Calculation of the total corneal astigmatism using the virtual cross cylinder method on the secondary principal plane of the cornea

Abstract

Abstract This study aimed to establish a virtual cross cylinder method to calculate total corneal astigmatism by combining anterior corneal astigmatism and posterior corneal astigmatism. The virtual cross cylinder method combines anterior and posterior corneal astigmatism on the secondary principal plane of the cornea based on Gaussian optics. The meridian with the least refractive power, namely, the flattest meridian of the virtual cross cylinder of a ± 0.5×C diopter, is set as the reference meridian, and the power (F) at an angle of φ between an arbitrary meridian and the reference meridian is defined as F(φ) = − 0.5×C×cos2φ. The magnitude and axis of the total corneal astigmatism were calculated by applying trigonometric functions and the atan2 function based on the combination of the virtual cross cylinders of the anterior corneal astigmatism and the posterior corneal astigmatism. To verify the performance of the virtual cross cylinder method, a verification experiment with two Jackson cross cylinders and a lensmeter was performed, and the measured and calculated values were compared. The verification experiment results showed good agreement between the measured and calculated values. A novel technique for calculating total corneal astigmatism, the virtual cross cylinder method, was developed and verified.