The DOI matches its Crossref record; 27 of the 27 references it cites were found in a registry or an index.
Natural demodulation of two-dimensional fringe patterns I General background of the spiral phase quadrature transform
Abstract
It is widely believed, in the areas of optics, image analysis, and visual perception, that the Hilbert transform does not extend naturally and isotropically beyond one dimension. In some areas of image analysis, this belief has restricted the application of the analytic signal concept to multiple dimensions. We show that, contrary to this view, there is a natural, isotropic, and elegant extension. We develop a novel two-dimensional transform in terms of two multiplicative operators: a spiral phase spectral (Fourier) operator and an orientational phase spatial operator. Combining the two operators results in a meaningful two-dimensional quadrature (or Hilbert) transform. The new transform is applied to the problem of closed fringe pattern demodulation in two dimensions, resulting in a direct solution. The new transform has connections with the Riesz transform of classical harmonic analysis. We consider these connections, as well as others such as the propagation of optical phase singularities and the reconstruction of geomagnetic fields.
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Cited by
Felsberg, M., & Sommer, G. (2001) · IEEE Transactions on Signal Processing · doi:10.1109/78.969520 · Cited by 802
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Spiral phase contrast imaging in microscopy
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Transforms and Operators for Directional Bioimage Analysis: A Survey
Püspöki, Z., Storath, M., Sage, D., & Unser, M. (2016) · Advances in Anatomy, Embryology and Cell Biology · doi:10.1007/978-3-319-28549-8_3 · Cited by 522
Metadata
- Authors
- Larkin, K. G., Bone, D. J., & Oldfield, M. A.
- Venue
- Journal of the Optical Society of America A
- Publisher
- Optica Publishing Group
- Published
- 2001-08-01
- Volume
- 18
- Issue
- 8
- Pages
- 1862
- ISSN
- 1084-7529 (ISSN-L)
- 1520-8532
- OpenAlex
- W2023204304
- Cited by
- 421
- References
- 27
- FWCI
- 10.17
- Type
- journal article
- Language
- en
- Open access
- closed
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- Larkin, K. G., Bone, D. J., & Oldfield, M. A. (2001). Natural demodulation of two-dimensional fringe patterns I General background of the spiral phase quadrature transform. Journal of the Optical Society of America A. https://doi.org/10.1364/josaa.18.001862
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