Abstract

Light scattering in the eye affects the quality of vision and its effect increases with aging and related pathologies, such as cataracts. Simulating methods were developed in order to reproduce the effects of this phenomenon. We introduce a statistical model of wavefront perturbations at the pupil plane of the eye that replicates the characteristic angular distribution of the light distribution over the retina. Our approach is based on the parameterization of the discrete cosine spectrum of the wavefront perturbation. The model performance was experimentally validated with a dedicated setup using a liquid crystal on silicon device as a spatial phase modulator. This instrument can be used for further visual experiments with controlled induction of light scattering.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [PubMed]
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    [Crossref] [PubMed]
  4. J. J. Vos and T. J. T. P. van den Berg, “Report on disability glare,” CIE Collect. 135, 1–9 (1999).
  5. I. Kelly-Pérez, N. C. Bruce, L. R. Berriel-Valdos, A. Werner, and J. A. Delgado Atencio, “Computational model of the effect of light scattering from cataracts in the human eye,” J. Opt. Soc. Am. A 30(12), 2585–2594 (2013).
    [Crossref] [PubMed]
  6. R. Paeglis, M. Ozolinsh, P. Cikmacs, and S. Andersson-Engels, “Eye model with controllable lens scattering,” in (2001), Vol. 4434, pp. 233–238.
  7. G. C. de Wit, L. Franssen, J. E. Coppens, and T. J. T. P. van den Berg, “Simulating the straylight effects of cataracts,” J. Cataract Refract. Surg. 32(2), 294–300 (2006).
    [Crossref] [PubMed]
  8. H. Ginis, O. Sahin, A. Pennos, and P. Artal, “Compact optical integration instrument to measure intraocular straylight,” Biomed. Opt. Express 5(9), 3036–3041 (2014).
    [Crossref] [PubMed]
  9. H. Ginis, G. M. Pérez, J. M. Bueno, and P. Artal, “The wide-angle point spread function of the human eye reconstructed by a new optical method,” J. Vis. 12(3), 20 (2012).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  14. A. Arias, H. Ginis, and P. Artal, “Physical Model of Intraocular Scattering using a Spatial Light Modulator,” Invest. Ophthalmol. Vis. Sci. 56, 1066 (2015).
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    [Crossref]
  16. T. Coleman, M. A. Branch, and A. Grace, “Matlab Optimization Toolbox,” Change, 42 (2008).
  17. P. Szendro, G. Vincze, and A. Szasz, “Pink-noise behaviour of biosystems,” Eur. Biophys. J. 30(3), 227–231 (2001).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  20. T. J. van den Berg, “Analysis of intraocular straylight, especially in relation to age,” Optom. Vis. Sci. 72(2), 52–59 (1995).
    [Crossref] [PubMed]

2016 (1)

2015 (1)

A. Arias, H. Ginis, and P. Artal, “Physical Model of Intraocular Scattering using a Spatial Light Modulator,” Invest. Ophthalmol. Vis. Sci. 56, 1066 (2015).

2014 (2)

H. Ginis, J. J. Rozema, M.-J. B. R. Tassignon, and P. Artal, “A phase perturbation model of light scattering in the human eye,” Invest. Ophthalmol. Vis. Sci. 55, 2120 (2014).

H. Ginis, O. Sahin, A. Pennos, and P. Artal, “Compact optical integration instrument to measure intraocular straylight,” Biomed. Opt. Express 5(9), 3036–3041 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (2)

H. Ginis, G. M. Pérez, J. M. Bueno, and P. Artal, “The wide-angle point spread function of the human eye reconstructed by a new optical method,” J. Vis. 12(3), 20 (2012).
[Crossref] [PubMed]

Y.-C. Chen, C.-J. Jiang, T.-H. Yang, and C.-C. Sun, “Development of a human eye model incorporated with intraocular scattering for visual performance assessment,” J. Biomed. Opt. 17(7), 0750091 (2012).
[Crossref] [PubMed]

