Abstract

A rigid contact lens on an eye can produce levels of spherical aberration very different from those produced by a spectacle lens in front of the eye. These levels are considerably affected by contact lens surface asphericity. Change in longitudinal spherical aberration associated with aspherizing a contact lens surface is well predicted by a simple equation for change in sagittal power of the surface. Displacing an aspheric contact lens on the eye can produce considerable defocus, which is well predicted by simple equations for change in sagittal and tangential surface powers. The best refractive correction with contact lenses can be determined only by overrefraction with a patient wearing a contact lens of power and characteristics similar to that which will be prescribed. An aspheric contact lens that moves to a considerable extent on the eye will cause more unstable vision than will a spherical lens that moves to the same extent.

© 1995 Optical Society of America

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References

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  1. L. N. Thibos, A. Bradley, X. Zhang, “Effect of ocular chromatic aberration on monocular visual performance,” Optom. Vis. Sci. 68, 599–607 (1991).
    [CrossRef] [PubMed]
  2. D. A. Atchison, “Modern optical design assessment and spectacle lenses,” Opt. Acta 32, 607–634 (1984).
    [CrossRef]
  3. H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. 67, 1508–1518 (1977).
    [CrossRef] [PubMed]
  4. G. Walsh, W. N. Charman, H. Howland, “Objective technique for the determination of monochromatic aberrations of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
    [CrossRef] [PubMed]
  5. G. Walsh, W. N. Charman, “Measurement of the axial wavefront of the human eye,” Ophth. Physiol. Opt. 5, 23–31 (1985).
    [CrossRef]
  6. P. Kiely, G. Smith, L. G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
    [CrossRef]
  7. M. Guillon, D. P. M. Lydon, C. Wilson, “Corneal topography: a clinical model,” Ophthalmic Physiol. Opt. 6, 47–56 (1986).
    [CrossRef] [PubMed]
  8. G. Westheimer, “Aberrations of contact lenses,” Am. J. Optom. Arch. Am. Acad. Optom. 38, 445–448 (1961).
    [CrossRef] [PubMed]
  9. G. L. Bauer, “Longitudinal spherical aberration of modern ophthalmic lenses and its effect on visual acuity,” Appl. Opt. 19, 2226–2234 (1980).
    [CrossRef] [PubMed]
  10. C. E. Campbell, “The effect of spherical aberration of contact lenses to the wearer,” Am. J. Optom. Physiol. Opt. 58, 212–217 (1981).
    [CrossRef] [PubMed]
  11. C. E. Campbell, Humphrey Instruments, Inc., San Leandro, Calif. 94577-0700 (personal communication, 1994).
  12. I. Cox, “Theoretical calculation of the longitudinal spherical aberration of rigid and soft contact lenses,” Optom. Vis. Sci. 67, 277–282 (1990).
    [CrossRef] [PubMed]
  13. R. M. Hammer, B. A. Holden, “Spherical aberration of aspheric contact lenses on eye,” Optom. Vis. Sci. 71, 522–528 (1994).
    [CrossRef] [PubMed]
  14. W. N. Charman, G. Walsh, “Properties of conicoidal surfaces and the Bausch and Lomb PA1 Soflens bifocal,” Optom. Today 26(17), 573–574, 576–578, 580 (1986).
  15. W. N. Charman, G. Walsh, “Retinal images with different designs of bifocal contact lenses,” in Transactions of the British Contact Lens Association. Annual Clinical Conference 1986 (British Contact Lens Association, London, 1986), pp. 13–19.
  16. M. J. Collins, B. Brown, D. A. Atchison, S. D. Newman, “Tolerance to spherical aberration induced by rigid contact lenses,” Ophth. Physiol. Opt. 12, 24–28 (1992).
    [CrossRef]
  17. A. G. Bennett, “Aspherical and continuous curve contact lenses. Part one,” Optom. Today 28(1), 11–14 (1988).
  18. H. H. Hopkins, The Wave Theory of Aberrations (Clarendon, Oxford, 1950).
  19. G. Smith, C-W Lu, “The spherical aberration of intraocular lenses,” Ophth. Physiol. Opt. 8, 287–294 (1988).
    [CrossRef]
  20. A. G. Bennett, “Aspherical contact lens surfaces. Part two,” Ophth. Optician 8, 1297–1300, 1311 (1968).
  21. W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
    [CrossRef]
  22. R. A. Applegate, V. Lakshminarayanan, “Parametric representation of Stiles–Crawford functions: normal variation of peak location and directionality,” J. Opt. Soc. Am. A 10, 1611–1623 (1993).
    [CrossRef] [PubMed]
  23. J. P. Carroll, “Apodization model of the Stiles–Crawford effect,” J. Opt. Soc. Am. 70, 1155–1156 (1980).
    [CrossRef] [PubMed]
  24. A. van Meeteren, “Calculation on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
    [CrossRef]
  25. D. A. Atchison, “Visual optics in man,” Aust. J. Optom. 67, 141–150 (1984).
  26. G. Smith, “The spherical aberration of aphakic eyes corrected with intraocular lenses,” Clin. Exp. Optom. 75, 27–34 (1992).
    [CrossRef]
  27. D. A. Atchison, G. Smith, N. Efron, “The effect of pupil size on visual acuity in uncorrected and corrected myopia,” Am. J. Optom. Physiol. Opt. 56, 315–323 (1979).
    [CrossRef] [PubMed]
  28. T. D. Winkler, “A new model for determining add power,” Contact Lens Spectrum 7(12), 23, 25, 28 (1992).

