Theory of Incoherent-Light Temporal Imaging Systems Based on a Temporal Pinhole

We present a comprehensive consistent theoretical analysis of a set of recently demonstrated schemes for temporal imaging of incoherent-light intensity waveforms based on the time-domain pinhole concept. Schemes analyzed here include temporal magnification and compression systems, time-to-frequency mapping, and frequency-to-time mapping processes, all involving a suitable combination of optical dispersive lines and a short temporal gate (time-domain pinhole). This paper reports formal derivations of the main performance specifications in the studied incoherent-light schemes, including mapping factors and precise estimates of time/frequency resolutions and operation windows (temporal/spectral field of view), as a function of design parameters, namely dispersion values and pinhole duration. Design equations for system performance optimization are also obtained and theoretical assumptions and design tradeoffs are pointed out and discussed. Our theoretical findings are in agreement with previous simulation and experimental results and are further validated in this report.