- FIG. 7 is a diagram conceptually illustrating an example of the structure of the sensor according to the first embodiment.
- FIG. 8 is a diagram illustrating a configuration of the distribution analysis apparatus according to the first embodiment.
- FIG. 9 is a flowchart showing the operation of the distribution analysis apparatus according to the first embodiment.
- FIG. 10 is a diagram illustrating a configuration of a variation of the distribution analysis apparatus according to the first embodiment.
- FIG. 11 is a flowchart showing an operation of a modification of the distribution analysis apparatus according to the first embodiment.
- FIG. 12 is a diagram for explaining an arithmetic expression according to the first embodiment.
- FIG. 13 is a diagram for explaining an arithmetic expression according to the second embodiment.
- FIG. 14 is a diagram conceptually showing a measurement surface according to the second embodiment.
- FIG. 15 is a diagram illustrating the direction of the radius vector according to the second embodiment.
- FIG. 16 is a diagram conceptually illustrating an example of an analysis region according to the third embodiment.
- FIG. 17 is a diagram illustrating a distribution analysis apparatus according to the fourth embodiment.
- FIG. 18 is a diagram illustrating a distribution analysis apparatus according to the fifth embodiment.
- FIG. 1 is a diagram showing an overview of the distribution analysis apparatus according to the first embodiment.
- the sensor 21 shown in FIG. 1 measures the distribution of the field (field to be analyzed).
- the distribution analyzer 10 analyzes the field distribution from the measurement data obtained by the sensor 21.
- the distribution analyzer 10 calculates analysis data indicating the spatial distribution with higher spatial resolution than the spatial distribution indicated by the measurement data from the measurement data.
- the calculated analysis data may be processed into an image or may be output as it is.
- the distribution analyzer 10 may include a sensor 21.
- Equation 1 F (x, y, z) in Equation 1 is a function that satisfies Laplace's equation, and is also called a harmonic function.
- ⁇ in Equation 1 is called Laplacian.
- the field having the characteristics satisfying the Laplace equation is a magnetic field in a place without current and spontaneous magnetization, an electric field in a place without charge, or a steady-state temperature field.
- the distribution analyzer 10 analyzes the field distribution and calculates analysis data. In the following, a plurality of embodiments including this embodiment are shown on the assumption that the field is a magnetic field. However, as described above, the field may not be a magnetic field as long as it has characteristics that satisfy the Laplace equation.
- FIG. 2 is a diagram showing a mode when the sensor 21 shown in FIG. 1 is used.
- the sensor 21 measures the magnetic field around the inspection object 22 placed on the table 23. At this time, the sensor 21 measures the magnetic field along the measurement surface 31.
- the sensor 21 sequentially measures the magnetic field in a sensor sensitive area including a part of the measurement surface 31.
- the sensor sensitive area is an area where a magnetic field is sensed and has a finite size.
- the sensor 21 measures the magnetic field along the measurement surface 31 while moving. It should be noted that the sensor 21 and the sensor sensing area may move relative to each other as the table 23 moves.
- the distribution analyzer 10 acquires magnetic field measurement data from the sensor 21. Then, the distribution analysis device 10 calculates analysis data from the measurement data.
- the analysis data calculated by the distribution analyzer 10 is typically used for generating a two-dimensional image. Therefore, as shown in FIG. 2, the sensor 21 preferably measures the magnetic field along the measurement surface 31. Thereby, the distribution analyzer 10 can calculate analysis data suitable for generating a two-dimensional image along the measurement surface 31 from the measurement data along the measurement surface 31 that is a plane. Such generation of a two-dimensional image is an example, and analysis data may be used for generation of a three-dimensional image.
- the inspection object 22 is, for example, an LSI (Large Scale Integration).
- the distribution analysis apparatus 10 can calculate analysis data indicating a wiring defect of the electronic circuit from the information on the magnetic field around the inspection object 22.
- LSI wiring is very small, image information with high spatial resolution is required.
- FIG. 3 is a diagram showing the aspect shown in FIG. 2 from the side.
- the inspection object 22 is on the table 23.
- the measurement surface 31 is on the inspection object 22.
- the sensor 21 measures the magnetic field along the measurement surface 31.
- the sensor 21 has a sensor sensitive area for measuring a magnetic field on the measurement surface 31. Thereby, the sensor 21 measures the magnetic field around the inspection object 22.
- FIG. 4 is a diagram showing a sensor sensing area of the sensor 21 shown in FIG.
- a sensor sensing area 41 is provided at the tip of the sensor 21.
- the sensor 21 measures the magnetic field in the sensor sensing area 41.
- the sensor sensing area 41 has a finite size.
- the sensor 21 generates a signal from the magnetic field in the entire sensor sensing area 41. That is, the sensor 21 acquires magnetic field information integrated (summed) by the size of the sensor sensing area 41. Therefore, it is difficult for the sensor 21 to measure the spatial distribution of the magnetic field with a spatial resolution finer than the size of the sensor sensitive area 41.