1994 (1)

R. M. Hammer, B. A. Holden, “Spherical aberration of aspheric contact lenses on eye,” Optom. Vis. Sci. 71, 522–528 (1994).
[CrossRef] [PubMed]

1993 (1)

1992 (3)

G. Smith, “The spherical aberration of aphakic eyes corrected with intraocular lenses,” Clin. Exp. Optom. 75, 27–34 (1992).
[CrossRef]

T. D. Winkler, “A new model for determining add power,” Contact Lens Spectrum 7(12), 23, 25, 28 (1992).

M. J. Collins, B. Brown, D. A. Atchison, S. D. Newman, “Tolerance to spherical aberration induced by rigid contact lenses,” Ophth. Physiol. Opt. 12, 24–28 (1992).
[CrossRef]

1991 (1)

L. N. Thibos, A. Bradley, X. Zhang, “Effect of ocular chromatic aberration on monocular visual performance,” Optom. Vis. Sci. 68, 599–607 (1991).
[CrossRef] [PubMed]

1990 (1)

I. Cox, “Theoretical calculation of the longitudinal spherical aberration of rigid and soft contact lenses,” Optom. Vis. Sci. 67, 277–282 (1990).
[CrossRef] [PubMed]

1988 (2)

A. G. Bennett, “Aspherical and continuous curve contact lenses. Part one,” Optom. Today 28(1), 11–14 (1988).

G. Smith, C-W Lu, “The spherical aberration of intraocular lenses,” Ophth. Physiol. Opt. 8, 287–294 (1988).
[CrossRef]

1986 (2)

W. N. Charman, G. Walsh, “Properties of conicoidal surfaces and the Bausch and Lomb PA1 Soflens bifocal,” Optom. Today 26(17), 573–574, 576–578, 580 (1986).

M. Guillon, D. P. M. Lydon, C. Wilson, “Corneal topography: a clinical model,” Ophthalmic Physiol. Opt. 6, 47–56 (1986).
[CrossRef] [PubMed]

1985 (1)

G. Walsh, W. N. Charman, “Measurement of the axial wavefront of the human eye,” Ophth. Physiol. Opt. 5, 23–31 (1985).
[CrossRef]

1984 (3)

D. A. Atchison, “Modern optical design assessment and spectacle lenses,” Opt. Acta 32, 607–634 (1984).
[CrossRef]

G. Walsh, W. N. Charman, H. Howland, “Objective technique for the determination of monochromatic aberrations of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
[CrossRef] [PubMed]

D. A. Atchison, “Visual optics in man,” Aust. J. Optom. 67, 141–150 (1984).

1982 (1)

