The Approximation of Vignetted Pupil Shape by an Ellipse

For many optical systems with zero obscuration, it has been found that, for extraaxial pencils, the periphery of the vignetted pupil shape may be represented by an ellipse with good approximation. A computer program is described which first determines the rim rays and then fits the ray coordinates to an ellipse by the method of least squares. Some examples are included showing the accuracy of the elliptical pupil.