Abstract

This work presents a compact statistical model of the retinal image quality in a large population of human eyes following two objectives. The first was to develop a general modal representation of the optical transfer function (OTF) in terms of orthogonal functions and construct a basis composed of cross-correlations between pairs of complex Zernike polynomials. That basis was not orthogonal and highly redundant, requiring the application of singular value decomposition (SVD) to obtain an orthogonal basis with a significantly lower dimensionality. The first mode is the OTF of the perfect system, and hence the modal representation, is highly compact for well-corrected optical systems, and vice-versa. The second objective is to apply this modal representation to the OTFs of a large population of human eyes for a pupil diameter of 5 mm. This permits an initial strong data compression. Next, principal component analysis (PCA) is applied to obtain further data compression, leading to a compact statistical model of the initial population. In this model each OTF is approximated by the sum of the population mean plus a linear combination of orthogonal eigenfunctions (eigen-OTF) accounting for a selected percentage (90%) of the population variance. This type of models can be useful for Monte Carlo simulations among other applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]

2017 (1)

J. J. Rozema, P. Rodriguez, R. Navarro, and C. Koppen, “Bigaussian wavefront model for normal and keratoconic eyes based on PCA,” Optom. Vis. Sci. 94(6), 680–687 (2017).
[Crossref]

2016 (3)

J. J. Rozema, P. Rodriguez, R. Navarro, and M.-J. Tassignon, “SyntEyes: a higher-order statistical eye model for healthy eyes,” Invest. Ophthalmol. Visual Sci. 57(2), 683–691 (2016).
[Crossref]

J. A. Díaz, “Relating wavefront error, apodization, and the optical transfer function: Comment,” Opt. Soc. Am A 33(8), 1622–1625 (2016).
[Crossref]

C. Ferreira, J. L. López, R. Navarro, and E. Pérez-Sinusía, “Orthogonal basis for the optical transfer function,” Appl. Opt. 55(34), 9688–9694 (2016).
[Crossref]

2014 (3)

2013 (2)

A. B. Watson, “A formula for the mean human optical modulation transfer function as a function of pupil size,” J. Vision 13(6), 18 (2013).
[Crossref]

S. van Haver and A. J. E. M. Janssen, “Advanced analytic treatment and efficient computation of the diffraction integrals in the extended Nijboer-Zernike theory,” J. Europ. Opt. Soc. Rap. Public. 8, 13044 (2013).
[Crossref]

2010 (2)

2009 (1)

J. Arines, E. Pailos, P. Prado, and S. Bará, “The contribution of the fixational eye movements to the variability of the measured ocular aberration,” Ophthalm. Physiol. Opt. 29(3), 281–287 (2009).
[Crossref]

2008 (1)

Y. Oie, N. Maeda, R. Kosaki, A. Suzaki, Y. Hirohara, T. Mihashi, Y. Hori, T. Inoue, K. Nishida, T. Fujikado, and Y. Tano, “Characteristics of ocular higher-order aberrations in patients with pellucid marginal corneal degeneration,” J. Cataract Refractive Surg. 34(11), 1928–1934 (2008).
[Crossref]

2007 (1)

M. J. Jee, J. P. Blakeslee, M. Sirianni, A. R. Martel, R. L. White, and H. C. Ford, “Principal component analysis of the time-and position-dependent point-spread function of the advanced camera for surveys,” Publ. Astron. Soc. Pac. 119(862), 1403–1419 (2007).
[Crossref]

2006 (3)

S. Koh, N. Maeda, Y. Hirohara, T. Mihashi, S. Ninomiya, K. Bessho, and Y. Tano, “Serial measurements of higher-order aberrations after blinking in normal subjects,” Invest. Ophthalmol. Visual Sci. 47(8), 3318–3324 (2006).
[Crossref]

J. J. Rozema, D. E. M. Van Dyck, and M.-J. Tassignon, “Clinical comparison of 6 aberrometers. Part 2: Statistical comparison in a test group,” J. Cataract Refractive Surg. 32(1), 33–44 (2006).
[Crossref]

T. O. Salmon and C. van de Pol, “Normal-eye Zernike coefficients and root-mean-square wavefront errors,” J. Cataract Refractive Surg. 32(12), 2064–2074 (2006).
[Crossref]

2004 (2)

J. D. Marsack, L. N. Thibos, and R. A. Applegate, “Metrics of optical quality derived from wave aberrations predict visual performance,” J. Vision 4(4), 8–328 (2004).
[Crossref]

P. Rodriguez, R. Navarro, L. González, and J. L. Hernández, “Accuracy and Reproducibility of Zywave, Tracey, and Experimental Aberrometers,” J. Refract. Surg. 20(6), 810–817 (2004).

2003 (2)

X. Cheng, A. Bradley, X. Hong, and L. N. Thibos, “Relationship between refractive error and monochromatic aberrations of the eye,” Optom. Vis. Sci. 80(1), 43–49 (2003).
[Crossref]

S. Shah, S. Naroo, S. Hosking, D. Gherghel, S. Mantry, S. Bannerjee, K. Pedwell, and H. S. Bains, “Nidek OPD-scan analysis of normal, keratoconic, and penetrating keratoplasty eyes,” J. Refract. Surg. 19(2), S255–S259 (2003).

2002 (6)

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18(5), S652–S660 (2002).

N. Maeda, T. Fujikado, T. Kuroda, T. Mihashi, Y. Hirohara, K. Nishida, H. Watanabe, and Y. Tano, “Wavefront aberrations measured with Hartmann-Shack sensor in patients with keratoconus,” Ophthalmology 109(11), 1996–2003 (2002).
[Crossref]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, “Statistical variation of aberration structure and image quality in a normal population of healthy eyes,” J. Opt. Soc. Am. A 19(12), 2329–2348 (2002).
[Crossref]

T. Kuroda, T. Fujikado, N. Maeda, T. Oshika, Y. Hirohara, and T. Mihashi, “Wavefront analysis in eyes with nuclear or cortical cataract,” Am. J. Ophthalmol. 134(1), 1–9 (2002).
[Crossref]

X. Cheng, L. N. Thibos, and A. Bradley, “Estimating visual quality from wavefront aberration measurements,” J. Refract. Surg. 19(5), S579–S584 (2002).

