Comparing optical systems, and the concept of the converter system

The purpose of this article was to present a complete and general method for comparing the first-order optical character of optical systems. The method provides a common basis for quantifying the difference between systems of all kinds including thin lenses, ophthalmic prisms, eyes before and after accommodation, eyes before and after refractive surgery, etc. Systems may be astigmatic or stigmatic, coaxial or noncoaxial. In special cases, the method reduces to being equivalent in essence to ostensibly incommensurate comparisons implicit or explicit in current optometric and ophthalmological usage (difference in power for refractions, corneas, and thin lenses, difference in prismatic power for prisms, ratio of magnifications for afocal telescopes, etc.). The method uses the concept of a converter system that when placed in front of or behind one system, converts its first-order optical character to the equivalent of a second system. Equations are presented for the ray transferences of the anterior and posterior converter systems for pair-wise comparisons in general. For any two systems, the transferences of the converter systems always exist and are unique. Numerical examples are presented; they illustrate converter systems that may be thin in special cases but thick otherwise. The transference of a converter system embodies and quantifies the optical difference between systems or characterizes the change from one state of a system (presurgical or preaccommodative, for example) to another (postsurgical or postaccommodative). The method provides a rational and uniform methodology for research and clinical applications in many areas of optometry and ophthalmology.