阅读说明：本技术 一种复杂曲面超声阵列换能器阵元位置误差校正方法 (Complex curved surface ultrasonic array transducer array position error correction method ) 是由 孟彧仟 施钧辉 尹永刚 陈睿黾 李驰野 于 2021-10-27 设计创作，主要内容包括：本发明公开了一种复杂曲面超声阵列换能器阵元位置误差校正方法,该方法首先将待校正位置阵元坐标作为初始值；设定误差平方和比较阈值；然后获取点声源坐标及其到待校正位置阵元的距离；最后将非线性方程组线性化；根据最小二乘法解算坐标；将误差平方和预设门限比较。本发明以最小二乘法为基础,通过迭代解算出阵列换能器中各阵元的位置坐标,利用校正后的阵元位置坐标进行超声和光声成像,可以有效解决复杂曲面超声阵列换能器因阵元位置误差导致的图像发散和伪影问题,从而得到物体高精度的重构图像。(The invention discloses a position error correction method for a transducer array element of a complex curved surface ultrasonic array, which comprises the steps of firstly taking an array element coordinate of a position to be corrected as an initial value; setting a square error sum comparison threshold; then, acquiring the coordinates of the point sound source and the distance between the point sound source and the array element at the position to be corrected; finally, linearizing the nonlinear equation set; resolving coordinates according to a least square method; the squared error is compared to a preset threshold. The invention is based on least square method, calculates the position coordinates of each array element in the array transducer by iterative solution, and utilizes the corrected position coordinates of the array elements to carry out ultrasonic and photoacoustic imaging, thereby effectively solving the problems of image divergence and artifacts caused by the position error of the array elements of the ultrasonic array transducer with complex curved surfaces, and obtaining the high-precision reconstructed image of the object.)

1. A position error correction method for a complex curved surface ultrasonic array transducer array element is characterized by comprising the following steps:

s1, calculating to obtain the array element coordinate of the position to be corrected of the ultrasonic array transducer through the radius of the circular array and the number of the ultrasonic array transducer elements, and taking the coordinate as the initial value of the array element coordinate;

s2, setting an error square and a comparison threshold;

s3, acquiring externally introduced point sound source coordinates, and respectively calculating the distance from the point sound source coordinates to the array element to be corrected position of the ultrasonic array transducer obtained in the step S1 to obtain a nonlinear distance equation set;

s4, linearizing the nonlinear distance equation set obtained in the step S3;

s5, solving the distance equation set linearized in the step S4 according to a least square method, calculating coordinate value estimation errors, and obtaining accurate array element coordinates of the position array elements to be corrected;

s6, comparing the sum of squared errors with the comparison threshold set in step S2: if the sum of squared errors is less than the comparison threshold, stopping iteration; and if the sum of the squared errors is larger than the comparison threshold, repeating the steps S3-S5 for iteration until the sum of the squared errors is smaller than the comparison threshold.

2. The method for correcting the position error of the transducer element of the complex curved surface ultrasonic array according to claim 1, wherein the step S2 specifically comprises: and setting an error square sum comparison threshold according to the square sum of the precision of the space coordinate measuring equipment in the array element position correction system and the iterative convergence speed.

3. The method for correcting the position error of the transducer element of the complex curved surface ultrasonic array according to claim 1, wherein the step S3 specifically comprises:

obtaining three point sound source space coordinates for array element position correctionAnd respectively calculating the distances from the point sound source to the array elements to be corrected of the ultrasonic array transducer in the step S1 according to the acquired time delay information of the photoacoustic signals(ii) a Setting the coordinates of the array element of the position to be corrected as(ii) a The distances from the three point sound source space coordinates to the array element to be corrected respectively can beExpressed as the following system of equations:

。

4. the method for correcting the position error of the transducer element of the complex curved surface ultrasonic array according to claim 1, wherein the step S4 specifically comprises:

order toRespectively expressed as coordinates of array elements of the position to be correctedIs determined by the estimated value of (c),for the error of the estimated value, there are:

order toIs shown asIs determined by the estimated value of (c),for the error of the estimated value, there are:

will be provided withAt the point ofAnd performing Taylor series expansion to obtain:

thus, it is possible to obtain:

order toThen the following linearized system of equations can be obtained:

。

5. the method for correcting the position error of the transducer element of the complex curved surface ultrasonic array according to claim 1, wherein the step S5 specifically comprises:

order toComprises the following steps:

the estimation error of the coordinate values can be calculated as:

the finally obtained accurate coordinate of the array element of the position to be corrected is。

6. The method for correcting the position error of the transducer element of the complex curved surface ultrasonic array according to claim 1, wherein the step S6 specifically comprises:

if the sum of squared errors is less than the comparison threshold, i.e.Then stopping iteration; if the sum of the squared errors is greater than the comparison threshold, repeating the steps S3-S5, and using the estimated error of the coordinate value obtained in the step S5 to correctAndand iterating until the sum of squared errors is less than the comparison threshold.

