TWI764593B - Method of constructing three-dimensional model by tomographic reconstruction technology - Google Patents

Abstract

A method of constructing a three-dimensional model of an object to be inspected includes: obtaining a plurality of databases of two-dimensional tomographic images associated with the object to be inspected; constructing an initial three-dimensional model; and performing an iterative process, the iterative process comprising executing an iterative process. The rotation is transformed on the initial 3D model to obtain a 3D model to be replaced on a polar coordinate system in a 3D Fourier domain, the transformed database is used to replace a part of the 3D model to be replaced, and the above steps are repeated Until each of the converted images has been used to replace the three-dimensional model to be replaced, and the three-dimensional model of the object to be inspected is obtained according to the iterative process.

Description

A method of constructing a three-dimensional model by tomographic reconstruction technology

The present invention relates to a method for constructing a three-dimensional model of an object to be inspected, and more particularly to a method for constructing a three-dimensional model of an object to be inspected using tomographic reconstruction technology.

Conventionally, tomographic techniques enable imaging of the interior of an object. In use, a tomographic scan of the object may be performed by a tomographic imager (ie, a device for performing the tomography) to obtain a plurality of two-dimensional (two-dimensional) ( 2D) image. The 2D images are then used to construct a 3D model of the object for subsequent use (eg, inspection). Such operations may be referred to as tomographic reconstructions, and may be useful in fields such as wafer/metal defect inspection, semiconductor packaging, and health inspection.

Note that the tomography has a specific field of view (FoV), which may be smaller than the size of the object. In this case, the 2D images are caused by the fact that the information of the 2D images of the parts of the object may not include all the information of the object (eg, information at the edges of the object may be missing) does not accurately reflect the actual structure of the object. Alternatively, these two-dimensional images may have incomplete representations, resulting in artifacts.

One way to solve this problem is to place the object away from the tomograph to keep the whole of the object within the field of view of the tomograph, so that multiple two-dimensional images, each of the two-dimensional images showing an entire portion of the object. However, the 2D images obtained in this way have lower resolution and less image details.

Accordingly, it is an object of the present invention to provide a method that addresses at least one of the disadvantages of the prior art.

Therefore, the present invention provides a method for constructing a three-dimensional model of an object to be inspected. The method is implemented using a tomography device and a computing device. The method includes the following steps (a) to (e):

Step (a) obtaining by the tomograph a plurality of tomograms associated with the object to be inspected, each of the tomograms being at a specific angle relative to an axis of the object to be inspected location is extracted.

Step (b) generating, by the computing device, a plurality of two-dimensional tomographic image databases related to the object to be inspected according to the tomographic imaging, each of the tomographic image databases related to a respective one of the Isotomograms and data including the respective tomograms, the tomograms showing a portion of a polar coordinate system in a real domain of the object to be inspected.

Step (c) constructs an initial three-dimensional model of a rectangular coordinate system in the real domain by a processor.

(d) an iterative process is performed by the processor, and the iterative process includes the following sub-steps (d-1)~(d-4):

Sub-step (d-1) performs a spin transformation on the initial three-dimensional model in order to obtain a three-dimensional model to be replaced on a polar coordinate system in a three-dimensional Fourier domain, the three-dimensional model to be replaced by relative to The object to be inspected rotates at a spin angle of the axis,

Sub-step (d-2) performs a spatial transformation on each of the two-dimensional tomographic map databases to obtain a plurality of transformed databases obtained from the two-dimensional tomographic map databases, respectively and are respectively related to a plurality of transformed images on the polar coordinate system in the three-dimensional Fourier domain and respectively corresponding to the tomograms,

Sub-step (d-3) replaces the to-be-replaced image with one of the transformed images corresponding to one of the transformed databases on the polar coordinate system in the three-dimensional Fourier domain by the processor part of a 3D model, and

Sub-step (d-4) repeats sub-step (d-1) to sub-step (d-3) with the three-dimensional model to be replaced, the three-dimensional model to be replaced is performed in a previous sub-step (d-3) obtained in the process, as the initial 3D model will be processed during the execution of a current sub-step (d-1) until each of the converted images has been used to replace the 3D model to be replaced; and

Step (e) obtains, by the processor, the three-dimensional model of the object to be checked on the Cartesian coordinate system of the real domain according to a result of the iterative process of the sub-step (d-4).