A. J. E. M. Janssen, “Extended Nijboer–Zernike approach for the computation of optical point-spread functions,” J. Opt. Soc. Am. A 19(5), 849–857 (2002).
[Crossref]

2001 (2)

J. Porter, A. Guirao, I. G. Cox, and D. R. Williams, “Monochromatic aberrations of the human eye in a large population,” J. Opt. Soc. Am. A 18(8), 1793–1803 (2001).
[Crossref]

E. Moreno-Barriuso, J. M. Lloves, S. Marcos, R. Navarro, L. Llorente, and S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42(6), 1396–1403 (2001).

1997 (1)

1995 (2)

1994 (1)

1976 (1)

E. C. Kintner and R. M. Sillitto, “A new analytic’ method for computing the optical transfer function,” Opt. Acta 23(8), 607–619 (1976).
[Crossref]

Applegate, R. A.

J. D. Marsack, L. N. Thibos, and R. A. Applegate, “Metrics of optical quality derived from wave aberrations predict visual performance,” J. Vision 4(4), 8–328 (2004).
[Crossref]

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18(5), S652–S660 (2002).

Arines, J.

J. Arines, E. Pailos, P. Prado, and S. Bará, “The contribution of the fixational eye movements to the variability of the measured ocular aberration,” Ophthalm. Physiol. Opt. 29(3), 281–287 (2009).
[Crossref]

Ariste, A. L.

A. A. Ramos and A. L. Ariste, “Image reconstruction with analytical point spread functions,” Astron. Astrophys. 518, A6 (2010).
[Crossref]

Artal, P.

Bains, H. S.

S. Shah, S. Naroo, S. Hosking, D. Gherghel, S. Mantry, S. Bannerjee, K. Pedwell, and H. S. Bains, “Nidek OPD-scan analysis of normal, keratoconic, and penetrating keratoplasty eyes,” J. Refract. Surg. 19(2), S255–S259 (2003).

Bannerjee, S.

S. Shah, S. Naroo, S. Hosking, D. Gherghel, S. Mantry, S. Bannerjee, K. Pedwell, and H. S. Bains, “Nidek OPD-scan analysis of normal, keratoconic, and penetrating keratoplasty eyes,” J. Refract. Surg. 19(2), S255–S259 (2003).

Bará, S.

J. Arines, E. Pailos, P. Prado, and S. Bará, “The contribution of the fixational eye movements to the variability of the measured ocular aberration,” Ophthalm. Physiol. Opt. 29(3), 281–287 (2009).
[Crossref]

Barbero, S.

E. Moreno-Barriuso, J. M. Lloves, S. Marcos, R. Navarro, L. Llorente, and S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42(6), 1396–1403 (2001).

Bessho, K.

S. Koh, N. Maeda, Y. Hirohara, T. Mihashi, S. Ninomiya, K. Bessho, and Y. Tano, “Serial measurements of higher-order aberrations after blinking in normal subjects,” Invest. Ophthalmol. Visual Sci. 47(8), 3318–3324 (2006).
[Crossref]

Blakeslee, J. P.

M. J. Jee, J. P. Blakeslee, M. Sirianni, A. R. Martel, R. L. White, and H. C. Ford, “Principal component analysis of the time-and position-dependent point-spread function of the advanced camera for surveys,” Publ. Astron. Soc. Pac. 119(862), 1403–1419 (2007).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics(Pergamon Press, 1983).

Bradley, A.

X. Cheng, A. Bradley, X. Hong, and L. N. Thibos, “Relationship between refractive error and monochromatic aberrations of the eye,” Optom. Vis. Sci. 80(1), 43–49 (2003).
[Crossref]

X. Cheng, L. N. Thibos, and A. Bradley, “Estimating visual quality from wavefront aberration measurements,” J. Refract. Surg. 19(5), S579–S584 (2002).

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, “Statistical variation of aberration structure and image quality in a normal population of healthy eyes,” J. Opt. Soc. Am. A 19(12), 2329–2348 (2002).
[Crossref]

Cheng, X.

X. Cheng, A. Bradley, X. Hong, and L. N. Thibos, “Relationship between refractive error and monochromatic aberrations of the eye,” Optom. Vis. Sci. 80(1), 43–49 (2003).
[Crossref]

X. Cheng, L. N. Thibos, and A. Bradley, “Estimating visual quality from wavefront aberration measurements,” J. Refract. Surg. 19(5), S579–S584 (2002).

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, “Statistical variation of aberration structure and image quality in a normal population of healthy eyes,” J. Opt. Soc. Am. A 19(12), 2329–2348 (2002).
[Crossref]

Cox, I. G.

Dainty, C.

Díaz, J. A.

J. A. Díaz, “Relating wavefront error, apodization, and the optical transfer function: Comment,” Opt. Soc. Am A 33(8), 1622–1625 (2016).
[Crossref]

R. Navarro, J. L. López, J. A. Díaz, and E. Pérez Sinusía, “Generalization of Zernike polynomials for regular portions of circles and ellipses,” Opt. Express 22(18), 21263–21279 (2014).
[Crossref]

Diaz-Santana, L.

Ferreira, C.

Ford, H. C.

M. J. Jee, J. P. Blakeslee, M. Sirianni, A. R. Martel, R. L. White, and H. C. Ford, “Principal component analysis of the time-and position-dependent point-spread function of the advanced camera for surveys,” Publ. Astron. Soc. Pac. 119(862), 1403–1419 (2007).
[Crossref]

Fujikado, T.

