Abstract

This paper presents a deflectometric technique to measure the power of an ophthalmic lens as perceived by the user. It is based on a calibrated camera acting as a pinhole in order to measure ray deflection along the same path as the visual axis when the lens is held in front of the eye. We have analyzed numerically the accuracy of our technique, and it has been compared experimentally with a commercial “lens mapper” and with the real user power calculated from the measured topography of the lens surfaces to state the reliability and accuracy of the presented technique.

© 2010 Optical Society of America

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References

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  1. B. Bourdoncle, J. P. Chauveau, and J. L. Mercier, “Traps in displaying optical performances of a progressive-addition lens,” Appl. Opt. 31, 3586–3593 (1992).
    [CrossRef] [PubMed]
  2. D. A. Atchinson, M. Kris, J. E. Sheedy, and I. L. Bailey, “Use of the Humphrey Lens Analyzer for off-axis measurements of spectacle lenses,” Optom. Vis. Sci. 68, 299–308 (1991).
    [CrossRef]
  3. D. A. Atchinson and M. Kris, “Off- axis measurement of a plano distance power progressive addition lens,” Ophthal. Physiol. Opt. 13, 322–326 (1993).
    [CrossRef]
  4. K. Gnanvo, Z. Y. Wu, J. L. de Bougrenet de la Tocnaye, and L. Liu, “Large-aperture automatic focimeter for the measureement of optical power and other optical characteristics of ophthalmic lenses,” Appl. Opt. 41, 5997–6005 (2002).
    [CrossRef] [PubMed]
  5. H. Canabal and J. Alonso, “Automatic wavefront measurement technique using a computer display and a charge-coupled device camera,” Opt. Eng. 41, 822 (2002).
    [CrossRef]
  6. J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38, 974–982 (1999).
    [CrossRef]
  7. J. H. Massig, “Measurement of phase objects by simple means,” Appl. Opt. 38, 4103–4105 (1999).
    [CrossRef]
  8. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University Press, 2008).
  9. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
    [CrossRef]
  10. J. Y. Bouget, “Camera calibration toolbox for MatLab,” http://www.vision.caltech.edu/bouguetj/calib_doc/ (2010).
  11. J. Vargas, J. A. Quiroga, and M. J. Terrón, “Flexible calibration procedure for fringe projection profilometry,” Opt. Eng. 46, 023601 (2007).
    [CrossRef]
  12. J. Alonso, J. A. Gómez-Pedrero, and E. Bernabeu, “Local dioptric power matrix in a progressive addition lens,” Ophthal. Physiol. Opt. 17, 522–529 (1997).
    [CrossRef]
  13. J. A. Gómez-Pedrero, J. Alonso, H. Canabal, and E. Bernabeu, “A generalization of Prentice’s law for lenses with arbitrary refracting surfaces,” Ophthal. Physiol. Opt. 18, 514–520(1998).
    [CrossRef]
  14. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).
  15. O. Kafri, “Noncoherent method for mapping phase objects,” Opt. Lett. 5, 555–557 (1980).
    [CrossRef] [PubMed]

2007 (1)

J. Vargas, J. A. Quiroga, and M. J. Terrón, “Flexible calibration procedure for fringe projection profilometry,” Opt. Eng. 46, 023601 (2007).
[CrossRef]

2002 (2)

2000 (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[CrossRef]

1999 (2)

J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38, 974–982 (1999).
[CrossRef]

J. H. Massig, “Measurement of phase objects by simple means,” Appl. Opt. 38, 4103–4105 (1999).
[CrossRef]

1998 (1)

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

1997 (1)

J. Alonso, J. A. Gómez-Pedrero, and E. Bernabeu, “Local dioptric power matrix in a progressive addition lens,” Ophthal. Physiol. Opt. 17, 522–529 (1997).
[CrossRef]

1993 (1)

D. A. Atchinson and M. Kris, “Off- axis measurement of a plano distance power progressive addition lens,” Ophthal. Physiol. Opt. 13, 322–326 (1993).
[CrossRef]

1992 (1)

1991 (1)

D. A. Atchinson, M. Kris, J. E. Sheedy, and I. L. Bailey, “Use of the Humphrey Lens Analyzer for off-axis measurements of spectacle lenses,” Optom. Vis. Sci. 68, 299–308 (1991).
[CrossRef]

1980 (1)

Alonso, J.

