Figure 2.
Astigmatism is usually denned by 3 parameters: minimum defocus value, maximum defocus value and the angle between the X-axis and the direction of maximum defocus. In the CTF Challenge, the defocus angle is in the range [0, 180), so that a rotation by that angle brings the unit vector (1,0) to coincide with the direction of maximum defocus. In other words, the unit vector with coordinates (cos (astigmatism angle), sin(astigmatism angle)) is parallel to the direction of maximum defocus. Note that the Thon ring major axis is perpendicular to the direction of maximum defocus. Thus, this figure presents an astigmatism angle of +45 degrees.