Abstract

We present a method for measuring lens power from extended depth OCT biometry, corneal topography, and refraction using an improvement on the Bennett method. A reduced eye model was used to derive a formula for lens power in terms of ocular distances, corneal power, and objective spherical equivalent refraction. An error analysis shows that the formula predicts relaxed lens power with a theoretical accuracy of ± 0.5 D for refractive error ranging from −10 D to + 10 D. The formula was used to calculate lens power in 16 eyes of 8 human subjects. Mean lens power was 24.3 D ± 1.7 D.

© 2015 Optical Society of America

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  4. D. O. Mutti, G. L. Mitchell, L. A. Jones, N. E. Friedman, S. L. Frane, W. K. Lin, M. L. Moeschberger, and K. Zadnik, “Axial growth and changes in lenticular and corneal power during emmetropization in infants,” Invest. Ophthalmol. Vis. Sci. 46(9), 3074–3080 (2005).
    [Crossref] [PubMed]
  5. T. Olsen, A. Arnarsson, H. Sasaki, K. Sasaki, and F. Jonasson, “On the ocular refractive components: the Reykjavik eye study,” Acta Ophthalmol. Scand. 85(4), 361–366 (2007).
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  6. L. A. Jones, G. L. Mitchell, D. O. Mutti, J. R. Hayes, M. L. Moeschberger, and K. Zadnik, “Comparison of ocular component growth curves among refractive error groups in children,” Invest. Ophthalmol. Vis. Sci. 46(7), 2317–2327 (2005).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  29. M. Dubbelman, V. A. Sicam, and G. L. Van der Heijde, “The shape of the anterior and posterior surface of the aging human cornea,” Vision Res. 46(6-7), 993–1001 (2006).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2015 (2)

R. Iribarren, “Crystalline lens and refractive development,” Prog. Retin. Eye Res. 47, 86–106 (2015).
[Crossref] [PubMed]

S. M. Li, N. Wang, Y. Zhou, S. Y. Li, M. T. Kang, L. R. Liu, H. Li, Y. Y. Sun, B. Meng, S. Y. Zhan, and D. A. Atchison, “Paraxial schematic eye models for 7- and 14-year-old Chinese children,” Invest. Ophthalmol. Vis. Sci. 56(6), 3577–3583 (2015).
[Crossref] [PubMed]

2013 (1)

2012 (4)

S. Ortiz, P. Pérez-Merino, E. Gambra, A. de Castro, and S. Marcos, “In vivo human crystalline lens topography,” Biomed. Opt. Express 3(10), 2471–2488 (2012).
[Crossref] [PubMed]

R. Iribarren, I. G. Morgan, V. Nangia, and J. B. Jonas, “Crystalline lens power and refractive error,” Invest. Ophthalmol. Vis. Sci. 53(2), 543–550 (2012).
[Crossref] [PubMed]

M. Ruggeri, S. R. Uhlhorn, C. De Freitas, A. Ho, F. Manns, and J. M. Parel, “Imaging and full-length biometry of the eye during accommodation using spectral domain OCT with an optical switch,” Biomed. Opt. Express 3(7), 1506–1520 (2012).
[Crossref] [PubMed]

J. J. Rozema, D. A. Atchison, S. Kasthurirangan, J. M. Pope, and M. J. Tassignon, “Methods to estimate the size and shape of the unaccommodated crystalline lens in vivo,” Invest. Ophthalmol. Vis. Sci. 53(6), 2533–2540 (2012).
[Crossref] [PubMed]

2011 (1)

J. J. Rozema, D. A. Atchison, and M. J. Tassignon, “Comparing methods to estimate the human lens power,” Invest. Ophthalmol. Vis. Sci. 52(11), 7937–7942 (2011).
[Crossref] [PubMed]

2010 (1)

2008 (1)

D. Borja, F. Manns, A. Ho, N. Ziebarth, A. M. Rosen, R. Jain, A. Amelinckx, E. Arrieta, R. C. Augusteyn, and J. M. Parel, “Optical power of the isolated human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 49(6), 2541–2548 (2008).
[Crossref] [PubMed]

2007 (3)

C. E. Jones, D. A. Atchison, and J. M. Pope, “Changes in lens dimensions and refractive index with age and accommodation,” Optom. Vis. Sci. 84(10), 990–995 (2007).
[Crossref] [PubMed]

M. C. M. Dunne, L. N. Davies, and J. S. Wolffsohn, “Accuracy of cornea and lens biometry using anterior segment optical coherence tomography,” J. Biomed. Opt. 12(6), 064023 (2007).
[Crossref] [PubMed]

T. Olsen, A. Arnarsson, H. Sasaki, K. Sasaki, and F. Jonasson, “On the ocular refractive components: the Reykjavik eye study,” Acta Ophthalmol. Scand. 85(4), 361–366 (2007).
[Crossref] [PubMed]

2006 (2)

P. Rosales and S. Marcos, “Phakometry and lens tilt and decentration using a custom-developed Purkinje imaging apparatus: validation and measurements,” J. Opt. Soc. Am. A 23(3), 509–520 (2006).
[Crossref] [PubMed]

M. Dubbelman, V. A. Sicam, and G. L. Van der Heijde, “The shape of the anterior and posterior surface of the aging human cornea,” Vision Res. 46(6-7), 993–1001 (2006).
[Crossref] [PubMed]

2005 (3)

M. Dubbelman, G. L. Van der Heijde, and H. A. Weeber, “Change in shape of the aging human crystalline lens with accommodation,” Vision Res. 45(1), 117–132 (2005).
[Crossref] [PubMed]

L. A. Jones, G. L. Mitchell, D. O. Mutti, J. R. Hayes, M. L. Moeschberger, and K. Zadnik, “Comparison of ocular component growth curves among refractive error groups in children,” Invest. Ophthalmol. Vis. Sci. 46(7), 2317–2327 (2005).
[Crossref] [PubMed]

D. O. Mutti, G. L. Mitchell, L. A. Jones, N. E. Friedman, S. L. Frane, W. K. Lin, M. L. Moeschberger, and K. Zadnik, “Axial growth and changes in lenticular and corneal power during emmetropization in infants,” Invest. Ophthalmol. Vis. Sci. 46(9), 3074–3080 (2005).
[Crossref] [PubMed]

2001 (3)