Before the present invention is described in detail, it should be noted that where considered appropriate, reference numerals or terminal portions of reference numerals have been repeated in the figures to indicate corresponding or analogous elements, wherein such elements may alternatively have similar characteristics.

Throughout this invention, the word "coupled" may refer to a direct connection between a plurality of electrical equipment/devices/instruments through a conductive material (eg, a wire), or through another or more electrical equipment/devices/instruments or Wireless communication is an indirect connection between two electrical devices/devices/instruments.

1 is a block diagram illustrating a system 100 for implementing a method of constructing a three-dimensional model of the object 150 under investigation in accordance with an embodiment of the present invention. In this embodiment, the system 100 includes a tomograph 110 and a computing device 120 coupled to the tomograph 110 .

The tomography 110 may be implemented using a device capable of performing a tomography operation on the object 150 under investigation. The tomograph 110 may include elements configured to perform the tomography operation using X-rays, magnetic resonance imaging (MRI), optical projection, ultrasound, and the like. Through the tomography operation, the tomograph 110 can generate a plurality of two-dimensional (2D) images associated with the object 150 to be inspected. Specifically, the two-dimensional images respectively display various parts of the object to be inspected 150 . These two-dimensional images may be referred to as tomograms.

In the present embodiment, the object to be inspected 150 may be a fin field effect transistor (FinFET), a semiconductor device, a metal material, a biomedical material, or an object embedded in the object to be inspected 150 that may require structural inspection other kinds of objects.

The computing device 120 can be implemented using a server, a personal computer, a laptop, a tablet, a smart phone, or other devices with computing capabilities to perform the operations described below. In this embodiment, the computing device 120 can be a server and includes a processor 120 , a data storage 124 and a communication unit 126 .

The processor 122 may include, but is not limited to, a single-core processor, a multi-core processor, a dual-core mobile processor, a microprocessor, a microcontroller, a digital signal processor (DSP), a field programmable Logic gate array (FPGA), a special application integrated circuit (ASIC), a radio frequency integrated circuit (RFIC), etc.

The data storage 124 is coupled to the processor 122 and may use random access memory (RAM), read only memory (ROM), programmable read only memory (PROM), firmware, flash memory, etc. , or any combination thereof. The data storage 124 stores instructions that, when executed by the processor 122, cause the processor 122 to perform the operations described below.

The communication unit 126 may include at least a radio frequency integrated circuit (RFIC), a short-range wireless communication module that supports a short-range wireless communication network using wireless technologies such as a Bluetooth and/or wireless hotspot, and a short-range wireless communication module that supports the use of long-term evolution Long-distance communication technology (LTE), third-generation (3G) and/or fifth-generation (5G) wireless mobile long-distance communication technology, etc.

The tomograph 110 has a specific field of view (FoV). The system 100 may be configured to obtain a plurality of tomographic images of the object under investigation 150 and perform a method of constructing a three-dimensional (3D) model of the object under inspection 150 from the tomographic images.

FIG. 2 is a flowchart illustrating the steps of a method of constructing a three-dimensional model of the object 150 under investigation according to an embodiment of the present invention. In this embodiment, the method is implemented using the system 100 shown in FIG. 1 .

In step 202, the tomograph 110 is configured to obtain a plurality of tomograms of the object under investigation 150 on a polar coordinate system in a real field. In this embodiment, a plurality of tomograms are extracted, and each of the tomograms is extracted at a specific angular position relative to an axis of the object under investigation 150 (eg, a vertical penetration the central axis passing through the center of the object 150 to be inspected). FIG. 5 illustrates exemplary tomograms (64 in total) of the object 150 under investigation. Each of the tomograms can be extracted at a particular and different angular position relative to the axis of the object 150 under investigation.

