Abstract

We present a new algorithm to calculate the optical imbalances and differential prismatic effects that appear when two eyes look at an object through correcting eyeglasses. These are important magnitudes in ophthalmic optics because large amounts of them will disturb the binocular vision of the spectacle wearer. As a practical application of our algorithm, the distribution of optical imbalances and differential prismatic powers for a pair of progressive addition lenses has been calculated, and we obtain information about the effects of this kind of lens on the binocular vision of the wearer.

© 2001 Optical Society of America

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References

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  1. Y. LeGrand, Optique Physiologique, la dioptrique de l’oeil et sa correction, 3èmeed. (Masson, Paris, 1965).
  2. R. W. Reading, Binocular Vision: Foundations and Applications (Butterworth, Boston, Mass, 1983).
  3. J. A. Gómez-Pedrero, J. Alonso, H. Canabal, E. Bernabeu, “A generalization of Prentice’s law for ophthalmic lenses with arbitrary refracting surfaces,” Ophthalmic Physiol. Opt. 18, 514–520 (1998).
    [CrossRef]
  4. J. A. Gómez-Pedrero, PhD. dissertation (Universidad Complutense de Madrid, Madrid, Spain1999).
  5. T. Fannin, T. Grosvernor, Clinical Optics, 1st ed. (Butterworth–Heinemann, Boston, Mass., 1996).
  6. M. Jalie, The Principles of Ophthalmic Lenses, 4th ed. (ABDO, London, 1988).
  7. J. A. Gómez-Pedrero, J. Alonso, E. Bernabeu, “Local dioptric power matrix and prismatic effects of spherical, aspherical, and spherotorical ophthalmic lenses,” in OPTIKA 98: 5th Conference on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds. Proc. SPIE3573, 405–408 (1998).
  8. W. H. Press, S. A. Teukolsky, W. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).
  9. J. Alonso, J. A. Gómez-Pedrero, E. Bernabeu, “Local dioptric power matrix in progressive addition lenses,” Ophthalmic Physiol. Opt. 17, 522–529 (1998).
    [CrossRef]
  10. B. Rassow, W. Wesemann, “Fusion and stereopsis under artificially impaired conditions of the binocular system,” Optometrie 2, 21–28 (1989).
  11. R. K. Luneburg, “The metric of binocular visual space,” J. Opt. Soc. Am. 40, 627–642 (1950).
    [CrossRef]
  12. K. N. Ogle, “Stereopsis and vertical disparity,” A. M. A. Arch. Opthal. 53, 495–504 (1955).
    [CrossRef]
  13. K. N. Ogle, “Distortion of the image by prism,” J. Opt. Soc. Am. 41, 1023–28 (1951).
    [CrossRef]

1998 (2)

J. A. Gómez-Pedrero, J. Alonso, H. Canabal, E. Bernabeu, “A generalization of Prentice’s law for ophthalmic lenses with arbitrary refracting surfaces,” Ophthalmic Physiol. Opt. 18, 514–520 (1998).
[CrossRef]

J. Alonso, J. A. Gómez-Pedrero, E. Bernabeu, “Local dioptric power matrix in progressive addition lenses,” Ophthalmic Physiol. Opt. 17, 522–529 (1998).
[CrossRef]

1989 (1)

B. Rassow, W. Wesemann, “Fusion and stereopsis under artificially impaired conditions of the binocular system,” Optometrie 2, 21–28 (1989).

1955 (1)

K. N. Ogle, “Stereopsis and vertical disparity,” A. M. A. Arch. Opthal. 53, 495–504 (1955).
[CrossRef]

1951 (1)

1950 (1)

Alonso, J.

J. A. Gómez-Pedrero, J. Alonso, H. Canabal, E. Bernabeu, “A generalization of Prentice’s law for ophthalmic lenses with arbitrary refracting surfaces,” Ophthalmic Physiol. Opt. 18, 514–520 (1998).
[CrossRef]

J. Alonso, J. A. Gómez-Pedrero, E. Bernabeu, “Local dioptric power matrix in progressive addition lenses,” Ophthalmic Physiol. Opt. 17, 522–529 (1998).
[CrossRef]

J. A. Gómez-Pedrero, J. Alonso, E. Bernabeu, “Local dioptric power matrix and prismatic effects of spherical, aspherical, and spherotorical ophthalmic lenses,” in OPTIKA 98: 5th Conference on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds. Proc. SPIE3573, 405–408 (1998).