- the sensor 21 measures the magnetic field along the measurement surface 31.
- the sensor 21 measures the magnetic field in a region including a region above or below the measurement surface 31 based on the size of the sensor sensing region 41. Therefore, it is difficult to obtain image information relating to the magnetic field distribution directly from the measurement data obtained by the sensor 21 with high spatial resolution. Therefore, the distribution analysis apparatus 10 calculates analysis data indicating a spatial distribution (magnetic field distribution or the like) with high spatial resolution using a predetermined arithmetic expression.
- FIG. 5 is a diagram showing the mode shown in FIG. 2 from above. As shown in FIG. 5, the sensor 21 moves so that the sensor sensitive area 41 scans the measurement surface 31. The sensor 21 measures the magnetic field of the sensor sensitive area 41 at each position on the measurement surface 31 while moving. Thereby, the whole information in the measurement surface 31 is obtained.
- FIG. 6 is a diagram showing an aspect when the sensor 21 shown in FIG. 1 measures different measurement surfaces.
- the sensor 21 measures the magnetic field along the measurement surface 32 above the measurement surface 31 shown in FIG.
- the sensor 21 may measure the magnetic fields of a plurality of measurement surfaces.
- the sensor 21 can measure the distribution of the magnetic field in the three-dimensional space.
- the distribution analysis apparatus 10 may calculate the magnetic field distribution inside the inspection object 22 based on the magnetic field distribution on the plurality of measurement surfaces.
- the sensor 21 may measure the magnetic field so that the sensor sensitive area 41 partially overlaps when the measurement surface 31 is measured and when the measurement surface 32 is measured.
- the distribution analysis apparatus 10 may perform an operation such as an averaging process on the information obtained in this way.
- FIG. 7 is a diagram conceptually showing an example of the structure of the sensor 21 shown in FIG. In FIG. 7, in particular, a portion corresponding to the sensor sensing area 41 of the sensor 21 is shown.
- FIG. 7 shows an example of a TMR (Tunneling Magneto Resistive) element.
- the TMR element an insulating film layer is sandwiched between magnetic thin films of about 10 nm to 100 nm. More specifically, the TMR element is composed of three thin films: a soft layer 51, a tunnel layer 52, and a PIN layer (magnetization pinned layer) 53.
- the soft layer 51 is made of a magnetic material whose magnetization direction varies according to the direction of magnetization in the outside world.
- the PIN layer 53 is made of a magnetic material whose magnetization direction does not change.
- the tunnel layer 52 is an insulating film.
- the electric resistance is different between the case where the magnetization direction in the soft layer 51 and the magnetization direction in the PIN layer 53 are the same, and the case where the directions are different.
- the magnetic field is measured using the change in electrical resistance.
- the sensor 21 measures the magnetic field in the sensor sensitive area 41 using the above-described characteristics.
- the sensor 21 may be composed of other elements such as a GMR (Giant Magneto Resistive) element instead of the TMR element. Even when other elements such as a SQUID element are used, the sensor 21 can measure the magnetic field in the sensor sensitive area 41.
- GMR Gate Magneto Resistive
- FIG. 8 is a diagram showing a configuration of the distribution analysis apparatus 10 shown in FIG.
- the distribution analysis apparatus 10 shown in FIG. 8 analyzes the field distribution in the three-dimensional space.
- the distribution analysis device 10 includes an acquisition unit 11 and a calculation unit 12.
- the acquisition unit 11 acquires measurement data indicating the distribution measured through the sensor sensing area 41.
- the sensor sensing area 41 is disposed so as to include a part of the measurement surface 31 perpendicular to the Z direction, which is a predetermined direction, when the distribution is measured.
- the acquisition unit 11 may acquire measurement data from the sensor 21 that measures the distribution via the sensor sensing area 41.
- the acquisition unit 11 may acquire equivalent measurement data from another simulation device.
- the calculation unit 12 calculates analysis data indicating a distribution of a magnetic field or an electric field with higher spatial resolution than the spatial distribution indicated by the measurement data based on the measurement data. That is, the calculation unit 12 can calculate a structure included in a space smaller than the size of the sensor sensing area 41 from the spatial distribution indicated by the measurement data obtained in the sensor sensing area 41. The calculated structure may be imaged.
- the calculation unit 12 uses the fact that the integration of the Laplace equation solution in a finite interval corresponding to the size of the sensor sensing area 41 matches the measurement data as a boundary condition, and strictly calculates the Laplace equation solution. calculate. Therefore, the obtained analysis data is accurate and unique. Further, the calculation unit 12 can calculate analysis data regardless of the position of the sensor sensing area 41 and the position of the magnetic field generation source.
- the calculation unit 12 calculates analysis data mathematically strictly.