FIG. 3 is a front view of an example of the object 150 to be inspected. As shown in FIG. 3 , the object to be checked 150 includes a plurality of three-dimensional structures, each of which is similar to an English character. In one embodiment, the object under inspection 150 may include a plurality of three-dimensional structures embedded therein; for example, a three-dimensional structure may be a specific layer in a semiconductor wafer.

It should be noted that the specific field of view of the tomograph 110 may be larger than one of the structures embedded on the object to be inspected 150 , but smaller than the size of the object to be inspected 150 . Furthermore, only a portion of the object 150 to be inspected is of interest, such as the structure "E" shown in the middle of FIG. 3 . Thus, in step 202, the tomography operation may be accomplished by placing the structure "E" in the center of the particular field of view of the tomograph 110, and the results of the tomograms may include not only Information for this structure "E", and includes information about other structures around or near this structure "E".

The tomograms can be obtained in one of a variety of commercially available ways, and the details of which are omitted here for brevity. Then, the tomograms are sent to the computing device 120 .

In step 204, in response to receiving the tomograms, the processor 122 of the computing device 120 is configured to generate a plurality of two-dimensional tomograms about the object 150 under investigation based on the tomograms Imaging map database. Each of the tomogram databases is related to a respective one of the tomograms showing the object under investigation and a respective one of data including the tomograms part of 150. The data for one of the tomograms includes, for each of the pixels of the tomogram, a pixel value and a coordinate set for the pixel on the polar coordinate system of the real domain. In the example of FIG. 5, sixty-four two-dimensional tomogram databases may be generated. Each of the two-dimensional tomogram databases may be represented in the form of at least one matrix. Each of the at least one matrix includes a plurality of elements, and each of the elements has a value that can be used to represent pixel data of the object 150 under investigation. That is, the matrices are generated from the tomograms, and the value of the element of one of the matrices is a pixel value corresponding to one of the tomograms.

In step 206, the processor 122 constructs an initial three-dimensional (3D) model in the rectangular coordinate system of the real domain. The initial three-dimensional model may be represented in the form of a matrix array comprising one of a plurality of matrices. Each of the matrices includes a plurality of elements, each of the elements having a value that can be used to represent pixel data for a three-dimensional object. It should be noted that the pixel data of the initial three-dimensional model may include any value in the matrix array.

In step 208 , the processor 122 performs an iterative process to extract the data of the tomographic images into the initial 3D model for constructing the 3D model of the object 150 under investigation. It should be noted that the purpose of performing the iterative process is to make the data of the tomograms (eg, the two-dimensional tomogram database) fit the initial three-dimensional model, so as to construct a structure that can accurately reflect the under-examination. The three-dimensional model of the object 150 .

Specifically, FIG. 5 is a flowchart illustrating exemplary sub-steps of the iterative process according to an embodiment of the present invention.

In sub-step 208a, the processor 122 performs a spin transformation on the initial 3D model. The spin transformation results in an alternate three-dimensional model being rotated on a polar coordinate system in the three-dimensional Fourier domain by a spin angle relative to the axis of the object 150 under investigation. It should be noted that the initial 3D model is used as the replacement 3D model of this generation in the first execution of sub-step 208a, and in subsequent iterations of sub-step 208a, the replacement 3D model of this generation is A 3D model of this generation replacement obtained in the latest execution.

Specifically, the spin transformation involves the operation of "spinning" the initial three-dimensional model originally on the Cartesian coordinate system to the polar coordinate system by a specific spin angle equal to the This angular position of one of the tomograms.

The reason for the spin transformation is that the tomogram is extracted on the polar coordinate system, which is different from the Cartesian coordinate system of the initial three-dimensional model, and in order to perform between the initial three-dimensional model and the slice For any operation between tomograms, both the initial three-dimensional model and the tomogram need to be represented on the same coordinate system in one of the same domains. Furthermore, the method involves frequently and correctly "spinning" the initial three-dimensional model at the equiangular positions relative to the tomograms on the polar coordinate system, and in the Cartesian coordinate system and the polar coordinate system There is no feasible fast Fourier transform in between, therefore, the present invention implements the spin transform in an efficient manner to achieve the desired operations, and is described below. Specifically, a plurality of geometric translation operations can be used to complete the operation of "translating a point of the initial three-dimensional system from the rectangular coordinate system of the real domain to a point of the polar coordinate system of the Fourier domain".

