The Kolmogorov‒Smirnov test showed that the distributions of angle kappa and angle alpha were both nonnormal and skewed. The proportion of eyes with an angle alpha less than 0.5 was 61.79%, and the proportion of eyes with an angle alpha less than 0.8 mm was 91.35% (Fig. 2A). The proportions of eyes with an angle kappa less than 0.5 and 0.8 mm were 88.79% and 98.24%, respectively, as shown in Fig. 2B.
Distribution of angle alpha in the population: The proportions of angle alpha in the right eye were 18.87%, 2.65%, 7.16%, and 71.31% under the nose, under the temple, above the nose, and above the temple, respectively; the left eye is infratemporal, supratemporal, infranasal and supranasal, and the proportions of angle alpha accounted for 22.92%, 2.37%, 6.26%, and 68.45%, respectively. The distribution characteristics of angle alpha in each quadrant: The lower part of the nose is the largest, and the upper part of the temple is the smallest. The size and distribution of the angle alpha in each quadrant are shown in Table 1 and Fig. 3.
The distribution of angle kappa in the population: The proportions of angle kappa in the right eye were 41.46%, 39.24%, 6.60%, and 12.70%. The proportions of angle kappa in the left eye were 42.41%, 30.48%, 11.68%, and 15.43%. The distribution characteristics of angle kappa in each quadrant: The upper part of the nose is the largest, and the lower part of the temple is the smallest. The size and distribution of the angle kappa in each quadrant are shown in Table 2 and Fig. 3.
The angle alpha was a median of 0.42 (0.26, 0.53) mm in the right eye and 0.41 (0.26, 0.52) mm in the left eye; the median size for males was 0.41 (0.26, 0.53) mm, and that for females was 0.40 (0.25, 0.52) mm, and the differences between males and females were statistically significant (Z=-3.177, P = 0.001). In addition, the differences in the angle alpha were statistically significant (Z=-2.855, P = 0.004) between the right eye and left eye.
The angle kappa was a median of 0.24 (0.14, 0.31) mm in the right eye and 0.23 (0.13,0.30) mm in the left eye; the median size for males was 0.23 (0.13,0.30) mm and that for females was 0.24 (0.13,0.31) mm. There was a statistically significant difference in the angle kappa between the right eye and left eye (Z=-9.383, P < 0.001), whereas there was no statistically significant difference between males and females (Z = 0.221, P = 0.825).
There was a moderate correlation between the angle alpha and angle kappa (r = 0.352, P < 0.001). The angle alpha of both eyes was linearly correlated, R2 = 0.2, P < 0.001 (Fig. 4A). The Spearman correlation coefficient was 0.49 (P < 0.001), and Cronbach’s coefficient was 0.62. The angle kappa of both eyes showed a linear correlation, R2 = 0.2, P < 0.001, as shown in Fig. 4B. The Spearman correlation coefficient was 0.51 (P < 0.001), and Cronbach’s coefficient was 0.64. The binocular polar diagram shows that the distribution of angle alpha and angle kappa is symmetrical, but the distribution of angle kappa is more concentrated, and the distribution of angle alpha is more variable than angle kappa, as shown in Fig. 4. There was no significant linear correlation between angle alpha and age (R2 = 0.03), and the best fitting coefficient R2 of the curve was R2 = 0.10 (P < 0.001); there was no significant linear correlation between angle kappa and age (R2 = 0.03), and the best fitting coefficient R2 of the curve was R2 = 0.11 (P < 0.001) (Fig. 5). With age as the independent variable and angle alpha or angle kappa as the dependent variable, regression equations were established: Angle alpha = 0.5076-0.0101Age + 0.0001Age2, angle kappa = 0.2139-0.0014Age + 0.00003Age2, as shown in Fig. 5.
From the perspective of age distribution, angle alpha and angle Kappa were the smallest in the 20–30 age group. Before the age of 20, angle alpha and angle kappa gradually decrease, and after the age of 30, angle alpha and angle kappa gradually increase; angle kappa in each age group was smaller than angle alpha, as shown in Fig. 6. Multivariate correlation analysis showed that angle kappa and angle alpha were positively correlated with age and lens thickness(LT) and negatively correlated with anterior chamber depth(ACD), axial length(AL), and white to white distance(WTW), but not with central corneal thickness(CT) and keratometry.