Paraxial optics of astigmatic systems: relations between the wavefront and the ray picture approaches.

PURPOSE The paraxial propagation of astigmatic wavefronts through astigmatic optical systems can be described by the augmented step-along method (ASAM). Its equivalence to the linear ray optics approach is considered in detail. METHODS The ASAM is exploited to derive paraxial ray paths through a general coaxial astigmatic system. RESULTS Starting from the information inherent in the ASAM all 2x2 submatrices rendering the general 4x4 transference of linear optics can be generated. This proves the complete equivalence of both approaches. Additionally, we show that the symplectic relations are automatically obeyed in the ASAM. CONCLUSIONS The ASAM offers a complete alternative to describe the paraxial optics of astigmatic optical systems. According to the ASAM, an optical system is fully characterized by the back vertex vergence and the angular magnification matrix. Hence, a complete description of the paraxial optics of an eye should not only report the state of refraction but the angular magnification matrix as well, although it is not yet very common. The magnification matrix might be important in cases of anisometropia or the design of progressive addition lenses. Yet, a simple clinical procedure to determine the angular magnification matrix is missing.