- the magnetic field generation source to be analyzed there may be a magnetic field generation source such as an electronic circuit or a sensor driving unit in the vicinity of the sensor sensing area 41.
- the calculation unit 12 mathematically strictly calculates analysis data regardless of the position where the magnetic field generation source exists.
- FIG. 9 is a flowchart showing the operation of the distribution analysis apparatus 10 shown in FIG.
- the acquisition part 11 acquires the measurement data measured via the sensor sensitive area 41 which senses a field (S11).
- the calculation unit 12 calculates analysis data having a spatial resolution higher than that of the measurement data using an arithmetic expression obtained by calculating the solution of the Laplace equation using the measurement data as a boundary condition (S12).
- the distribution analysis apparatus 10 can obtain analysis data having a higher spatial resolution than the measurement data.
- FIG. 10 is a diagram showing a configuration of a modified example of the distribution analysis apparatus 10 shown in FIG.
- the distribution analysis apparatus 10 illustrated in FIG. 10 includes an acquisition unit 11, a calculation unit 12, a measurement unit 13, and an image processing unit 14. That is, a measurement unit 13 and an image processing unit 14 are added to the distribution analysis apparatus 10 shown in FIG.
- the measurement unit 13 measures the field distribution through the sensor sensing area 41.
- the measurement unit 13 includes a sensor or a probe.
- the measurement unit 13 may be the sensor 21 shown in FIG.
- the sensor sensing area 41 includes a part of the measurement surface 31.
- the sensor sensing area 41 may be an area inside the measurement unit 13 or an area outside the measurement unit 13.
- the acquisition unit 11 acquires measurement data from the measurement unit 13.
- the image processing unit 14 uses the analysis data calculated by the calculation unit 12 to generate an image corresponding to the field distribution.
- the generated image is displayed on an external display device or the like.
- the distribution analysis device 10 may include a display unit that displays the generated image.
- FIG. 11 is a flowchart showing the operation of the distribution analysis apparatus 10 shown in FIG. First, the measuring unit 13 measures the field distribution through the sensor sensing area 41 (S21). Next, the acquisition unit 11 acquires measurement data indicating the distribution measured by the measurement unit 13 (S22).
- the calculation unit 12 calculates analysis data indicating the field distribution with higher resolution than the measurement data based on the measurement data (S23). At this time, the calculation unit 12 uses an arithmetic expression obtained by deriving a solution of the Laplace equation using the measurement data as a boundary condition. Then, the image processing unit 14 generates an image using the analysis data (S24).
- FIG. 12 is a diagram for explaining an arithmetic expression according to the first embodiment.
- the distribution of the magnetic field is measured via the sensor sensing area 41 in the three-dimensional space shown in FIG.
- the sensor sensitive area 41 has ⁇ x as a finite size in the X direction and ⁇ z as a finite size in the Z direction.
- the measurement surface 31 passes through the center of the sensor sensing area 41.
- the sensor sensing area 41 moves according to the scanning direction. Thereby, the spatial distribution of the magnetic field is measured along the measurement surface 31.
- the measurement data on the measurement surface 31 is actually measurement data of a field sensed in the entire sensor sensing area 41 having a width in the X direction and the Z direction. Therefore, there is an error between the measurement data and the actual magnetic field distribution.
- the calculation unit 12 calculates analysis data that does not depend on the size of the sensor sensitive area 41 with high spatial resolution using an arithmetic expression obtained by deriving a solution of the Laplace equation using the measurement data as a boundary condition. .
- Equation 2 shows Maxwell's equation when there is spontaneous magnetization like a ferromagnet.
- Equation 3 E indicates an electric field.
- B indicates the magnetic flux density.
- t indicates time.
- H indicates a magnetic field.
- j e represents a current.
- ⁇ represents conductivity.
- M indicates magnetization.
- ⁇ 0 indicates the permeability of vacuum.
- ⁇ represents magnetic permeability.
- Equation 3 is calculated as Equation 5 based on the result of Equation 4.
- Equation 6 the relationship between the magnetic field and the current is expressed by Equation 6 from Equation 3 and Equation 5.
- Equation 7 the relationship between the magnetic field and the current is expressed as Equation 7.
- Equation 7 is an equation of a stationary magnetic field due to current and spontaneous magnetization. In a place where there is no current and no spontaneous magnetization, the right side of Equation 7 is zero. Therefore, in such a location, the magnetic field satisfies Equation 8.
- Equation 9 the three-dimensional spatial distribution of the magnetic field is specified.
- the following shows the procedure for deriving an exact solution.
- a two-dimensional Fourier transform in the X direction and the Y direction is performed on ⁇ (x, y, z).
- Equation 10 shows a two-dimensional Fourier transform.
- Equation 11 is derived.
- Equation 11 is a differential equation for z twice. Therefore, the general solution of the equation of Equation 11 is expressed by Equation 12.
