Using the propagator method, the quasi-geometric transmittance function and complex amplitude distribution produced by a GRIN lens are evaluated when it is illuminated by a Gaussian beam and the pupil effect is taken into account. The effective pupil is defined and derived by both quasi-geometrical optics and the exact Fresnel diffraction, which it is evaluated in a Rubinowicz representation.
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Liñares et al. (1991) studied this question.
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