Fig. 2

Vector analysis of refractive astigmatism in G1 and G2.. Refractive astigmatism was converted to vector notations by using equations by Fourier analysis (J0 = −(C/2)*cos2θ, J45 = −(C/2)*sin2θ (C = minus cylinder power of refractive errors, θ = cylinder axis of refractive errors, J0 < 0 against the rule astigmatism, J0 > 0 with the rule astigmatism, J45 accounts for oblique astigmatism), x axis = J0, y axis = J45). In both groups, clustering of dots toward (0, 0), postoperatively (b: G1, d: G2) compared to preoperative J0 / J45 (a: G1, c: G2) was observed. G1 = normal corneal astigmatism group, G2 = post-penetrating keratoplasty astigmatism group