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Y. Gagnon, R.H. H. Kröger, The Lund Vision Group; Gradient Index Models of Monofocal and Multifocal Spherical Fish Lenses . Invest. Ophthalmol. Vis. Sci. 2006;47(13):1211.
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© ARVO (1962-2015); The Authors (2016-present)
Many fish lenses are corrected for longitudinal chromatic aberration (LCA) by longitudinal spherical aberration (LSA) of complex shape. This leads to multiple focal lengths in a single lens. Each focal length focuses a different spectral band on the retina. A ray–tracing model was constructed to explore the internal optical structure of fish lenses.
The model was created using MATLAB R14. It was based on a spherical lens consisting of 1400 layers, which is about the number of cell layers in a fish lens 1 mm in radius. Two refractive index gradients (RIGs) were then determined by iterative optimization, one for a monofocal and one for a multifocal lens. The multifocal lens was divided into three zones, each focusing a different wavelength. The chosen wavelengths corresponded to the three cone pigments of the African cichlid fish Astatotilapia (formerly Haplochromis) burtoni (455, 523, and 562 nm for the inner, middle, and peripheral zones, respectively). Chromatic dispersion in the crystalline lens was estimated by using data from the literature. The refractive index profile was optimized such that the achieved back centre distances of rays entering the lens at positions between 0 and 0.95 R (R = lens radius) differed from the target focal length by at most 10–6 R. The refractive index distribution in the outer periphery of the lenses was chosen to match data from the literature.
The algorithm achieved a high degree of accuracy for both the monofocal and multifocal lenses despite the low number of layers. The multifocal RIG closely followed the monofocal RIG. Refractive index was at most 2 · 10–3 higher than the monofocal RIG for the outer and middle zones (1 down to 0.5 R), and lower in the inner zone.
The striking similarity between the multifocal and monofocal RIGs suggests stringent regulation of the RIGs in real fish lenses. This raises interesting questions on how lens fiber cells can control refractive index with such high accuracy, and on the nature of the regulatory feedback processes.
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