Intrinsic Image-Error Theory*

Abstract

Image-error theories are usually based on the coefficients of a characteristic function, and these coefficients are geometrically interpreted in the present paper. The choice of the characteristic function, particularly the choice of variables, is arbitrary. A normal bundle of rays is analyzed here to obtain intrinsic error coefficients which have a geometrical significance, that is, which are independent of the variables used. The connections of these coefficients with the classical image-error theory, the theory of diapoints, the geometry of the caustic, the spot-diagram analysis, and the normal evaluation of the meridional-ray trace are analyzed. This ireatment is based on fifth-order theory since this is the simplest approximation having all the complexity of real optical systems. The interpretation of the sine condition and the Petzval condition in the light of these coefficients is explained.