We introduce a model of the human eye for which we take into consideration the laminated nature of lens fibers. The thickness of each lamina is 5.6 µm; thus the lens comprises 300 eccentric lenses of minute dimensions. The index gradient of the lens is such that the index of refraction increases exponentially from the lens core to its peripheral zone. A vector ray-tracing technique is employed to study the optical haracteristics of the system. Both paraxial and marginal rays are simulated, and the angles of incidence vary from 0° to ±20°. Special attention is given to the meridional caustic surfaces as well as the wave-front distortion of the refracted rays. A quasi-Newton optimization technique is employed to obtain the best parameters for the system. A computer modeling program, written in FORTRAN 77, is used to simulate a ray's refraction through the multisurfaces of the eye. The results show full agreement with previous data and that the cornea is responsible for eliminating possible spherical aberration of the system.

For an imaging optical system it is, in general, desirable to transform a collection of point sources of light into point images distributed over the focal plane with the appropriate magnification. In practice, this is achieved by varying the lens system parameters such that the spread of a bundle of rays from each object point over the image plane has been minimized. In this study, caustic surfaces are used to construct a merit function that describes the spread of the caustic surfaces from an ideal image point. This caustic merit function has been used to optimize a large collection of three- and four-element lens systems. The performance of the optimized lenses has been evaluated by comparing the rms blur circle radii vs field angle to that of similar lenses designed by conventional techniques. The average rms improvement has been calculated for optimized systems. Results indicate that minimizing the caustic merit function reduces the rms blur radii over the field of view and the total aberrations of the lens systems, particularly for systems with large apertures and wide fields of view.

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This study presents a new method for designing algorithm for a triplet lens with one or two elements that are made of a gradient index medium (GRIN). This method is based upon considering a well-known designed triplet lens (Cooke triplet lens) as a target lens for designing of the Hybrid Triplet Lens (HTL). Our design was based upon keeping the total optical path length for the axial ray fixed for each case of design. The results showed that several designs for the HTL have the same total powers of the target lens. These designs depend on the variation of the GRIN element parameter values and the order of the GRIN element position in the system. These HTL designs have been evaluated by considering several optical merit functions, i.e., the root mean square (RMS) spot radius, wave front error and the spherical aberration. To achieve the optimal design, these functions are compared for the target lens and the HTL designs through a wide range of field angles.

For an imaging optical system it is, in general, desirable to transform a collection of point sources of light into point images distributed over the focal plane with the appropriate magnification. In practice this is achieved by varying the lens system parameters such that the spread of a bundle of rays from each object point over the image plane has been minimized. A new generalized ray tracing program has been constructed to calculate the principal curvatures of the wavefront associated with a bundle of rays as it passes through an optical system. The caustic surfaces are formed by an optical system and can be determined from the results of the generalized ray tracing program. In this study, the caustic surfaces are used to construct a merit function that describes the spread of the caustic surfaces from an ideal image point. The caustic merit function has been used to optimize a large collection of three- and four-element lenses. The performance of the optimized systems has been evaluated for different field angles by comparing the rms blur circle radii of lenses designed by conventional techniques. Results indicate that minimizing the caustic merit function reduces the rms blur radii over the field of view and the total aberrations of the lens system.