P. Kiely, G. Smith, L. G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
[CrossRef]

1981 (1)

C. E. Campbell, “The effect of spherical aberration of contact lenses to the wearer,” Am. J. Optom. Physiol. Opt. 58, 212–217 (1981).
[CrossRef] [PubMed]

1980 (2)

1979 (1)

D. A. Atchison, G. Smith, N. Efron, “The effect of pupil size on visual acuity in uncorrected and corrected myopia,” Am. J. Optom. Physiol. Opt. 56, 315–323 (1979).
[CrossRef] [PubMed]

1977 (1)

1974 (1)

A. van Meeteren, “Calculation on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
[CrossRef]

1968 (1)

A. G. Bennett, “Aspherical contact lens surfaces. Part two,” Ophth. Optician 8, 1297–1300, 1311 (1968).

1961 (1)

G. Westheimer, “Aberrations of contact lenses,” Am. J. Optom. Arch. Am. Acad. Optom. 38, 445–448 (1961).
[CrossRef] [PubMed]

1933 (1)

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Applegate, R. A.

Atchison, D. A.

M. J. Collins, B. Brown, D. A. Atchison, S. D. Newman, “Tolerance to spherical aberration induced by rigid contact lenses,” Ophth. Physiol. Opt. 12, 24–28 (1992).
[CrossRef]

D. A. Atchison, “Visual optics in man,” Aust. J. Optom. 67, 141–150 (1984).

D. A. Atchison, “Modern optical design assessment and spectacle lenses,” Opt. Acta 32, 607–634 (1984).
[CrossRef]

D. A. Atchison, G. Smith, N. Efron, “The effect of pupil size on visual acuity in uncorrected and corrected myopia,” Am. J. Optom. Physiol. Opt. 56, 315–323 (1979).
[CrossRef] [PubMed]

Bauer, G. L.

Bennett, A. G.

A. G. Bennett, “Aspherical and continuous curve contact lenses. Part one,” Optom. Today 28(1), 11–14 (1988).

A. G. Bennett, “Aspherical contact lens surfaces. Part two,” Ophth. Optician 8, 1297–1300, 1311 (1968).

Bradley, A.

L. N. Thibos, A. Bradley, X. Zhang, “Effect of ocular chromatic aberration on monocular visual performance,” Optom. Vis. Sci. 68, 599–607 (1991).
[CrossRef] [PubMed]

Brown, B.

M. J. Collins, B. Brown, D. A. Atchison, S. D. Newman, “Tolerance to spherical aberration induced by rigid contact lenses,” Ophth. Physiol. Opt. 12, 24–28 (1992).
[CrossRef]

Campbell, C. E.

C. E. Campbell, “The effect of spherical aberration of contact lenses to the wearer,” Am. J. Optom. Physiol. Opt. 58, 212–217 (1981).
[CrossRef] [PubMed]

C. E. Campbell, Humphrey Instruments, Inc., San Leandro, Calif. 94577-0700 (personal communication, 1994).

Carney, L. G.

P. Kiely, G. Smith, L. G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
[CrossRef]

Carroll, J. P.

Charman, W. N.

W. N. Charman, G. Walsh, “Properties of conicoidal surfaces and the Bausch and Lomb PA1 Soflens bifocal,” Optom. Today 26(17), 573–574, 576–578, 580 (1986).

G. Walsh, W. N. Charman, “Measurement of the axial wavefront of the human eye,” Ophth. Physiol. Opt. 5, 23–31 (1985).
[CrossRef]

G. Walsh, W. N. Charman, H. Howland, “Objective technique for the determination of monochromatic aberrations of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
[CrossRef] [PubMed]

W. N. Charman, G. Walsh, “Retinal images with different designs of bifocal contact lenses,” in Transactions of the British Contact Lens Association. Annual Clinical Conference 1986 (British Contact Lens Association, London, 1986), pp. 13–19.

Collins, M. J.

