Dispersive Fourier transformation for fast continuous single-shot measurements

102 NATURE PHOTONICS | VOL 7 | FEBRUARY 2013 | www.nature.com/naturephotonics The real-time measurement of fast non-repetitive events is arguably the most challenging problem in the field of instrumentation and measurement1–4. These instruments are needed for investigating rapid transient phenomena such as chemical reactions, phase transitions, protein dynamics in living cells and impairments in data networks. Optical spectrometers are the basic instrument for performing sensing and detection in chemical and biological applications1–6. Unfortunately, the scan rate of a spectrometer is often too long compared with the timescale of the physical processes of interest. In terms of conventional optical spectroscopy, this temporal mismatch means that the instrument is too slow to perform real-time single-shot spectroscopic measurements because it either employs a moving component, such as a translating slit, or relies on a detector array, such as a charge-coupled device (CCD), with limited refresh rate (typically up to ~10 kHz)1–6. Single-shot measurement tools7–15 such as frequency-resolved optical gating (FROG)8–13 and spectral phase interferometry for direct electric-field reconstruction (SPIDER)14,15 are, although powerful, therefore unable to perform pulse-resolved spectral measurements in real time. Although pump–probe methods offer the ability to perform time-resolved spectroscopic analysis with extremely fine temporal resolutions of less than 1 ps, they are based on the stroboscopic measurement technique and hence do not operate in real time16–19, thus making them unable to capture non-repetitive and rare events such as those found in complex physical, chemical and biological systems. Dispersive Fourier transformation (DFT)20–23 — also known as real-time Fourier transformation24–27 — is a powerful method that overcomes the speed limitation of traditional spectrometers and hence enables fast real-time spectroscopic measurements. DFT is an example of the analogy between paraxial diffraction (that is, Fraunhofer diffraction) and temporal dispersion28,29. This analogy, known as space–time duality, emerges from Maxwell’s equations and has been employed to produce a wide variety of elegant methods (including DFT) for high-speed all-optical signal processing such as Fourier optics30,31 and temporal imaging (the temporal equivalent of Dispersive Fourier transformation for fast continuous single-shot measurements