Patent Application
20130148894
The present invention relates to an image reconstruction method and device of transmitting and receiving signals to and from a measurement region as a measurement object and determining the quantity of a physical property of the measurement region based on the actual receive signal. The present invention relates to a technique with which, even when the distribution of a physical property value such as a density inside the measurement object is non-uniform, the distribution of the physical property value inside the measurement region can be calculated within a feasible period of time without causing image deterioration due to phenomena such as refraction and multiple-reflections caused by the non-uniformity.
A measuring apparatus is an apparatus to form an image of the interior of a measurement object in non-invasive manner. The measuring apparatus transmits a measurement signal (for example, ultrasonic waves) to the interior of the measurement object from the boundary of the measurement object, and converts a measurement value measured at the boundary into a distribution of physical property value of the interior in accordance with an algorithm based on a physical equation which expresses a propagation phenomenon of the measurement signal. The measurement signal serves as a variable of the physical equation, the physical property values serve as a coefficient and an external force term of the physical equation, and the physical equation is used as an equation expressing a relationship between the measurement signal and the physical property values.
Algorithms for converting a measurement signal into physical property values based on physical equations have been studied as a coefficient identification problem and a boundary value problem in the field of scientific computing. Algorithms actually installed in devices are configured with their conversion accuracy reduced by applying approximation to equations in order to reduce the computation amount to an implementable level. An algorithm in a currently-commercialized product is a method of synthesizing directivities on the basis of an antenna technology, and makes such an approximation that each kind of physical property values of the interior of a measurement object is regarded as uniform. A breast-dedicated system, which is an advanced prototype equipped with a projection mapping algorithm similar to that for CT, also makes such an approximation that the physical property value is regarded as uniform, which means to assume the linearity of a measurement signal.
Moreover, as described in Patent Literature 1, a receive waveform is computed from a transmitted waveform in consideration of the non-uniformity of in-vivo physical property value and in consideration of wave propagation defined by the Helmholtz equation or the like. There is also a method of estimating an in-vivo physical property value by iterating a step of correcting the in-vivo physical property value so that a difference between the measured receive waveform and the calculated receive waveform can be made small.
A Method represented by Non-Patent Literature 1 described above can achieve short processing time because the method is based on approximate equations. In the case where a measurement object has a non-uniform interior structure, however, the method has a problem of being incapable of eliminating, in principle, image deterioration due to phenomena such as refraction and multiple-reflections caused by the non-uniformity.
In addition, the method represented by Patent Literature 1 consumes a time to calculate wave propagation inside a measurement object, and also requires this calculation to be iterated until the difference between the actually-measured receive data and the calculated receive data converges. Hence, the method has a problem of being unpractical when used as a medical apparatus which is required to achieve real-time performance.
The present inventors propose a method and device of transmitting and receiving measurement signals to and from the interior of a measurement object at a boundary of the object, and calculating a physical property value inside the measurement object from the measured value at the boundary, and propose a technique capable of calculating a distribution of physical property value inside the measurement object with an implementable calculation scale, even if the measurement object has a non-uniform internal structure, without having image deterioration due to phenomena such as refraction and multiple-reflections caused by the non-uniformity.
In particular, the present inventors propose a technique of achieving a significant reduction in a calculation scale for estimating a distribution of physical property value from receive data of actual measurement.
The present invention obtains a physical property value of a measurement object by using an evaluation quantity derived from physical equations without approximation. The present invention employs a method of estimating a deviation quantity that makes an assumed physical property value closer to a true physical property value, and thereby finding the true physical property value through update of the deviation quantity. Note that it is preferable to use a transmit sequence in which only signals making a large contribution to the image reconstruction are acquired. To be more specific, (a) the present invention proposes an image reconstruction method of transmitting and receiving signals to and from a measurement region as a measurement object and determining a quantity of a physical property of the measurement region through numerical calculation, the method including the following steps:
(1) a transmit-receive data acquisition step (means) of transmitting and receiving signals to and from the measurement region;
(2) a physical property value calculation step (means) of calculating a physical property value from an actual receive signal received from the measurement region; and
(3) a physical property value-display value conversion step (means) of converting the physical property value into a display value.