Technical Field

The invention relates to the field of ultrasonic and photoacoustic imaging, in particular to a method for correcting position errors of a transducer array element of a complex curved surface ultrasonic array.

Background

Ultrasonic Tomography (UCT) refers to a technique for reconstructing internal (cross-sectional) information of an object from ultrasonic signal data detected from the outside of the object. According to the technology, multiple sound wave rays passing through the medium are extracted according to the difference of the propagation speeds of sound waves in different media, and the sound wave speed spatial distribution image of the medium is inverted to accurately describe the aggregate form and physical characteristics of the target body.

Photoacoustic tomography (PACT) is an emerging imaging technology for acquiring two-dimensional tomographic images or three-dimensional stereoscopic images of objects by using the Photoacoustic effect. The technology combines the advantages of optical imaging and ultrasonic imaging, and can realize biological tissue imaging with high resolution and contrast. Especially the non-invasive and non-ionizing imaging characteristics, has important application value in the biomedical field.

Both ultrasound imaging and photoacoustic imaging use ultrasound array transducers that contain multiple elements. In the reconstruction of the tomography image, only the accurate position of each array element is obtained, and the accurate image can be obtained. However, due to the limitation of the existing process conditions, in complex curved surface ultrasonic array transducers such as bowl-shaped arrays, annular arrays, flexible arrays and the like, a certain error exists between the actual position of each array element and the theoretical design position, and the position error of the array element can seriously affect the reconstructed image, so that the image has the phenomena of divergence, artifact and the like. Therefore, the research on the array element position error correction method has important application value for ultrasonic imaging and photoacoustic imaging.

Disclosure of Invention

The invention aims to provide a position error correction method for a transducer array element of a complex curved surface ultrasonic array aiming at the defects of the prior art so as to obtain the actual position of each array element and accurately reconstruct an image.

In order to achieve the purpose, the invention adopts the technical scheme that: a position error correction method for a complex curved surface ultrasonic array transducer array element comprises the following steps:

s1, calculating to obtain the array element coordinate of the position to be corrected of the ultrasonic array transducer through the radius of the circular array and the number of the ultrasonic array transducer elements, and taking the coordinate as the initial value of the array element coordinate;

s2, setting an error square and a comparison threshold;

s3, acquiring externally introduced point sound source coordinates, and respectively calculating the distance from the point sound source coordinates to the array element to be corrected position of the ultrasonic array transducer obtained in the step S1 to obtain a nonlinear distance equation set;

s4, linearizing the nonlinear distance equation set obtained in the step S3;

s5, solving the distance equation set linearized in the step S4 according to a least square method, calculating coordinate value estimation errors, and obtaining accurate array element coordinates of the position array elements to be corrected;

s6, comparing the sum of squared errors with the comparison threshold set in step S2: if the sum of squared errors is less than the comparison threshold, stopping iteration; and if the sum of the squared errors is larger than the comparison threshold, repeating the steps S3-S5 for iteration until the sum of the squared errors is smaller than the comparison threshold.

Further, the step S2 is specifically: and setting an error square sum comparison threshold according to the square sum of the precision of the space coordinate measuring equipment in the array element position correction system and the iterative convergence speed.

Further, the step S3 is specifically: obtaining three point sound source space coordinates for array element position correctionAnd respectively calculating the distances from the point sound source to the array elements to be corrected of the ultrasonic array transducer in the step S1 according to the acquired time delay information of the photoacoustic signals(ii) a Setting the coordinates of the array element of the position to be corrected as(ii) a The distances from the three point sound source space coordinates to the array element to be corrected can be expressed as the following equation set:

。

further, the step S4 is specifically:

order toRespectively expressed as coordinates of array elements of the position to be correctedIs determined by the estimated value of (c),for the error of the estimated value, there are:

order toIs shown asIs determined by the estimated value of (c),for the error of the estimated value, there are:

will be provided withAt the point ofAnd performing Taylor series expansion to obtain:

thus, it is possible to obtain:

order toThen the following linearized system of equations can be obtained:

。

further, the step S5 is specifically:

order toComprises the following steps:

the estimation error of the coordinate values can be calculated as:

the finally obtained accurate coordinate of the array element of the position to be corrected is。

Further, the step S6 is specifically:

if the sum of squared errors is less than the comparison threshold, i.e.Then stopping iteration; if the sum of the squared errors is greater than the comparison threshold, repeating the steps S3-S5, and obtaining the result S5The estimated error of the coordinate value is used for correctionAnduntil the sum of squared errors is less than the comparison threshold.

