Fast Fourier method for the accurate rotation of sampled images

Larkin, Kieran G.; Oldfield, Michael A.; Klemm, H.

doi:10.1016/s0030-4018(97)00097-7

Cited by 54 publications

(51 citation statements)

References 8 publications

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“…For a propagated distance from zero to infinity, the rotation angle α corresponds to 0°up to 90°. According to Larkin [10] and Lohmann [11], an arbitrary rotation matrix can be expressed as a product of three shearing matrices. When the fast Fourier transform is used to implement these shearing operations, this way produces accurate results for the rotated image.…”

Section: Results and Discussion Of Methodsmentioning

confidence: 99%

Propagation algorithms for Wigner functions

Zhong

Groß

2016

J. Eur. Opt. Soc.-Rapid Publ.

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We propose an algorithm to remove a parabolic wavefront from a convergent or divergent beam in the Wigner function. Using this approach we numerically collimate the beam. This avoids a dense sampling in phase space to describe a convergent wavefront. Thereby we reduce the required computer memory, but maintain computational accuracy and physical effects. Furthermore, we compare two algorithms, shearing and Radon transform, to propagate the Wigner function in free space. We use the fast Fourier transform to accurately perform shearing. However, zero-padding is necessary to circumvent aliasing. We prove that the Radon transform is a more efficient approach for a long propagated distance.

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Section: Results and Discussion Of Methodsmentioning

confidence: 99%

Propagation algorithms for Wigner functions

Zhong

Groß

2016

J. Eur. Opt. Soc.-Rapid Publ.

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“…Figure 5 (a) is an example of STEM image with accelerating voltage of 200 kV and magnification of 3,000,000. The inside of Si lattice (red frame of 700 × 700 pixels) is extracted and transformed to a frequency domain image ( Figure 5 (b)) with zero padding method 15,16 . The positions of peaks of the frequency domain image shown in Table 2 are compared with the Si lattice pattern ( Figure 5 (c)), then, an image pixel size and inclination angles of the image are calculated.…”

Section: Image Parameters Of Stem Image By 2d Fourier Analysismentioning

confidence: 99%

Sub-nanometer calibration of CD-SEM line width by using STEM

et al. 2010

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The novel calibration method of sub-nanometer accuracy for the line width measurement using STEM images is proposed to calibrate CD-SEM line width measurements. In accordance with the proposed method, the traceability and reference metrology of line width standards are established using Si lattice structures. First, we define the edge of a line as the end of Si lattice structure as the interface between Si lattice and oxide film. Second, an image magnification and inclination angles are calculated using 2D Fourier analysis of a STEM image. Third, the edge positions of the line are detected after the novel noise reduction method using averaging by Si lattice patterns. Then, the uncertainty of the line width measurement is evaluated with the uncertainty contributors of pixel size, edge detections and repeatability. Using the proposed method, the expanded uncertainty less than 0.5 nm for the line width of 45 nm is established.

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“…Local interpolation is an inexact step that destroys global information about the image. In spite of these disadvantages, an FFT-based rotation algorithm using three shears shows fast and accurate results [8, 19]. The basic concept of that method is that one can apply the 3 shear processes to the original image and each shear process is implemented by the FFT.…”

Section: Related Workmentioning

confidence: 99%

“…We report the results by the two methods (Method A and Method B) for computing S m ( θ ). We also report the test results of the FFT-based image rotation method developed by Larkin et al [8] and Owen et al [19] by applying their method to our example images. As mentioned earlier, in this FFT-based method, three consecutive shears are implemented using FFT.…”

Section: Rotation Of Images and Accuracy Testmentioning

confidence: 99%

Accurate Image Rotation Using Hermite Expansions

Park

Leibon

Rockmore

et al. 2009

IEEE Trans. on Image Process.

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In this paper we propose an approach for the accurate rotation of a digital image using Hermite expansions. This exploits the fact that if a 2D continuous band-limited Hermite expansion is rotated, the resulting function can be expressed as a Hermite expansion with the same band limit. Furthermore, the Hermite coefficients of the initial 2D expansion and the rotated expansion are mapped through an invertible linear relationship. Two efficient methods to compute the mapping between Hermite coefficients during rotation are proposed. We also propose a method for connecting the Hermite expansion and a discrete image. Using this method, we can obtain the Hermite expansion from a discrete image and vice versa. Combining these techniques, we propose new methods for the rotation of discrete images. We assess the accuracy of our methods and compare with existing FFT-based methods implementing three shears. We find that the method proposed here consistently has better accuracy than FFT-based methods.

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Fast Fourier method for the accurate rotation of sampled images

Cited by 54 publications

References 8 publications

Propagation algorithms for Wigner functions

Propagation algorithms for Wigner functions

Sub-nanometer calibration of CD-SEM line width by using STEM

Accurate Image Rotation Using Hermite Expansions

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