Bernabeu, E.

J. A. Gómez-Pedrero, J. Alonso, H. Canabal, E. Bernabeu, “A generalization of Prentice’s law for ophthalmic lenses with arbitrary refracting surfaces,” Ophthalmic Physiol. Opt. 18, 514–520 (1998).
[CrossRef]

J. Alonso, J. A. Gómez-Pedrero, E. Bernabeu, “Local dioptric power matrix in progressive addition lenses,” Ophthalmic Physiol. Opt. 17, 522–529 (1998).
[CrossRef]

J. A. Gómez-Pedrero, J. Alonso, E. Bernabeu, “Local dioptric power matrix and prismatic effects of spherical, aspherical, and spherotorical ophthalmic lenses,” in OPTIKA 98: 5th Conference on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds. Proc. SPIE3573, 405–408 (1998).

Canabal, H.

J. A. Gómez-Pedrero, J. Alonso, H. Canabal, E. Bernabeu, “A generalization of Prentice’s law for ophthalmic lenses with arbitrary refracting surfaces,” Ophthalmic Physiol. Opt. 18, 514–520 (1998).
[CrossRef]

Fannin, T.

T. Fannin, T. Grosvernor, Clinical Optics, 1st ed. (Butterworth–Heinemann, Boston, Mass., 1996).

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Gómez-Pedrero, J. A.

J. Alonso, J. A. Gómez-Pedrero, E. Bernabeu, “Local dioptric power matrix in progressive addition lenses,” Ophthalmic Physiol. Opt. 17, 522–529 (1998).
[CrossRef]

J. A. Gómez-Pedrero, J. Alonso, H. Canabal, E. Bernabeu, “A generalization of Prentice’s law for ophthalmic lenses with arbitrary refracting surfaces,” Ophthalmic Physiol. Opt. 18, 514–520 (1998).
[CrossRef]

J. A. Gómez-Pedrero, J. Alonso, E. Bernabeu, “Local dioptric power matrix and prismatic effects of spherical, aspherical, and spherotorical ophthalmic lenses,” in OPTIKA 98: 5th Conference on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds. Proc. SPIE3573, 405–408 (1998).

J. A. Gómez-Pedrero, PhD. dissertation (Universidad Complutense de Madrid, Madrid, Spain1999).

Grosvernor, T.

T. Fannin, T. Grosvernor, Clinical Optics, 1st ed. (Butterworth–Heinemann, Boston, Mass., 1996).

Jalie, M.

M. Jalie, The Principles of Ophthalmic Lenses, 4th ed. (ABDO, London, 1988).

LeGrand, Y.

Y. LeGrand, Optique Physiologique, la dioptrique de l’oeil et sa correction, 3èmeed. (Masson, Paris, 1965).

Luneburg, R. K.

Ogle, K. N.

K. N. Ogle, “Stereopsis and vertical disparity,” A. M. A. Arch. Opthal. 53, 495–504 (1955).
[CrossRef]

K. N. Ogle, “Distortion of the image by prism,” J. Opt. Soc. Am. 41, 1023–28 (1951).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Rassow, B.

B. Rassow, W. Wesemann, “Fusion and stereopsis under artificially impaired conditions of the binocular system,” Optometrie 2, 21–28 (1989).

Reading, R. W.

R. W. Reading, Binocular Vision: Foundations and Applications (Butterworth, Boston, Mass, 1983).

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Vettering, W.

W. H. Press, S. A. Teukolsky, W. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Wesemann, W.

B. Rassow, W. Wesemann, “Fusion and stereopsis under artificially impaired conditions of the binocular system,” Optometrie 2, 21–28 (1989).

A. M. A. Arch. Opthal. (1)

K. N. Ogle, “Stereopsis and vertical disparity,” A. M. A. Arch. Opthal. 53, 495–504 (1955).
[CrossRef]

J. Opt. Soc. Am. (2)

Ophthalmic Physiol. Opt. (2)

J. A. Gómez-Pedrero, J. Alonso, H. Canabal, E. Bernabeu, “A generalization of Prentice’s law for ophthalmic lenses with arbitrary refracting surfaces,” Ophthalmic Physiol. Opt. 18, 514–520 (1998).
[CrossRef]

J. Alonso, J. A. Gómez-Pedrero, E. Bernabeu, “Local dioptric power matrix in progressive addition lenses,” Ophthalmic Physiol. Opt. 17, 522–529 (1998).
[CrossRef]

Optometrie (1)

B. Rassow, W. Wesemann, “Fusion and stereopsis under artificially impaired conditions of the binocular system,” Optometrie 2, 21–28 (1989).