M. J. Collins, B. Brown, D. A. Atchison, S. D. Newman, “Tolerance to spherical aberration induced by rigid contact lenses,” Ophth. Physiol. Opt. 12, 24–28 (1992).
[CrossRef]

Cox, I.

I. Cox, “Theoretical calculation of the longitudinal spherical aberration of rigid and soft contact lenses,” Optom. Vis. Sci. 67, 277–282 (1990).
[CrossRef] [PubMed]

Crawford, B. H.

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Efron, N.

D. A. Atchison, G. Smith, N. Efron, “The effect of pupil size on visual acuity in uncorrected and corrected myopia,” Am. J. Optom. Physiol. Opt. 56, 315–323 (1979).
[CrossRef] [PubMed]

Guillon, M.

M. Guillon, D. P. M. Lydon, C. Wilson, “Corneal topography: a clinical model,” Ophthalmic Physiol. Opt. 6, 47–56 (1986).
[CrossRef] [PubMed]

Hammer, R. M.

R. M. Hammer, B. A. Holden, “Spherical aberration of aspheric contact lenses on eye,” Optom. Vis. Sci. 71, 522–528 (1994).
[CrossRef] [PubMed]

Holden, B. A.

R. M. Hammer, B. A. Holden, “Spherical aberration of aspheric contact lenses on eye,” Optom. Vis. Sci. 71, 522–528 (1994).
[CrossRef] [PubMed]

Hopkins, H. H.

H. H. Hopkins, The Wave Theory of Aberrations (Clarendon, Oxford, 1950).

Howland, B.

Howland, H.

Howland, H. C.

Kiely, P.

P. Kiely, G. Smith, L. G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
[CrossRef]

Lakshminarayanan, V.

Lu, C-W

G. Smith, C-W Lu, “The spherical aberration of intraocular lenses,” Ophth. Physiol. Opt. 8, 287–294 (1988).
[CrossRef]

Lydon, D. P. M.

M. Guillon, D. P. M. Lydon, C. Wilson, “Corneal topography: a clinical model,” Ophthalmic Physiol. Opt. 6, 47–56 (1986).
[CrossRef] [PubMed]

Newman, S. D.

M. J. Collins, B. Brown, D. A. Atchison, S. D. Newman, “Tolerance to spherical aberration induced by rigid contact lenses,” Ophth. Physiol. Opt. 12, 24–28 (1992).
[CrossRef]

Smith, G.

G. Smith, “The spherical aberration of aphakic eyes corrected with intraocular lenses,” Clin. Exp. Optom. 75, 27–34 (1992).
[CrossRef]

G. Smith, C-W Lu, “The spherical aberration of intraocular lenses,” Ophth. Physiol. Opt. 8, 287–294 (1988).
[CrossRef]

P. Kiely, G. Smith, L. G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
[CrossRef]

D. A. Atchison, G. Smith, N. Efron, “The effect of pupil size on visual acuity in uncorrected and corrected myopia,” Am. J. Optom. Physiol. Opt. 56, 315–323 (1979).
[CrossRef] [PubMed]

Stiles, W. S.

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Thibos, L. N.

L. N. Thibos, A. Bradley, X. Zhang, “Effect of ocular chromatic aberration on monocular visual performance,” Optom. Vis. Sci. 68, 599–607 (1991).
[CrossRef] [PubMed]

van Meeteren, A.

A. van Meeteren, “Calculation on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
[CrossRef]

Walsh, G.

W. N. Charman, G. Walsh, “Properties of conicoidal surfaces and the Bausch and Lomb PA1 Soflens bifocal,” Optom. Today 26(17), 573–574, 576–578, 580 (1986).

G. Walsh, W. N. Charman, “Measurement of the axial wavefront of the human eye,” Ophth. Physiol. Opt. 5, 23–31 (1985).
[CrossRef]

G. Walsh, W. N. Charman, H. Howland, “Objective technique for the determination of monochromatic aberrations of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
[CrossRef] [PubMed]

W. N. Charman, G. Walsh, “Retinal images with different designs of bifocal contact lenses,” in Transactions of the British Contact Lens Association. Annual Clinical Conference 1986 (British Contact Lens Association, London, 1986), pp. 13–19.

