On Extensions of the Optical Optimization

We offer an optimized image formation by considering the focal length of a lens/ mirror or their combination as the objective function. We characterize the stability and correlation properties of an image under fluctuations of the lateral magnification and object distance. The local stability of an image thus formed is determined by the positivity of the pure fluctuation components, while its global counterpart as that of the determinant of the fluctuation matrix. We find that the concave and convex systems render disjoint fluctuation surfaces about the line of the unit lateral magnification. Extended objective functions are constructed for optical systems with finitely many constrained and unconstrained components