Contribution of the gradient refractive index and shape to the crystalline lens spherical aberration and astigmatism

Abstract

The optical properties of the crystalline lens are determined by its shape and refractive index distribution. However, to date, those properties have not been measured together in the same lens, and therefore their relative contributions to optical aberrations are not fully understood. The shape, the optical path difference, and the focal length of ten porcine lenses (age around 6 months) were measured in vitro using Optical Coherence Tomography and laser ray tracing. The 3D Gradient Refractive Index distribution (GRIN) was reconstructed by means of an optimization method based on genetic algorithms. The optimization method searched for the parameters of a 4-variable GRIN model that best fits the distorted posterior surface of the lens in 18 different meridians. Spherical aberration and astigmatism of the lenses were estimated using computational ray tracing, with the reconstructed GRIN lens and an equivalent homogeneous refractive index. For all lenses the posterior radius of curvature was systematically steeper than the anterior one, and the conic constant of both the anterior and posterior positive surfaces was positive. In average, the measured focal length increased with increasing pupil diameter, consistent with a crystalline lens negative spherical aberration. The refractive index of nucleus and surface was reconstructed to an average value of 1.427 and 1.364, respectively, for 633 nm. The results of the GRIN reconstruction showed a wide distribution of the index in all lens samples. The GRIN shifted spherical aberration towards negative values when compared to a homogeneous index. A negative spherical aberration with GRIN was found in 8 of the 10 lenses. The presence of GRIN also produced a decrease in the total amount of lens astigmatism in most lenses, while the axis of astigmatism was only little influenced by the presence of GRIN. To our knowledge, this study is the first systematic experimental study of the relative contribution of geometry and GRIN to the aberrations in a mammal lens.

Influence of Shape and Gradient Refractive Index in the Accommodative Changes of Spherical Aberration in Nonhuman Primate Crystalline Lenses

“…We have recently shown that the presence of the GRIN plays a critical role in the negative spherical aberration of the isolated porcine, 28,31 Observations of the shift of spherical aberration in isolated porcine lens from negative values in virgin lenses to positive values after lens refilling with a homogeneous refractive index polymer also point to a fundamental role of the GRIN in the crystalline lens optical properties. 32 Although there is increasing experimental evidence of GRIN distribution in the crystalline lens of several species, the redistribution of the GRIN in the accommodating lens has remained relatively unexplored.…”

OCT-based crystalline lens topography in accommodating eyes

“…However, although posterior lens surface shape estimation could have a benefit by increasing knowledge of the lens GRIN (especially in the spherical Zernike terms), it should be noted that the ex vivo GRIN distribution represents more closely values the GRIN in a maximally accommodated state and it is unlikely that GRIN plays a major role in non-rotationally symmetric aberrations. In fact, in a recent study on the impact of shape and GRIN on the astigmatism of isolated lenses, Birkenfeld et al [22] found little influence of GRIN on the magnitude and axis of lens astigmatism.…”

“…Lens aberrations have been measured either ex vivo (using laser ray tracing [22] or Hartmann-Shack [23]), or in vivo by subtracting corneal aberrations from total aberrations [24,25]. However, although aberrometers allow measuring the relative contribution of the crystalline lens to the optics of the eye, the relative contribution of the lens surfaces themselves to aberrations is still poorly understood.…”

OCT 3-D surface topography of isolated human crystalline lenses

“…To obtain the shape of the lens surfaces, a surface segmentation algorithm previously described [4] was used. The segmented surfaces were fit to biconical surfaces and spheres.…”

“…In addition, the crystalline lens shows a gradient refractive index (GRIN) distribution, which also changes with age [4][5][6][7][8]. Recent work has shown that in human [9], as well as monkey [10] and porcine lenses [4], both the lens shape and the GRIN play a role in the negative spherical aberration of the lens.…”