- Equation 13 shows a two-dimensional inverse Fourier transform.
- the sensor sensing area 41 has a finite size. Therefore, the sensor 21 in FIG. 1 can acquire only the information added in the sensor sensing area 41 in FIG. Therefore, it is difficult to directly measure ⁇ (x, y, z). That is, it is difficult to directly determine unknown functions a (k x , k y ) and b (k x , k y ) from the measurement data.
- Expression 14 is obtained by integrating Expression 13 in a finite interval corresponding to the finite size of the sensor sensing area 41.
- ⁇ m (x, y, z) corresponds to the measurement data. That is, the sensor 21 can measure ⁇ m (x, y, z).
- ⁇ x indicates the size of the sensor sensing area 41 in the X direction.
- ⁇ z indicates the size of the sensor sensing area 41 in the Z direction.
- the size of the sensor sensing area 41 in the Y direction is very small and is not considered. Note that an arithmetic expression when the size in the Y direction is taken into account can be derived by the same procedure as the procedure according to the present disclosure.
- Equation 15 shows a two-dimensional Fourier transform. Equation 15 corresponds to a function after the two-dimensional Fourier transform of the measurement data.
- the measurement surface 31 is used as a boundary condition.
- a function after Fourier transform of f (x, y) and g (x, y) is defined as in Expression 16.
- Equation 17 is derived from Equation 15 and Equation 16.
- Equation 17 is a simultaneous equation for a (k x , k y ) and b (k x , k y ). Therefore, from Expression 17, Expression 18 is obtained as a solution of a (k x , k y ) and b (k x , k y ).
- the solutions of a (k x , k y ) and b (k x , k y ) are obtained from the actual measurement data.
- analytical data indicating the distribution with higher spatial resolution than the spatial distribution indicated by the measurement data is calculated. Is obtained.
- Expression 19 shows an arithmetic expression obtained by substitution.
- Equation 20 represents the inverse Fourier transform, and is the same as Expression 13.
- the calculation unit 12 can calculate analysis data with high spatial resolution from the measurement data using the equations 19 and 20 derived as described above.
- the above-described arithmetic expression and its derivation procedure are examples, and modifications may be made to them. Further, the size of the sensor sensing area 41 in the Y direction may be included in the calculation formula and the derivation procedure.
- Equation 19 the sinh function is monotonically increasing, but the sin function has 0 points. Therefore, it is desirable that k x is not so large as compared to a given ⁇ x. Further, as compared with a given Delta] z k x, the k y increases, sinh function of the denominator rapidly rises right side of Equation 19 is rapidly reduced. Therefore, in Patent Document 2 based on the theory that the finite size of the sensor sensing area 41 is not considered, it is difficult to reconstruct an image showing a magnetic field distribution unless a spatial high-frequency component is cut.
- the distribution analysis apparatus 10 can calculate analysis data using an arithmetic expression. Therefore, even when the sensor sensitive area 41 or the like larger than the structure of the magnetic field generation source is used, the distribution analysis apparatus 10 substitutes the measurement data for the arithmetic expression and converts the analysis data indicating the field distribution to high spatial resolution. Can be calculated.
- Emodiment 2 In the second embodiment, the same configuration as that of the distribution analysis apparatus 10 according to the first embodiment shown in FIGS. 8 and 10 is used.
- the operation of the distribution analysis apparatus 10 according to the second embodiment is the same as the operation of the distribution analysis apparatus 10 according to the first embodiment shown in FIGS.
- the sensor sensing area 41 rotates. This further improves the spatial resolution.
- FIG. 13 is a diagram for explaining an arithmetic expression according to the second embodiment.
- the magnetic field is measured in the sensor sensing area 41 in the three-dimensional space shown in FIG. Then, the sensor sensing area 41 moves according to the scanning direction. Thereby, the magnetic field is measured along the Y direction of the measurement surface 31.
- the sensor sensing area 41 rotates around a straight line parallel to the Z direction.
- the sensor 21 may rotate the sensor sensing area 41 by rotating the sensor 21 shown in FIG.
- the sensor 21 may rotate only the sensor sensing area 41 such as a TMR element.
- the senor 21 may rotate the scanning direction. That is, the sensor 21 may change the angle in the scanning direction by changing the moving direction according to the rotation angle of the sensor sensing area 41.
- the scanning direction of the sensor 21 is preferably normal to the sensing surface of the sensor sensing area 41.
- the calculation part 12 calculates analysis data with high spatial resolution using a predetermined arithmetic expression.
- the predetermined arithmetic expression is an arithmetic expression obtained by solving the Laplace equation using the measurement data as a boundary condition. Further, in this calculation formula, the size of the sensor sensing area 41 is taken into consideration. This arithmetic expression is derived as follows.
- Equation 21 holds for the component of the magnetic field in the z-axis direction.