M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, “The thickness of the aging human lens obtained from corrected Scheimpflug images,” Optom. Vis. Sci. 78(6), 411–416 (2001).
[Crossref] [PubMed]

M. Dubbelman and G. L. Van der Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41(14), 1867–1877 (2001).
[Crossref] [PubMed]

A. Ho, P. Erickson, F. Manns, T. Pham, and J. M. Parel, “Theoretical analysis of accommodation amplitude and ametropia correction by varying refractive index in Phaco-Ersatz,” Optom. Vis. Sci. 78(6), 405–410 (2001).
[Crossref] [PubMed]

1997 (2)

L. F. Garner, “Calculation of the radii of curvature of the crystalline lens surfaces,” Ophthalmic Physiol. Opt. 17(1), 75–80 (1997).
[Crossref] [PubMed]

J. F. Koretz, C. A. Cook, and P. L. Kaufman, “Accommodation and presbyopia in the human eye. Changes in the anterior segment and crystalline lens with focus,” Invest. Ophthalmol. Vis. Sci. 38(3), 569–578 (1997).
[PubMed]

1995 (1)

D. O. Mutti, K. Zadnik, and A. J. Adams, “The equivalent refractive index of the crystalline lens in childhood,” Vision Res. 35(11), 1565–1573 (1995).
[Crossref] [PubMed]

1992 (2)

D. O. Mutti, K. Zadnik, and A. J. Adams, “A video technique for phakometry of the human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 33(5), 1771–1782 (1992).
[PubMed]

M. C. Dunne, J. M. Royston, and D. A. Barnes, “Normal variations of the posterior corneal surface,” Acta Ophthalmol. (Copenh.) 70(2), 255–261 (1992).
[Crossref] [PubMed]

1989 (2)

M. C. M. Dunne, D. A. Barnes, and J. M. Royston, “An evaluation of Bennett’s method for determining the equivalent powers of the eye and its crystalline lens without resort to phakometry,” Ophthalmic Physiol. Opt. 9(1), 69–71 (1989).
[Crossref] [PubMed]

J. M. Royston, M. C. M. Dunne, and D. A. Barnes, “Calculation of crystalline lens radii without resort to phakometry,” Ophthalmic Physiol. Opt. 9(4), 412–414 (1989).
[Crossref] [PubMed]

1988 (1)

A. G. Bennett, “A method of determining the equivalent powers of the eye and its crystalline lens without resort to phakometry,” Ophthalmic Physiol. Opt. 8(1), 53–59 (1988).
[Crossref] [PubMed]

1855 (1)

H. von Helmholtz, “Uber die akkommodation des auges,” Arch. Ophthalmol. 2(2), 1–74 (1855).

Adams, A. J.

D. O. Mutti, K. Zadnik, and A. J. Adams, “The equivalent refractive index of the crystalline lens in childhood,” Vision Res. 35(11), 1565–1573 (1995).
[Crossref] [PubMed]

D. O. Mutti, K. Zadnik, and A. J. Adams, “A video technique for phakometry of the human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 33(5), 1771–1782 (1992).
[PubMed]

Amelinckx, A.

D. Borja, F. Manns, A. Ho, N. Ziebarth, A. M. Rosen, R. Jain, A. Amelinckx, E. Arrieta, R. C. Augusteyn, and J. M. Parel, “Optical power of the isolated human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 49(6), 2541–2548 (2008).
[Crossref] [PubMed]

Arnarsson, A.

T. Olsen, A. Arnarsson, H. Sasaki, K. Sasaki, and F. Jonasson, “On the ocular refractive components: the Reykjavik eye study,” Acta Ophthalmol. Scand. 85(4), 361–366 (2007).
[Crossref] [PubMed]

Arrieta, E.

D. Borja, F. Manns, A. Ho, N. Ziebarth, A. M. Rosen, R. Jain, A. Amelinckx, E. Arrieta, R. C. Augusteyn, and J. M. Parel, “Optical power of the isolated human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 49(6), 2541–2548 (2008).
[Crossref] [PubMed]

Atchison, D. A.

S. M. Li, N. Wang, Y. Zhou, S. Y. Li, M. T. Kang, L. R. Liu, H. Li, Y. Y. Sun, B. Meng, S. Y. Zhan, and D. A. Atchison, “Paraxial schematic eye models for 7- and 14-year-old Chinese children,” Invest. Ophthalmol. Vis. Sci. 56(6), 3577–3583 (2015).
[Crossref] [PubMed]

J. J. Rozema, D. A. Atchison, S. Kasthurirangan, J. M. Pope, and M. J. Tassignon, “Methods to estimate the size and shape of the unaccommodated crystalline lens in vivo,” Invest. Ophthalmol. Vis. Sci. 53(6), 2533–2540 (2012).
[Crossref] [PubMed]

J. J. Rozema, D. A. Atchison, and M. J. Tassignon, “Comparing methods to estimate the human lens power,” Invest. Ophthalmol. Vis. Sci. 52(11), 7937–7942 (2011).
[Crossref] [PubMed]

C. E. Jones, D. A. Atchison, and J. M. Pope, “Changes in lens dimensions and refractive index with age and accommodation,” Optom. Vis. Sci. 84(10), 990–995 (2007).
[Crossref] [PubMed]

Augusteyn, R. C.

D. Borja, F. Manns, A. Ho, N. Ziebarth, A. M. Rosen, R. Jain, A. Amelinckx, E. Arrieta, R. C. Augusteyn, and J. M. Parel, “Optical power of the isolated human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 49(6), 2541–2548 (2008).
[Crossref] [PubMed]

Barnes, D. A.

M. C. Dunne, J. M. Royston, and D. A. Barnes, “Normal variations of the posterior corneal surface,” Acta Ophthalmol. (Copenh.) 70(2), 255–261 (1992).
[Crossref] [PubMed]

J. M. Royston, M. C. M. Dunne, and D. A. Barnes, “Calculation of crystalline lens radii without resort to phakometry,” Ophthalmic Physiol. Opt. 9(4), 412–414 (1989).
[Crossref] [PubMed]

M. C. M. Dunne, D. A. Barnes, and J. M. Royston, “An evaluation of Bennett’s method for determining the equivalent powers of the eye and its crystalline lens without resort to phakometry,” Ophthalmic Physiol. Opt. 9(1), 69–71 (1989).
[Crossref] [PubMed]

Bennett, A. G.

