Reconstruction in time-bandwidth compression systems

Abstract

Recently, it has been shown that the intensity time-bandwidth product of optical signals can be engineered to match that of the data acquisition instrument. In particular, it is possible to slow down an ultrafast signal, resulting in compressed RF bandwidth-a similar benefit to that offered by the Time-Stretch Dispersive Fourier Transform-but with reduced temporal record length leading to time-bandwidth compression. The compression is implemented using a warped group delay dispersion leading to non-uniform time stretching of the signal's intensity envelope. Decoding requires optical phase retrieval and reconstruction of the input temporal profile, for the case where information of interest resides in the complex field. In this paper, we present results on the general behavior of the reconstruction process and its dependence on the signal-to-noise ratio. We also discuss the role of chirp in the input signal. V C 2014 AIP Publishing LLC.Capturing wide-bandwidth ultrafast signals in real-time is restricted by the time-bandwidth product of the data acquisition instrument. Here, the "product" does not refer to the uncertainty limit but rather to that imposed by the digitizer's bandwidth and record length. The time-stretch dispersive Fourier transformation (TS-DFT) has proven to be very useful in digitizing ultrafast optical signals in real-time. It has led to the discovery of optical rogue waves, 1 the study of supercontinuum noise, 2 and the detection of cancer cells in blood with one-in-a-million sensitivity. 3,4 TS-DFT allows real-time analog-to-digital conversion by reducing the intensity (envelope) bandwidth of information-carrying optical signals to match the much smaller bandwidth of the electronic digitizer. 5,6 However, it does not address the generation of big data volumes inherent in high-throughput realtime measurements. This has fueled interest in non-uniform time stretch transformations that take advantage of sparsity in physical signals to achieve both bandwidth compression as well as reduction in the temporal length. 7-10 Compared to linear time stretch achieved with TS-DFT, such transforms lead to savings in the amount of digital data required for transfer. The aim of this technique is to transform a signal such that its intensity matches not only the digitizer's bandwidth but also its temporal record length. The latter is typically limited by the digitizer's storage capacity. To be sure, reduction of digital data size also facilitates its transmission over communication networks.To this end, it was shown that it is possible to reshape the spectro-temporal profile of optical signals in the analog domain such that signal intensity's time-bandwidth product is commensurate with the acquisition instrument and the big data problem is alleviated. 7-10 The compression is achieved through a warped time-stretch dispersive Fourier transform, in which the transformation is intentionally warped using an engineered group delay (GD) dispersion profile. The transformation causes a frequency-dependent reshaping of th...

Optical Data Compression in Time Stretch Imaging

“…In the time stretch camera, the image is encoded into the amplitude of the spectrum of a broadband optical pulse, and reconstruction consists of a time-to-frequency mapping using the inverse of the measured or simulated group delay profile followed by a frequency-tospace mapping. The compression ratio depends on the group delay characteristics and the sparsity of the image [21,22]. This method offers similar functionality as compressive sampling [25][26][27][28][29][30][31] albeit it achieves it via an entirely different approach, namely by reshaping the analog image using warped time-stretch dispersive Fourier transform.…”

“…Using warped group delay dispersion, it has been shown that one can reshape the spectrotemporal profile of optical signals such that signal envelope's time-bandwidth product is compressed [1,[19][20][21][22]. The compression is achieved through time-stretch dispersive Fourier transform in which the frequency-to-time mapping is intentionally warped, using an engineered group delay dispersion profile, to match the sparsity of the image.…”

“…Detecting rare events such as cancer cells or rogue signals requires that data be recorded continuously and for a long time to catch the rare events. The need to compress massive volumes of data in real-time has fueled interest in nonuniform time stretch transformation that takes advantage of sparsity in physical signals to achieve both bandwidth compression as well as reduction in the temporal length [1,[19][20][21][22]. The aim of this technique is to transform a signal such that its intensity matches not only the digitizer's bandwidth, but also its temporal record length.…”

Design of Warped Stretch Transform

“…Generally known as a phase retrieval method, there are numerous digital algorithms available for recovering the complex amplitude from intensity-only measurements 25,26 . The reconstruction accuracy and lossy nature of this compression have been analyzed previously 18 . The system reshapes the spectrotemporal structure of the signal such that nearly all the signal energy is within the bandwidth of the photodetector and the real-time digitizer of the acquisition system.…”

“…For example, direct frequency-to-time mapping can be replaced by phase retrieval 13 or coherent detection after the dispersion 14 followed by back propagation. Using warped group delay dispersion as a photonic hardware accelerator 15 , an optical signal's intensity envelope can be engineered to match the specifications of the data acquisition back-end [16][17][18] . One can slow down an ultra-fast burst of data, and at the same time, achieve data compression by exploiting sparsity in the original data 19 .…”