- Equation 21 a two-dimensional Fourier transform of ⁇ (x, y, z) is performed for x and y.
- Equation 22 shows a two-dimensional Fourier transform.
- FIG. 14 is a diagram conceptually showing the measurement surface 31 shown in FIG.
- the sensor 21 measures a measurable field on the measurement surface 31 by the rotation of the sensor sensing area 41.
- the straight line l shown in FIG. 14 indicates the sensor sensing area 41 at a specific time point. Since the sensor sensing area 41 can be configured by a thin film, it is represented by a line.
- the thickness of the thin film is not considered here.
- An arithmetic expression in the case where the thickness of the thin film is taken into consideration can be derived by the same procedure as the procedure according to the present disclosure. However, it is difficult to calculate a field in a space smaller than the thickness of the thin film with high accuracy.
- the sensor 21 measures the field distribution of the entire measurement surface 31 as the sensor sensing area 41 (straight line 1) rotates.
- ⁇ corresponds to the deflection angle of rotation of the sensor sensing area 41.
- p corresponds to the shortest distance from the predetermined origin to the sensor sensing area 41 and corresponds to the moving radius.
- (P, ⁇ ) is an expression based on polar coordinates.
- (P, ⁇ , z) obtained by a combination of polar coordinates and coordinate values in the Z direction is cylindrical coordinates.
- the measurement data in the sensor sensing area 41 is expressed by Expression 24.
- Equation 24 is proportional to the actual measurement data.
- Equation 25 shows the Fourier transform of Equation 24 with respect to p.
- FIG. 15 is a diagram illustrating the direction of the radius vector according to the second embodiment.
- FIG. 15 shows a radial direction 61 (also referred to as a radial direction P or P direction).
- a rotation (deflection) direction 62 corresponding to the radial direction 61 is shown.
- Equation 27 is obtained by substituting Equation 26 into Equation 25. Equation 27 corresponds to actual measurement data.
- Equation 29 is obtained from Equation 27 and Equation 28.
- Equation 29 is a simultaneous equation for a (k cos ⁇ , k sin ⁇ ), b (k cos ⁇ , k sin ⁇ ). From Expression 29, Expression 30 that is a solution of a (k cos ⁇ , k sin ⁇ ) and b (k cos ⁇ , k sin ⁇ ) is derived.
- Equation 31 corresponds to a function obtained by executing two-dimensional Fourier transform of ⁇ (x, y, z) in the X direction and the Y direction. From Expression 31, a two-dimensional Fourier transform image in the X direction and the Y direction at an arbitrary z is obtained. By performing a two-dimensional inverse Fourier transform on Equation 31, ⁇ (x, y, z) is obtained. Equation 32 shows a two-dimensional inverse Fourier transform. The calculation of Equation 32 requires conversion from polar coordinates to orthogonal coordinates in the wave number space.
- the equation 31 is an arithmetic expression obtained by solving the Laplace equation using the measurement data as the boundary condition in consideration of the finite size of the sensor sensing area 41. is there. It is possible to directly substitute actual measurement data into this arithmetic expression.
- the calculation unit 12 can calculate analysis data indicating the field distribution with high spatial resolution from the measurement data using the equation 31 derived as described above.
- the distribution analysis apparatus 10 can calculate analysis data indicating a field distribution with high spatial resolution using an arithmetic expression.
- Formula 19 shown in Embodiment 1 includes a sin function in the denominator. Therefore, the denominator has 0 points. Therefore, when k x is larger than the given ⁇ x, there is a possibility that appropriate analysis data cannot be obtained. That is, in the first embodiment, it is difficult to reconstruct a distribution image without cutting spatial high-frequency components. On the other hand, in Formula 31 shown in Embodiment 2, there is no sin function in the denominator. Therefore, in the second embodiment, it is possible to reconstruct a distribution image with high resolution without cutting spatial high-frequency components.
- the same configuration as that of the distribution analysis apparatus 10 according to the first embodiment shown in FIGS. 8 and 10 is used.
- the operation of the distribution analysis apparatus 10 according to the third embodiment is the same as the operation of the distribution analysis apparatus 10 according to the first embodiment shown in FIG. 9 and FIG.
- the sensor sensing area 41 according to the third embodiment may rotate as in the second embodiment.
- the third embodiment shows a method for realizing local Radon transformation as a method added to the first and second embodiments.
- the measurement unit 13 measures the field distribution in the region scanned by the sensor sensing region 41. In the area that is not scanned by the sensor sensitive area 41, the field distribution is not measured.
- the measurement unit 13 desirably measures the field distribution in a peripheral region covering the inspection object 22 in order to analyze the inspection object 22. Therefore, it is desirable that the size of the sensor sensing area 41 corresponds to the size of the inspection object 22.