For instance, the physical property value calculation step uses, as an evaluation quantity, a linear sum of: (i) an equation residual quantity that is a residual being a difference between an operator term and an external force term of an equation of motion; (ii) a non-uniformity detection equation residual quantity that is a residual of an equation of detecting non-uniformity of the physical property value by using a matching degree of solutions of the equation of motion under two types of boundary conditions; and (iii) a conditional equation residual quantity that is a residual of a constraint condition, and outputs the physical property value that makes the evaluation quantity be an extremum to the physical property value-display value conversion step (means).
(b) Here, the transmit-receive data acquisition step preferably includes a transmit-receive sequence determination step of determining: (i) the number of times of performing transmissions-and-receptions by transceiver elements, (ii) a spatial layout of the transceiver elements and (iii) transmit-and-receive waveforms, and obtaining results of the transmissions-and-receptions.
In this connection, a receive sequence determination step preferably determines that the number of times of performing transmissions-and-receptions by the transceiver elements is two or more, that the transmit waveform at least includes a plurality of plane burst waves having an equal burst length but having different carrier frequencies within a range of 0.5 MHz to 10 MHz, both inclusive, that the spatial layout of the transmitter elements has spacing inversely proportional to the carrier frequencies, and that a spatial layout of receiver elements is a layout that maximizes an angle of view in the measurement region.
(c) Moreover, the transmit-receive sequence determination step preferably outputs a transmit-receive sequence in which: the number of times of performing transmissions-and-receptions is two or more; and the frequency used in the transmission-and-reception becomes lower as a transmission-and-reception time becomes earlier.
(d) Additionally, the non-uniformity detection equation residual quantity is preferably a residual being a difference between: (i) a differential vector that is a difference between a solution under a Neumann boundary condition and a solution under a Dirichlet boundary condition in a case where a boundary value is actual transmit-receive data, and (ii) a product of a vector expressing the non-uniformity of the physical property value and an operator matrix that is a difference between a Green's function of the equation of motion under a Neumann boundary condition and a Green's function of the equation of motion under a Dirichlet boundary condition in a case where the boundary value is zero.
(e) Further, a conditional equation residual quantity of the evaluation quantity preferably includes at least one of a prior probability quantity that is a prior probability expressing the nature of a distribution of the evaluation quantity of the physical property value, and a low order approximation matching quantity indicating a matching degree with an image reconstructed by a method of synthesizing directivities or projection mapping.
(f) Furthermore, the physical property value calculation step preferably calculates the physical property value that makes the evaluation quantity be an extremum, by using metropolis sampling that is one of stochastic methods.
(g) The evaluation quantity or the equation residual is preferably a residual of any equation among a frequency representation of an elastodynamic equation, a time response representation of the elastodynamic equation and a Helmholtz potential representation value. Moreover, the physical property value is preferably one or more of a Lamé's constant λ, a Lamé's constant μ, a density of inertia ρ, an attenuation coefficient c, ratios therebetween, and a force source f. In addition, the display quantity is preferably any one or more of the λ, the μ, the ρ, the c, and functions thereof including a bulk modulus, a longitudinal wave velocity, a transverse wave velocity, a Poisson's ratio, and a Young's modulus, an impedance, and the force source f.
The present invention uses physical equations without approximation, and thereby enables image reconstruction without having image deterioration due to phenomena such as refraction and multiple-reflections caused by the non-uniformity. Moreover, the processing speed of the image reconstruction is determined depending on a period of time for signal acquisition and a period of time for calculation. In this regard, the period of time for signal acquisition is reduced by use of a transmit sequence in which only signals making large contribution to the image reconstruction are acquired, and the period of time for calculation is reduced by use of the equation of estimating the deviation quantity of the assumed physical property value from the true physical property value. Thus, the present invention achieves a feasible processing period of time of the image reconstruction.