Y. Oie, N. Maeda, R. Kosaki, A. Suzaki, Y. Hirohara, T. Mihashi, Y. Hori, T. Inoue, K. Nishida, T. Fujikado, and Y. Tano, “Characteristics of ocular higher-order aberrations in patients with pellucid marginal corneal degeneration,” J. Cataract Refractive Surg. 34(11), 1928–1934 (2008).
[Crossref]

N. Maeda, T. Fujikado, T. Kuroda, T. Mihashi, Y. Hirohara, K. Nishida, H. Watanabe, and Y. Tano, “Wavefront aberrations measured with Hartmann-Shack sensor in patients with keratoconus,” Ophthalmology 109(11), 1996–2003 (2002).
[Crossref]

T. Kuroda, T. Fujikado, N. Maeda, T. Oshika, Y. Hirohara, and T. Mihashi, “Wavefront analysis in eyes with nuclear or cortical cataract,” Am. J. Ophthalmol. 134(1), 1–9 (2002).
[Crossref]

Gherghel, D.

S. Shah, S. Naroo, S. Hosking, D. Gherghel, S. Mantry, S. Bannerjee, K. Pedwell, and H. S. Bains, “Nidek OPD-scan analysis of normal, keratoconic, and penetrating keratoplasty eyes,” J. Refract. Surg. 19(2), S255–S259 (2003).

González, L.

P. Rodriguez, R. Navarro, L. González, and J. L. Hernández, “Accuracy and Reproducibility of Zywave, Tracey, and Experimental Aberrometers,” J. Refract. Surg. 20(6), 810–817 (2004).

Guirao, A.

Hernández, J. L.

P. Rodriguez, R. Navarro, L. González, and J. L. Hernández, “Accuracy and Reproducibility of Zywave, Tracey, and Experimental Aberrometers,” J. Refract. Surg. 20(6), 810–817 (2004).

Hirohara, Y.

Y. Oie, N. Maeda, R. Kosaki, A. Suzaki, Y. Hirohara, T. Mihashi, Y. Hori, T. Inoue, K. Nishida, T. Fujikado, and Y. Tano, “Characteristics of ocular higher-order aberrations in patients with pellucid marginal corneal degeneration,” J. Cataract Refractive Surg. 34(11), 1928–1934 (2008).
[Crossref]

S. Koh, N. Maeda, Y. Hirohara, T. Mihashi, S. Ninomiya, K. Bessho, and Y. Tano, “Serial measurements of higher-order aberrations after blinking in normal subjects,” Invest. Ophthalmol. Visual Sci. 47(8), 3318–3324 (2006).
[Crossref]

N. Maeda, T. Fujikado, T. Kuroda, T. Mihashi, Y. Hirohara, K. Nishida, H. Watanabe, and Y. Tano, “Wavefront aberrations measured with Hartmann-Shack sensor in patients with keratoconus,” Ophthalmology 109(11), 1996–2003 (2002).
[Crossref]

T. Kuroda, T. Fujikado, N. Maeda, T. Oshika, Y. Hirohara, and T. Mihashi, “Wavefront analysis in eyes with nuclear or cortical cataract,” Am. J. Ophthalmol. 134(1), 1–9 (2002).
[Crossref]

Hong, X.

X. Cheng, A. Bradley, X. Hong, and L. N. Thibos, “Relationship between refractive error and monochromatic aberrations of the eye,” Optom. Vis. Sci. 80(1), 43–49 (2003).
[Crossref]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, “Statistical variation of aberration structure and image quality in a normal population of healthy eyes,” J. Opt. Soc. Am. A 19(12), 2329–2348 (2002).
[Crossref]

Hori, Y.

Y. Oie, N. Maeda, R. Kosaki, A. Suzaki, Y. Hirohara, T. Mihashi, Y. Hori, T. Inoue, K. Nishida, T. Fujikado, and Y. Tano, “Characteristics of ocular higher-order aberrations in patients with pellucid marginal corneal degeneration,” J. Cataract Refractive Surg. 34(11), 1928–1934 (2008).
[Crossref]

Hosking, S.

S. Shah, S. Naroo, S. Hosking, D. Gherghel, S. Mantry, S. Bannerjee, K. Pedwell, and H. S. Bains, “Nidek OPD-scan analysis of normal, keratoconic, and penetrating keratoplasty eyes,” J. Refract. Surg. 19(2), S255–S259 (2003).

Inoue, T.

Y. Oie, N. Maeda, R. Kosaki, A. Suzaki, Y. Hirohara, T. Mihashi, Y. Hori, T. Inoue, K. Nishida, T. Fujikado, and Y. Tano, “Characteristics of ocular higher-order aberrations in patients with pellucid marginal corneal degeneration,” J. Cataract Refractive Surg. 34(11), 1928–1934 (2008).
[Crossref]

Janssen, A. J. E. M.

S. van Haver and A. J. E. M. Janssen, “Advanced analytic treatment and efficient computation of the diffraction integrals in the extended Nijboer-Zernike theory,” J. Europ. Opt. Soc. Rap. Public. 8, 13044 (2013).
[Crossref]

A. J. E. M. Janssen, “Extended Nijboer–Zernike approach for the computation of optical point-spread functions,” J. Opt. Soc. Am. A 19(5), 849–857 (2002).
[Crossref]

Jee, M. J.

M. J. Jee, J. P. Blakeslee, M. Sirianni, A. R. Martel, R. L. White, and H. C. Ford, “Principal component analysis of the time-and position-dependent point-spread function of the advanced camera for surveys,” Publ. Astron. Soc. Pac. 119(862), 1403–1419 (2007).
[Crossref]

Jolliffe, I. T.

