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The complex amplitude distribution transmitted by a refracting surface of revolution between two homogeneous media when it is illuminated by a plane wavefront is determined. In particular, the diffraction pattern associated with the primary spherical aberration is studied.

The method of the transmission function is used to determine the complex amplitude distribution transmitted by a conical lens illuminated by a plane or spherical wave. We study the transmission function of the conical lens and determine the focal curve which coincides with that obtained by the ray-tracing method.

In this paper we determine the location of image and transform planes and the equivalent focal length for a parabolic gradient-index rod, and we consider the problem of modal propagation.

The objective of this paper is to show that it is possible to transmit a paraxial optical image and transform through a dielectric inhomogeneous medium whose refractive index is given by n^2=n12(z)+n02[h_1(z)x+h_2(z)y−g^2(z)(x^2+y^2)], where n_0 = n_1(0), and n_1, g, h_1, and h_2 are arbitrary functions of z. The optical image transmission, with a scaling factor F = H_2(zm), m being an integer, is obtained at planes z = zm such that H_1(zm) = 0 (the image condition), and the optical transform transmission is obtained at planes z=z˜_m such that H_2(z˜_m)=0 (the transform condition), where H_1(z) and H_2(z) are two independent solutions of the paraxial ray equation ?(z) + g^2(z)H(z) = 0 with the initial conditions H_1(0) = 0,?_1(0) = 1,H_2(0) = 1, and ?_2(0) = 0, where the point denotes the derivative with respect to z. Finally, we show that this medium can be represented by a transmittance function similar to the spherical-lens transmittance function and thus can be an element of image-forming systems.

Validity conditions of the thickness function method for determining the transmittance function are obtained by a general method developed by the authors.

Three equivalent methods are presented for determining the complex amplitude distribution transmitted by a refracting surface between two homogeneous media when it is illuminated by a plane or spherical wavefront.

The effect on the transmittance function in gradient-index material due to a circular pupil is studied, and we characterize this material by its effective transmittance function.

In this paper we study the paraxial imaging and transforming in a medium with gradient index obtaining the image and transform conditions. The medium is characterized by a transmittance function at the output plane similar to a thin lens. This medium can be an element of imaging and optical data processing systems.

In this paper, we use the matrix wave equation to solve the propagation problem of a monochromatic wave through a square law medium.

The propagation of a complex amplitude distribution in quadratix-index material is studied by the characteristic point function, and we determine the maximum distance for which an optical image and transform can be transmitted without estimable loss of information due to modal dispersion.

In this paper we determine the image planes and the transmittance function for a conical gradient-index (GRIN) rod, and we consider the problem of modal propagation.