Westheimer, G.

G. Westheimer, “Aberrations of contact lenses,” Am. J. Optom. Arch. Am. Acad. Optom. 38, 445–448 (1961).
[CrossRef] [PubMed]

Wilson, C.

M. Guillon, D. P. M. Lydon, C. Wilson, “Corneal topography: a clinical model,” Ophthalmic Physiol. Opt. 6, 47–56 (1986).
[CrossRef] [PubMed]

Winkler, T. D.

T. D. Winkler, “A new model for determining add power,” Contact Lens Spectrum 7(12), 23, 25, 28 (1992).

Zhang, X.

L. N. Thibos, A. Bradley, X. Zhang, “Effect of ocular chromatic aberration on monocular visual performance,” Optom. Vis. Sci. 68, 599–607 (1991).
[CrossRef] [PubMed]

Am. J. Optom. Arch. Am. Acad. Optom. (1)

G. Westheimer, “Aberrations of contact lenses,” Am. J. Optom. Arch. Am. Acad. Optom. 38, 445–448 (1961).
[CrossRef] [PubMed]

Am. J. Optom. Physiol. Opt. (2)

C. E. Campbell, “The effect of spherical aberration of contact lenses to the wearer,” Am. J. Optom. Physiol. Opt. 58, 212–217 (1981).
[CrossRef] [PubMed]

D. A. Atchison, G. Smith, N. Efron, “The effect of pupil size on visual acuity in uncorrected and corrected myopia,” Am. J. Optom. Physiol. Opt. 56, 315–323 (1979).
[CrossRef] [PubMed]

Appl. Opt. (1)

Aust. J. Optom. (1)

D. A. Atchison, “Visual optics in man,” Aust. J. Optom. 67, 141–150 (1984).

Clin. Exp. Optom. (1)

G. Smith, “The spherical aberration of aphakic eyes corrected with intraocular lenses,” Clin. Exp. Optom. 75, 27–34 (1992).
[CrossRef]

Contact Lens Spectrum (1)

T. D. Winkler, “A new model for determining add power,” Contact Lens Spectrum 7(12), 23, 25, 28 (1992).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Ophth. Optician (1)

A. G. Bennett, “Aspherical contact lens surfaces. Part two,” Ophth. Optician 8, 1297–1300, 1311 (1968).

Ophth. Physiol. Opt. (3)

G. Walsh, W. N. Charman, “Measurement of the axial wavefront of the human eye,” Ophth. Physiol. Opt. 5, 23–31 (1985).
[CrossRef]

G. Smith, C-W Lu, “The spherical aberration of intraocular lenses,” Ophth. Physiol. Opt. 8, 287–294 (1988).
[CrossRef]

M. J. Collins, B. Brown, D. A. Atchison, S. D. Newman, “Tolerance to spherical aberration induced by rigid contact lenses,” Ophth. Physiol. Opt. 12, 24–28 (1992).
[CrossRef]

Ophthalmic Physiol. Opt. (1)

M. Guillon, D. P. M. Lydon, C. Wilson, “Corneal topography: a clinical model,” Ophthalmic Physiol. Opt. 6, 47–56 (1986).
[CrossRef] [PubMed]

Opt. Acta (3)

A. van Meeteren, “Calculation on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
[CrossRef]

P. Kiely, G. Smith, L. G. Carney, “The mean shape of the human cornea,” Opt. Acta 29, 1027–1040 (1982).
[CrossRef]

D. A. Atchison, “Modern optical design assessment and spectacle lenses,” Opt. Acta 32, 607–634 (1984).
[CrossRef]

Optom. Today (2)

A. G. Bennett, “Aspherical and continuous curve contact lenses. Part one,” Optom. Today 28(1), 11–14 (1988).

W. N. Charman, G. Walsh, “Properties of conicoidal surfaces and the Bausch and Lomb PA1 Soflens bifocal,” Optom. Today 26(17), 573–574, 576–578, 580 (1986).

