  4-dimensional optics is based on the use 4-dimensional movement space,
resulting from the consideration of the usual 3-dimensional coordinates
complemented by proper time. The paper uses the established K-calculus to make
a parallel derivation of special relativity and 4-dimensional optics, allowing
a real possibility of comparison between the two theories. The significance of
proper time coordinate is given special attention and its definition is made
very clear in terms of just send and receive instants of radar pulses. The
4-dimensional optics equivalent to relativistic Lorentz transformations is
reviewed.
  Special relativity and 4-dimensional optics are also compared in terms of
Lagrangian definition of worldlines and movement Hamiltonian. The final section
of the paper discusses simultaneity through the solution of a two particle
head-on collision problem. It is shown that a very simple graphical
construction automatically solves energy and momentum conservation when the
observer is located at the collision position. A further discussion of the
representation for a distant observer further clarifies how simultaneity is
accommodated by 4DO.
