Ever since the discovery of space-time duality, several methods have been developed to perform temporal imaging, and there are two major categories: the quadratic signal onto the phase modulator and the parametric mixer with a linear chirped pump. The features of each mechanism have been thoroughly and quantitatively explored and optimized for certain kinds of applications, but a comparison of some key parameters, especially in the aspect of the repetition rate, is required. In this paper, we will first review the theoretical models and existing performance of these two mechanisms and, consequently, compare them quantitatively in different aspects: the focal group delay dispersion, the pupil size, the effective duty ratio, and the temporal numerical aperture. All these fundamental parameters are related to the repetition rate. The results obtained in this study would provide some important guidelines for the time-lens design, so as to be optimized in different kinds of applications with different repetition rate requirements, such as ultrafast optical communication and real-time bio-imaging systems.
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