  Observing and studying the evolution of rare non-repetitive natural phenomena
such as optical rogue waves or dynamic chemical processes in living cells is a
crucial necessity for developing science and technologies relating to them. One
indispensable technique for investigating these fast evolutions is temporal
imaging systems. However, just as conventional spatial imaging systems are
incapable of capturing depth information of a three-dimensional scene, typical
temporal imaging systems also lack this ability to retrieve depth information;
different dispersions in a complex pulse. Therefore, enabling temporal imaging
systems to provide these information with great detail would add a new facet to
the analysis of ultrafast pulses. In this paper, after discussing how spatial
three-dimensional integral imaging could be generalized to the time domain, two
distinct methods have been proposed in order to compensate for its shortcomings
such as relatively low depth resolution and limited depth-of-field. The first
method utilizes a curved time-lens array instead of a flat one, which leads to
an improved viewing zone and depth resolution, simultaneously. The second one
which widens the depth-of-field is based on the non-uniformity of focal lengths
of time-lenses in the time-lens array. It has been shown that compared with
conventional setup for temporal integral imaging, depth resolution, i.e.
dispersion resolvability, and depth-of-field, i.e. the range of resolvable
dispersions, have been improved by a factor of 2.5 and 1.87, respectively.