In this embodiment, each of the geometric translation operations is a two-dimensional Fast Fourier Transform (FFT) operation, which may be a sheared Fast Fourier Transform.

，其中，(x, y)代表該原點的坐標，及(

,

)代表該常規旋轉操作後的一新點的坐標。 It should be noted that, in order to achieve the result of a conventional rotation operation of an origin by an angle (θ), a plurality of shift operations respectively in different directions may be employed. This general rotation operation can be expressed in the form of a matrix operation:

, where (x, y) represent the coordinates of the origin, and (

,

) represents the coordinates of a new point after the normal rotation operation.

，其中，(x, y)代表該原點的坐標，及(

,

)代表該剪切變換操作後的一新點的坐標。圖6說明一相對於一水平方向的示例性剪切變換。 By a shear factor (α) in one direction, the shift operation of the origin (also called a "shear" transformation) can be expressed in the form of a matrix operation:

, where (x, y) represent the coordinates of the origin, and (

,

) represents the coordinates of a new point after the clipping transformation operation. FIG. 6 illustrates an exemplary shear transformation relative to a horizontal direction.

，及分別用於該剪切變換的該剪切因子α、β及γ可被計算為

、β=-sinθ。因此，子步驟208a的該等操作可使用三個基於上述之剪切因子的剪切快速傅立葉變換操作來完成。 Note that this spin transformation of sub-step 208a can be accomplished using multiple shear transformations with respect to different directions. The corresponding operation can be expressed as

, and the shearing factors α, β and γ for the shearing transformation, respectively, can be calculated as

, β=-sinθ. Thus, the operations of sub-step 208a can be accomplished using three sheared fast Fourier transform operations based on the shearing factors described above.

A spin operation as described above can be decomposed into three shear operations, each of which can be implemented in the Fourier domain by means of a fast Fourier transform. Specifically, each of the shear Fourier operations can be performed using a two-dimensional expansion of a one-dimensional (1D) Fourier shift theorem (ie, a one-dimensional Fourier transform).

In sub-step 208b, the processor 122 performs a spatial transformation on each of the two-dimensional tomographic image databases to obtain a plurality of transformed databases from the two-dimensional layers, respectively The analytical image database is obtained and separately correlated to the plurality of transformed images. The transformed images are on the polar coordinate system in the three-dimensional Fourier domain and respectively correspond to the tomograms.

It should be noted in this embodiment that the spatial transformation may be a two-dimensional fast Fourier operation. The purpose of sub-step 208b is to place the replacement 3D model and each of the transformed images on the same coordinate system (polar coordinate system) in the same domain (3D Fourier domain). Similar to the two-dimensional tomographic databases, each of the transformed databases may be in the form of at least one matrix.

In sub-step 208c, the processor 122 is programmed to replace the substitute with one of the transformed images corresponding to one of the transformed databases on the polar coordinate system in the three-dimensional Fourier domain Part of the replacement 3D model.

That is, after the replacement 3D model has been spun at an angle corresponding to one of the corners of the transformed images in sub-step 208a, the processor 122 may be configured to use the angular spin corresponding to the transformed images The transformed database of one of the images directly replaces a portion of the replacement 3D model that passes through the axis and has an angular position equal to the corner of one of the equally transformed images. In this manner, after each use of the converted images to replace portions of the replacement 3D model, the result of the 3D model can be an approximation of the 3D model forming the object 150 under investigation.