- the size of the sensor sensing area 41 and the size of the inspection object 22 are not balanced, it may take a long time to acquire measurement data, and measurement data may not be acquired properly.
- a relatively large sensor sensing area 41 is scanned so as to cover the inspection object 22, whereby the magnetic field in the area around the inspection object 22 is measured.
- the sensor sensing area 41 is configured in advance with a large size. Even when the inspection object 22 smaller than the sensor sensing area 41 is used, the magnetic field around the inspection object 22 can be measured by the sensor sensing area 41 having a large size.
- the measurement unit 13 measures the magnetic field distribution in the sensor sensing area 41 having a large size, the magnetic field distribution in an area where the magnetic field distribution need not be measured is also measured. Thereby, it may take a long time to analyze the distribution of the magnetic field. In addition, an appropriate distribution may not be obtained due to unnecessary magnetic field information.
- a window function is used to amplify a necessary part of measurement data and attenuate an unnecessary part. Thereby, the time required for analyzing the distribution of the magnetic field is reduced. Moreover, an appropriate distribution can be obtained locally. Then, based on this locally obtained distribution, Radon transformation that locally generates a three-dimensional image is possible.
- the acquisition unit 11 multiplies the field value sensed in the sensor sensing area 41 by a window function. And the acquisition part 11 acquires the measurement data comprised by the value by which the window function was multiplied.
- the window function may be a function that depends on the distance from a predetermined position to the sensor sensing area 41.
- FIG. 16 is a diagram conceptually illustrating an example of an analysis region according to the third embodiment.
- FIG. 16 corresponds to a top view of the measurement surface 31.
- the sensor sensing area 41 scans the scan area 85.
- the inspection object 22 is disposed below the measurement surface 31.
- the inspection object 22 is arranged on a turntable, and the area around the inspection object 22 is scanned in a plurality of directions.
- the state in which the inspection object 22 is rotating by ⁇ corresponds to the state in which the sensor sensing area 41 is rotating by ⁇ .
- the inspection object 22 is arranged below the analysis region 82 on the measurement surface 31.
- the analysis area 82 is included in the measurement area 83.
- the measurement unit 13 measures the magnetic field distribution in the measurement region 83.
- the acquisition unit 11 acquires measurement data indicating the measured distribution.
- the calculation unit 12 analyzes the magnetic field distribution in the analysis region 82 based on the measurement data. In these series of procedures, unnecessary data is removed from the measurement data by the window function w (p).
- FIG. 16 conceptually shows the window function w (p).
- p represents a moving radius.
- the window function w (p) converges to zero.
- the window function w (p) By multiplying the measurement data by the window function w (p), data outside the analysis region 82 is excluded from the measurement data.
- the size of the analysis region 82 varies depending on the window function w (p).
- the half-width region 84 is a region that affects the analysis of the magnetic field distribution even when the measurement data is multiplied by the window function w (p).
- the half width region 84 is a region corresponding to the half width of the window function w (p).
- the window function w (p) is sharper than the example of FIG. Therefore, the impact is small.
- G (p, ⁇ ) in Expression 33 represents a function corresponding to the magnetic field sensed in the sensor sensing area 41.
- p represents a moving radius.
- ⁇ represents the deflection angle.
- D indicates a plane.
- H z (x, y) represents a magnetic field.
- x represents a coordinate value in the X direction.
- y represents a coordinate value in the Y direction.
- Expression 34 shows a relational expression obtained by multiplying g (p, ⁇ ) by a window function and performing Fourier transform in the P direction.
- G (k, ⁇ ) represents a function obtained by Fourier transformation in the P direction.
- k represents the wave number in the P direction.
- w (xcos ⁇ + ysin ⁇ ) in Expression 34 the approximate expression shown in Expression 35 holds.
- Expression 35 is applied to Expression 34. Thereby, the relational expression of Expression 36 is obtained.
- the measurement data multiplied by the window function w (p) is analyzed using the arithmetic expression obtained in the second embodiment. As a result, analysis data showing a highly accurate distribution locally can be obtained with a small amount of calculation.
- the original measurement data can be obtained except for the portion where the window function w (p) is zero.
- the window function w ′ (x, y) may be used for the divisor.
- the measurement data divided by the window function w (p) or the window function w ′ (x, y) may be analyzed using the arithmetic expression obtained in the second embodiment or the like.
- window function w (p) and calculation are examples.
- a window function w (p) that amplifies magnetic field information at a position other than the center of the measurement region 83 may be used.
- the window function w (p) may be a window function called a rectangular window.
- the method shown in the third embodiment is mainly a method corresponding to the second embodiment, the same concept may be applied to the first embodiment.
- the method shown in the third embodiment may be used independently as a method for acquiring appropriate measurement data locally, regardless of the first and second embodiments.
- the fourth embodiment shows a first application example related to the distribution analysis apparatus 10 shown in the first to third embodiments.