H. Canabal and J. Alonso, “Automatic wavefront measurement technique using a computer display and a charge-coupled device camera,” Opt. Eng. 41, 822 (2002).
[CrossRef]

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

J. Alonso, J. A. Gómez-Pedrero, and E. Bernabeu, “Local dioptric power matrix in a progressive addition lens,” Ophthal. Physiol. Opt. 17, 522–529 (1997).
[CrossRef]

Atchinson, D. A.

D. A. Atchinson and M. Kris, “Off- axis measurement of a plano distance power progressive addition lens,” Ophthal. Physiol. Opt. 13, 322–326 (1993).
[CrossRef]

D. A. Atchinson, M. Kris, J. E. Sheedy, and I. L. Bailey, “Use of the Humphrey Lens Analyzer for off-axis measurements of spectacle lenses,” Optom. Vis. Sci. 68, 299–308 (1991).
[CrossRef]

Bailey, I. L.

D. A. Atchinson, M. Kris, J. E. Sheedy, and I. L. Bailey, “Use of the Humphrey Lens Analyzer for off-axis measurements of spectacle lenses,” Optom. Vis. Sci. 68, 299–308 (1991).
[CrossRef]

Bernabeu, E.

J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38, 974–982 (1999).
[CrossRef]

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

J. Alonso, J. A. Gómez-Pedrero, and E. Bernabeu, “Local dioptric power matrix in a progressive addition lens,” Ophthal. Physiol. Opt. 17, 522–529 (1997).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

Bouget, J. Y.

J. Y. Bouget, “Camera calibration toolbox for MatLab,” http://www.vision.caltech.edu/bouguetj/calib_doc/ (2010).

Bourdoncle, B.

Canabal, H.

H. Canabal and J. Alonso, “Automatic wavefront measurement technique using a computer display and a charge-coupled device camera,” Opt. Eng. 41, 822 (2002).
[CrossRef]

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

Chauveau, J. P.

Crespo, D.

J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38, 974–982 (1999).
[CrossRef]

de Bougrenet de la Tocnaye, J. L.

Gnanvo, K.

Gómez-Pedrero, J. A.

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

J. Alonso, J. A. Gómez-Pedrero, and E. Bernabeu, “Local dioptric power matrix in a progressive addition lens,” Ophthal. Physiol. Opt. 17, 522–529 (1997).
[CrossRef]

Hartley, R.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University Press, 2008).

Kafri, O.

Kris, M.

D. A. Atchinson and M. Kris, “Off- axis measurement of a plano distance power progressive addition lens,” Ophthal. Physiol. Opt. 13, 322–326 (1993).
[CrossRef]

D. A. Atchinson, M. Kris, J. E. Sheedy, and I. L. Bailey, “Use of the Humphrey Lens Analyzer for off-axis measurements of spectacle lenses,” Optom. Vis. Sci. 68, 299–308 (1991).
[CrossRef]

Liu, L.

Massig, J. H.

Mercier, J. L.

Quiroga, J. A.

J. Vargas, J. A. Quiroga, and M. J. Terrón, “Flexible calibration procedure for fringe projection profilometry,” Opt. Eng. 46, 023601 (2007).
[CrossRef]

J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38, 974–982 (1999).
[CrossRef]

Sheedy, J. E.

D. A. Atchinson, M. Kris, J. E. Sheedy, and I. L. Bailey, “Use of the Humphrey Lens Analyzer for off-axis measurements of spectacle lenses,” Optom. Vis. Sci. 68, 299–308 (1991).
[CrossRef]

Terrón, M. J.

J. Vargas, J. A. Quiroga, and M. J. Terrón, “Flexible calibration procedure for fringe projection profilometry,” Opt. Eng. 46, 023601 (2007).
[CrossRef]

Vargas, J.

J. Vargas, J. A. Quiroga, and M. J. Terrón, “Flexible calibration procedure for fringe projection profilometry,” Opt. Eng. 46, 023601 (2007).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

Wu, Z. Y.

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[CrossRef]

Zisserman, A.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University Press, 2008).

