Third-Order Aberrations of Inhomogeneous Lenses
01 Nov 1970-Journal of the Optical Society of America (Optical Society of America)-Vol. 60, Iss: 11, pp 1436-1443
TL;DR: In this article, the third-order aberration coefficients of a symmetric system may be computed when the lenses are manufactured from glasses with continuously varying refractive indices, and the surface contribution consists of the usual contribution based on the assumption that the media are homogeneous, and an additional term that takes into account the variation of the index along the surface.
Abstract: Various organizations in the United States and abroad are experimenting with techniques for manufacturing glass with a continuously varying refractive index. Use of such glasses in lens design would provide valuable additional degrees of freedom for the control of aberrations. This paper presents formulas by means of which the third-order (monochromatic) aberration coefficients of a symmetric system may be computed when the lenses are manufactured from glasses with continuously varying refractive indices. Each coefficient is expressed as a sum of contributions by each surface separating two distinct media and a sum of integrals over each inhomogeneous medium. The surface contribution consists of the usual contribution based on the assumption that the media are homogeneous, and an additional term that takes into account the variation of the index along the surface.
Citations
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TL;DR: The subject of gradient-index optics dates from the 1850s but only in the last 10 years has it been possible to design lenses, manufacture materials, measure the properties, and fabricate finished lens elements.
Abstract: The subject of gradient-index optics dates from the 1850s. However, only in the last 10 years has it been possible to design lenses, manufacture materials, measure the properties, and fabricate finished lens elements. The current status of gradient-index optics is reviewed.
254 citations
TL;DR: The proposed wide-field schematic eye model incorporates a gradient-index (GRIN) lens, which enables it to fulfill properties of two well-known schematic eye models, namely, Navarro's model for off-axis aberrations and Thibos's chromatic on-axis model.
Abstract: We propose a wide-field schematic eye model, which provides a more realistic description of the optical system of the eye in relation to its anatomical structure. The wide-field model incorporates a gradient-index (GRIN) lens, which enables it to fulfill properties of two well-known schematic eye models, namely, Navarro's model for off-axis aberrations and Thibos's chromatic on-axis model (the Indiana eye). These two models are based on extensive experimental data, which makes the derived wide-field eye model also consistent with that data. A mathematical method to construct a GRIN lens with its iso-indicial contours following the optical surfaces of given asphericity is presented. The efficiency of the method is demonstrated with three variants related to different age groups. The role of the GRIN structure in relation to the lens paradox is analyzed. The wide-field model with a GRIN lens can be used as a starting design for the eye inverse problem, i.e., reconstructing the optical structure of the eye from off-axis wavefront measurements. Anatomically more accurate age-dependent optical models of the eye could ultimately help an optical designer to improve wide-field retinal imaging.
156 citations
TL;DR: For all the subjects and for a wide range of possible aberration levels at the posterior corneal surface, the spherical aberration of the relaxed lens was found to be negative.
138 citations
Additional excerpts
...Equations for calculating the aberration contribution from the surfaces can be found in texts by Welford (1986), Smith and Atchison (1997) and equations for calculating the aberrations of gradient index structures have been given by Sands (1970)....
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TL;DR: In this article, the effect of varying lens shape factors and refractive index distribution on two lens performance characteristics (equivalent power and spherical aberration) were considered, using a mathematical model of the human lens which is based upon ellipsoidal iso-indical contours.
104 citations
01 Oct 1991
TL;DR: The shape of the index profile was found to have a significant effect on the equivalent power and spherical aberration of the lens and the results indicate that more information on surface asphericity and accurate measurement of theindex profile in the sagittal plane are required for more accurate modelling of the human lens.
Abstract: The effect of varying lens shape factors and refractive index distribution on two lens performance characteristics (equivalent power and spherical aberration) are considered, using a mathematical model of the human lens which is based upon ellipsoidal iso-indical contours. Values of radii of curvature based on the work of various authors are used to determine asphericity and these inferred values compared with previous measurement. Discrepancies are found and although asphericity has no effect on equivalent power, it does affect the spherical aberration. Based on preliminary findings of the refractive index distribution in the equatorial plane of human lenses, the index distribution is described by a polynomial in the Y (the distance from the optical axis in the equatorial plane), the coefficients of which are polynomials in Z (the distance along the optical axis). The shape of the index profile was found to have a significant effect on the equivalent power and spherical aberration of the lens. The results indicate that more information on surface asphericity and accurate measurement of the index profile in the sagittal plane are required for more accurate modelling of the human lens.
99 citations
References
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TL;DR: No one refractive index distribution can be "ideal" for both meridional and skew rays, and the optimal index distribution varies with the ratio of rod length to radius and the relative aperture and is intermediate between the helically ideal and the meridionally ideal distributions.
Abstract: Cylindrical transparent media whose refractive index decreases with increasing cylinder radius have been investigated in connection with coherent light propagation in gas waveguides. Recently, graded index glass rods (trade named SELFOC rods) have been used as imaging devices. We report here on a geometrical optical study of graded index systems used for relaying images at unit magnification. We have found that two index distributions previously studied result in large image aberrations when the presence of skew rays is taken into account. We have derived an index distribution which is “ideal” for helical skew rays. Using ray tracing methods we have examined image aberrations for various index distributions and for various rod geometries. We find that (1) no one refractive index distribution can be “ideal” for both meridional and skew rays, (2) image resolution is generally low, reaching about 1000 spots per field, and (3) the optimal index distribution varies with the ratio of rod length to radius and the relative aperture and is intermediate between the helically ideal and the meridionally ideal distributions.
105 citations
TL;DR: In this paper, a glass rod with a radially graduated refractive index was produced by replacing the lithium ions contained in the glass composition with sodium ions from a fused salt bath.
Abstract: A glass rod with a radially graduated refractive index was produced by replacing the lithium ions contained in the glass composition with sodium ions from a fused salt bath. Glass rods with such refractive index gradients are potentially useful as low resolution imaging devices.
70 citations
TL;DR: In this article, the authors deal with practical methods of tracing rays through a gradient-index element, one in which the refractive index varies appreciably in a layer just below the surface of the glass.
Abstract: A gradient-index element is one in which the refractive index varies appreciably in a layer just below the surface of the glass. The present paper deals with practical methods of tracing rays through such a medium. One method, due to L. Montagnino, lends itself to rapid computer ray tracing. A second method, through restricted to the case of spherical symmetry in the index function, lends itself both to computer tracing and to analytical investigations.
67 citations