Therefore, an object of the disclosure is to provide a three-dimensional (3D) reconstruction method and a 3D reconstruction device that are adapted for a thin film including a light element and that can alleviate at least one drawback of the prior art.
According to one aspect of the disclosure, the 3D reconstruction method is to be implemented by a scanning transmission electron microscope (STEM) and a processor, and includes the following steps.
In one step, by the STEM, N number of original projection images of a target area of the thin film sample are captured when the target area is at N number of different angles with respect to a horizontal plane, respectively, where N is a positive integer and the N number of different angles include a zero-degree angle, a plurality of positive angles and a plurality of negative angles.
In one step, by the processor, preprocessing is performed on the N number of original projection images to obtain N number of two-dimensional (2D) images that respectively correspond to the N number of different angles, where the preprocessing includes noise removal, field-of-view correction and background subtraction.
In one step, by the processor, a 3D reconstruction procedure is performed based on the N number of 2D images and N number of reference images that respectively correspond to the N number of different angles to obtain a piece of reconstructed 3D image data related to the target area. The 3D reconstruction procedure includes:
for each of the N number of 2D images, performing an alignment process on the 2D image so as to obtain an aligned 2D image that corresponds to the respective one of the N number of different angles, where the alignment process includes image shifting and image rotation, the 2D image is shifted by a pixel shifting amount that falls within a specific pixel range and rotated by an angle rotating amount that falls within a specific angular range to result in the aligned 2D image such that the aligned 2D image has minimum error in terms of pixel values with respect to the corresponding one of the N number of reference images, and the pixel shifting amount and the angle rotating amount for each of the N number of 2D images are recorded,
generating an initial 3D data distribution in reciprocal space based on the aligned 2D images that respectively correspond to the N number of different angles by using discrete Fourier transform and interpolation,
combining the initial 3D data distribution and an arbitrary data distribution to obtain a piece of 3D distribution data related to the target area in the reciprocal space, where the arbitrary data distribution is related to reciprocal lattice points in the reciprocal space without the initial 3D data distribution,
performing an iterative algorithm based on the piece of 3D distribution data to obtain a piece of iterative 3D distribution data in the reciprocal space, the iterative algorithm including performing inverse Fourier transform on the piece of 3D distribution data to obtain a piece of 3D image data in real space, extracting a 3D image data part that corresponds to the target area from the piece of 3D image data, and performing Fourier transform on the 3D image data part to obtain the piece of iterative 3D distribution data,
substituting a piece of 3D data in the reciprocal space for a data part of the piece of iterative 3D distribution data that corresponds to the target area to obtain a piece of updated 3D distribution data which serves as the piece of 3D distribution data for a next round of the iterative algorithm, the piece of 3D data being obtained by performing Fourier transform on the N number of 2D images,
repeating performing the iterative algorithm and substituting the piece of 3D data until it is determined that an error between the 3D image data part that was extracted in a latest round of the iterative algorithm and the 3D image data part that was extracted in a second latest round of the iterative algorithm is smaller than a threshold value, and
making the 3D image data part that was extracted in the latest round of the iterative algorithm serve as a piece of reconstructed 3D image data that is obtained in this round of the 3D reconstruction procedure.
In one step, by the processor, from the piece of reconstructed 3D image data, N pieces of 2D image data that respectively correspond to the N number of different angles are extracted to serve as the N number of reference images for a next round of the 3D reconstruction procedure.
In one step, by the processor, performing the 3D reconstruction procedure and extracting the N pieces of 2D image data are repeated until it is determined that the pixel shifting amounts and the angle rotating amounts recorded for the N number of 2D images in a latest round of the 3D reconstruction procedure match the pixel shifting amounts and the angle rotating amounts recorded for the N number of 2D images in a second latest round of the 3D reconstruction procedure.
In one step, by the processor, a reconstructed 3D image of the target area is generated based on the piece of reconstructed 3D image data that was obtained in the latest round of the 3D reconstruction procedure.
In one step, by the processor, a display device is controlled to display the reconstructed 3D image thus generated.