With further reference to FIG. 7, there are presented five exemplary converted images, each of which is at a particular corner. For each of the exemplary transformed images, in sub-step 208a, the initial 3D model is assigned a spin transformation, and in sub-step 208b, the transformed image is subjected to the spatial transformation and in sub-step 208b In step 208c, a portion of the three-dimensional model used to replace the replacement is obtained. That is, in the example of FIG. 5, sub-steps 208a-208c are repeated five times until each of the transformed images has been used to replace the portion of the replacement 3D model. It should be noted that, in other embodiments, multiple tomograms may be obtained, and sub-steps 208a-208c may be repeated to replace the alternate 3D generation with all combined images corresponding to the tomograms, respectively. Model.

Then, in sub-step 208d, the processor 122 performs a filtering noise operation on each of the converted databases.

Specifically, the processor 122 can be programmed to first perform an inverse spin operation (ie, a set of operations that achieves the opposite of the spin operations) after replacing the replacement three-dimensional image with the transformed images On the model, the replacement three-dimensional model is placed back on the Cartesian coordinate system of the real domain with a spin angle of zero.

Thereafter, the processor 122 determines whether any of the transformed databases contain values that are not possible for the replacement three-dimensional model of that generation.

For example, each of the transformed databases is in the form of at least one matrix, each of the matrices including a plurality of elements having a value. In this embodiment, the processor 122 determines, for each element, whether the element has a negative value and an imaginary value (based on noise results from the aforementioned operations). For any of a plurality of elements, when it is determined that the element has one of a negative value and an imaginary value, the processor 122 can be programmed to replace the value of the element with a zero value.

It should be noted that, in other embodiments, various noise filtering methods may be implemented. In this embodiment, for example, the noise filtering operation includes the processor 122 first determining that any of the elements is part of the object 150 to be inspected.

When determining that one of the elements is part of the associated object 150 and has a non-zero value, the processor 122 replaces the value of one of the elements with a zero value.

At this stage, the iterative process has completed once. In step 210, the processor 122 may determine whether to iterate the iterative process based on whether a predetermined convergence condition related to the iterative process is satisfied. The predetermined convergence condition may be that the equivalent values of the elements on the transformed database see no substantial change (substantially no change) between executions or iterations of the iterative process.

When the predetermined convergence condition is not met, the determination of step 210 is correct, and the flow returns to sub-step 208a and repeats the iteration for the three-dimensional model to be replaced that has been processed in the last iteration of step 208 generation process. Otherwise, the process proceeds to step 212 where the processor 122 obtains the three-dimensional model of the object 150 under investigation at the Cartesian coordinates of the real domain based on a result of the iterative process. This iterative process may need to be performed about three hundred times in order to satisfy the predetermined convergence condition. In other embodiments, a user may input a predetermined number (eg, 300), and then the processor 122 performs the iterative process for the predetermined number of times before obtaining the three-dimensional model.

FIG. 8 illustrates an image of the result of the 3D model of the object 150 under investigation, the image focusing on the middle structure "E". It should be noted that the resolution of the 3D model constructed using the aforementioned method (see part (a) of Fig. 8) is significantly higher than other conventional methods such as filtered back projection (FBP) (see Fig. 8(b) part) and the resolution of the three-dimensional model constructed by equal slope tomography (EST) (see part (c) of Fig. 8). FIG. 9 is a schematic perspective view of a portion of the three-dimensional model of the object 150 under investigation.

To sum up, the embodiments of the present invention provide a method for constructing a three-dimensional model of an object to be inspected. Since completing the job can be computationally intensive, the method includes an emerging way of efficiently "spinning" the three-dimensional model of the object under investigation. By using the two-dimensional fast Fourier transform operation, a time complexity of the spin transform may be (N logN), and a time complexity of the spin transform using the discrete Fourier transform is N ² . This greatly improves the efficiency of the operations in the iterative process, allowing the iterative process to be performed multiple times to achieve a more desirable result without spending a lot of time and computing power.