I. T. Jolliffe, Principal Component Analysis, 2nd edition (Springer-Verlag, 2002).

Kintner, E. C.

E. C. Kintner and R. M. Sillitto, “A new analytic’ method for computing the optical transfer function,” Opt. Acta 23(8), 607–619 (1976).
[Crossref]

Koh, S.

S. Koh, N. Maeda, Y. Hirohara, T. Mihashi, S. Ninomiya, K. Bessho, and Y. Tano, “Serial measurements of higher-order aberrations after blinking in normal subjects,” Invest. Ophthalmol. Visual Sci. 47(8), 3318–3324 (2006).
[Crossref]

Koppen, C.

J. J. Rozema, P. Rodriguez, R. Navarro, and C. Koppen, “Bigaussian wavefront model for normal and keratoconic eyes based on PCA,” Optom. Vis. Sci. 94(6), 680–687 (2017).
[Crossref]

Kosaki, R.

Y. Oie, N. Maeda, R. Kosaki, A. Suzaki, Y. Hirohara, T. Mihashi, Y. Hori, T. Inoue, K. Nishida, T. Fujikado, and Y. Tano, “Characteristics of ocular higher-order aberrations in patients with pellucid marginal corneal degeneration,” J. Cataract Refractive Surg. 34(11), 1928–1934 (2008).
[Crossref]

Kuroda, T.

N. Maeda, T. Fujikado, T. Kuroda, T. Mihashi, Y. Hirohara, K. Nishida, H. Watanabe, and Y. Tano, “Wavefront aberrations measured with Hartmann-Shack sensor in patients with keratoconus,” Ophthalmology 109(11), 1996–2003 (2002).
[Crossref]

T. Kuroda, T. Fujikado, N. Maeda, T. Oshika, Y. Hirohara, and T. Mihashi, “Wavefront analysis in eyes with nuclear or cortical cataract,” Am. J. Ophthalmol. 134(1), 1–9 (2002).
[Crossref]

Leahy, C.

Leroux, C.

Llorente, L.

E. Moreno-Barriuso, J. M. Lloves, S. Marcos, R. Navarro, L. Llorente, and S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42(6), 1396–1403 (2001).

Lloves, J. M.

E. Moreno-Barriuso, J. M. Lloves, S. Marcos, R. Navarro, L. Llorente, and S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42(6), 1396–1403 (2001).

López, J. L.

Losada, M. A.

Maeda, N.

Y. Oie, N. Maeda, R. Kosaki, A. Suzaki, Y. Hirohara, T. Mihashi, Y. Hori, T. Inoue, K. Nishida, T. Fujikado, and Y. Tano, “Characteristics of ocular higher-order aberrations in patients with pellucid marginal corneal degeneration,” J. Cataract Refractive Surg. 34(11), 1928–1934 (2008).
[Crossref]

S. Koh, N. Maeda, Y. Hirohara, T. Mihashi, S. Ninomiya, K. Bessho, and Y. Tano, “Serial measurements of higher-order aberrations after blinking in normal subjects,” Invest. Ophthalmol. Visual Sci. 47(8), 3318–3324 (2006).
[Crossref]

T. Kuroda, T. Fujikado, N. Maeda, T. Oshika, Y. Hirohara, and T. Mihashi, “Wavefront analysis in eyes with nuclear or cortical cataract,” Am. J. Ophthalmol. 134(1), 1–9 (2002).
[Crossref]

N. Maeda, T. Fujikado, T. Kuroda, T. Mihashi, Y. Hirohara, K. Nishida, H. Watanabe, and Y. Tano, “Wavefront aberrations measured with Hartmann-Shack sensor in patients with keratoconus,” Ophthalmology 109(11), 1996–2003 (2002).
[Crossref]

Mantry, S.

S. Shah, S. Naroo, S. Hosking, D. Gherghel, S. Mantry, S. Bannerjee, K. Pedwell, and H. S. Bains, “Nidek OPD-scan analysis of normal, keratoconic, and penetrating keratoplasty eyes,” J. Refract. Surg. 19(2), S255–S259 (2003).

Marcos, S.

E. Moreno-Barriuso, J. M. Lloves, S. Marcos, R. Navarro, L. Llorente, and S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42(6), 1396–1403 (2001).

P. Artal, S. Marcos, D. R. Williams, and R. Navarro, “Odd aberrations and double-pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12(2), 195–201 (1995).
[Crossref]

Marsack, J. D.

J. D. Marsack, L. N. Thibos, and R. A. Applegate, “Metrics of optical quality derived from wave aberrations predict visual performance,” J. Vision 4(4), 8–328 (2004).
[Crossref]

Martel, A. R.

M. J. Jee, J. P. Blakeslee, M. Sirianni, A. R. Martel, R. L. White, and H. C. Ford, “Principal component analysis of the time-and position-dependent point-spread function of the advanced camera for surveys,” Publ. Astron. Soc. Pac. 119(862), 1403–1419 (2007).
[Crossref]

Mihashi, T.

Y. Oie, N. Maeda, R. Kosaki, A. Suzaki, Y. Hirohara, T. Mihashi, Y. Hori, T. Inoue, K. Nishida, T. Fujikado, and Y. Tano, “Characteristics of ocular higher-order aberrations in patients with pellucid marginal corneal degeneration,” J. Cataract Refractive Surg. 34(11), 1928–1934 (2008).
[Crossref]

S. Koh, N. Maeda, Y. Hirohara, T. Mihashi, S. Ninomiya, K. Bessho, and Y. Tano, “Serial measurements of higher-order aberrations after blinking in normal subjects,” Invest. Ophthalmol. Visual Sci. 47(8), 3318–3324 (2006).
[Crossref]

N. Maeda, T. Fujikado, T. Kuroda, T. Mihashi, Y. Hirohara, K. Nishida, H. Watanabe, and Y. Tano, “Wavefront aberrations measured with Hartmann-Shack sensor in patients with keratoconus,” Ophthalmology 109(11), 1996–2003 (2002).
[Crossref]

T. Kuroda, T. Fujikado, N. Maeda, T. Oshika, Y. Hirohara, and T. Mihashi, “Wavefront analysis in eyes with nuclear or cortical cataract,” Am. J. Ophthalmol. 134(1), 1–9 (2002).
[Crossref]

Moreno-Barriuso, E.

