Differential equations for a constant-angular-magnification aspheric-m
irror 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 part
icular values of the angular magnification. For a series of odd intege
r values of the angular magnification, 10th-order polynomial approxima
tions of the mirror surface are presented. The imaging performance of
such a mirror with an angular magnification of 7 is analyzed and compa
red with a spherical mirror. The main cause of image blur in all-sky c
ameras 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.