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Power Vectors: An Application of Fourier Analysis to the Description and Statistical Analysis of Refractive Error
Abstract
The description of sphero-cylinder lenses is approached from the viewpoint of Fourier analysis of the power profile. It is shown that the familiar sine-squared law leads naturally to a Fourier series representation with exactly three Fourier coefficients, representing the natural parameters of a thin lens. The constant term corresponds to the mean spherical equivalent (MSE) power, whereas the amplitude and phase of the harmonic correspond to the power and axis of a Jackson cross-cylinder (JCC) lens, respectively. Expressing the Fourier series in rectangular form leads to the representation of an arbitrary sphero-cylinder lens as the sum of a spherical lens and two cross-cylinders, one at axis 0 degree and the other at axis 45 degrees. The power of these three component lenses may be interpreted as (x,y,z) coordinates of a vector representation of the power profile. Advantages of this power vector representation of a sphero-cylinder lens for numerical and graphical analysis of optometric data are described for problems involving lens combinations, comparison of different lenses, and the statistical distribution of refractive errors.
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Citations
Cited by
Thibos, L. N., Hong, X., Bradley, A., & Cheng, X. (2002) · Journal of the Optical Society of America A · doi:10.1364/josaa.19.002329 · Cited by 622
Self-citationPower vector analysis of the optical outcome of refractive surgery
Thibos, L. N., & Horner, D. (2001) · Journal of Cataract and Refractive Surgery · doi:10.1016/s0886-3350(00)00797-5 · Cited by 477
Self-citationEffect of Dual-Focus Soft Contact Lens Wear on Axial Myopia Progression in Children
Anstice, N. S., & Phillips, J. R. (2011) · Ophthalmology · doi:10.1016/j.ophtha.2010.10.035 · Cited by 422
A new non-contact optical device for ocular biometry
Santodomingo-Rubido, J. (2002) · British Journal of Ophthalmology · doi:10.1136/bjo.86.4.458 · Cited by 294
Theoretical performance of progressive addition lenses with poorly measured individual parameters
Pascual, E., Gómez‐Pedrero, J. A., & Alonso, J. (2023) · Ophthalmic and Physiological Optics · doi:10.1111/opo.13088 · Cited by 11
Metadata
- Authors
- Thibos, L. N., WHEELER, W., & Horner, D. G.
- Venue
- Optometry and Vision Science
- Publisher
- Wiley
- Published
- 1997-06
- Volume
- 74
- Issue
- 6
- Pages
- 367-375
- ISSN
- 1040-5488 (ISSN-L)
- 1538-9235
- OpenAlex
- W2012640979
- Cited by
- 1,238
- References
- 0
- FWCI
- 4.39
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- onlinelibrary.wiley.com/termsAndConditions#vor (vor)
- doi.wiley.com/10.1002/tdm_license_1.1 (tdm)
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- CoChat. (2026). Citation check: Power Vectors: An Application of Fourier Analysis to the Description and Statistical Analysis of Refractive Error. https://app.cochat.ai/papers/10.1002/j.1538-9235.1997.tb04707.x
- The paper
- Thibos, L. N., WHEELER, W., & Horner, D. G. (1997). Power Vectors: An Application of Fourier Analysis to the Description and Statistical Analysis of Refractive Error. Optometry and Vision Science. https://doi.org/10.1002/j.1538-9235.1997.tb04707.x
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