E. Moreno-Barriuso, J. M. Lloves, S. Marcos, R. Navarro, L. Llorente, and S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42(6), 1396–1403 (2001).

Naroo, S.

S. Shah, S. Naroo, S. Hosking, D. Gherghel, S. Mantry, S. Bannerjee, K. Pedwell, and H. S. Bains, “Nidek OPD-scan analysis of normal, keratoconic, and penetrating keratoplasty eyes,” J. Refract. Surg. 19(2), S255–S259 (2003).

Navarro, R.

J. J. Rozema, P. Rodriguez, R. Navarro, and C. Koppen, “Bigaussian wavefront model for normal and keratoconic eyes based on PCA,” Optom. Vis. Sci. 94(6), 680–687 (2017).
[Crossref]

C. Ferreira, J. L. López, R. Navarro, and E. Pérez-Sinusía, “Orthogonal basis for the optical transfer function,” Appl. Opt. 55(34), 9688–9694 (2016).
[Crossref]

J. J. Rozema, P. Rodriguez, R. Navarro, and M.-J. Tassignon, “SyntEyes: a higher-order statistical eye model for healthy eyes,” Invest. Ophthalmol. Visual Sci. 57(2), 683–691 (2016).
[Crossref]

P. Rodríguez, R. Navarro, and J. J. Rozema, “Eigencorneas: application of principal component analysis to corneal topography,” Ophthalm. Physiol. Opt. 34(6), 667–677 (2014).
[Crossref]

R. Navarro, J. L. López, J. A. Díaz, and E. Pérez Sinusía, “Generalization of Zernike polynomials for regular portions of circles and ellipses,” Opt. Express 22(18), 21263–21279 (2014).
[Crossref]

P. Rodriguez, R. Navarro, L. González, and J. L. Hernández, “Accuracy and Reproducibility of Zywave, Tracey, and Experimental Aberrometers,” J. Refract. Surg. 20(6), 810–817 (2004).

E. Moreno-Barriuso, J. M. Lloves, S. Marcos, R. Navarro, L. Llorente, and S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42(6), 1396–1403 (2001).

R. Navarro and M. A. Losada, “Shape of stars and optical quality of the human eye,” J. Opt. Soc. Am. A 14(2), 353–359 (1997).
[Crossref]

P. Artal, S. Marcos, D. R. Williams, and R. Navarro, “Odd aberrations and double-pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12(2), 195–201 (1995).
[Crossref]

R. Navarro and M. A. Losada, “Phase transfer and point-spread function of the human eye determined by a new asymmetric double-pass method,” J. Opt. Soc. Am. A 12(11), 2385–2392 (1995).
[Crossref]

P. Artal and R. Navarro, “Monochromatic modulation transfer function of the human eye for different pupil diameters: an analytical expression,” J. Opt. Soc. Am. A 11(1), 246–249 (1994).
[Crossref]

Ninomiya, S.

S. Koh, N. Maeda, Y. Hirohara, T. Mihashi, S. Ninomiya, K. Bessho, and Y. Tano, “Serial measurements of higher-order aberrations after blinking in normal subjects,” Invest. Ophthalmol. Visual Sci. 47(8), 3318–3324 (2006).
[Crossref]

Nishida, K.

Y. Oie, N. Maeda, R. Kosaki, A. Suzaki, Y. Hirohara, T. Mihashi, Y. Hori, T. Inoue, K. Nishida, T. Fujikado, and Y. Tano, “Characteristics of ocular higher-order aberrations in patients with pellucid marginal corneal degeneration,” J. Cataract Refractive Surg. 34(11), 1928–1934 (2008).
[Crossref]

N. Maeda, T. Fujikado, T. Kuroda, T. Mihashi, Y. Hirohara, K. Nishida, H. Watanabe, and Y. Tano, “Wavefront aberrations measured with Hartmann-Shack sensor in patients with keratoconus,” Ophthalmology 109(11), 1996–2003 (2002).
[Crossref]

Oie, Y.

Y. Oie, N. Maeda, R. Kosaki, A. Suzaki, Y. Hirohara, T. Mihashi, Y. Hori, T. Inoue, K. Nishida, T. Fujikado, and Y. Tano, “Characteristics of ocular higher-order aberrations in patients with pellucid marginal corneal degeneration,” J. Cataract Refractive Surg. 34(11), 1928–1934 (2008).
[Crossref]

Oshika, T.

T. Kuroda, T. Fujikado, N. Maeda, T. Oshika, Y. Hirohara, and T. Mihashi, “Wavefront analysis in eyes with nuclear or cortical cataract,” Am. J. Ophthalmol. 134(1), 1–9 (2002).
[Crossref]

Pailos, E.

J. Arines, E. Pailos, P. Prado, and S. Bará, “The contribution of the fixational eye movements to the variability of the measured ocular aberration,” Ophthalm. Physiol. Opt. 29(3), 281–287 (2009).
[Crossref]

Pedwell, K.

S. Shah, S. Naroo, S. Hosking, D. Gherghel, S. Mantry, S. Bannerjee, K. Pedwell, and H. S. Bains, “Nidek OPD-scan analysis of normal, keratoconic, and penetrating keratoplasty eyes,” J. Refract. Surg. 19(2), S255–S259 (2003).

Pérez Sinusía, E.

