Forms of the characteristic function for asymmetric systems that form sharp images to first order

The coefficients of the terms of second degree in the Taylor series of any of Hamilton’s characteristic functions, together with the indices of refraction in object and image space, completely characterize the first-order imaging properties of an optical system. Constraints on the first-order imaging properties (such as requiring that a system possess a given focal length) are, therefore, associated with constraints on the coefficients of second degree. This correspondence is discussed for asymmetric systems that, to first order, form a sharp image of one or more objects. The further requirement of nonanamorphic imagery of a specified magnification is also addressed. The ideas developed here enable the first-order layout of an asymmetric system to be realized by using methods for determining a system’s configuration in terms of desired values for the coefficients of the characteristic function.