2009 (2)

P. H. B. Kok, H. W. van Dijk, T. J. T. P. van den Berg, and F. D. Verbraak, “A model for the effect of disturbances in the optical media on the OCT image quality,” Invest. Ophthalmol. Vis. Sci. 50(2), 787–792 (2009).
[Crossref] [PubMed]

H. Ginis, I. Pentari, D. de Brouwere, D. Bouzoukis, I. Naoumidi, and I. Pallikaris, “Narrow angle light scatter in rabbit corneas after excimer laser surface ablation,” Ophthalmic Physiol. Opt. 29(3), 357–362 (2009).
[Crossref] [PubMed]

2006 (1)

G. C. de Wit, L. Franssen, J. E. Coppens, and T. J. T. P. van den Berg, “Simulating the straylight effects of cataracts,” J. Cataract Refract. Surg. 32(2), 294–300 (2006).
[Crossref] [PubMed]

2005 (1)

2001 (1)

P. Szendro, G. Vincze, and A. Szasz, “Pink-noise behaviour of biosystems,” Eur. Biophys. J. 30(3), 227–231 (2001).
[Crossref] [PubMed]

1999 (2)

J. J. Vos and T. J. T. P. van den Berg, “Report on disability glare,” CIE Collect. 135, 1–9 (1999).

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[Crossref]

1997 (1)

T. J. van den Berg, “Light scattering by donor lenses as a function of depth and wavelength,” Invest. Ophthalmol. Vis. Sci. 38(7), 1321–1332 (1997).
[PubMed]

1996 (1)

M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, “Observation of light diffusion and correlation transport in nematic liquid crystals,” Phys. Rev. Lett. 77(11), 2233–2236 (1996).
[Crossref] [PubMed]

1995 (1)

T. J. van den Berg, “Analysis of intraocular straylight, especially in relation to age,” Optom. Vis. Sci. 72(2), 52–59 (1995).
[Crossref] [PubMed]

1985 (1)

Alfano, R. R.

Andersson-Engels, S.

R. Paeglis, M. Ozolinsh, P. Cikmacs, and S. Andersson-Engels, “Eye model with controllable lens scattering,” in (2001), Vol. 4434, pp. 233–238.

Arias, A.

A. Arias, H. Ginis, and P. Artal, “Physical Model of Intraocular Scattering using a Spatial Light Modulator,” Invest. Ophthalmol. Vis. Sci. 56, 1066 (2015).

Artal, P.

D. Christaras, H. Ginis, A. Pennos, and P. Artal, “Intraocular scattering compensation in retinal imaging,” Biomed. Opt. Express 7(10), 3996–4006 (2016).
[Crossref] [PubMed]

A. Arias, H. Ginis, and P. Artal, “Physical Model of Intraocular Scattering using a Spatial Light Modulator,” Invest. Ophthalmol. Vis. Sci. 56, 1066 (2015).

H. Ginis, J. J. Rozema, M.-J. B. R. Tassignon, and P. Artal, “A phase perturbation model of light scattering in the human eye,” Invest. Ophthalmol. Vis. Sci. 55, 2120 (2014).

H. Ginis, O. Sahin, A. Pennos, and P. Artal, “Compact optical integration instrument to measure intraocular straylight,” Biomed. Opt. Express 5(9), 3036–3041 (2014).
[Crossref] [PubMed]

H. Ginis, G. M. Pérez, J. M. Bueno, and P. Artal, “The wide-angle point spread function of the human eye reconstructed by a new optical method,” J. Vis. 12(3), 20 (2012).
[Crossref] [PubMed]

Bernardo, L. M.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[Crossref]

Berriel-Valdos, L. R.

Bouzoukis, D.

H. Ginis, I. Pentari, D. de Brouwere, D. Bouzoukis, I. Naoumidi, and I. Pallikaris, “Narrow angle light scatter in rabbit corneas after excimer laser surface ablation,” Ophthalmic Physiol. Opt. 29(3), 357–362 (2009).
[Crossref] [PubMed]

Bruce, N. C.