Pérez-Sinusía, E.

Porter, J.

Prado, P.

J. Arines, E. Pailos, P. Prado, and S. Bará, “The contribution of the fixational eye movements to the variability of the measured ocular aberration,” Ophthalm. Physiol. Opt. 29(3), 281–287 (2009).
[Crossref]

Ramos, A. A.

A. A. Ramos and A. L. Ariste, “Image reconstruction with analytical point spread functions,” Astron. Astrophys. 518, A6 (2010).
[Crossref]

Rodriguez, P.

J. J. Rozema, P. Rodriguez, R. Navarro, and C. Koppen, “Bigaussian wavefront model for normal and keratoconic eyes based on PCA,” Optom. Vis. Sci. 94(6), 680–687 (2017).
[Crossref]

J. J. Rozema, P. Rodriguez, R. Navarro, and M.-J. Tassignon, “SyntEyes: a higher-order statistical eye model for healthy eyes,” Invest. Ophthalmol. Visual Sci. 57(2), 683–691 (2016).
[Crossref]

P. Rodriguez, R. Navarro, L. González, and J. L. Hernández, “Accuracy and Reproducibility of Zywave, Tracey, and Experimental Aberrometers,” J. Refract. Surg. 20(6), 810–817 (2004).

Rodríguez, P.

P. Rodríguez, R. Navarro, and J. J. Rozema, “Eigencorneas: application of principal component analysis to corneal topography,” Ophthalm. Physiol. Opt. 34(6), 667–677 (2014).
[Crossref]

Rozema, J. J.

J. J. Rozema, P. Rodriguez, R. Navarro, and C. Koppen, “Bigaussian wavefront model for normal and keratoconic eyes based on PCA,” Optom. Vis. Sci. 94(6), 680–687 (2017).
[Crossref]

J. J. Rozema, P. Rodriguez, R. Navarro, and M.-J. Tassignon, “SyntEyes: a higher-order statistical eye model for healthy eyes,” Invest. Ophthalmol. Visual Sci. 57(2), 683–691 (2016).
[Crossref]

P. Rodríguez, R. Navarro, and J. J. Rozema, “Eigencorneas: application of principal component analysis to corneal topography,” Ophthalm. Physiol. Opt. 34(6), 667–677 (2014).
[Crossref]

J. J. Rozema, D. E. M. Van Dyck, and M.-J. Tassignon, “Clinical comparison of 6 aberrometers. Part 2: Statistical comparison in a test group,” J. Cataract Refractive Surg. 32(1), 33–44 (2006).
[Crossref]

Salmon, T. O.

T. O. Salmon and C. van de Pol, “Normal-eye Zernike coefficients and root-mean-square wavefront errors,” J. Cataract Refractive Surg. 32(12), 2064–2074 (2006).
[Crossref]

Schwiegerling, J.

Schwiegerling, J. T.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18(5), S652–S660 (2002).

Shah, S.

S. Shah, S. Naroo, S. Hosking, D. Gherghel, S. Mantry, S. Bannerjee, K. Pedwell, and H. S. Bains, “Nidek OPD-scan analysis of normal, keratoconic, and penetrating keratoplasty eyes,” J. Refract. Surg. 19(2), S255–S259 (2003).

Sillitto, R. M.

E. C. Kintner and R. M. Sillitto, “A new analytic’ method for computing the optical transfer function,” Opt. Acta 23(8), 607–619 (1976).
[Crossref]

Sirianni, M.

M. J. Jee, J. P. Blakeslee, M. Sirianni, A. R. Martel, R. L. White, and H. C. Ford, “Principal component analysis of the time-and position-dependent point-spread function of the advanced camera for surveys,” Publ. Astron. Soc. Pac. 119(862), 1403–1419 (2007).
[Crossref]

Suzaki, A.

Y. Oie, N. Maeda, R. Kosaki, A. Suzaki, Y. Hirohara, T. Mihashi, Y. Hori, T. Inoue, K. Nishida, T. Fujikado, and Y. Tano, “Characteristics of ocular higher-order aberrations in patients with pellucid marginal corneal degeneration,” J. Cataract Refractive Surg. 34(11), 1928–1934 (2008).
[Crossref]

Tano, Y.

Y. Oie, N. Maeda, R. Kosaki, A. Suzaki, Y. Hirohara, T. Mihashi, Y. Hori, T. Inoue, K. Nishida, T. Fujikado, and Y. Tano, “Characteristics of ocular higher-order aberrations in patients with pellucid marginal corneal degeneration,” J. Cataract Refractive Surg. 34(11), 1928–1934 (2008).
[Crossref]

S. Koh, N. Maeda, Y. Hirohara, T. Mihashi, S. Ninomiya, K. Bessho, and Y. Tano, “Serial measurements of higher-order aberrations after blinking in normal subjects,” Invest. Ophthalmol. Visual Sci. 47(8), 3318–3324 (2006).
[Crossref]

N. Maeda, T. Fujikado, T. Kuroda, T. Mihashi, Y. Hirohara, K. Nishida, H. Watanabe, and Y. Tano, “Wavefront aberrations measured with Hartmann-Shack sensor in patients with keratoconus,” Ophthalmology 109(11), 1996–2003 (2002).
[Crossref]

Tassignon, M.-J.

J. J. Rozema, P. Rodriguez, R. Navarro, and M.-J. Tassignon, “SyntEyes: a higher-order statistical eye model for healthy eyes,” Invest. Ophthalmol. Visual Sci. 57(2), 683–691 (2016).
[Crossref]

J. J. Rozema, D. E. M. Van Dyck, and M.-J. Tassignon, “Clinical comparison of 6 aberrometers. Part 2: Statistical comparison in a test group,” J. Cataract Refractive Surg. 32(1), 33–44 (2006).
[Crossref]

Thibos, L. N.