- FIG. 17 is a diagram illustrating the distribution analysis apparatus 10 according to the fourth embodiment.
- the distribution analysis apparatus 10 shown in FIG. 17 is a computer represented by a personal computer (PC).
- the distribution analysis apparatus 10 includes a CPU (Central Processing Unit), a memory, an input / output interface, and the like.
- CPU Central Processing Unit
- the distribution analyzer 10 acquires measurement data from the sensor 21. Then, the distribution analyzer 10 calculates analysis data having a higher spatial resolution from the measurement data using a predetermined arithmetic expression. Then, the distribution analysis device 10 displays the analysis data on the display device 71.
- the distribution analyzer 10 can be applied to a computer such as a personal computer.
- the fifth embodiment shows a second application example related to the distribution analysis apparatus 10 shown in the first to third embodiments.
- FIG. 18 is a diagram showing the distribution analysis apparatus 10 according to the fifth embodiment.
- the distribution analyzer 10 shown in FIG. 18 analyzes the magnetic field distribution inside the inspection object 91.
- the inspection object 91 is a building made of reinforced concrete, for example.
- the worker 92 uses the sensor 21 to measure the magnetic field inside and around the inspection object 91.
- the distribution analyzer 10 acquires measurement data from the sensor 21. Then, the distribution analyzer 10 calculates highly accurate analysis data from the measurement data using a predetermined arithmetic expression. Then, the distribution analysis device 10 displays the analysis data on the display device 71.
- the operator 92 can use the distribution analysis apparatus 10 for the inspection of the reinforcing bar corrosion inside the concrete.
- the distribution analyzer concerning the present invention was explained based on a plurality of embodiments, the present invention is not limited to the embodiments. Embodiments obtained by subjecting the embodiments to modifications conceivable by those skilled in the art and other embodiments realized by arbitrarily combining components in the embodiments are also included in the present invention.
- another processing unit may execute a process executed by a specific processing unit.
- the order in which the processes are executed may be changed, or a plurality of processes may be executed in parallel.
- the present invention can be realized not only as a distribution analysis apparatus but also as a method having steps as processing means constituting the distribution analysis apparatus. For example, these steps are performed by a computer.
- the present invention can be realized as a program for causing a computer to execute the steps included in these methods.
- the present invention can be realized as a non-transitory computer-readable recording medium such as a CD-ROM in which the program is recorded.
- the plurality of components included in the distribution analysis apparatus may be realized as an LSI that is an integrated circuit. These components may be individually made into one chip, or may be made into one chip so as to include a part or all of them. Although referred to here as an LSI, it may be referred to as an IC (Integrated Circuit), a system LSI, a super LSI, or an ultra LSI depending on the degree of integration.
- LSI Integrated Circuit
- the method of circuit integration is not limited to LSI, and implementation with a dedicated circuit or a general-purpose processor is also possible.