Hereinafter, embodiments of the present invention are described based on the drawings. It should be noted that the details of device configurations and processing operations described below are one example for explaining the present invention. The present invention also includes any combination of the device configurations and processing operations described below, a combination in which an existing technique is added to any of the device configurations and processing operations described below, and a combination in which part of the device configurations and processing operations described below is replaced with an existing technique.
In the first place, an outline of characteristic features of the present invention is described by using
On the other hand, the present invention employs a configuration in part (b) of
(Configuration of Image Reconstruction Apparatus)
Hereinafter, an embodiment is explained with reference to
The probe 2 includes multiple transceiver elements 21. The main body 1 includes a transmitter 3, a receiver 4, a signal processor 5, a memory 6, a display 7, an input means 8, and a controller 9. The signal processor 5 further includes: a transmit-receive data acquisition part 51 transmitting and receiving measurement signals to and from a measurement region, and outputting an actual receive signal that is the signal thus received; a physical property value calculation part 52 receiving the actual receive signal from the transmit-receive data acquisition part, converting the actual receive signal into a physical property value of the measurement region, and outputting the physical property value; and a physical property value-display quantity conversion part 53 receiving the physical property value from the physical property value calculation part and converting the physical property value into a display quantity. The physical property value calculation part 52 indicated by a thick frame in
(Measurement Operations of Image Reconstruction Apparatus)
The image reconstruction device according to the embodiment performs signal processing in the following procedure.
Firstly, the transmit-receive data acquisition part 51 of the signal processor 5 determines a transmit sequence that is composed of transmission waveforms for the respective transceiver elements 21. The determined transmit sequence is outputted directly to the transmitter 3 from or is written to the memory 6 by the transmit-receive data acquisition part 51. The transmit sequence written in the memory 6 is read from the memory 6 and outputted to the transmitter 3 at predetermined timing.
Next, an operator performing the measurement operation while viewing a display screen of the display 7 performs manual input for start of imaging of a measurement region by using the input means 8 such as a mouse, a keyboard, an operation bottom or another means. Upon detection of the manual input, the input means 8 outputs an imaging start signal to the controller 9. Upon receipt of the imaging start signal, the controller 9 notifies the signal processor 5 of the start of imaging processing.
Upon receipt of the transmit sequence from the signal processor 5 or the memory 6, the transmitter 3 sends the signals to the measurement object from the transceiver elements 21 corresponding to the transmit sequence. For instance, ultrasonic signals are transmitted to an imaging subject such as a living body.
At the same time as the transmission start of the transmit sequence, the receiver 4 receives, via the transceiver elements 21, receive signals corresponding to signals reflected from the imaging subject or transmitted through the imaging subject. The receiver 4 outputs the receive signals from the respective transceiver elements 21 to the signal processor 5.
The signal processor 5 firstly receives, at the transmit-receive data acquisition part 51, the transmit-receive data from the respective transceiver elements 21. Then, the signal processor 5 calculates, at the physical property value calculation part 52, physical property values such as Lamé's constants λ, μ, and a density of inertia ρ on the basis of the transmit-receive data from the respective transceiver elements 21. Subsequently, the signal processor 5 converts the physical property values such as the Lamé's constants and the density of inertia ρ into display quantities of the physical property values to themselves, or other values such as a longitudinal wave velocity (λ+2μ)/ρ, a transverse wave velocity μ/ρ, and a bulk modulus (λ+2μ)/ρ and outputs the display quantities to the memory 6.
The memory 6 outputs the written display quantities to a monitor or the like of the display 7. The display 7 shows the display quantities corresponding to the physical property values on the screen.