J. D. Marsack, L. N. Thibos, and R. A. Applegate, “Metrics of optical quality derived from wave aberrations predict visual performance,” J. Vision 4(4), 8–328 (2004).
[Crossref]

X. Cheng, A. Bradley, X. Hong, and L. N. Thibos, “Relationship between refractive error and monochromatic aberrations of the eye,” Optom. Vis. Sci. 80(1), 43–49 (2003).
[Crossref]

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18(5), S652–S660 (2002).

X. Cheng, L. N. Thibos, and A. Bradley, “Estimating visual quality from wavefront aberration measurements,” J. Refract. Surg. 19(5), S579–S584 (2002).

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, “Statistical variation of aberration structure and image quality in a normal population of healthy eyes,” J. Opt. Soc. Am. A 19(12), 2329–2348 (2002).
[Crossref]

van de Pol, C.

T. O. Salmon and C. van de Pol, “Normal-eye Zernike coefficients and root-mean-square wavefront errors,” J. Cataract Refractive Surg. 32(12), 2064–2074 (2006).
[Crossref]

Van Dyck, D. E. M.

J. J. Rozema, D. E. M. Van Dyck, and M.-J. Tassignon, “Clinical comparison of 6 aberrometers. Part 2: Statistical comparison in a test group,” J. Cataract Refractive Surg. 32(1), 33–44 (2006).
[Crossref]

van Haver, S.

S. van Haver and A. J. E. M. Janssen, “Advanced analytic treatment and efficient computation of the diffraction integrals in the extended Nijboer-Zernike theory,” J. Europ. Opt. Soc. Rap. Public. 8, 13044 (2013).
[Crossref]

Watanabe, H.

N. Maeda, T. Fujikado, T. Kuroda, T. Mihashi, Y. Hirohara, K. Nishida, H. Watanabe, and Y. Tano, “Wavefront aberrations measured with Hartmann-Shack sensor in patients with keratoconus,” Ophthalmology 109(11), 1996–2003 (2002).
[Crossref]

Watson, A. B.

A. B. Watson, “A formula for the mean human optical modulation transfer function as a function of pupil size,” J. Vision 13(6), 18 (2013).
[Crossref]

Webb, R.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18(5), S652–S660 (2002).

White, R. L.

M. J. Jee, J. P. Blakeslee, M. Sirianni, A. R. Martel, R. L. White, and H. C. Ford, “Principal component analysis of the time-and position-dependent point-spread function of the advanced camera for surveys,” Publ. Astron. Soc. Pac. 119(862), 1403–1419 (2007).
[Crossref]

Williams, D. R.

Wolf, E.

M. Born and E. Wolf, Principles of Optics(Pergamon Press, 1983).

Am. J. Ophthalmol. (1)

T. Kuroda, T. Fujikado, N. Maeda, T. Oshika, Y. Hirohara, and T. Mihashi, “Wavefront analysis in eyes with nuclear or cortical cataract,” Am. J. Ophthalmol. 134(1), 1–9 (2002).
[Crossref]

Appl. Opt. (1)

Astron. Astrophys. (1)

A. A. Ramos and A. L. Ariste, “Image reconstruction with analytical point spread functions,” Astron. Astrophys. 518, A6 (2010).
[Crossref]

Invest. Ophthalmol. Visual Sci. (3)

J. J. Rozema, P. Rodriguez, R. Navarro, and M.-J. Tassignon, “SyntEyes: a higher-order statistical eye model for healthy eyes,” Invest. Ophthalmol. Visual Sci. 57(2), 683–691 (2016).
[Crossref]

S. Koh, N. Maeda, Y. Hirohara, T. Mihashi, S. Ninomiya, K. Bessho, and Y. Tano, “Serial measurements of higher-order aberrations after blinking in normal subjects,” Invest. Ophthalmol. Visual Sci. 47(8), 3318–3324 (2006).
[Crossref]

E. Moreno-Barriuso, J. M. Lloves, S. Marcos, R. Navarro, L. Llorente, and S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42(6), 1396–1403 (2001).

J. Cataract Refractive Surg. (3)

Y. Oie, N. Maeda, R. Kosaki, A. Suzaki, Y. Hirohara, T. Mihashi, Y. Hori, T. Inoue, K. Nishida, T. Fujikado, and Y. Tano, “Characteristics of ocular higher-order aberrations in patients with pellucid marginal corneal degeneration,” J. Cataract Refractive Surg. 34(11), 1928–1934 (2008).
[Crossref]

J. J. Rozema, D. E. M. Van Dyck, and M.-J. Tassignon, “Clinical comparison of 6 aberrometers. Part 2: Statistical comparison in a test group,” J. Cataract Refractive Surg. 32(1), 33–44 (2006).
[Crossref]

T. O. Salmon and C. van de Pol, “Normal-eye Zernike coefficients and root-mean-square wavefront errors,” J. Cataract Refractive Surg. 32(12), 2064–2074 (2006).
[Crossref]

J. Europ. Opt. Soc. Rap. Public. (1)

S. van Haver and A. J. E. M. Janssen, “Advanced analytic treatment and efficient computation of the diffraction integrals in the extended Nijboer-Zernike theory,” J. Europ. Opt. Soc. Rap. Public. 8, 13044 (2013).
[Crossref]

J. Opt. Soc. Am. A (8)

J. Refract. Surg. (4)

P. Rodriguez, R. Navarro, L. González, and J. L. Hernández, “Accuracy and Reproducibility of Zywave, Tracey, and Experimental Aberrometers,” J. Refract. Surg. 20(6), 810–817 (2004).

S. Shah, S. Naroo, S. Hosking, D. Gherghel, S. Mantry, S. Bannerjee, K. Pedwell, and H. S. Bains, “Nidek OPD-scan analysis of normal, keratoconic, and penetrating keratoplasty eyes,” J. Refract. Surg. 19(2), S255–S259 (2003).

