Abbe Number and Longitudinal Chromatic Aberration (LCA)

jose 24 April, 2018 2657 No Comments

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In natural conditions with polychromatic light, retinal image quality is affected both by monochromatic and chromatic aberrations of the ocular optics and their interactions. As a consequence, Retinal image could be blurred and contrast sensitivity reduced.

Chromatic aberrations are induced by the dispersion of light in the ocular media: this is caused by the wavelength dependence of the refractive index of the cornea and the natural lens.

There are different types of chromatic aberrations:

– Longitudinal chromatic aberration (short wavelengths to focus in front of long wavelengths, producing a chromatic difference of focus between the shorter and longer wavelengths)

– Transverse chromatic aberration: the difference in the angular displacement of the retinal image for different wavelengths.

Unlike transverse chromatic aberration (TCA), which shows a high intersubjective variability, LCA is less variable across subjects, and seems to remain fairly constant with age.1

In the normal phakic eye, contribution of the natural lens to LCA has been reported to be 28, 5 % of the entire eye.2 However in phakic eye, if LCA could be higher than 2D across the visible spectrum, experimental studies did not show significant impact on visual performance: this is mainly explains because the greatest amount of defocus is produced by those wavelengths that are least visible. In addition, individual accommodate to focus a wavelength in the middle of the spectrum.2

Moreover, in phakic eyes, it has been shown that monochromatic aberrations play a protective role against chromatic aberrations.3Chromatic and spherical aberrations depend differently on the pupil diameter. For smaller pupil diameters, LCA correction alone could have a superior impact than correcting SA.4

The interactions between these aberrations and the role of the accommodation are of special concern when the crystalline lens of the eye is replaced by an intraocular lens (IOL).

Pseudophakic optical performance is limited by light scattering foci or surfaces, ocular media in homogeneities, pupillary diffraction, and monochromatic or chromatic aberrations of the cornea and intraocular lens (IOL). Most pseudophakic longitudinal chromatic aberration arises from the chromatic dispersion of IOLs rather than the cornea and other ocular media.5

The dispersion properties of the IOL are defined by the Abbe number (ranging in most designs from 35 to 60): the refractive index of optical materials typically decreases when the wavelength increases,

The Abbe number, also called the V-number, is a measure of the material dispersion properties and it is sometimes referred to as the refractive efficiency.6 The Abbe number (VD) is defined as follows:

Where nD, nF, and nC are the refractive indices of the material at the wavelengths of the Fraunhofer spectral lines D (587.6 nm), F (486.1 nm), and C (656.3 nm).

The following table provides examples of the Abbe numbers and refraction index of various IOLs:

Index of refraction Abbe number
Crystalline lens 1.40 47
Hydrophobic lenses
   Acrysof model 1.55 37
   Hoya acrylic 1.51 43
   Tecnis models 1.47 55
Hydrophilic lenses 1.46 58

 

The higher the Abbe number, the lower the longitudinal chromatic aberration.

Experimental measurements,5,7 as well in vivo measurements,8,9 of chromatic difference of focus reported consistently that in pseudophakic eyes, IOLs with higher chromatic dispersion produce greater longitudinal chromatic aberration. Additionally, Zhao and Mainster have shown that pseudophakic performance improves with increasing Abbe number when IOL parameters are otherwise equivalent.5 Higher Abbe number acrylic materials provide better optical performance in spherical aberration correcting IOLs.

Thus, combining correction of spherical and chromatic aberration would provide superior performance for a larger range of pupil diameters. For the smaller pupil range, LCA would do more, while SA would have a smaller impact and for larger pupils the opposite situation would occur.4

Moreover , with the increase of  multifocal IOLs, the pattern of LCA with  this new diffractive optic should also be considered: Millan,10  has reported evaluating experimentally two bifocal diffractive lenses, that in distance vision, bifocal diffractive IOLs increase the positive LCA of prior ocular media. The more dispersive the IOL material (lower Abbe value), the greater is the LCA. In contrast, in near vision, bifocal diffractive IOLs tend to reduce the amount of LCA. This achromatizing effect varies linearly with the addition power and, depending on the IOL material and the amount of refractive LCA produced, may compensate, in part, the LCA of the eye in near vision.

Chromatic aberration is a fundamental property of IOLs. The human visual system can tolerate a significant amount of monochromatic aberrations, but it is unclear how much LCA can be tolerated.

Further studies are needed to understand the clinical significance of chromatic refractive differences. Low-contrast sensitivity and glare situations might be affected by LCA and chromatic refractive differences.

Minimal residual aberration remains a goal of the IOL design. Lenses with a higher Abbe number causes less light dispersion, therefore, less chromatic aberration, potentially resulting in better quality of vision.

 

References:

  1. Marcos, S., Burns, S. A., Moreno-Barriusop, E. & Navarro, R. A new approach to the study of ocular chromatic aberrations. Vision Res. 39, 4309–4323 (1999).
  2. Negishi, K., Ohnuma, K., Hirayama, N. & Noda, T. Effect of chromatic aberration on contrast sensitivity in pseudophakic eyes. Arch. Ophthalmol. 119, 1154–1158 (2001).
  3. McLellan, J. S., Marcos, S., Prieto, P. M. & Burns, S. A. Imperfect optics may be the eye’s defence against chromatic blur. Nature 417, 174–176 (2002).
  4. Artal, P., Manzanera, S., Piers, P. & Weeber, H. Visual effect of the combined correction of spherical and longitudinal chromatic aberrations. Opt. Express 18, 1637–48 (2010).
  5. Zhao, H. & Mainster, M. A. The effect of chromatic dispersion on pseudophakic optical performance. Br. J. Ophthalmol. 91, 1225–1229 (2007).
  6. Huang, T.-T., Cheng, S.-W., Tsai, C.-L. & Liou, G.-S. Optically Isotropic, Colorless, and Flexible PITEs/TiO2 and ZrO2 Hybrid Films with Tunable Refractive Index, Abbe Number, and Memory Properties. Sci. Rep. 7, 7978 (2017).
  7. Nagata, T., Kubota, S., Watanabe, I. & Aoshima, S. [Chromatic aberration in pseudophakic eyes]. Nihon. Ganka Gakkai Zasshi 103, 237–42 (1999).
  8. Vinas, M., Dorronsoro, C., Garzón, N., Poyales, F. & Marcos, S. In vivo subjective and objective longitudinal chromatic aberration after bilateral implantation of the same design of hydrophobic and hydrophilic intraocular lenses. J. Cataract Refract. Surg. 41, 2115–2124 (2015).
  9. Pérez-Merino, P. et al. In vivo chromatic aberration in eyes implanted with intraocular lenses. Investig. Ophthalmol. Vis. Sci. 54, 2654–2661 (2013).
  10. Millán, M. S., Vega, F. & Ríos-López, I. Polychromatic image performance of diffractive bifocal intraocular lenses: Longitudinal chromatic aberration and energy efficiency. Investig. Ophthalmol. Vis. Sci. 57, 2021–2028 (2016).

 

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