(Outline of Processing Operation)
Part (a) of
As illustrated in part (a) of
(Details of Transmit-Receive Data Acquisition Step)
Part (b) in
(Details of Physical Property Value Calculation Step)
Part (a) of
Upon start of the physical property value calculation step (S200), an initial value of a physical property value is set in an initial physical property value setting step (S201). Then, a transmit-receive data calculation step (S202) calculates an actual receive signal that is a receive signal corresponding to the initial value of the physical property value. The subsequent convergence determination step (S203) determines whether or not the calculation result is converged depending on whether or not the evaluation quantity J is an extremum. When the determination result in the step (S203) is negative (No), the physical property value update step (S204) updates the physical property value, and returns to the calculate-and-receive data calculation step (S202) for the updated physical property value. This loop processing is iterated until the determination result in the step (S203) becomes affirmative (Yes). The physical property value in the case where the determination result in the step (S203) is affirmative (Yes) is outputted to the physical property value-display quantity conversion step (S300). The convergence determination step (S203) and the physical property value update step (S204), indicated by thick frames among the processing steps illustrated part (a) of
In the case of the present embodiment, the “evaluation quantity” is given as a linear sum of (1) an equation residual quantity that is a residual being a difference between an operator term and an external force term of an equation of motion, (2) a non-uniformity detection equation residual quantity that is a residual of an equation of detecting the non-uniformity of physical property value depending on the matching degree between solutions of the equation of motion under two types of boundary conditions, and (3) a conditional equation residual quantity that is a residual of a constraint condition. It should be noted that the evaluation quantity may be given as any one of these residual quantities, a linear sum or a product of plural ones of them, or an exponential function including them as exponents.
(Details of Evaluation Quantity)
The following provides explanation of details of the evaluation quantity. First of all, the explanation is provided for a case where whether or not the evaluation quantity J is converged is determined depending on whether the evaluation quantity J takes an extremum (zero in this embodiment). This determination, however, is equivalent to maximizing P=exp(−Ĵ2) that is an exponential function of the “non-uniformity detection equation residual quantity” J. In other words, the calculus of variations using the evaluation quantity J can be also expressed as processing of maximizing an exponential function P representing a probability density.
In the case where the measurement signals are ultrasonic waves, an equation of motion is given using a frequency representation of an elastodynamic equation, a time response representation of the elastodynamic equation or a Helmholtz potential representation of the elastodynamic equation. In this case, the physical property values are a Lamé's constant λ, a Lamé's constant μ, and a density of inertia ρ. In the case where a measurement region is a human body, the initial physical property values λ and ρ are given as 2e9 [kg/m/seĉ2] and 1e3 [kg/m̂3], respectively, which are set to be uniform within the entire measurement region.
Firstly, a basic evaluation quantity is explained. The basic evaluation quantity is a residual being a difference between an operator term and an external force term of an equation of motion and is called as an equation residual quantity Jeq. Here, in the equation of motion, the operator is expressed by a matrix G(ε)[i][j], a displacement is expressed by a vector p, and the external force is expressed by a vector f, where G is a function of a physical property value ε to be obtained. In this case, a relationship G*p=f holds among these quantities. Hence, if the equation residual quantity Jeq is defined as Jeq=G*p−f, Jeq is a function of the physical property value ε, and the equation residual quantity Jeq is 0 when εA is a true value. A generally-known method may be used as a method of obtaining the physical property value εA that makes the equation residual quantity be 0. For instance, use of the method of steepest descent with Jeq=−(G*p−f)2 or the like can be cited as one example.
By use of this evaluation quantity Jeq, a solution satisfying an ideal (not-approximated) physical equation can be obtained as a physical property value that gives the extremum (zero in this embodiment) of the evaluation quantity J. In addition, influences of refraction and scattering can be eliminated from the physical property value thus obtained.
Next, an evaluation quantity for obtaining a physical property value at high speed is explained.