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18(5), S652–S660 (2002).

X. Cheng, L. N. Thibos, and A. Bradley, “Estimating visual quality from wavefront aberration measurements,” J. Refract. Surg. 19(5), S579–S584 (2002).

J. Vision (2)

J. D. Marsack, L. N. Thibos, and R. A. Applegate, “Metrics of optical quality derived from wave aberrations predict visual performance,” J. Vision 4(4), 8–328 (2004).
[Crossref]

A. B. Watson, “A formula for the mean human optical modulation transfer function as a function of pupil size,” J. Vision 13(6), 18 (2013).
[Crossref]

Ophthalm. Physiol. Opt. (2)

P. Rodríguez, R. Navarro, and J. J. Rozema, “Eigencorneas: application of principal component analysis to corneal topography,” Ophthalm. Physiol. Opt. 34(6), 667–677 (2014).
[Crossref]

J. Arines, E. Pailos, P. Prado, and S. Bará, “The contribution of the fixational eye movements to the variability of the measured ocular aberration,” Ophthalm. Physiol. Opt. 29(3), 281–287 (2009).
[Crossref]

Ophthalmology (1)

N. Maeda, T. Fujikado, T. Kuroda, T. Mihashi, Y. Hirohara, K. Nishida, H. Watanabe, and Y. Tano, “Wavefront aberrations measured with Hartmann-Shack sensor in patients with keratoconus,” Ophthalmology 109(11), 1996–2003 (2002).
[Crossref]

Opt. Acta (1)

E. C. Kintner and R. M. Sillitto, “A new analytic’ method for computing the optical transfer function,” Opt. Acta 23(8), 607–619 (1976).
[Crossref]

Opt. Express (2)

Opt. Soc. Am A (1)

J. A. Díaz, “Relating wavefront error, apodization, and the optical transfer function: Comment,” Opt. Soc. Am A 33(8), 1622–1625 (2016).
[Crossref]

Optom. Vis. Sci. (2)

J. J. Rozema, P. Rodriguez, R. Navarro, and C. Koppen, “Bigaussian wavefront model for normal and keratoconic eyes based on PCA,” Optom. Vis. Sci. 94(6), 680–687 (2017).
[Crossref]

X. Cheng, A. Bradley, X. Hong, and L. N. Thibos, “Relationship between refractive error and monochromatic aberrations of the eye,” Optom. Vis. Sci. 80(1), 43–49 (2003).
[Crossref]

Publ. Astron. Soc. Pac. (1)

M. J. Jee, J. P. Blakeslee, M. Sirianni, A. R. Martel, R. L. White, and H. C. Ford, “Principal component analysis of the time-and position-dependent point-spread function of the advanced camera for surveys,” Publ. Astron. Soc. Pac. 119(862), 1403–1419 (2007).
[Crossref]

Other (3)

M. Born and E. Wolf, Principles of Optics(Pergamon Press, 1983).

ISO (International Organisation for Standardization), “ISO 24157:2008 - Ophthalmic optics and instruments: Reporting aberrations of the human eye,” (2008).

I. T. Jolliffe, Principal Component Analysis, 2nd edition (Springer-Verlag, 2002).

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Figures (9)

Fig. 1.
Fig. 1. Block diagram of the method.
Fig. 2.
Fig. 2. Real and imaginary parts of first cross-correlations between complex Zernike polynomials
Fig. 3.
Fig. 3. Orthogonal OTF modes, after applying SVD to complex Zernike cross-correlations. Each pair of upper and lower circles represents amplitude (MTF) and phase (PTF) respectively. Rotated versions are not included.
Fig. 4.
Fig. 4. SVD threshold versus number of retained OTF basis functions.
Fig. 5.
Fig. 5. Average population OTF and first 10 eigenfunctions (pairs of MTF and PTF).
Fig. 6.
Fig. 6. Normalized cumulative variance versus number of eigenfunctions for an 80% SVD threshold (blue line) and 95% SVD threshold (red line).
Fig. 7.
Fig. 7. Number of OTF basis functions obtained with different SVD and PCA thresholds.
Fig. 8.
Fig. 8. MTF reconstruction with OTF basis (SVD and PCA thresholds, 99% and 90%) for two random subjects in the dataset. Original (blue dotted line), reconstructed (red solid line) and diffraction limited MTF (black dash-dotted line) are displayed.
Fig. 9.
Fig. 9. Reconstruction error (Strehl ratio dimensionless units) histograms for the lowest (80%, upper panel) and highest (99%, lower panel) SVD and PCA thresholds investigated.

Tables (1)

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Table 1. Statistical median of the reconstruction error (Strehl ratio dimensionless units) for different combinations of SVD (columns) and PCA (rows) thresholds

Equations (6)

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P ( ρ , θ ) = e i k W = e i k j = 1 J = 44 a j Z j ( ρ , θ )
P ( ρ , θ ) k = 1 K b k C k ( ρ , θ )
C k = C n m ( ρ , ϕ ) := 1 2 N n m R n | m | ( ρ ) exp ( i m ϕ )
O T F ( ρ , θ ) k = 1 K l = 1 K b k b l C k ( ρ , θ ) C l ( ρ , θ ) = n = 1 N o n O n ( ρ , θ ) .
O T F i ( ρ , θ ) M ( ρ , θ ) + j = 1 J c j i E j ( ρ , θ )
f n 1 n 2 m ( ρ , θ ) = { a n 1 n 2 m J n 1 + 1 ( 2 π ρ ) ρ J n 2 + 1 ( 2 π ρ ) ρ cos m θ , m 0 a n 1 n 2 m J n 1 + 1 ( 2 π ρ ) ρ J n 2 + 1 ( 2 π ρ ) ρ sin m θ , m < 0

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