According to another aspect of the disclosure, the 3D reconstruction system includes a STEM, a storage device, a display device and a processor. The STEM includes a platform that is rotatable about an axis. The thin film sample is disposed on the platform and has a target area that corresponds in position to the axis. The STEM is configured to capture N number of original projection images of the target area when the target area is at N number of different angles with respect to a horizontal plane, respectively, where N is a positive integer and the N number of different angles include a zero-degree angle, a plurality of positive angles and a plurality of negative angles. The storage device is configured for data storage. The display device is configured for image display. The processor is electrically connected to the STEM, the storage device and the display device.
The processor is configured to receive the N number of original projection images from the STEM, and store the N number of original projection images in the storage device.
The processor includes a preprocessing module, an alignment module, a processing module, an iterative algorithm module, an iterative determination module, a reconstruction determination module and a reconstruction module.
The preprocessing module performs preprocessing on the N number of original projection images to obtain N number of two-dimensional (2D) images that respectively correspond to the N number of different angles. The preprocessing includes noise removal, field-of-view correction and background subtraction.
The processor performs a 3D reconstruction procedure based on the N number of 2D images and N number of reference images that respectively correspond to the N number of different angles to obtain a piece of reconstructed 3D image data related to the target area.
During the 3D reconstruction procedure,
the alignment module, for each of the N number of 2D images, performs an alignment process on the 2D image so as to obtain an aligned 2D image that corresponds to the respective one of the N number of different angles, where the alignment process that includes image shifting and image rotation, the 2D image is shifted by a pixel shifting amount that falls within a specific pixel range and rotated by an angle rotating amount that falls within a specific angular range to result in the aligned 2D image such that the aligned 2D image has minimum error in terms of pixel values with respect to the corresponding one of the N number of reference images,
the alignment module, for each of the N number of 2D images, records the pixel shifting amount and the angle rotating amount in the storage device,
the processing module generates an initial 3D data distribution in reciprocal space based on the aligned 2D images that respectively correspond to the N number of different angles by using discrete Fourier transform and interpolation,
the processing module combines the initial 3D data distribution and an arbitrary data distribution to obtain a piece of 3D distribution data related to the target area in the reciprocal space, where the arbitrary data distribution is related to reciprocal lattice points in the reciprocal space without the initial 3D data distribution,
the iterative algorithm module performs an iterative algorithm based on the piece of 3D distribution data to obtain a piece of iterative 3D distribution data in the reciprocal space, where the iterative algorithm includes performing inverse Fourier transform on the piece of 3D distribution data to obtain a piece of 3D image data in real space, extracting a 3D image data part corresponding to the target area from the piece of 3D image data, and performing Fourier transform on the 3D image data part to obtain the piece of iterative 3D distribution data,
the iterative algorithm module substitutes a piece of 3D data in the reciprocal space for a data part of the piece of iterative 3D distribution data that corresponds to the target area to obtain a piece of updated 3D distribution data that serves as the piece of 3D distribution data for a next round of the iterative algorithm, where the piece of 3D data is obtained by performing Fourier transform on the N number of 2D images and being stored in the storage device,
the iterative algorithm module repeatedly performing the iterative algorithm and substituting the piece of 3D data until it is determined by the iterative determination module that an error between the 3D image data part that was extracted in a latest round of the iterative algorithm and the 3D image data part that was extracted in a second latest round of the iterative algorithm is smaller than a threshold value,
the iterative determination module makes the 3D image data part that was extracted in the latest round of the iterative algorithm serve as a piece of reconstructed 3D image data that is obtained in this round of the 3D reconstruction procedure.
The processor is configured to extract, from the piece of reconstructed 3D image data, N pieces of 2D image data that respectively correspond to the N number of different angles to serve as the N number of reference images for a next round of the 3D reconstruction procedure.
The processor is configured to repeatedly perform the 3D reconstruction procedure and extract the N pieces of 2D image data until it is determined by the iterative determination module that the pixel shifting amounts and the angle rotating amounts recorded for the N number of 2D images in a latest round of the 3D reconstruction procedure match the pixel shifting amounts and the angle rotating amounts recorded for the N number of 2D images in a second latest round of the 3D reconstruction procedure.
The reconstruction module is configured to generate a reconstructed 3D image of the target area based on the piece of reconstructed 3D image data that was obtained in the latest round of the 3D reconstruction procedure.
The processor is configured to control a display device to display the reconstructed 3D image thus generated. |