The boundary conditions of the equation of motion are two types, that is, the Neumann condition and the Dirichlet condition. Here, for the equation of motion having a set physical property value as a coefficient, a solution under the Neumann condition (the boundary value=the actual transmit-receive data) is denoted by h1, and a solution under the Dirichlet condition (the boundary value=the actual transmit-receive data) is denoted by d1. In addition, for the equation of motion having the set physical property value as the coefficient, a solution under the Neumann condition (the boundary value=0; the non-uniformity is taken into account) is denoted by h2, and a solution under the Dirichlet condition (the boundary value=0; the non-uniformity is taken into account) is denoted by d2. In this case, the solution obtained in consideration of the non-uniformity with the actual transmit-receive data used as the boundary value is given as h1+d1 under the Neumann condition or as h2+d2 under the Dirichlet condition. If the non-uniformity is estimated precisely, the two conditions match with each other. That is to way, h1+d1=h2+d2 holds.
For this reason, in this description, the evaluation quantity J defined as the following equation the solution of which is 0 if the non-uniformity is estimated precisely is used as an equation of detecting the non-uniformity of the physical property value depending on the matching degree between the solutions of the equation of motion.
J
dh=(−h1+h2)−(d1−d2) (1) Equation
This evaluation quantity J (Jdh) serves as a “non-uniformity detection equation residual quantity” in Claims.
Here, σ denotes a quantity indicating a difference between a set value and a true value of the Lamé's constant λ, and μ denotes a quantity indicating a difference between a set value and a true value of the density of inertia ρ. By using a matrix representation GN[i][j] of a Green's function of the equation of motion under the Neumann condition (this is configured in the same manner with a method such as the finite element method), and the matrix representation GD[i][j] of the Green's function of the equation of motion under the Dirichlet condition, the second quantity on the right side of (1) Equation (i.e., d1−d2) can be expressed as a product of a matrix (GD−1-GN−1) and a vector (σ, μ).
In the present embodiment, a deviation quantity dεI of the physical property value is calculated (deviation quantity estimation step) by using the following relation derived for σ based on the foregoing relation:
GN(dεi)*(h1+d1)=σ (2) Equation,
and the set value εi of the physical property value is sequentially updated to εi+1=εi+dεi (physical property value update step). The deviation quantity dεi herein is a value relative to the initial valuesI0 of the physical property value. The derivation of the (2) Equation is described in details later.
The setting and update of the physical property value (S204) are iterated until the fulfillment of a condition (S203), for a set minute quantity e, in which the evaluation quantity Jdh(εi) having as a variable the physical property value εi updated by an i-th update can be regarded as 0 (i.e., |Jdh(εi)|<e), or in which the exponential function exp(−|Jdh(εi)|2) of the evaluation quantity can be regarded as maximum (i.e., |exp(−|Jdh(εi+1)|2)−exp(−|Jdh(εi)|2)|<e). Then, the set value of the physical property value taken when the condition (convergence condition) is fulfilled is used as an estimated value for output of the physical property value calculation step (S205). Note that, the evaluation quantity J is calculated from the transmit-receive data (S202).
By use of this evaluation quantity J, the solution satisfying the ideal (not-approximated) physical equation can be obtained as the physical property value that gives the extremum (zero in this embodiment) of the evaluation quantity J. In addition, the influences of refraction and scattering can be eliminated from the physical property value thus obtained. Moreover, the physical property value can be obtained within a short calculation period of time.
Next, description is provided for a case where the convergence determination step (S203) is executed as processing of maximizing the exponential function P. When a constraint condition includes a prior probability, the convergence determination step (S203) can be expressed as in part (b) of
Here, “c” denotes a physical property value within a measurement region, and “lc” denotes a linear process that takes a value “1” at a discontinuous portion and takes a value “0” at a continuous portion. In this case, a prior probability quantity Jc expressing an assumption that the physical property value distribution is composed of a domain in which constant values continue and its boundary in space can be expressed as, the following equation:
Jc=(∇c)̂2(1−lc)+lc (3) Equation.
