Differential equations for a constant-angular-magnification aspheric-mirror surface shape are derived for a general dependence of the camera image height on the camera field angle. The explicit equations of the constant-angular-magnification mirror surface are given for some particular values of the angular magnification. For a series of odd integer values of the angular magnification, 10th-order polynomial approximations of the mirror surface are presented. The imaging performance of such a mirror with an angular magnification of 7 is analyzed and compared with a spherical mirror. The main cause of image blur in all-sky cameras at the edge of the field of view was found to be a strong image curvature. We show that increasing the camera-to-mirror distance and/or stopping down the camera lens reduces the image blur.
© 1994 Optical Society of America
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