The invention has the beneficial effects that: the method for correcting the position error of the transducer array element of the ultrasonic array by using the optical fiber induced photoacoustic point sound source can accurately calculate the actual position of each array element, brings the position coordinate information of each array element into image reconstruction, and can obtain a clear and accurate reconstructed image of a phantom. The problems of image divergence and artifacts caused by array element position errors of the complex curved surface ultrasonic array transducer are solved.

Drawings

FIG. 1 is a process of solving array element coordinates according to an embodiment of the present invention;

FIG. 2 is a schematic diagram of the position correction of the array elements of the circular array in the embodiment of the present invention;

FIG. 3 is a diagram illustrating distances from the array elements to the center of the array before and after the array calibration according to an embodiment of the present invention;

FIG. 4 is a reconstructed image of a point source before array correction according to an embodiment of the present invention;

FIG. 5 is a point light source reconstructed image after array correction in an embodiment of the present invention;

FIG. 6 is a cross-hair reconstructed image before array correction in an embodiment of the invention;

FIG. 7 is a cross-hair reconstructed image after array correction in an embodiment of the invention.

Detailed Description

In order to make the aforementioned objects, features and advantages of the present application more comprehensible, embodiments accompanying the present application are described in detail below with reference to the accompanying drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application. This application is capable of embodiments in many different forms than those described herein and those skilled in the art will be able to make similar modifications without departing from the spirit of the application and it is therefore not intended to be limited to the embodiments disclosed below.

The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate preferred embodiments of the invention and together with the description, serve to explain the principles of the invention and not to limit the scope of the invention.

Locating an unknown point in a three-dimensional space, selecting at least three different position points in the space as known points, respectively drawing a spherical surface by taking the known points as the center of a circle and the distance between the unknown point and the known points as the radius, wherein the three spherical surfaces have two intersection points. According to the geometrical relationship between the unknown point and the three spherical surfaces, one of the points can be excluded, and the rest of the points are the unknown points to be positioned. If the coordinate values of the unknown points can be solved by a least square method of multiple iterations by taking the measurement error into consideration, the model can obtain more accurate results by using multiple known points. The invention is introduced based on a three-point positioning model, and the steps under the multi-point condition are similar to the three-point positioning model, so that the description is omitted.

And S1, calculating to obtain the array element coordinate of the position to be corrected of the ultrasonic array transducer through the radius of the circular array and the number of the elements of the ultrasonic array transducer, and taking the coordinate as the initial value of the array element coordinate.

And S2, setting error square sum comparison threshold according to the square sum of the precision of the space coordinate measuring equipment in the array element position correction system and combining the iterative convergence speed.

S3, acquiring externally introduced point sound source coordinates, and respectively calculating the distance from the point sound source coordinates to the array element to be corrected position of the ultrasonic array transducer obtained in the step S1 to obtain a nonlinear distance equation set; the method specifically comprises the following steps:

obtaining three point sound source space coordinates for array element position correctionAnd respectively calculating the distances from the point sound source to the array elements to be corrected of the ultrasonic array transducer in the step S1 according to the acquired time delay information of the photoacoustic signals(ii) a Setting the coordinates of the array element of the position to be corrected as(ii) a The distances from the three point sound source space coordinates to the array element to be corrected can be expressed as the following equation set:

。

s4, linearizing the nonlinear distance equation set obtained in the step S3; the method specifically comprises the following steps:

order toRespectively expressed as coordinates of array elements of the position to be correctedIs determined by the estimated value of (c),for the error of the estimated value, there are:

。

order toIs shown asIs determined by the estimated value of (c),for the error of the estimated value, there are:

。

will be provided withAt the point ofAnd performing Taylor series expansion to obtain:

。

thus, it is possible to obtain:

。

order toThen the following linearized system of equations can be obtained:

。

s5, solving the distance equation set linearized in the step S4 according to a least square method, calculating coordinate value estimation errors, and obtaining accurate array element coordinates of the position array elements to be corrected; the method specifically comprises the following steps:

order toComprises the following steps:

。

the estimation error of the coordinate values can be calculated as:

。

the finally obtained accurate coordinate of the array element of the position to be corrected is。

S6, comparing the sum of squared errors with the comparison threshold set in step S2: if the sum of squared errors is less than the comparison threshold, i.e.Then stopping iteration; if the sum of the squared errors is greater than the comparison threshold, repeating the steps S3-S5, and using the estimated error of the coordinate value obtained in the step S5 to correctAnduntil the sum of squared errors is less than the comparison threshold.