This prior probability quantity Jc serves as the “conditional equation residual quantity” Jc in Claims. The prior probability quantity Jc can be also expressed as an exponential function Pc=exp(−Jĉ2) as in the case with the “non-uniformity detection equation residual quantity” J. When the physical property value is calculated with the prior probability quantity introduced as described above, an information quantity necessary for the calculation of the physical property value can be complemented. Hence, even if there is a shortage of measurement points, the physical property value in the measurement region can be calculated. Note that the evaluation quantity in the case where the evaluation quantity J is complemented by the prior probability quantity Jc is given as Ĵ2+Jĉ2 or P*Pc(=exp(−(Ĵ2+Jĉ2)).
Here, the evaluation quantity J is given as a primary expression of receive data, and the exponent (−Ĵ2) of the exponential function P is given as a secondary expression of the receive data. A calculation of an inverse matrix generally requires a long period of time. When each function is a primary or secondary expression, however, the Sherman-Morrison formula, the Woodbury formula or any other perturbation expansion formula for a matrix can be applied to a small change in the matrix (GN-GD) associated with a small change in the physical property value in step S204, and accordingly the calculation amount required to update the calculation result of the evaluation quantity J can be reduced. Specifically, a significant reduction in the time for the calculation of the inverse matrix leads to a reduction in the time for the whole calculation of the evaluation quantity J.
The foregoing description is provided for the case where the quantity (conditional equation residual quantity) in which the conditional expression assisting the calculation of the physical property value is reflected is expressed by using the prior probability quantity Jc. Instead, it is also possible to define a low order approximation matching quantity using an image calculated by a conventional image reconstruction method as a complement, and to define the aforementioned “conditional equation residual quantity” Jc as a sum of the prior probability quantity and the low order approximation matching quantity.
More specifically, the prior probability calculation step S2031 may include (1) the prior probability quantity calculation step, and (2) a low order approximation matching quantity calculation step. Here, the low order approximation matching quantity calculation step may include (1) an image formation step of forming an image of a physical property value distribution c′ by the directivity synthesizing method, projection mapping or any other conventional method; and (2) a low order approximation matching quantity calculation step of calculating a low order approximation matching quantity that is a secondary expression (c-c′)̂2 of a difference (=c-c′) between the physical property value distribution c assumed in the physical property value update step S204 and a physical property value distribution c′ (image) obtained by the conventional method. Then, the “conditional equation residual quantity” Jc may be calculated as a sum of the prior probability quantity and the low order approximation matching quantity:
Jc=(∇c)̂2(1−lc)+lc+(c-c′)̂2 (4) Equation.
The foregoing description is provided for the method of obtaining the physical property value that minimizes the linear sum of secondary expressions of Ĵ2+Jĉ2 specified by the “non-uniformity inspection equation residual quantity” J and the “conditional equation residual quantity” Jc or that maximizes the exponential function P*Pc=exp(−(Ĵ2+Jĉ2)) specified by these two residual quantities. Instead, the evaluation quantity may include an equation residual quantity Je that is given as a secondary expression of a difference between the right side and the left side of an equation of motion. In this case, the physical property value may be obtained which minimizes a linear sum of secondary expressions of Ĵ2+Jĉ2+Jê2, or maximizes the exponential function P*Pc*Pe=exp(−(Ĵ2+Jĉ2+Jê2)).
In the present invention, if the conditional equation residual quantity of the evaluation quantity includes at least one of: the prior probability quantity that is a prior probability indicating the nature of a physical property value distribution; and the low order approximation matching quantity that indicates the matching degree with an image reconstructed by a method of modeling receive signals by use of the directivity synthesizing method or projection mapping, the introduction of the prior probability can complement the information quantity. Thus, even if there is a shortage of measurement points, the physical property value in the measurement region can be calculated.
Moreover, the aforementioned matrix (GN-GD) is not a full rank matrix. For this reason, (σ*, μ*) that is a solution to the matrix (GN-GD)×vector(σ, μ)=0 is a variable quantity. Hence, one possible example of the above physical property value update step (S204) is to update the physical property value by sampling this variable quantity.
