A Unified Framework for Photonic Time-Stretch Systems

Photonic time stretch is the key enabling technology for a wide variety of instruments with unparalleled single-shot data acquisition performance at high throughput and continuous operation. These systems have established landmark performance in spectroscopy and imaging including flow-through microscopy, velocimetry, lidar, and other measurements. The evolution of the original time-stretch technique into such diverse instruments and applications over the last 25 years has created the need for a unified theoretical framework. This paper represents the first step toward a universal mathematical model for time-stretch instruments. It shows that the "stretch factor"-the fundamental performance metric-is governed by a single canonical equation in a wide range of seemingly diverse time-stretch instruments. The paper also provides new insight into the operation of time-stretch imaging and light scattering systems. The stretch factor is derived for time-stretch systems that operate in temporal, spatial, angular, and Doppler domains. The analysis and mathematical tools provided here can facilitate understanding and analysis of such systems and help future developments in this field.