Modified Lagrange invariants and their role in determining transverse and axial imaging resolutions of self-interference incoherent holographic systems

The Lagrange invariant is a well-known law for optical imaging systems formulated in the frame of ray optics. In this study, we reformulate this law in terms of wave optics and relate it to the resolution limits of various imaging systems. Furthermore, this modified Lagrange invariant is generalized for imaging along the z axis, resulting with the axial Lagrange invariant which can be used to analyze the axial resolution of various imaging systems. To demonstrate the effectiveness of the theory, analysis of the lateral and the axial imaging resolutions is provided for Fresnel incoherent correlation holography (FINCH) systems.