It should be noted that the foregoing method is particularly useful when only this portion of the object 150 to be inspected is of interest (eg, structure "E" in the middle of FIG. 3 ). Because the iterative process can be repeated more efficiently, the structure of the portion of the three-dimensional model of interest can be more focused on the portion of interest without obtaining a tomogram of the entire object 150 under investigation. Thus, it is possible to focus more on the tomograms of the portion of interest, allowing a higher resolution for the results of the obtained tomograms and the three-dimensional model.

It should also be noted that, in some embodiments, the tomographic images are obtained to reflect a specific part inside the object 150 to be inspected, wherein the object to be inspected 150 may have a larger size than the tomographic imager inside Neither the size of the specific field of view 110 nor the converted images correspond to the entirety of the object to be inspected 150 . That is, it is not necessary to obtain a tomographic image covering the entirety of the object to be inspected 150 in order to perform the aforementioned operations. In the example of Figure 10, a portion of the initial three-dimensional model corresponding to one of the tomograms may be selected, and the spin transformation performed relative to the portion of the initial three-dimensional model.

In the above description, for purposes of explanation, numerous specific details have been set forth in order to provide a thorough understanding of the embodiments. It will be apparent, however, to one skilled in the art that one or more other embodiments may be practiced without some of these specific details. It should also be understood that, in this specification, references to "an embodiment," an embodiment with an ordinal designation, mean that a particular feature, structure, or characteristic can be included in the practice of the invention. It will be further understood that in this specification, for the purpose of streamlining the invention and to assist in understanding its various aspects, various features are sometimes grouped together in the illustrations or descriptions of a single embodiment, and Where appropriate, one or more features or specific details from one embodiment may be practiced with one or more features or specific details from another embodiment in the practice of implementing the invention.

While the present invention has been described in connection with the exemplary embodiments, it should be understood that the invention is not limited to the disclosed embodiments, but is intended to cover various arrangements within the spirit and scope of the broadest interpretation to encompass all such Modifications and Equivalent Arrangements.

However, the above are only examples of the present invention, and should not limit the scope of implementation of the present invention. Any simple equivalent changes and modifications made according to the scope of the patent application of the present invention and the contents of the patent specification are still included in the scope of the present invention. within the scope of the invention patent.

202: Steps for obtaining multiple tomograms 204: Steps of generating a two-dimensional tomographic image database 206: Steps to construct an initial 3D model 208: the step of constructing the three-dimensional model of the object to be inspected 208a: Substep of performing a spin transformation on the initial 3D model 208b: Substep of performing a spatial transformation 208c: Substep of replacing part of the 3D model replaced by this generation 208d: Substep of performing a noise filtering operation on the converted databases 210: The step of determining whether to iterate 212: Steps based on a result of the iterative process 110: Tomography 120: Computing device 122: Processor 124: data storage 126: Communication unit 150: Object to be checked

Other features and effects of the present invention will be clearly presented in the embodiments with reference to the drawings, wherein: 1 is a block diagram of a system for implementing a method of constructing a three-dimensional model of the object 150 under investigation according to an embodiment of the present invention; 2 is a flowchart illustrating the steps of a method of constructing a three-dimensional model of the object to be inspected according to an embodiment of the present invention; 3 is a front view of an example of the object to be checked; Fig. 4 is a front view of an example of the object to be checked; FIG. 5 is an illustration of a plurality of example tomograms for obtaining the object under investigation; 6 is a schematic diagram illustrating an exemplary shear transformation relative to a horizontal direction; 7 is a schematic diagram illustrating that five exemplary converted images are used to replace the 3D model of the generation; 8 is a schematic diagram illustrating an image of the 3D model result of the object to be inspected; Figure 9 is a schematic perspective view of a portion of the three-dimensional model of the object to be inspected; and 10 is an example of a schematic diagram of a portion of the initial 3D model corresponding to the iterative process.

