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An optical analysis of eccentric photorefraction (photoretinoscopy) of astigmatic eyes is presented. The size and the angular tilt of the dark crescent appearing in the subject's pupil are derived as a function of five variables: the ametropia of the eye (Dsph, Dcyl, axis), the eccentricity of the flash, e, and the distance of the camera from the subject's eye, dc. A simplified solution and a solution of the inverse problem, which enable one to calculate the degree of ametropia from the size and the tilt of the crescent, are also presented. If the crescent is smaller than the pupil, both the size and the tilt of the dark crescent are independent of the pupil size. The angular tilt of the crescent is also independent of the eccentricity. Characteristic changes of the crescent as a function of the cylinder axis are illustrated for compound and mixed astigmatisms. The validity of the theoretical predictions was experimentally verified on a model eye.
Wesemann et al. (Sun,) studied this question.