Bueno, J. M.

H. Ginis, G. M. Pérez, J. M. Bueno, and P. Artal, “The wide-angle point spread function of the human eye reconstructed by a new optical method,” J. Vis. 12(3), 20 (2012).
[Crossref] [PubMed]

Chen, Y.-C.

Y.-C. Chen, C.-J. Jiang, T.-H. Yang, and C.-C. Sun, “Development of a human eye model incorporated with intraocular scattering for visual performance assessment,” J. Biomed. Opt. 17(7), 0750091 (2012).
[Crossref] [PubMed]

Christaras, D.

Cikmacs, P.

R. Paeglis, M. Ozolinsh, P. Cikmacs, and S. Andersson-Engels, “Eye model with controllable lens scattering,” in (2001), Vol. 4434, pp. 233–238.

Collings, P. J.

M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, “Observation of light diffusion and correlation transport in nematic liquid crystals,” Phys. Rev. Lett. 77(11), 2233–2236 (1996).
[Crossref] [PubMed]

Coppens, J. E.

G. C. de Wit, L. Franssen, J. E. Coppens, and T. J. T. P. van den Berg, “Simulating the straylight effects of cataracts,” J. Cataract Refract. Surg. 32(2), 294–300 (2006).
[Crossref] [PubMed]

de Brouwere, D.

H. Ginis, I. Pentari, D. de Brouwere, D. Bouzoukis, I. Naoumidi, and I. Pallikaris, “Narrow angle light scatter in rabbit corneas after excimer laser surface ablation,” Ophthalmic Physiol. Opt. 29(3), 357–362 (2009).
[Crossref] [PubMed]

de Wit, G. C.

G. C. de Wit, L. Franssen, J. E. Coppens, and T. J. T. P. van den Berg, “Simulating the straylight effects of cataracts,” J. Cataract Refract. Surg. 32(2), 294–300 (2006).
[Crossref] [PubMed]

Delgado Atencio, J. A.

Ferreira, C.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[Crossref]

Franssen, L.

G. C. de Wit, L. Franssen, J. E. Coppens, and T. J. T. P. van den Berg, “Simulating the straylight effects of cataracts,” J. Cataract Refract. Surg. 32(2), 294–300 (2006).
[Crossref] [PubMed]

Garcia, J.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[Crossref]

Ginis, H.

D. Christaras, H. Ginis, A. Pennos, and P. Artal, “Intraocular scattering compensation in retinal imaging,” Biomed. Opt. Express 7(10), 3996–4006 (2016).
[Crossref] [PubMed]

A. Arias, H. Ginis, and P. Artal, “Physical Model of Intraocular Scattering using a Spatial Light Modulator,” Invest. Ophthalmol. Vis. Sci. 56, 1066 (2015).

H. Ginis, J. J. Rozema, M.-J. B. R. Tassignon, and P. Artal, “A phase perturbation model of light scattering in the human eye,” Invest. Ophthalmol. Vis. Sci. 55, 2120 (2014).

H. Ginis, O. Sahin, A. Pennos, and P. Artal, “Compact optical integration instrument to measure intraocular straylight,” Biomed. Opt. Express 5(9), 3036–3041 (2014).
[Crossref] [PubMed]

H. Ginis, G. M. Pérez, J. M. Bueno, and P. Artal, “The wide-angle point spread function of the human eye reconstructed by a new optical method,” J. Vis. 12(3), 20 (2012).
[Crossref] [PubMed]

H. Ginis, I. Pentari, D. de Brouwere, D. Bouzoukis, I. Naoumidi, and I. Pallikaris, “Narrow angle light scatter in rabbit corneas after excimer laser surface ablation,” Ophthalmic Physiol. Opt. 29(3), 357–362 (2009).
[Crossref] [PubMed]

Jester, K. A.