A. G. Bennett, “A method of determining the equivalent powers of the eye and its crystalline lens without resort to phakometry,” Ophthalmic Physiol. Opt. 8(1), 53–59 (1988).
[Crossref] [PubMed]

Borja, D.

D. Borja, F. Manns, A. Ho, N. Ziebarth, A. M. Rosen, R. Jain, A. Amelinckx, E. Arrieta, R. C. Augusteyn, and J. M. Parel, “Optical power of the isolated human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 49(6), 2541–2548 (2008).
[Crossref] [PubMed]

Cook, C. A.

J. F. Koretz, C. A. Cook, and P. L. Kaufman, “Accommodation and presbyopia in the human eye. Changes in the anterior segment and crystalline lens with focus,” Invest. Ophthalmol. Vis. Sci. 38(3), 569–578 (1997).
[PubMed]

Davies, L. N.

M. C. M. Dunne, L. N. Davies, and J. S. Wolffsohn, “Accuracy of cornea and lens biometry using anterior segment optical coherence tomography,” J. Biomed. Opt. 12(6), 064023 (2007).
[Crossref] [PubMed]

de Castro, A.

De Freitas, C.

Dubbelman, M.

M. Dubbelman, V. A. Sicam, and G. L. Van der Heijde, “The shape of the anterior and posterior surface of the aging human cornea,” Vision Res. 46(6-7), 993–1001 (2006).
[Crossref] [PubMed]

M. Dubbelman, G. L. Van der Heijde, and H. A. Weeber, “Change in shape of the aging human crystalline lens with accommodation,” Vision Res. 45(1), 117–132 (2005).
[Crossref] [PubMed]

M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, “The thickness of the aging human lens obtained from corrected Scheimpflug images,” Optom. Vis. Sci. 78(6), 411–416 (2001).
[Crossref] [PubMed]

M. Dubbelman and G. L. Van der Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41(14), 1867–1877 (2001).
[Crossref] [PubMed]

Dunne, M. C.

M. C. Dunne, J. M. Royston, and D. A. Barnes, “Normal variations of the posterior corneal surface,” Acta Ophthalmol. (Copenh.) 70(2), 255–261 (1992).
[Crossref] [PubMed]

Dunne, M. C. M.

M. C. M. Dunne, L. N. Davies, and J. S. Wolffsohn, “Accuracy of cornea and lens biometry using anterior segment optical coherence tomography,” J. Biomed. Opt. 12(6), 064023 (2007).
[Crossref] [PubMed]

M. C. M. Dunne, D. A. Barnes, and J. M. Royston, “An evaluation of Bennett’s method for determining the equivalent powers of the eye and its crystalline lens without resort to phakometry,” Ophthalmic Physiol. Opt. 9(1), 69–71 (1989).
[Crossref] [PubMed]

J. M. Royston, M. C. M. Dunne, and D. A. Barnes, “Calculation of crystalline lens radii without resort to phakometry,” Ophthalmic Physiol. Opt. 9(4), 412–414 (1989).
[Crossref] [PubMed]

Erickson, P.

A. Ho, P. Erickson, F. Manns, T. Pham, and J. M. Parel, “Theoretical analysis of accommodation amplitude and ametropia correction by varying refractive index in Phaco-Ersatz,” Optom. Vis. Sci. 78(6), 405–410 (2001).
[Crossref] [PubMed]

Frane, S. L.

D. O. Mutti, G. L. Mitchell, L. A. Jones, N. E. Friedman, S. L. Frane, W. K. Lin, M. L. Moeschberger, and K. Zadnik, “Axial growth and changes in lenticular and corneal power during emmetropization in infants,” Invest. Ophthalmol. Vis. Sci. 46(9), 3074–3080 (2005).
[Crossref] [PubMed]

Friedman, N. E.

D. O. Mutti, G. L. Mitchell, L. A. Jones, N. E. Friedman, S. L. Frane, W. K. Lin, M. L. Moeschberger, and K. Zadnik, “Axial growth and changes in lenticular and corneal power during emmetropization in infants,” Invest. Ophthalmol. Vis. Sci. 46(9), 3074–3080 (2005).
[Crossref] [PubMed]

Gambra, E.

Garner, L. F.

L. F. Garner, “Calculation of the radii of curvature of the crystalline lens surfaces,” Ophthalmic Physiol. Opt. 17(1), 75–80 (1997).
[Crossref] [PubMed]

Gora, M.

Hayes, J. R.

L. A. Jones, G. L. Mitchell, D. O. Mutti, J. R. Hayes, M. L. Moeschberger, and K. Zadnik, “Comparison of ocular component growth curves among refractive error groups in children,” Invest. Ophthalmol. Vis. Sci. 46(7), 2317–2327 (2005).
[Crossref] [PubMed]

Ho, A.

M. Ruggeri, S. R. Uhlhorn, C. De Freitas, A. Ho, F. Manns, and J. M. Parel, “Imaging and full-length biometry of the eye during accommodation using spectral domain OCT with an optical switch,” Biomed. Opt. Express 3(7), 1506–1520 (2012).
[Crossref] [PubMed]

D. Borja, F. Manns, A. Ho, N. Ziebarth, A. M. Rosen, R. Jain, A. Amelinckx, E. Arrieta, R. C. Augusteyn, and J. M. Parel, “Optical power of the isolated human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 49(6), 2541–2548 (2008).
[Crossref] [PubMed]

A. Ho, P. Erickson, F. Manns, T. Pham, and J. M. Parel, “Theoretical analysis of accommodation amplitude and ametropia correction by varying refractive index in Phaco-Ersatz,” Optom. Vis. Sci. 78(6), 405–410 (2001).
[Crossref] [PubMed]

Iribarren, R.

R. Iribarren, “Crystalline lens and refractive development,” Prog. Retin. Eye Res. 47, 86–106 (2015).
[Crossref] [PubMed]

R. Iribarren, I. G. Morgan, V. Nangia, and J. B. Jonas, “Crystalline lens power and refractive error,” Invest. Ophthalmol. Vis. Sci. 53(2), 543–550 (2012).
[Crossref] [PubMed]

Izatt, J. A.

Jain, R.