- An FPGA Field Programmable Gate Array
- a reconfigurable processor that can reconfigure the connection and setting of circuit cells inside the LSI may be used.
- the distribution analysis apparatus can analyze the distribution of various fields, for example, magnetic field diagnostic equipment, inspection of electronic components, inspection of rebar corrosion inside concrete, seismic inspection of rebar structures in disaster areas, And applicable to medical diagnosis.
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Abstract
Description
図1は、実施の形態1に係る分布解析装置の概要を示す図である。図1に示されたセンサ21は、場(解析対象の場)の分布を測定する。そして、分布解析装置10は、センサ21で得られた測定データから、場の分布を解析する。この時、分布解析装置10は、測定データで示される空間分布よりも高い空間分解能で空間分布を示す解析データを測定データから算出する。算出された解析データは、画像に加工されてもよいし、そのまま出力されてもよい。なお、分布解析装置10は、センサ21を備えていてもよい。
実施の形態2では、図8および図10等に示された実施の形態1に係る分布解析装置10と同様の構成が用いられる。そして、実施の形態2に係る分布解析装置10の動作は、図9および図11等に示された実施の形態1に係る分布解析装置10の動作と同様である。実施の形態2では、センサ感受領域41が回転する。これにより、さらに、空間分解能が向上する。
実施の形態3では、図8および図10等に示された実施の形態1に係る分布解析装置10と同様の構成が用いられる。そして、実施の形態3に係る分布解析装置10の動作は、図9および図11等に示された実施の形態1に係る分布解析装置10の動作と同様である。また、実施の形態3に係るセンサ感受領域41は、実施の形態2のように回転してもよい。実施の形態3は、実施の形態1および実施の形態2に追加される方法として、局所的なラドン変換を実現するための方法を示す。
実施の形態4は、実施の形態1~3に示された分布解析装置10に係る第1の適用例を示す。
実施の形態5は、実施の形態1~3に示された分布解析装置10に係る第2の適用例を示す。
11 取得部
12 算出部
13 測定部
14 画像処理部
21 センサ
22、91 検査対象物
23 台
31、32 測定面
41 センサ感受領域
51 ソフト層
52 トンネル層
53 PIN層(磁化固定層)
61、62 方向
71 表示装置
82 解析領域
83 測定領域
84 半値幅領域
85 スキャン領域
92 作業者
Claims (10)
- ラプラス方程式を満たす特性を有する場の分布を解析する分布解析装置であって、
前記場の分布が測定される測定領域において移動する領域であり当該領域において前記場が合算されて感受される領域であるセンサ感受領域を介して測定された前記分布を示す測定データを取得する取得部と、
前記センサ感受領域の大きさに対応する有限の区間での前記ラプラス方程式の解の積分が前記測定データに適合することを境界条件として用いて前記ラプラス方程式の解を導出することによって得られる演算式を用いて、前記測定データよりも高い分解能で前記場の分布を示す解析データを算出する算出部とを備える
分布解析装置。 - 前記取得部は、磁場、電場または温度場である前記場の分布を示す前記測定データを取得し、
前記算出部は、前記場の分布を示す前記解析データを算出する
請求項1に記載の分布解析装置。 - 前記取得部は、予め定められた方向であるZ方向に垂直な平面である測定面に交わる前記センサ感受領域を介して測定された前記場の分布を示す前記測定データを取得し、
前記算出部は、前記センサ感受領域の前記Z方向の大きさに対応する前記有限の区間での前記ラプラス方程式の解の積分が前記測定データに適合することを前記境界条件として用いて前記ラプラス方程式の解を導出することで得られる前記演算式を用いて、前記解析データを算出する
請求項1または2に記載の分布解析装置。 - 互いに垂直なX方向、Y方向およびZ方向を含む3次元空間において、zが前記Z方向の座標値を示し、kxが前記X方向の波数を示し、kyが前記Y方向の波数を示し、Δxが前記センサ感受領域の前記X方向の大きさを示し、Δzが前記センサ感受領域の前記Z方向の大きさを示し、φm(x,y,z)が前記Z方向の座標値がzである場合における前記測定データを示し、f(x,y)がφm(x,y,z)のzが0である場合における前記測定データを示し、g(x,y)がφm(x,y,z)をzで微分することで得られる関数のzに0を代入することで得られる関数を示し、
前記算出部は、
請求項1~3のいずれか1項に記載の分布解析装置。 - 前記取得部は、予め定められたZ方向に平行な直線を軸として回転する前記センサ感受領域を介して測定された前記分布を示す前記測定データを取得する
請求項1~3のいずれか1項に記載の分布解析装置。 - 3次元空間が、前記Z方向の座標値を示すzと、偏角を示すθと、動径を示すpとを用いて円柱座標で表現され、kが前記動径の方向であるP方向の波数を示し、Δzが前記センサ感受領域の前記Z方向の大きさを示し、gme(p,θ,z)が前記Z方向の座標値がzである場合における前記測定データを示し、fm(k,θ)がgme(p,θ,z)のzが0である場合におけるgme(p,θ,z)の前記P方向についてのフーリエ変換後の関数を示し、gm(k,θ)がgme(p,θ,z)をzで微分することで得られる関数のzに0を代入することで得られる関数の前記P方向についてのフーリエ変換後の関数を示す場合、
前記算出部は、
請求項5に記載の分布解析装置。 - 前記取得部は、前記センサ感受領域で感受された前記場の値にウィンドウ関数を掛けて、前記ウィンドウ関数が掛けられた前記値で構成される前記測定データを取得する
請求項1~6のいずれか1項に記載の分布解析装置。 - 前記取得部は、予め定められた位置から前記センサ感受領域までの距離に依存する前記ウィンドウ関数を前記値に掛けて、前記ウィンドウ関数が掛けられた前記値で構成される前記測定データを取得する
請求項7に記載の分布解析装置。 - 前記分布解析装置は、さらに、前記センサ感受領域を介して前記場の分布を測定する測定部を備え、
前記取得部は、前記測定部で測定された前記分布を示す前記測定データを取得する
請求項1~8のいずれか1項に記載の分布解析装置。 - 前記分布解析装置は、さらに、前記算出部で算出された前記解析データで示される前記分布を示す画像を生成する画像処理部を備える
請求項1~9のいずれか1項に記載の分布解析装置。
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EP2708884B1 (en) | 2018-07-11 |
US9568567B2 (en) | 2017-02-14 |
US20140081584A1 (en) | 2014-03-20 |
EP2708884A1 (en) | 2014-03-19 |
EP2708884A4 (en) | 2016-01-06 |
TW201300811A (zh) | 2013-01-01 |
JP6035535B2 (ja) | 2016-11-30 |
TWI463161B (zh) | 2014-12-01 |
JPWO2012153496A1 (ja) | 2014-07-31 |
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