The power of a cylinder in an oblique meridian: Revisiting an old controversy

Ophthalmic and Physiological Optics

Volumn 26, Issue 2, 2006, Pages 189-198

  Naeser, Kristian ^a,b   Hjortdal, Jesper ^a  

^a AARHUS UNIVERSITY HOSPITAL   (Denmark)

^b Randers Centralsygehus ^*  (Denmark)

Author keywords

Astigmatism; Curvital power; Fourier decomposition; Polar values; Sine squared correlation; Torsional power

Indexed keywords

CORRELATION ANALYSIS; FOURIER ANALYSIS; GEOMETRY; LENS; LIGHT; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; OPHTHALMOLOGY; OPTOMETRY; PRIORITY JOURNAL; REFRACTION INDEX; REVIEW;

ASTIGMATISM; DIAGNOSTIC TECHNIQUES, OPHTHALMOLOGICAL; FOURIER ANALYSIS; HUMANS; MODELS, BIOLOGICAL; OPTICS; REFRACTION, OCULAR;

EID: 33645118045     PISSN: 02755408     EISSN: 14751313     Source Type: Journal    
DOI: 10.1111/j.1475-1313.2006.00369.x     Document Type: Review

References (40)

1. Bennett A. G. 1950 Prismatic effects of cylinders: a recurrent fallacy Manuf Optician 3 575 577
2. Bennett A. G. 1976 ''Power'' in an oblique meridian Manuf. Optics Int. 29 357 359
3. Bennett A. G. Rabbetts R. B. 1978 Refraction in oblique meridians of the astigmatic eye Br. J. Physiol. Opt. 32 59 77
4. Bennett A. G. 1990 The sine-squared expression and torsional prismatic effects in astigmatic lenses Ophthal. Physiol. Opt. 10 399 402
5. Brubaker R. F. Reinicke R. D. Copeland J.C. 1969 Meridional refractometry. I. Derivation of equations Arch. Ophthal. 81 849 852
6. Burek H. 1990 Tri-meridional analysis using arbitrary meridians Ophthal. Physiol. Opt. 10 280 285
7. Dam-Johansen M. 1996 Corneal astigmatisme efter katarakt kirurgi Ph.D. Thesis Det Sundhedsvidenskalbelige Fakultet, Aarhus Universitet Århus, Denmark pp 100 101
8. Furlan W. D. Muñoz-Escrivá L. 2002 Author's reply Ophthal. Physiol. Opt. 22 263 265
9. Goldstein D. A. 1964 A critique of the sine-squared law Am. J. Optom. Arch. Am. Acad. Optom. 41 549 560
10. Graustein W. C. 1966 Differential Geometry Dover Publications New York
11. Guggenheimer H. W. 1963 Differential Geometry McGraw-Hill Book Company, Inc. New York pp 206 214
12. Haine C. Long W. Reading R. 1976 Laser meridional refractometry Am. J. Optom. Physiol. Opt. 53 194 204
13. Harris W. F. 1990 Elements of the dioptric power matrix and the concept of torsional power: a reinterpretation Optom. Vis. Sci. 67 36 37
14. Harris W. F. 1992 Relation between meridional power and the dioptric power matrix Optom. Vis. Sci. 69 159 161
15. Harris W. F. 1997 Dioptric power: its representation in three- and four-dimensional space Optom. Vis. Sci. 74 349 366
16. Harris W. F. 1998 Signs of surface torsion and torsional dioptric power Optom. Vis. Sci. 75 670 673
17. Harris W. F. Gool R. D. 1998 Curvital and torsional dioptric power and their polar profiles across meridians S. Afr. Optom. 57 3 17
18. Harris W. F. 2000 Astigmatism Ophthal. Physiol. Opt. 20 11 30
19. Hjortdal J. Ø. Erdman L. Bek T. 1995 Fourier analysis of video-keratographic data Ophthal. Physiol. Opt. 15 171 185
20. Keating M. P. Carroll J. P. 1976 Blurred imagery and the cylinder sine-squared law Am. J. Optom. Physiol. Opt. 53 66 69
21. Keating M. P. 1986 Dioptric power in an off-axis meridian: the torsional component Am. J. Optom. Physiol. Opt. 63 830 838
22. Keating M. P. 2002 Geometric, Physical and Visual Optics Butterworth-Heinemann Boston, MA pp 101 and 233 237
23. Laurance L. 1920 General and Practical Optics 3rd edn School of Optics, Ltd London, UK pp 248 252 and 308 309
24. Linksz A. 1942 Determination of axis and amount of astigmatic error by rotation of trial cylinder Arch. Ophthalmol. 28 632 651
25. Martin L.C. Welford W. T. 1966 Technical Optics 2nd edn Sir Isaac Pitman & Sons, Ltd London
26. Muñoz-Escrivá L. Furlan W. D. 2001 The stenopaeic slit: an analytical expression to quantify its optical effect in front of an astigmatic eye Ophthal. Physiol. Opt. 21 327 333
27. Naeser K. 1990 Conversion of keratometer readings to polar values J. Cataract Refract. Surg. 16 741 745
28. Naeser K. 2002 Letter Ophthal. Physiol. Opt. 22 262
29. Naeser K. Behrens J. K. 1997 Correlation between polar values and vector analysis J. Cataract Refract. Surg. 23 76 81
30. Naeser K. Hjortdal J. 1999 Bivariate analysis of surgically induced regular astigmatism. Mathematical analysis and graphical display Ophthal. Physiol. Opt. 19 50 61
31. Naeser K. Hjortdal J. 2001 Multivariate analysis of refractive data. Mathematics and statistics of spherocylinders J. Cataract Refract. Surg. 27 129 142
32. Naeser K. Behrens J.K. Naeser E.V. 1994 Quantitative assessment of corneal astigmatic surgery: expanding the polar values concept J. Cataract Refract. Surg. 20 162 168
33. Oechsner U. Kusel R. 1997 Multimeridional refraction: dependence of the measurement accuracy on the number of meridians refracted Optom. Vis. Sci. 74 425 433
34. Pascal J. I. 1939 Power of cylinders in oblique meridians Arch. Ophthalmol. 22 290 291
35. Rosenfield M. Portello J. K. 1996 Multi-meridional keratometry Ophthal. Physiol. Opt. 16 83 85
36. Seiler T. Wollensak J. 1993 Über die mathematische darstellung des postoperatives regulären Hornhautastigmatismus Klin. Monatsbl. Augenheilkd 203 70 76
37. Thibos L. N. Wheeler W. Horner P. G. 1997 Power vectors: an application of Fourier analysis to the description and statistical analysis of refractive error Optom. Vis. Sci. 74 367 375
38. Worthey J. A. 1977 Simplified analysis of meridional refraction data Am. J. Optom. Physiol. Opt. 54 771 775
39. Whitwell A. 1905 On the focal power of an oblique section of a cylinder lens Br. Opt. J. 4 195 197
40. Wunsh S. E. 1971 The cross cylinder Int. Ophthalmol. Clin. 11 131 153