Optom. Vis. Sci. (3)

I. Cox, “Theoretical calculation of the longitudinal spherical aberration of rigid and soft contact lenses,” Optom. Vis. Sci. 67, 277–282 (1990).
[CrossRef] [PubMed]

R. M. Hammer, B. A. Holden, “Spherical aberration of aspheric contact lenses on eye,” Optom. Vis. Sci. 71, 522–528 (1994).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, X. Zhang, “Effect of ocular chromatic aberration on monocular visual performance,” Optom. Vis. Sci. 68, 599–607 (1991).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. B (1)

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Other (3)

C. E. Campbell, Humphrey Instruments, Inc., San Leandro, Calif. 94577-0700 (personal communication, 1994).

W. N. Charman, G. Walsh, “Retinal images with different designs of bifocal contact lenses,” in Transactions of the British Contact Lens Association. Annual Clinical Conference 1986 (British Contact Lens Association, London, 1986), pp. 13–19.

H. H. Hopkins, The Wave Theory of Aberrations (Clarendon, Oxford, 1950).

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Figures (5)

Fig. 1
Fig. 1

Parameters needed for determining the change in spherical aberration with contact lenses on an eye relative to the change obtained with spectacle lenses in front of the eye. Not to scale.

Fig. 2
Fig. 2

LSA for contact lenses and spectacle lenses of various lens powers in combination with the anterior cornea. ●: Distance object, spherical cornea (Q = 0.0); ■: distance object, aspheric cornea (Q = −0.26); ○: near object (200-mm distance), spherical cornea. Stop diameter, 5.0 mm. Other details are given in the text.

Fig. 3
Fig. 3

Differences in LSA between contact lens and spectacle lens wear for various lens powers in combination with a spherical anterior cornea. ●: Distance object, spherical cornea (Q = 0.0); ■: distance object, aspheric cornea (Q = −0.26); ○: near object (200-mm distance), spherical cornea. Stop diameter, 5.0 mm. Other details are given in the text.

Fig. 4
Fig. 4

LSA of contact lenses combined with an anterior corneal surface, as a function of anterior lens surface asphericity, for distance vision. ▲: +6-D power, Δ: −6-D power. Third-order predictions of changes in LSA are also shown. Distance object; stop diameter, 5.0 mm. Note the different vertical scale from that of Figs. 2 and 3. Other details are given in the text.

Fig. 5
Fig. 5

Spot diagrams for a +6-D contact lens combined with a spherical cornea. (a) Spherical contact lens, (b) aspherical front surface (Q = −0.4) contact lens. Lens displacements of 0 mm (top row), 1 mm (middle row), and 1.5 mm (bottom row) are shown. Results are for the Gaussian image plane and for the planes in front of it (−0.6, −0.4, −0.2 mm) and behind it (+0.2 mm). Distance object; stop diameter, 5.0 mm. Other details are given in the text.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

LSA = n / l f - n l g ,
z = c ( x 2 + y 2 ) 1 + [ 1 - c 2 ( 1 + Q ) ( x 2 + y 2 ) ] 0.5 ,
( 1 + Q ) = p ,
Q = - e 2 ,
Δ S 1 = c 3 h 4 Q ( n - n ) ,
LSA = 2 S 1 / D 2 ,
h D / 2 ,
Δ LSA = c 3 h 2 Q ( n - n ) / 2.
r s = ( r 2 - Q h 2 ) 0.5 .
c s = c / ( 1 - Q c 2 h 2 ) 0.5 c ( 1 + Q c 2 h 2 / 2 ) .
Δ c s c 3 h 2 Q / 2.
Δ F s = Δ c s ( n - n ) c 3 h 2 Q ( n - n ) / 2.
Δ LSA Δ F s ;
r t = r s 3 / r 2 .
c t = c s 3 / c 2 ,
c t = c / ( 1 - Q c 2 h 2 ) 1.5 c ( 1 + 3 Q c 2 h 2 / 2 ) .
Δ c t 3 c 3 h 2 Q / 2 ,
Δ F t = Δ c t ( n - n ) 3 c 3 h 2 Q ( n - n ) / 2 = 3 Δ F s .

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