D. Borja, F. Manns, A. Ho, N. Ziebarth, A. M. Rosen, R. Jain, A. Amelinckx, E. Arrieta, R. C. Augusteyn, and J. M. Parel, “Optical power of the isolated human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 49(6), 2541–2548 (2008).
[Crossref] [PubMed]

Jonas, J. B.

R. Iribarren, I. G. Morgan, V. Nangia, and J. B. Jonas, “Crystalline lens power and refractive error,” Invest. Ophthalmol. Vis. Sci. 53(2), 543–550 (2012).
[Crossref] [PubMed]

Jonasson, F.

T. Olsen, A. Arnarsson, H. Sasaki, K. Sasaki, and F. Jonasson, “On the ocular refractive components: the Reykjavik eye study,” Acta Ophthalmol. Scand. 85(4), 361–366 (2007).
[Crossref] [PubMed]

Jones, C. E.

C. E. Jones, D. A. Atchison, and J. M. Pope, “Changes in lens dimensions and refractive index with age and accommodation,” Optom. Vis. Sci. 84(10), 990–995 (2007).
[Crossref] [PubMed]

Jones, L. A.

L. A. Jones, G. L. Mitchell, D. O. Mutti, J. R. Hayes, M. L. Moeschberger, and K. Zadnik, “Comparison of ocular component growth curves among refractive error groups in children,” Invest. Ophthalmol. Vis. Sci. 46(7), 2317–2327 (2005).
[Crossref] [PubMed]

D. O. Mutti, G. L. Mitchell, L. A. Jones, N. E. Friedman, S. L. Frane, W. K. Lin, M. L. Moeschberger, and K. Zadnik, “Axial growth and changes in lenticular and corneal power during emmetropization in infants,” Invest. Ophthalmol. Vis. Sci. 46(9), 3074–3080 (2005).
[Crossref] [PubMed]

Kang, M. T.

S. M. Li, N. Wang, Y. Zhou, S. Y. Li, M. T. Kang, L. R. Liu, H. Li, Y. Y. Sun, B. Meng, S. Y. Zhan, and D. A. Atchison, “Paraxial schematic eye models for 7- and 14-year-old Chinese children,” Invest. Ophthalmol. Vis. Sci. 56(6), 3577–3583 (2015).
[Crossref] [PubMed]

Kasthurirangan, S.

J. J. Rozema, D. A. Atchison, S. Kasthurirangan, J. M. Pope, and M. J. Tassignon, “Methods to estimate the size and shape of the unaccommodated crystalline lens in vivo,” Invest. Ophthalmol. Vis. Sci. 53(6), 2533–2540 (2012).
[Crossref] [PubMed]

Kaufman, P. L.

J. F. Koretz, C. A. Cook, and P. L. Kaufman, “Accommodation and presbyopia in the human eye. Changes in the anterior segment and crystalline lens with focus,” Invest. Ophthalmol. Vis. Sci. 38(3), 569–578 (1997).
[PubMed]

Koretz, J. F.

J. F. Koretz, C. A. Cook, and P. L. Kaufman, “Accommodation and presbyopia in the human eye. Changes in the anterior segment and crystalline lens with focus,” Invest. Ophthalmol. Vis. Sci. 38(3), 569–578 (1997).
[PubMed]

Kuo, A. N.

Li, H.

S. M. Li, N. Wang, Y. Zhou, S. Y. Li, M. T. Kang, L. R. Liu, H. Li, Y. Y. Sun, B. Meng, S. Y. Zhan, and D. A. Atchison, “Paraxial schematic eye models for 7- and 14-year-old Chinese children,” Invest. Ophthalmol. Vis. Sci. 56(6), 3577–3583 (2015).
[Crossref] [PubMed]

Li, S. M.

S. M. Li, N. Wang, Y. Zhou, S. Y. Li, M. T. Kang, L. R. Liu, H. Li, Y. Y. Sun, B. Meng, S. Y. Zhan, and D. A. Atchison, “Paraxial schematic eye models for 7- and 14-year-old Chinese children,” Invest. Ophthalmol. Vis. Sci. 56(6), 3577–3583 (2015).
[Crossref] [PubMed]

Li, S. Y.

S. M. Li, N. Wang, Y. Zhou, S. Y. Li, M. T. Kang, L. R. Liu, H. Li, Y. Y. Sun, B. Meng, S. Y. Zhan, and D. A. Atchison, “Paraxial schematic eye models for 7- and 14-year-old Chinese children,” Invest. Ophthalmol. Vis. Sci. 56(6), 3577–3583 (2015).
[Crossref] [PubMed]

Lin, W. K.

D. O. Mutti, G. L. Mitchell, L. A. Jones, N. E. Friedman, S. L. Frane, W. K. Lin, M. L. Moeschberger, and K. Zadnik, “Axial growth and changes in lenticular and corneal power during emmetropization in infants,” Invest. Ophthalmol. Vis. Sci. 46(9), 3074–3080 (2005).
[Crossref] [PubMed]

Liu, L. R.

S. M. Li, N. Wang, Y. Zhou, S. Y. Li, M. T. Kang, L. R. Liu, H. Li, Y. Y. Sun, B. Meng, S. Y. Zhan, and D. A. Atchison, “Paraxial schematic eye models for 7- and 14-year-old Chinese children,” Invest. Ophthalmol. Vis. Sci. 56(6), 3577–3583 (2015).
[Crossref] [PubMed]

Manns, F.

M. Ruggeri, S. R. Uhlhorn, C. De Freitas, A. Ho, F. Manns, and J. M. Parel, “Imaging and full-length biometry of the eye during accommodation using spectral domain OCT with an optical switch,” Biomed. Opt. Express 3(7), 1506–1520 (2012).
[Crossref] [PubMed]

D. Borja, F. Manns, A. Ho, N. Ziebarth, A. M. Rosen, R. Jain, A. Amelinckx, E. Arrieta, R. C. Augusteyn, and J. M. Parel, “Optical power of the isolated human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 49(6), 2541–2548 (2008).
[Crossref] [PubMed]

A. Ho, P. Erickson, F. Manns, T. Pham, and J. M. Parel, “Theoretical analysis of accommodation amplitude and ametropia correction by varying refractive index in Phaco-Ersatz,” Optom. Vis. Sci. 78(6), 405–410 (2001).
[Crossref] [PubMed]

Marcos, S.

Meng, B.