Other (7)

Y. LeGrand, Optique Physiologique, la dioptrique de l’oeil et sa correction, 3èmeed. (Masson, Paris, 1965).

R. W. Reading, Binocular Vision: Foundations and Applications (Butterworth, Boston, Mass, 1983).

J. A. Gómez-Pedrero, PhD. dissertation (Universidad Complutense de Madrid, Madrid, Spain1999).

T. Fannin, T. Grosvernor, Clinical Optics, 1st ed. (Butterworth–Heinemann, Boston, Mass., 1996).

M. Jalie, The Principles of Ophthalmic Lenses, 4th ed. (ABDO, London, 1988).

J. A. Gómez-Pedrero, J. Alonso, E. Bernabeu, “Local dioptric power matrix and prismatic effects of spherical, aspherical, and spherotorical ophthalmic lenses,” in OPTIKA 98: 5th Conference on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds. Proc. SPIE3573, 405–408 (1998).

W. H. Press, S. A. Teukolsky, W. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

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Figures (4)

Fig. 1
Fig. 1

(a) Scheme of the principal rays’ path from the object point O to the left- and right-eye rotation centers: d is the nasopupillary distance (assumed equal for the two eyes), z is the object distance, and l2 is the distance between the back surface of the lens and the rotation center of the eye. (b) Plot representing the coordinate system employed, referring to the respective centers of left and right lenses.

Fig. 2
Fig. 2

Plots of the calculated differential spherical power versus the horizontal sight angle ωx for three object distances: (a) near, (b) intermediate, and (c) far. Each line indicates a different value of the vertical sight angle.

Fig. 3
Fig. 3

Plots of the calculated differential cylindrical power versus the horizontal sight angle ωx for three object distances: (a) near, (b) intermediate, and (c) far. Each line indicates a different value of the vertical sight angle.

Fig. 4
Fig. 4

Plots of the calculated vertical differential prismatic power versus the horizontal sight angle ωx for three object distances: (a) near, (b) intermediate, and (c) far. Each line indicates a different value of the vertical sight angle.

Equations (23)

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ΔE(x, y, z)=ER(ξR, ηR)-EL(ξL, ηL),
ΔC(x, y, z)=CR(ξR, ηR)-CL(ξL, ηL),
ΔPx(x, y, z)=PxR(rR)-PxL(rR),
ΔPy(x, y, z)=PyR(rL)-PyL(rL),
kiR=(d+ξR-x, ηR-y, l2-z)[(d+ξR-x)2+(ηR-y)2+(l2-z)2]1/2,
krR=(-ξR, -ηR, l2)[(ξR)2+(ηR)2+(l2)2]1/2.
kiR=d+ξR-xz-l2, ηR-yz-l2,-1,
krR=-ξRl2, -ηRl2,-1.
Px(rR)=krxR-kixR,
Py(rR)=kryR-kiyR.
Px(rR)+1z-l2+1l2ξR-x-dz-l2=0,
Py(rR)+1z-l2+1l2ηR-yz-l2=0.
Px(rL)+1z-l2+1l2ξL-x+dz-l2=0,
Py(rL)+1z-l2+1l2ηL-yz-l2=0.
SR(rR)=0,
SL(rL)=0,
SR(rR)=Px(rR)+1z-l2+1l2ξR-x-dz-l2Py(rR)+1z-l2+1l2ηR-yz-l2,
SL(rL)=Px(rL)+1z-l2+1l2ξL-x-dz-l2Py(rL)+1z-l2+1l2ηL-yz-l2.
JR(rR)=ξSx(rR)ηSx(rR)ξSy(rR)ηSy(rR),
JR(rR)=ξPx(rR)ηPx(rR)ξPy(rR)ηPy(rR)+1z-l2+1l2I,
JR(rR)=FR(rR)+1z-l2+1l2I,
m=1-dvE,
δm=mR-mLmR=dv|ΔE|1-dvER,

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