Celestial sphere diagram showing the deviation of the optical centre from the zenith and a target star in a different coordinate system. It is presented in plane rather than spherical projection for easier viewing. In the upper left, a sketch shows the location of the optical centre and the zenith relative to the whole image. The optical centre (x₀, y₀) is slightly off the zenith (x_c, y_c), and the parameters (E, ϵ) refer to the deviation in azimuth and zenith, respectively. The planar polar coordinates (θ, r) and spherical projection coordinates (b, u) are based on the optical centre (x₀, y₀), while the horizontal coordinates (a, ɀ) are based on the zenith (x_c, y_c). N is true north, whereas n is the direction of the initial ray of the polar coordinates (where θ = 0°); a₀ is their difference in azimuth.