S. M. Li, N. Wang, Y. Zhou, S. Y. Li, M. T. Kang, L. R. Liu, H. Li, Y. Y. Sun, B. Meng, S. Y. Zhan, and D. A. Atchison, “Paraxial schematic eye models for 7- and 14-year-old Chinese children,” Invest. Ophthalmol. Vis. Sci. 56(6), 3577–3583 (2015).
[Crossref] [PubMed]

Mitchell, G. L.

D. O. Mutti, G. L. Mitchell, L. A. Jones, N. E. Friedman, S. L. Frane, W. K. Lin, M. L. Moeschberger, and K. Zadnik, “Axial growth and changes in lenticular and corneal power during emmetropization in infants,” Invest. Ophthalmol. Vis. Sci. 46(9), 3074–3080 (2005).
[Crossref] [PubMed]

L. A. Jones, G. L. Mitchell, D. O. Mutti, J. R. Hayes, M. L. Moeschberger, and K. Zadnik, “Comparison of ocular component growth curves among refractive error groups in children,” Invest. Ophthalmol. Vis. Sci. 46(7), 2317–2327 (2005).
[Crossref] [PubMed]

Moeschberger, M. L.

L. A. Jones, G. L. Mitchell, D. O. Mutti, J. R. Hayes, M. L. Moeschberger, and K. Zadnik, “Comparison of ocular component growth curves among refractive error groups in children,” Invest. Ophthalmol. Vis. Sci. 46(7), 2317–2327 (2005).
[Crossref] [PubMed]

D. O. Mutti, G. L. Mitchell, L. A. Jones, N. E. Friedman, S. L. Frane, W. K. Lin, M. L. Moeschberger, and K. Zadnik, “Axial growth and changes in lenticular and corneal power during emmetropization in infants,” Invest. Ophthalmol. Vis. Sci. 46(9), 3074–3080 (2005).
[Crossref] [PubMed]

Morgan, I. G.

R. Iribarren, I. G. Morgan, V. Nangia, and J. B. Jonas, “Crystalline lens power and refractive error,” Invest. Ophthalmol. Vis. Sci. 53(2), 543–550 (2012).
[Crossref] [PubMed]

Mutti, D. O.

D. O. Mutti, G. L. Mitchell, L. A. Jones, N. E. Friedman, S. L. Frane, W. K. Lin, M. L. Moeschberger, and K. Zadnik, “Axial growth and changes in lenticular and corneal power during emmetropization in infants,” Invest. Ophthalmol. Vis. Sci. 46(9), 3074–3080 (2005).
[Crossref] [PubMed]

L. A. Jones, G. L. Mitchell, D. O. Mutti, J. R. Hayes, M. L. Moeschberger, and K. Zadnik, “Comparison of ocular component growth curves among refractive error groups in children,” Invest. Ophthalmol. Vis. Sci. 46(7), 2317–2327 (2005).
[Crossref] [PubMed]

D. O. Mutti, K. Zadnik, and A. J. Adams, “The equivalent refractive index of the crystalline lens in childhood,” Vision Res. 35(11), 1565–1573 (1995).
[Crossref] [PubMed]

D. O. Mutti, K. Zadnik, and A. J. Adams, “A video technique for phakometry of the human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 33(5), 1771–1782 (1992).
[PubMed]

Nangia, V.

R. Iribarren, I. G. Morgan, V. Nangia, and J. B. Jonas, “Crystalline lens power and refractive error,” Invest. Ophthalmol. Vis. Sci. 53(2), 543–550 (2012).
[Crossref] [PubMed]

Olsen, T.

T. Olsen, A. Arnarsson, H. Sasaki, K. Sasaki, and F. Jonasson, “On the ocular refractive components: the Reykjavik eye study,” Acta Ophthalmol. Scand. 85(4), 361–366 (2007).
[Crossref] [PubMed]

Ortiz, S.

Parel, J. M.

M. Ruggeri, S. R. Uhlhorn, C. De Freitas, A. Ho, F. Manns, and J. M. Parel, “Imaging and full-length biometry of the eye during accommodation using spectral domain OCT with an optical switch,” Biomed. Opt. Express 3(7), 1506–1520 (2012).
[Crossref] [PubMed]

D. Borja, F. Manns, A. Ho, N. Ziebarth, A. M. Rosen, R. Jain, A. Amelinckx, E. Arrieta, R. C. Augusteyn, and J. M. Parel, “Optical power of the isolated human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 49(6), 2541–2548 (2008).
[Crossref] [PubMed]

A. Ho, P. Erickson, F. Manns, T. Pham, and J. M. Parel, “Theoretical analysis of accommodation amplitude and ametropia correction by varying refractive index in Phaco-Ersatz,” Optom. Vis. Sci. 78(6), 405–410 (2001).
[Crossref] [PubMed]

Perez-Merino, P.

Pérez-Merino, P.

Pham, T.

A. Ho, P. Erickson, F. Manns, T. Pham, and J. M. Parel, “Theoretical analysis of accommodation amplitude and ametropia correction by varying refractive index in Phaco-Ersatz,” Optom. Vis. Sci. 78(6), 405–410 (2001).
[Crossref] [PubMed]

Pope, J. M.

J. J. Rozema, D. A. Atchison, S. Kasthurirangan, J. M. Pope, and M. J. Tassignon, “Methods to estimate the size and shape of the unaccommodated crystalline lens in vivo,” Invest. Ophthalmol. Vis. Sci. 53(6), 2533–2540 (2012).
[Crossref] [PubMed]

C. E. Jones, D. A. Atchison, and J. M. Pope, “Changes in lens dimensions and refractive index with age and accommodation,” Optom. Vis. Sci. 84(10), 990–995 (2007).
[Crossref] [PubMed]

Rosales, P.

Rosen, A. M.

D. Borja, F. Manns, A. Ho, N. Ziebarth, A. M. Rosen, R. Jain, A. Amelinckx, E. Arrieta, R. C. Augusteyn, and J. M. Parel, “Optical power of the isolated human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 49(6), 2541–2548 (2008).
[Crossref] [PubMed]

Royston, J. M.

