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.
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