M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, “Observation of light diffusion and correlation transport in nematic liquid crystals,” Phys. Rev. Lett. 77(11), 2233–2236 (1996).
[Crossref] [PubMed]

Jiang, C.-J.

Y.-C. Chen, C.-J. Jiang, T.-H. Yang, and C.-C. Sun, “Development of a human eye model incorporated with intraocular scattering for visual performance assessment,” J. Biomed. Opt. 17(7), 0750091 (2012).
[Crossref] [PubMed]

Kao, M. H.

M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, “Observation of light diffusion and correlation transport in nematic liquid crystals,” Phys. Rev. Lett. 77(11), 2233–2236 (1996).
[Crossref] [PubMed]

Kelly-Pérez, I.

Kok, P. H. B.

P. H. B. Kok, H. W. van Dijk, T. J. T. P. van den Berg, and F. D. Verbraak, “A model for the effect of disturbances in the optical media on the OCT image quality,” Invest. Ophthalmol. Vis. Sci. 50(2), 787–792 (2009).
[Crossref] [PubMed]

Marinho, F.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[Crossref]

Mas, D.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[Crossref]

Naoumidi, I.

H. Ginis, I. Pentari, D. de Brouwere, D. Bouzoukis, I. Naoumidi, and I. Pallikaris, “Narrow angle light scatter in rabbit corneas after excimer laser surface ablation,” Ophthalmic Physiol. Opt. 29(3), 357–362 (2009).
[Crossref] [PubMed]

Navarro, R.

Ozolinsh, M.

R. Paeglis, M. Ozolinsh, P. Cikmacs, and S. Andersson-Engels, “Eye model with controllable lens scattering,” in (2001), Vol. 4434, pp. 233–238.

Paeglis, R.

R. Paeglis, M. Ozolinsh, P. Cikmacs, and S. Andersson-Engels, “Eye model with controllable lens scattering,” in (2001), Vol. 4434, pp. 233–238.

Pallikaris, I.

H. Ginis, I. Pentari, D. de Brouwere, D. Bouzoukis, I. Naoumidi, and I. Pallikaris, “Narrow angle light scatter in rabbit corneas after excimer laser surface ablation,” Ophthalmic Physiol. Opt. 29(3), 357–362 (2009).
[Crossref] [PubMed]

Pennos, A.

Pentari, I.

H. Ginis, I. Pentari, D. de Brouwere, D. Bouzoukis, I. Naoumidi, and I. Pallikaris, “Narrow angle light scatter in rabbit corneas after excimer laser surface ablation,” Ophthalmic Physiol. Opt. 29(3), 357–362 (2009).
[Crossref] [PubMed]

Pérez, G. M.

H. Ginis, G. M. Pérez, J. M. Bueno, and P. Artal, “The wide-angle point spread function of the human eye reconstructed by a new optical method,” J. Vis. 12(3), 20 (2012).
[Crossref] [PubMed]

Rozema, J. J.

H. Ginis, J. J. Rozema, M.-J. B. R. Tassignon, and P. Artal, “A phase perturbation model of light scattering in the human eye,” Invest. Ophthalmol. Vis. Sci. 55, 2120 (2014).

Sahin, O.

Sun, C.-C.

Y.-C. Chen, C.-J. Jiang, T.-H. Yang, and C.-C. Sun, “Development of a human eye model incorporated with intraocular scattering for visual performance assessment,” J. Biomed. Opt. 17(7), 0750091 (2012).
[Crossref] [PubMed]

Szasz, A.

P. Szendro, G. Vincze, and A. Szasz, “Pink-noise behaviour of biosystems,” Eur. Biophys. J. 30(3), 227–231 (2001).
[Crossref] [PubMed]

Szendro, P.

P. Szendro, G. Vincze, and A. Szasz, “Pink-noise behaviour of biosystems,” Eur. Biophys. J. 30(3), 227–231 (2001).
[Crossref] [PubMed]

Tassignon, M.-J. B. R.

