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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.
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.
This book employs homogeneous coordinate notation to compute the
first- and second-order derivative matrices of various optical
quantities. It will be one of the important mathematical tools for
automatic optical design. The traditional geometrical optics is
based on raytracing only. It is very difficult, if possible, to
compute the first- and second-order derivatives of a ray and
optical path length with respect to system variables, since they
are recursive functions. Consequently, current commercial software
packages use a finite difference approximation methodology to
estimate these derivatives for use in optical design and analysis.
Furthermore, previous publications of geometrical optics use vector
notation, which is comparatively awkward for computations for
non-axially symmetrical systems.
This book employs homogeneous coordinate notation to compute the
first- and second-order derivative matrices of various optical
quantities. It will be one of the important mathematical tools for
automatic optical design. The traditional geometrical optics is
based on raytracing only. It is very difficult, if possible, to
compute the first- and second-order derivatives of a ray and
optical path length with respect to system variables, since they
are recursive functions. Consequently, current commercial software
packages use a finite difference approximation methodology to
estimate these derivatives for use in optical design and analysis.
Furthermore, previous publications of geometrical optics use vector
notation, which is comparatively awkward for computations for
non-axially symmetrical systems.
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