Appl. Opt. (3)

IEEE Trans. Pattern Anal. Mach. Intell. (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[CrossRef]

Ophthal. Physiol. Opt. (3)

D. A. Atchinson and M. Kris, “Off- axis measurement of a plano distance power progressive addition lens,” Ophthal. Physiol. Opt. 13, 322–326 (1993).
[CrossRef]

J. Alonso, J. A. Gómez-Pedrero, and E. Bernabeu, “Local dioptric power matrix in a progressive addition lens,” Ophthal. Physiol. Opt. 17, 522–529 (1997).
[CrossRef]

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

Opt. Eng. (3)

J. Vargas, J. A. Quiroga, and M. J. Terrón, “Flexible calibration procedure for fringe projection profilometry,” Opt. Eng. 46, 023601 (2007).
[CrossRef]

H. Canabal and J. Alonso, “Automatic wavefront measurement technique using a computer display and a charge-coupled device camera,” Opt. Eng. 41, 822 (2002).
[CrossRef]

J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38, 974–982 (1999).
[CrossRef]

Opt. Lett. (1)

Optom. Vis. Sci. (1)

D. A. Atchinson, M. Kris, J. E. Sheedy, and I. L. Bailey, “Use of the Humphrey Lens Analyzer for off-axis measurements of spectacle lenses,” Optom. Vis. Sci. 68, 299–308 (1991).
[CrossRef]

Other (3)

J. Y. Bouget, “Camera calibration toolbox for MatLab,” http://www.vision.caltech.edu/bouguetj/calib_doc/ (2010).

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University Press, 2008).

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

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Figures (8)

Fig. 1
Fig. 1

Ophthalmic lens-rotating eye scheme. An object O is observed through an ophthalmic lens by a rotating eye, represented by a diaphragm located at the rotation center of the eye, point C. The vertex sphere is also represented in this picture.

Fig. 2
Fig. 2

Image formation by a pinhole camera. Object point O is mapped onto an image point O , defined by the intersection of the principal ray (which passes through the projection center C) with the CCD plane. Note that both the World Reference System and the Camera Reference System have been represented in this figure as W and C for its respective origins.

Fig. 3
Fig. 3

Scheme of the experimental setup employed to measure the prismatic power formed by a flat screen, a CCD camera (modeled as a pinhole camera), and the lens to be measured. The World and Camera Reference Systems employed are also depicted with points W and C as the centers of these reference systems, respectively.

Fig. 4
Fig. 4

Image formation from an ophthalmic lens, plus a pinhole camera. Object point O is imaged onto the image plane at O , where the principal ray intercepts the CCD plane. The backprojection of O gives the point O at the screen.

Fig. 5
Fig. 5

Ray-tracing drawings of the three configurations studied: (a) configuration A, with the objective entrance pupil placed at the eye’s rotation center, (b) configuration B, with the objective nodal point (space object) placed at the same point, and (c) configuration C with the objective separated a greater distance from the lens.

Fig. 6
Fig. 6

Prismatic power obtained in the (a) horizontal and (b) vertical directions using our technique for a progressive addition lens. Also represented are the (c) spherical and (d) cylindrical power maps obtained from them.

Fig. 7
Fig. 7

(a) Spherical and (b) cylindrical power maps of the same lens from Fig. 6, obtained using a lens mapper (Rotlex’s Class Plus).

Fig. 8
Fig. 8

Actual (a) spherical and (b) cylindrical user power maps derived through ray tracing from the measured surface of the progressive addition lens studied in this paper.

Tables (1)

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Table 1 Prismatic Power (Ray Deviation) Both in Degrees and Prismatic Diopters Calculated in Three Different Experimental Configurations for the Lens–Camera System a

Equations (6)

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

F u = V B V A ,
( u v 1 ) = [ f x 0 c x 0 0 f y c y 0 0 0 0 1 ] [ r X X r X Y r X Z t X r Y X r Y Y r Z Z t Y r Z X r Z Y r Z Z t Z 0 0 0 1 ] ( X Y Z 1 ) = P · ( X Y Z 1 ) ,
( u i v i 1 ) = [ f x 0 c x 0 0 f y c y 0 0 0 0 1 ] ( X i c Y i c Z i c 1 ) ,
Φ X = 2 π p X X , Φ Y = 2 π p Y Y ,
δ Y = tan ( Y O Y O z ) ,
δ X = tan ( X O X O z ) , δ Y = tan ( Y O Y O z ) .

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