M. C. Dunne, J. M. Royston, and D. A. Barnes, “Normal variations of the posterior corneal surface,” Acta Ophthalmol. (Copenh.) 70(2), 255–261 (1992).
[Crossref] [PubMed]

M. C. M. Dunne, D. A. Barnes, and J. M. Royston, “An evaluation of Bennett’s method for determining the equivalent powers of the eye and its crystalline lens without resort to phakometry,” Ophthalmic Physiol. Opt. 9(1), 69–71 (1989).
[Crossref] [PubMed]

J. M. Royston, M. C. M. Dunne, and D. A. Barnes, “Calculation of crystalline lens radii without resort to phakometry,” Ophthalmic Physiol. Opt. 9(4), 412–414 (1989).
[Crossref] [PubMed]

Rozema, J. J.

J. J. Rozema, D. A. Atchison, S. Kasthurirangan, J. M. Pope, and M. J. Tassignon, “Methods to estimate the size and shape of the unaccommodated crystalline lens in vivo,” Invest. Ophthalmol. Vis. Sci. 53(6), 2533–2540 (2012).
[Crossref] [PubMed]

J. J. Rozema, D. A. Atchison, and M. J. Tassignon, “Comparing methods to estimate the human lens power,” Invest. Ophthalmol. Vis. Sci. 52(11), 7937–7942 (2011).
[Crossref] [PubMed]

Ruggeri, M.

Sasaki, H.

T. Olsen, A. Arnarsson, H. Sasaki, K. Sasaki, and F. Jonasson, “On the ocular refractive components: the Reykjavik eye study,” Acta Ophthalmol. Scand. 85(4), 361–366 (2007).
[Crossref] [PubMed]

Sasaki, K.

T. Olsen, A. Arnarsson, H. Sasaki, K. Sasaki, and F. Jonasson, “On the ocular refractive components: the Reykjavik eye study,” Acta Ophthalmol. Scand. 85(4), 361–366 (2007).
[Crossref] [PubMed]

Sicam, V. A.

M. Dubbelman, V. A. Sicam, and G. L. Van der Heijde, “The shape of the anterior and posterior surface of the aging human cornea,” Vision Res. 46(6-7), 993–1001 (2006).
[Crossref] [PubMed]

Sun, Y. Y.

S. M. Li, N. Wang, Y. Zhou, S. Y. Li, M. T. Kang, L. R. Liu, H. Li, Y. Y. Sun, B. Meng, S. Y. Zhan, and D. A. Atchison, “Paraxial schematic eye models for 7- and 14-year-old Chinese children,” Invest. Ophthalmol. Vis. Sci. 56(6), 3577–3583 (2015).
[Crossref] [PubMed]

Tassignon, M. J.

J. J. Rozema, D. A. Atchison, S. Kasthurirangan, J. M. Pope, and M. J. Tassignon, “Methods to estimate the size and shape of the unaccommodated crystalline lens in vivo,” Invest. Ophthalmol. Vis. Sci. 53(6), 2533–2540 (2012).
[Crossref] [PubMed]

J. J. Rozema, D. A. Atchison, and M. J. Tassignon, “Comparing methods to estimate the human lens power,” Invest. Ophthalmol. Vis. Sci. 52(11), 7937–7942 (2011).
[Crossref] [PubMed]

Uhlhorn, S. R.

Van der Heijde, G. L.

M. Dubbelman, V. A. Sicam, and G. L. Van der Heijde, “The shape of the anterior and posterior surface of the aging human cornea,” Vision Res. 46(6-7), 993–1001 (2006).
[Crossref] [PubMed]

M. Dubbelman, G. L. Van der Heijde, and H. A. Weeber, “Change in shape of the aging human crystalline lens with accommodation,” Vision Res. 45(1), 117–132 (2005).
[Crossref] [PubMed]

M. Dubbelman and G. L. Van der Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41(14), 1867–1877 (2001).
[Crossref] [PubMed]

M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, “The thickness of the aging human lens obtained from corrected Scheimpflug images,” Optom. Vis. Sci. 78(6), 411–416 (2001).
[Crossref] [PubMed]

von Helmholtz, H.

H. von Helmholtz, “Uber die akkommodation des auges,” Arch. Ophthalmol. 2(2), 1–74 (1855).

Wang, N.

S. M. Li, N. Wang, Y. Zhou, S. Y. Li, M. T. Kang, L. R. Liu, H. Li, Y. Y. Sun, B. Meng, S. Y. Zhan, and D. A. Atchison, “Paraxial schematic eye models for 7- and 14-year-old Chinese children,” Invest. Ophthalmol. Vis. Sci. 56(6), 3577–3583 (2015).
[Crossref] [PubMed]

Weeber, H. A.

M. Dubbelman, G. L. Van der Heijde, and H. A. Weeber, “Change in shape of the aging human crystalline lens with accommodation,” Vision Res. 45(1), 117–132 (2005).
[Crossref] [PubMed]

M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, “The thickness of the aging human lens obtained from corrected Scheimpflug images,” Optom. Vis. Sci. 78(6), 411–416 (2001).
[Crossref] [PubMed]

Wojtkowski, M.

Wolffsohn, J. S.

M. C. M. Dunne, L. N. Davies, and J. S. Wolffsohn, “Accuracy of cornea and lens biometry using anterior segment optical coherence tomography,” J. Biomed. Opt. 12(6), 064023 (2007).
[Crossref] [PubMed]

Zadnik, K.

L. A. Jones, G. L. Mitchell, D. O. Mutti, J. R. Hayes, M. L. Moeschberger, and K. Zadnik, “Comparison of ocular component growth curves among refractive error groups in children,” Invest. Ophthalmol. Vis. Sci. 46(7), 2317–2327 (2005).
[Crossref] [PubMed]

D. O. Mutti, G. L. Mitchell, L. A. Jones, N. E. Friedman, S. L. Frane, W. K. Lin, M. L. Moeschberger, and K. Zadnik, “Axial growth and changes in lenticular and corneal power during emmetropization in infants,” Invest. Ophthalmol. Vis. Sci. 46(9), 3074–3080 (2005).
[Crossref] [PubMed]

D. O. Mutti, K. Zadnik, and A. J. Adams, “The equivalent refractive index of the crystalline lens in childhood,” Vision Res. 35(11), 1565–1573 (1995).
[Crossref] [PubMed]

D. O. Mutti, K. Zadnik, and A. J. Adams, “A video technique for phakometry of the human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 33(5), 1771–1782 (1992).
[PubMed]

Zhan, S. Y.