When an update value candidate (σ′, μ′) of the physical property value is stochastically sampled, the current physical property value (σ, μ) can be updated to an updated value according to the following equation:
P(σ,μ→σ′,μ′)=min(1,P(σ,μ)/P(σ′,μ′)) (5) Equation.
Here, P(σ, μ) is exp(−Jσ, μ̂2−J), and P(σ′, μ′) is exp(−Jσ′, μ′̂2−J). This update rule is called as the metropolis sampling method. The execution of the above processing makes the calculation scale small.
Hereinafter, description is provided for a case where the foregoing image reconstruction device is used to measure the interior of a human body.
In these drawings, “001” to “013” are internal structures that cause the non-uniformity. Incidentally, “001” is a cerebral gray matter, “002” is a cerebral white matter, “003” is the skull, “004” is an epithelium, “005” is a fat, “006” is an epithelium, “007” is a muscle, “008” is a body cavity, “009” is an organ, “010” is an epithelium, “011” is a fat, “012” is a fibroma, and “013” is a cancerous tissue. The placement position of the probe 2 on a space may be a part of the boundary of the measurement region as illustrated in
The physical property value calculation part 52 sets a measurement region 411 for numerical calculation within a space in the measurement object as illustrated in part (b) of
Parts (a) to (c) of
(Example of Data Format)
Under these settings, the physical property value εAi is calculated by using the data formats (b) to (e) in
The data (d1) is a matrix GD[i][j] expressing a Green's function of the equation of motion for the Dirichlet condition, whereas the data (d2) is a matrix GN[i][j] expressing a Green's function of the equation of motion for the Neumann condition. Both of (d1) and (d2) have a size of 24 (the number of sides) rows and 24 columns, and are functions of the set value of the physical property value. In other words, if the assumed value of the physical property value is changed, the values of the matrices are changed. Please see a general text book for relations between the physical property value and the matrices. By using these data, the physical property value described with reference to
In this calculation, a value of σ is calculated with Jdh=0, the deviation quantity dεi of the physical property value is calculated by using the relation expressed by (2) Equation (i.e., GN(dεi)*(h1+d1)=σ), and the set value εi of the physical property value is updated to εi+1=εi+dεi.
The transmit-receive wave data c1 and c2 in
(Relationship Between Evaluation Quantity and how to Calculate Physical Property Value)
(Example of Transmit Sequence Transmission)
In the case of
Note that 21L1 (indicated by hatching) in part (a) of
Employment of the basic sequence having the aforementioned transmission waveforms and spatial layout of the transceiver elements 21 enable generation of sound fields which have simple and similar forms only having a difference between their carrier frequencies. This results in an improvement of the identification accuracy of the sound speed that is a ratio between the Lamé's constants and the density of inertia by using the evaluation quantity. Moreover, identification accuracy of inertia mass can be improved by use of a difference between the carrier frequencies. In addition, use of plane burst waves as in this example can improve S/N due to measurement noise, as compared with a case where only one transceiver element 21 transmits a signal.
Parts (a1) and (a2) of
Parts (b1) to (b3) of
In the case where the probe 2 is in contact with part of the boundary of the measurement object 0 as illustrated in
On the other hand, in the case where the probe 2 is in contact with the entire boundary of the measurement object 0 as illustrated in
For instance, the example in
A low-frequency burst plane wave is transmitted in the directions in part (b1) of
The example in
The transmitter elements T placed on the upper side in the drawing with inter-element spacing of 2d transmit a low-frequency burst plane wave in the directions in part (b1) of
In this case, the same transceiver elements 21 placed on the circumference at equal intervals as illustrated in parts (a1) and (a2) of
The description has been provided for the examples in which the transmit-receive data is transmitted and received 6 times in
| Number | Date | Country | Kind |
|---|---|---|---|
| 2010-193031 | Aug 2010 | JP | national |
| Filing Document | Filing Date | Country | Kind | 371c Date |
|---|---|---|---|---|
| PCT/JP2011/067201 | 7/28/2011 | WO | 00 | 2/7/2013 |
