Purpose: To derive general equations that characterize rays, magnification, and blur at the retina in the case of distant object points for a naked eye and for an eye looking through an arbitrary optical instrument. The eye and optical instrument may be astigmatic and noncoaxial.
Method: The derivation is based on linear optics and makes use of the concept of the augmented ray transference of an optical system. Because the transference completely characterizes the linear optics, the analysis can claim completeness.
Results: Equations are presented for position and direction of rays at the retina from distant object points. They lead naturally to the definition of six properties that characterize blur, shape, size, orientation, and position of images of distant objects viewed by the naked eye and by the eye looking through an instrument. By way of example, the general equations are applied to the simple examples of a thin contact lens and a thin spectacle lens in particular.
Conclusion: The analysis provides a framework, complete as far as linear optics is concerned, for the analysis of light arriving at the retina through any instrument from a distant point. In so doing, it unifies and generalizes concepts like blur and spectacle magnification, which, in the past, have been treated separately.