S. M. Li, N. Wang, Y. Zhou, S. Y. Li, M. T. Kang, L. R. Liu, H. Li, Y. Y. Sun, B. Meng, S. Y. Zhan, and D. A. Atchison, “Paraxial schematic eye models for 7- and 14-year-old Chinese children,” Invest. Ophthalmol. Vis. Sci. 56(6), 3577–3583 (2015).
[Crossref] [PubMed]

Zhao, M.

Zhou, Y.

S. M. Li, N. Wang, Y. Zhou, S. Y. Li, M. T. Kang, L. R. Liu, H. Li, Y. Y. Sun, B. Meng, S. Y. Zhan, and D. A. Atchison, “Paraxial schematic eye models for 7- and 14-year-old Chinese children,” Invest. Ophthalmol. Vis. Sci. 56(6), 3577–3583 (2015).
[Crossref] [PubMed]

Ziebarth, N.

D. Borja, F. Manns, A. Ho, N. Ziebarth, A. M. Rosen, R. Jain, A. Amelinckx, E. Arrieta, R. C. Augusteyn, and J. M. Parel, “Optical power of the isolated human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 49(6), 2541–2548 (2008).
[Crossref] [PubMed]

Acta Ophthalmol. (Copenh.) (1)

M. C. Dunne, J. M. Royston, and D. A. Barnes, “Normal variations of the posterior corneal surface,” Acta Ophthalmol. (Copenh.) 70(2), 255–261 (1992).
[Crossref] [PubMed]

Acta Ophthalmol. Scand. (1)

T. Olsen, A. Arnarsson, H. Sasaki, K. Sasaki, and F. Jonasson, “On the ocular refractive components: the Reykjavik eye study,” Acta Ophthalmol. Scand. 85(4), 361–366 (2007).
[Crossref] [PubMed]

Arch. Ophthalmol. (1)

H. von Helmholtz, “Uber die akkommodation des auges,” Arch. Ophthalmol. 2(2), 1–74 (1855).

Biomed. Opt. Express (3)

Invest. Ophthalmol. Vis. Sci. (9)

J. J. Rozema, D. A. Atchison, S. Kasthurirangan, J. M. Pope, and M. J. Tassignon, “Methods to estimate the size and shape of the unaccommodated crystalline lens in vivo,” Invest. Ophthalmol. Vis. Sci. 53(6), 2533–2540 (2012).
[Crossref] [PubMed]

J. J. Rozema, D. A. Atchison, and M. J. Tassignon, “Comparing methods to estimate the human lens power,” Invest. Ophthalmol. Vis. Sci. 52(11), 7937–7942 (2011).
[Crossref] [PubMed]

S. M. Li, N. Wang, Y. Zhou, S. Y. Li, M. T. Kang, L. R. Liu, H. Li, Y. Y. Sun, B. Meng, S. Y. Zhan, and D. A. Atchison, “Paraxial schematic eye models for 7- and 14-year-old Chinese children,” Invest. Ophthalmol. Vis. Sci. 56(6), 3577–3583 (2015).
[Crossref] [PubMed]

D. Borja, F. Manns, A. Ho, N. Ziebarth, A. M. Rosen, R. Jain, A. Amelinckx, E. Arrieta, R. C. Augusteyn, and J. M. Parel, “Optical power of the isolated human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 49(6), 2541–2548 (2008).
[Crossref] [PubMed]

L. A. Jones, G. L. Mitchell, D. O. Mutti, J. R. Hayes, M. L. Moeschberger, and K. Zadnik, “Comparison of ocular component growth curves among refractive error groups in children,” Invest. Ophthalmol. Vis. Sci. 46(7), 2317–2327 (2005).
[Crossref] [PubMed]

J. F. Koretz, C. A. Cook, and P. L. Kaufman, “Accommodation and presbyopia in the human eye. Changes in the anterior segment and crystalline lens with focus,” Invest. Ophthalmol. Vis. Sci. 38(3), 569–578 (1997).
[PubMed]

D. O. Mutti, K. Zadnik, and A. J. Adams, “A video technique for phakometry of the human crystalline lens,” Invest. Ophthalmol. Vis. Sci. 33(5), 1771–1782 (1992).
[PubMed]

R. Iribarren, I. G. Morgan, V. Nangia, and J. B. Jonas, “Crystalline lens power and refractive error,” Invest. Ophthalmol. Vis. Sci. 53(2), 543–550 (2012).
[Crossref] [PubMed]

D. O. Mutti, G. L. Mitchell, L. A. Jones, N. E. Friedman, S. L. Frane, W. K. Lin, M. L. Moeschberger, and K. Zadnik, “Axial growth and changes in lenticular and corneal power during emmetropization in infants,” Invest. Ophthalmol. Vis. Sci. 46(9), 3074–3080 (2005).
[Crossref] [PubMed]

J. Biomed. Opt. (1)

M. C. M. Dunne, L. N. Davies, and J. S. Wolffsohn, “Accuracy of cornea and lens biometry using anterior segment optical coherence tomography,” J. Biomed. Opt. 12(6), 064023 (2007).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (1)

Ophthalmic Physiol. Opt. (4)

L. F. Garner, “Calculation of the radii of curvature of the crystalline lens surfaces,” Ophthalmic Physiol. Opt. 17(1), 75–80 (1997).
[Crossref] [PubMed]

A. G. Bennett, “A method of determining the equivalent powers of the eye and its crystalline lens without resort to phakometry,” Ophthalmic Physiol. Opt. 8(1), 53–59 (1988).
[Crossref] [PubMed]

M. C. M. Dunne, D. A. Barnes, and J. M. Royston, “An evaluation of Bennett’s method for determining the equivalent powers of the eye and its crystalline lens without resort to phakometry,” Ophthalmic Physiol. Opt. 9(1), 69–71 (1989).
[Crossref] [PubMed]

J. M. Royston, M. C. M. Dunne, and D. A. Barnes, “Calculation of crystalline lens radii without resort to phakometry,” Ophthalmic Physiol. Opt. 9(4), 412–414 (1989).
[Crossref] [PubMed]

Opt. Express (1)

Optom. Vis. Sci. (3)

C. E. Jones, D. A. Atchison, and J. M. Pope, “Changes in lens dimensions and refractive index with age and accommodation,” Optom. Vis. Sci. 84(10), 990–995 (2007).
[Crossref] [PubMed]

