Mathematical Background -- Skew-Ray Tracing of Geometrical Optics -- Geometrical Optical Model -- Ray tracing Equations for Paraxial Optics -- Cardinal Points and Image Equations -- Ray Aberrations -- Jacobian Matrix of Ray Ri with Respect to Incoming ray Ri-1 and Boundary Variable Vector Xi -- Jacobian Matrix of Boundary Variable Vector Xi¬ with Respect to System Variable Vector Xsys -- Prism Analysis -- Prism Design Based on Image Orientation -- Determination of Prism Reflectors to produce required image orientation -- Optically Stable Systems -- Point Spread Function, Caustic Surfaces and Modulation Transfer Function -- Optical Path Length and Its Jacobian Matrix -- Wavefront Aberration and Wavefront Shape -- Hessian Matrix of Ray Ri with Respect to Incoming ray Ri-1 and Boundary Variable Vector Xi -- Hessian Matrix of Boundary Variable Vector Xi with Respect to System Variable Vector Xsys -- Hessian Matrix of Optical Path Length.

This book computes the first- and second-order derivative matrices of skew ray and optical path length, while also providing an important mathematical tool for automatic optical design. This book consists of three parts. Part One reviews the basic theories of skew-ray tracing, paraxial optics and primary aberrations – essential reading that lays the foundation for the modeling work presented in the rest of this book. Part Two derives the Jacobian matrices of a ray and its optical path length. Although this issue is also addressed in other publications, they generally fail to consider all of the variables of a non-axially symmetrical system. The modeling work thus provides a more robust framework for the analysis and design of non-axially symmetrical systems such as prisms and head-up displays. Lastly, Part Three proposes a computational scheme for deriving the Hessian matrices of a ray and its optical path length, offering an effective means of determining an appropriate search direction when tuning the system variables in the system design process.