Example 1

The invention example 1 describes the correction of the position error of the transducer element of the annular ultrasonic array containing 512 array elements by the optical fiber induced photoacoustic point sound source, as shown in figure 2. This example 1 can be simplified to a two-dimensional plane positioning problem, that is, three different position points are selected as known points in a plane, and a circle is drawn by using the known points as the center of the circle and the distance between the unknown point and the known points as the radius, so that the three circles intersect at one point. This point is the unknown point that needs to be located. If the three circles do not intersect at one point, the least square method is adopted for iterative calculation, and the coordinate estimation value closest to the unknown point can be obtained.

And correcting the position error of the transducer array element of the ultrasonic array, and calculating the actual spatial position of each array element. An optical fiber photoacoustic point sound source is placed in a measuring area of the array, and photoacoustic signals received by all channels of the array are obtained through a data acquisition system. The operation is carried out at least three times, wherein the positions of the optical fiber photoacoustic point sound sources are different.

The array element coordinate calculation flowchart in embodiment 1 of the present invention is shown in fig. 1, and includes the following steps:

and S1, calculating to obtain the array element coordinate of the position to be corrected of the ultrasonic array transducer through the radius of the circular array and the number of the elements of the ultrasonic array transducer, and taking the coordinate as the initial value of the array element coordinate.

And S2, setting error square sum comparison threshold according to the square sum of the precision of the space coordinate measuring equipment in the array element position correction system and combining the iterative convergence speed.

And S3, acquiring the coordinates of the point sound source and the distance between the point sound source and the array element to be corrected.

Obtaining three point source spatial coordinates for array element position correction according to the above descriptionAnd calculating the distance from the point sound source to the array element to be corrected by acquiring the time delay information of the photoacoustic signal. Setting the coordinates of the array element of the position to be corrected as. The distances from the three point sound sources to the array element to be corrected can be expressed as the following equation system:

and S4, linearizing the nonlinear equation system.

Order toIs shown asEstimate of (b), QUOTEThe error of the estimated value is

。

Order toIs shown asIs determined by the estimated value of (c),the error of the estimated value is

。

Will be provided withAt the point ofThe Taylor series expansion is carried out, and high-order terms above the quadratic term are ignored, so that the method can obtain

。

Then can obtain

。

Order toThen the following system of equations can be obtained:

。

and S5, resolving the coordinates according to a least square method.

Order toThe method comprises the following steps:

。

the coordinate values can be calculated as follows:

。

the finally obtained array element coordinate is。

And S6, comparing the square of the error with a preset threshold.

The least square method is used for calculating the array element coordinates, and accurate space coordinates of each array element are finally calculated after repeated iterative convergence. If the sum of squared errors is less than the comparison threshold, i.e.Then stopping iteration; if the sum of the squares of the errors is larger than the comparison threshold, firstly, the coordinates of each array element calculated according to the array shape are used as initial values, the steps S3-S5 are repeated, and the coordinate value estimation errors obtained through iteration of the step S5 are used for correctingAnduntil the sum of squared errors is less than the comparison threshold, i.e.The iteration is stopped.

According to the steps, the plane positions of each array element in a regular linear array, a circular ring array and a planar array can be corrected, and the plane positions of each array element in a complex curved surface ultrasonic array transducer system with irregular space geometric distribution, such as a bowl-shaped array, a circular array, a flexible array and the like, can also be corrected.

The distances from the array elements to the center of the array before and after array correction are shown in fig. 3. The originally designed array has the radius of 50 mm, and 512 array elements are uniformly distributed along a circular ring. After correction, it can be seen that a certain error exists between the actual position of each array element and the design.

The results of the reconstructed images of the point source and the cross hair phantom in the gel before and after the array calibration are shown in fig. 4 to 7. Fig. 4 and 5 are respectively reconstructed images of point light sources before and after array correction in the embodiment of the present invention; fig. 6 and 7 are cross hair reconstructed images before and after array correction in the embodiment of the present invention. Comparing the four images, it can be seen that the system has divergence and artifact phenomena on the reconstructed image of the phantom before correcting the array, and the reconstructed image of the phantom can be clearly and accurately presented after correcting the array.

In summary, the method for correcting the position error of the transducer array element of the ultrasonic array by using the optical fiber-induced photoacoustic point sound source provided by the invention can accurately calculate the actual position of each array element, bring the position coordinate information of each array element into image reconstruction, and obtain a clear and accurate reconstructed image of a phantom.

The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.