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Eye gaze estimation via images has been well investigated and all methods worked on images with the full face. This makes the eye details small and accuracy is affected. We address this problem by zooming in on a single eye. In this paper, we will show the validity of the method and investigate the performance with controlled synthetic data and also with real images. The principle is to rely on the fact that the outer boundary of the iris is a circle. With a fully calibrated camera, its elliptical image can be back-projected into the 3D space yielding two possible circles. To disambiguate, the solution is found by making use of anthropomorphic knowledge of the structure of the eyeball. Hence, getting a larger eye image with a zoom camera enabled us to achieve higher resolutions and thereby higher accuracies. The robustness of the algorithm was verified by extensive statistical trials conducted on synthetic data and real images. The two key contributions in this paper are to show that it is possible to estimate eye gaze with only one eye image and that consequently this achieves higher accuracy of eye gaze estimation.