A. Ho, P. Erickson, F. Manns, T. Pham, and J. M. Parel, “Theoretical analysis of accommodation amplitude and ametropia correction by varying refractive index in Phaco-Ersatz,” Optom. Vis. Sci. 78(6), 405–410 (2001).
[Crossref] [PubMed]

M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, “The thickness of the aging human lens obtained from corrected Scheimpflug images,” Optom. Vis. Sci. 78(6), 411–416 (2001).
[Crossref] [PubMed]

Prog. Retin. Eye Res. (1)

R. Iribarren, “Crystalline lens and refractive development,” Prog. Retin. Eye Res. 47, 86–106 (2015).
[Crossref] [PubMed]

Vision Res. (4)

D. O. Mutti, K. Zadnik, and A. J. Adams, “The equivalent refractive index of the crystalline lens in childhood,” Vision Res. 35(11), 1565–1573 (1995).
[Crossref] [PubMed]

M. Dubbelman and G. L. Van der Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41(14), 1867–1877 (2001).
[Crossref] [PubMed]

M. Dubbelman, G. L. Van der Heijde, and H. A. Weeber, “Change in shape of the aging human crystalline lens with accommodation,” Vision Res. 45(1), 117–132 (2005).
[Crossref] [PubMed]

M. Dubbelman, V. A. Sicam, and G. L. Van der Heijde, “The shape of the anterior and posterior surface of the aging human cornea,” Vision Res. 46(6-7), 993–1001 (2006).
[Crossref] [PubMed]

Other (2)

F. A. Jenkins and H. E. White, Fundamentals of Optics (Mc Graw Hill Book Company, New York, 68 1957).

A. G. Bennett, R. B. Rabbetts, Clinical Visual Optics (Butterworth-Heinemann, Oxford, 1998).

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Figures (6)

Fig. 1
Fig. 1 Schematic representing the primary image formed by the cornea, which is subsequently imaged by the crystalline lens onto the retinal plane. Variable definitions can be found in Table 1. The figure shows the case of a myopic eye (the retinal conjugate is located at a finite distance in front of the eye). Solid vertical lines correspond to principal planes. Dashed vertical lines show the planes passing through the object, image, and surface vertices.
Fig. 2
Fig. 2 (Left) Exact and approximate conjugate ratio squared for a relaxed 20 year old eye (Dubbelman eye model) as a function of the refractive error. (Right) Exact and approximate conjugate ratio squared vs age for the relaxed age-dependent emmetropic Dubbelman eye model.
Fig. 3
Fig. 3 (Left) Predicted error the approximate constant b for the relaxed emmetropic eye vs age. (Right) Prediction error for the 20 year old relaxed and accommodated, and the 60 year old model in terms of refractive error.
Fig. 4
Fig. 4 Predicted error of the change in lens power for the 20 year old vs refractive error. The change in lens power is 9.1 D.
Fig. 5
Fig. 5 Image acquired using the extended-depth SD-OCT system. The image of the whole eye is acquired by using an optical switch and three reference arms. The switch allows the capture of the entire anterior segment in two successive frames and of the retina in a third frame. The vitreous is not imaged.
Fig. 6
Fig. 6 Lens power vs axial eye length for 16 eyes of 8 subjects.

Tables (4)

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Table 1 List of variables (in alphabetical order)

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Table 2 Eye model parameters for the error analysis (based on data from refs [16]. and [27]).

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Table 3 Data collected on 16 eyes of 8 subjects. See definition of symbols in Table 1.

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Table 4 Calculated values used in the equations for lens power.

Equations (28)

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L 0 = n s ' L n s L
L= n s ' L H 4 O ¯ n s L H 3 O ¯
L=n[ 1 s ' L ( 1+ H 4 O ¯ s ' L ) 1 s L ( 1+ H 3 O ¯ s L ) ]
L= L 0 +n ( H 4 O ¯ s ' L 2 H 3 O ¯ s L 2 )
ΔL=L L 0 =n ( H 3 O ¯ H 3 H 4 ¯ s L ' 2 H 3 O ¯ s L 2 )
H 3 O ¯ = H 3 H 4 ¯ 1 s ' L 2 s L 2
H 3 O ¯ = H 3 H 4 ¯ 1 M L 2
V 3 H 3 ¯ = n n L LT L 4 L 0
V 4 H 4 ¯ = n n L LT L 3 L 0
V 3 O ¯ =LT 1 1 M L 2 ( 1 n n L × L 3 + L 4 × M L 2 L 0 )
V 3 O ¯ =b LT
b= 1 1 M L 2 ( 1 n n L L 3 + L 4 × M L 2 L 3 + L 4 )
b= 1 1 M L 2 ( 1 n n L M L 2 R 4 R 3 1 R 4 R 3 )
s ' L =v ' L + H 4 V 4 ¯
s L = v L + H 3 V 3 ¯
L= n v ' L (b1) LT n v L b LT
v L = n R+K ACDCCT H 1 V 1 ¯
H 1 V 1 ¯ = 1 n K CCT K 2 K
L= n VD(b1)×LT n n R+K ACDCCT ( 1 1 n K K 2 K )b×LT
b= 0.6500.584 M L 2 1 M L 2
M L = VD+ LT 2 n R+K ACDCCT( 1 1 n K K 2 K ) LT 2
K 1 = n K 1 R 1 = 1.3761 0.00774 =48.58D
K 2 = n n K R 2 = 1.3361.376 0.00637 =6.28D
K= K 1 + K 2 CCT n K K 1 K 2 =48.586.28+ 0.000488 1.376 ×48.58×6.28=42.41D
M L = VD+ LT 2 n R+K ACDCCT( 1 1 n K K 2 K ) LT 2 = 18.302+ 3.438 2 1336 4.07+42.41 3.7830.4880.053 3.438 2 =0.695
b= 0.6500.584 M L 2 1 M L 2 = 0.6500.584× 0.695 2 1 0.695 2 =0.712
v L = n R+K ACDCCT ( 1 1 n K K 2 K ) = 1336 4.07+42.41 3.7830.488( 1+ 1 1.376 6.28 42.41 )=30.522mm
L= n v ' L (b1)×LT n v L b×LT = 1336 18.302(0.7121)×3.438 1336 30.5220.712×3.438 =21.66D

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