H. Ginis, J. J. Rozema, M.-J. B. R. Tassignon, and P. Artal, “A phase perturbation model of light scattering in the human eye,” Invest. Ophthalmol. Vis. Sci. 55, 2120 (2014).

van den Berg, T. J.

T. J. van den Berg, “Light scattering by donor lenses as a function of depth and wavelength,” Invest. Ophthalmol. Vis. Sci. 38(7), 1321–1332 (1997).
[PubMed]

T. J. van den Berg, “Analysis of intraocular straylight, especially in relation to age,” Optom. Vis. Sci. 72(2), 52–59 (1995).
[Crossref] [PubMed]

van den Berg, T. J. T. P.

P. H. B. Kok, H. W. van Dijk, T. J. T. P. van den Berg, and F. D. Verbraak, “A model for the effect of disturbances in the optical media on the OCT image quality,” Invest. Ophthalmol. Vis. Sci. 50(2), 787–792 (2009).
[Crossref] [PubMed]

G. C. de Wit, L. Franssen, J. E. Coppens, and T. J. T. P. van den Berg, “Simulating the straylight effects of cataracts,” J. Cataract Refract. Surg. 32(2), 294–300 (2006).
[Crossref] [PubMed]

J. J. Vos and T. J. T. P. van den Berg, “Report on disability glare,” CIE Collect. 135, 1–9 (1999).

van Dijk, H. W.

P. H. B. Kok, H. W. van Dijk, T. J. T. P. van den Berg, and F. D. Verbraak, “A model for the effect of disturbances in the optical media on the OCT image quality,” Invest. Ophthalmol. Vis. Sci. 50(2), 787–792 (2009).
[Crossref] [PubMed]

Verbraak, F. D.

P. H. B. Kok, H. W. van Dijk, T. J. T. P. van den Berg, and F. D. Verbraak, “A model for the effect of disturbances in the optical media on the OCT image quality,” Invest. Ophthalmol. Vis. Sci. 50(2), 787–792 (2009).
[Crossref] [PubMed]

Vincze, G.

P. Szendro, G. Vincze, and A. Szasz, “Pink-noise behaviour of biosystems,” Eur. Biophys. J. 30(3), 227–231 (2001).
[Crossref] [PubMed]

Vos, J. J.

J. J. Vos and T. J. T. P. van den Berg, “Report on disability glare,” CIE Collect. 135, 1–9 (1999).

Werner, A.

Xu, M.

Yang, T.-H.

Y.-C. Chen, C.-J. Jiang, T.-H. Yang, and C.-C. Sun, “Development of a human eye model incorporated with intraocular scattering for visual performance assessment,” J. Biomed. Opt. 17(7), 0750091 (2012).
[Crossref] [PubMed]

Yodh, A. G.

M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, “Observation of light diffusion and correlation transport in nematic liquid crystals,” Phys. Rev. Lett. 77(11), 2233–2236 (1996).
[Crossref] [PubMed]

Biomed. Opt. Express (2)

CIE Collect. (1)

J. J. Vos and T. J. T. P. van den Berg, “Report on disability glare,” CIE Collect. 135, 1–9 (1999).

Eur. Biophys. J. (1)

P. Szendro, G. Vincze, and A. Szasz, “Pink-noise behaviour of biosystems,” Eur. Biophys. J. 30(3), 227–231 (2001).
[Crossref] [PubMed]

Invest. Ophthalmol. Vis. Sci. (4)

H. Ginis, J. J. Rozema, M.-J. B. R. Tassignon, and P. Artal, “A phase perturbation model of light scattering in the human eye,” Invest. Ophthalmol. Vis. Sci. 55, 2120 (2014).

A. Arias, H. Ginis, and P. Artal, “Physical Model of Intraocular Scattering using a Spatial Light Modulator,” Invest. Ophthalmol. Vis. Sci. 56, 1066 (2015).

