Optimization of Optical Instruments Under Fluctuations of System Parameters

Optimization plays a fundamental role in understanding stability characteristics of optical systems, for example, lenses, mirrors, and their constrained counterparts. For a dynamical object, the authors address the issue of stability of an image formed under fluctuations of optimization variables. As per this analysis, for a given single lens, mirror, or optical instrument, the positivity of pure correlation components of the fluctuation matrix characterizes the local stability about a chosen fixed point, whilst the positivity of the determinant of the fluctuation matrix offers global stability of the image under variations of the object distance and lateral magnification. In this paper, they demonstrate that there exists a clear cut distinction between the positive and negative lenses and mirrors about the line of unit lateral magnification. Moreover, they propose the extension of the above model to a class of constraint optical system optimization. They also propose an extended formulation for an optimized designing of nonlinearly constrained optical systems with finitely many components.