206: Steps to construct an initial 3D model

208: the step of constructing the three-dimensional model of the object to be inspected

208a: Substep of performing a spin transformation on the initial 3D model

208b: Substep of performing a spatial transformation

208c: Substep of replacing part of the 3D model replaced by this generation

208d: Substep of performing a noise filtering operation on the converted databases

210: The step of determining whether to iterate

Claims (9)

A method of constructing a three-dimensional model of an object to be inspected, the method is implemented using a tomographic imager and a computing device, the method comprising the steps of: (a) obtaining a plurality of correlations with the tomography imager The tomographic images of the object to be inspected, each of the tomographic images is extracted at a specific angular position relative to an axis of the object to be inspected; (b) generating a plurality of images with the computing device Regarding the two-dimensional tomogram database of the object under investigation according to the tomography, each of the tomogram databases is related to a respective tomogram and includes the respective slices data of tomograms showing the object to be inspected as part of a polar coordinate system in a real domain; (c) constructing, by a processor, an initial rectangular coordinate system in the real domain three-dimensional model; (d) executing an iterative process by the processor, the iterative process including the following sub-steps: (d-1) performing a spin transformation on the initial three-dimensional model to obtain a three-dimensional model to be replaced The model is on a polar coordinate system in a three-dimensional Fourier domain, the three-dimensional model to be replaced is rotated by a spin angle relative to the axis of the object under investigation, (d-2) performs a spatial transformation on the each of the two-dimensional tomogram databases in order to obtain a plurality of transformed databases obtained from the two-dimensional tomogram databases and respectively related to a plurality of transformed images, the transformed databases After the image is in the 3D Fourier domain on the polar coordinate system and respectively corresponding to the tomograms, (d-3), by the processor, using one of the transformed databases on the polar coordinate system in the three-dimensional Fourier domain one of the converted images to replace a part of the three-dimensional model to be replaced, and (d-4) repeat the sub-steps (d-1) to sub-steps (d-3) with the three-dimensional model to be replaced, The 3D model to be replaced is obtained during the execution of a previous sub-step (d-3), as the initial 3D model will be processed during the execution of a current sub-step (d-1) until the converted images each of which has been used to replace the three-dimensional model to be replaced; and (e) obtain, by the processor, the three-dimensional model of the object to be inspected according to a result of the iterative process of the sub-step (d-4) The model is on the Cartesian coordinate system of the real domain. The method for constructing a three-dimensional model of an object to be inspected as claimed in claim 1, wherein the sub-step (d-1) includes performing three geometric translation operations to implement the spin transformation. The method of constructing a three-dimensional model of an object under investigation as claimed in claim 2, wherein each of the geometric translation operations is a two-dimensional fast Fourier transform operation. The method of constructing a three-dimensional model of an object to be inspected as claimed in claim 3, wherein the fast Fourier transform operation is a shear fast Fourier transform operation. The method for constructing a three-dimensional model of an object to be inspected as claimed in claim 1, wherein the iterative process further comprises, after the replacement, a noise filtering operation on each of these transformed databases. The method for constructing a three-dimensional model of an object to be inspected as claimed in claim 5, wherein each of the converted databases is in the form of a matrix, the matrix includes a plurality of elements, and each of the elements has a value, and for each of the elements, the filtering noise operation includes: determining whether the element has one of a negative value and an imaginary value; and when determining that the element has one of a negative value and an imaginary value one, replace the value of the element with a zero value. The method for constructing a three-dimensional model of an object to be inspected as claimed in claim 5, wherein each of the converted databases is in the form of a matrix, the matrix includes a plurality of elements, and each of the elements has a value, and the filtering noise operation includes: determining whether any of the elements is associated with a portion of the object to be inspected; and when determining that one of the elements is associated with a portion of the object to be inspected and has a non-zero value, replaces the value of one of the elements with a zero value. The method for constructing a three-dimensional model of an object to be inspected as claimed in claim 1, wherein step (d) is repeated before step (e) until a predetermined convergence condition is satisfied with the relative iterative process. The method for constructing a three-dimensional model of an object to be inspected as claimed in claim 1, wherein: the tomographic images are obtained to reflect a specific part inside the object to be inspected, and none of the converted images corresponds to the object to be investigated and in sub-step (d-1), the spin is performed relative to a portion of the initial three-dimensional model, the initial three-dimensional model corresponding to one of the tomograms.

Images