T. J. van den Berg, “Light scattering by donor lenses as a function of depth and wavelength,” Invest. Ophthalmol. Vis. Sci. 38(7), 1321–1332 (1997).
[PubMed]

P. H. B. Kok, H. W. van Dijk, T. J. T. P. van den Berg, and F. D. Verbraak, “A model for the effect of disturbances in the optical media on the OCT image quality,” Invest. Ophthalmol. Vis. Sci. 50(2), 787–792 (2009).
[Crossref] [PubMed]

J. Biomed. Opt. (1)

Y.-C. Chen, C.-J. Jiang, T.-H. Yang, and C.-C. Sun, “Development of a human eye model incorporated with intraocular scattering for visual performance assessment,” J. Biomed. Opt. 17(7), 0750091 (2012).
[Crossref] [PubMed]

J. Cataract Refract. Surg. (1)

G. C. de Wit, L. Franssen, J. E. Coppens, and T. J. T. P. van den Berg, “Simulating the straylight effects of cataracts,” J. Cataract Refract. Surg. 32(2), 294–300 (2006).
[Crossref] [PubMed]

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

J. Vis. (1)

H. Ginis, G. M. Pérez, J. M. Bueno, and P. Artal, “The wide-angle point spread function of the human eye reconstructed by a new optical method,” J. Vis. 12(3), 20 (2012).
[Crossref] [PubMed]

Ophthalmic Physiol. Opt. (1)

H. Ginis, I. Pentari, D. de Brouwere, D. Bouzoukis, I. Naoumidi, and I. Pallikaris, “Narrow angle light scatter in rabbit corneas after excimer laser surface ablation,” Ophthalmic Physiol. Opt. 29(3), 357–362 (2009).
[Crossref] [PubMed]

Opt. Commun. (1)

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999).
[Crossref]

Opt. Lett. (1)

Optom. Vis. Sci. (1)

T. J. van den Berg, “Analysis of intraocular straylight, especially in relation to age,” Optom. Vis. Sci. 72(2), 52–59 (1995).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, “Observation of light diffusion and correlation transport in nematic liquid crystals,” Phys. Rev. Lett. 77(11), 2233–2236 (1996).
[Crossref] [PubMed]

Other (2)

T. Coleman, M. A. Branch, and A. Grace, “Matlab Optimization Toolbox,” Change, 42 (2008).

R. Paeglis, M. Ozolinsh, P. Cikmacs, and S. Andersson-Engels, “Eye model with controllable lens scattering,” in (2001), Vol. 4434, pp. 233–238.

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Figures (4)

Fig. 1
Fig. 1 Phase map calculation.
Fig. 2
Fig. 2 Experimental setup for the dynamical generation and estimation of straylight.
Fig. 3
Fig. 3 Numerical optimization results.
Fig. 4
Fig. 4 Relationship among B parameter, RMS and the straylight at 6 degrees.

Equations (8)

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PS F CIE =[ 10.08 ( A 70 ) 4 ][ 9.2× 10 6 [ 1+ ( θ/ 0.0046 ) 2 ] 1.5 + 1.5× 10 5 [ 1+ ( θ/ 0.045 ) 2 ] 1.5 ] +[ 11.6 ( A 70 ) 4 ]{ [ 400 1+ ( θ/ 0.1 ) 2 +3× 10 8 . θ 2 ]+p[ 1300 [ 1+ ( θ/ 0.1 ) 2 ] 1.5 + 0.8 [ 1+ ( θ/ 0.1 ) 2 ] 0.5 ] } +2.5× 10 3 p
W i',j' =circ( i',j' ) i=0 N1 j=0 N1 U ij R ji cos( πϕ f i N i' )cos( πϕ f j N j' )
F( f )=B f β
I c ( θ )= 0 θ 2πPSF( ϕ ) dϕ
PSF( θ )= 1 2πθ d I c ( θ ) dθ
PSF( θ )=C( PS F dl )+D[ 1 ( θ+0.001 ) E ]
Ω αPSF dΩ=1
α= [ ( λ ϕ ) 2 x=1 N y=1 N PS F x,y ] 1

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