# Phase-Coded and Noise-Based Brillouin Optical Correlation-Domain Analysis
## 1 Introduction  
Distributed analysis of Brillouin gain spectra along optical fibers was first proposed as a means for temperature and strain sensing nearly 30 years ago [1; 2]. The first and most widely employed architectures of stimulated Brillouin scattering (SBS) sensors are based on time-domain analysis: a Brillouin pump pulse is launched from one end of the fiber, and the amplification of a counter-propagating Brillouin signal wave is being monitored as a function of time [1; 2]. The spatial resolution of the basic configuration of such Brillouin optical time-domain analysis (B-OTDA) protocols equals the duration of the pump pulse multiplied by the group velocity of light in the fiber [1; 2]. The pulse duration, in turn, must exceed the lifetime associated with the stimulation of hypersonic acoustic waves in the core of the fiber, on the order of 5-10 ns [3]. Consequently, the spatial resolution of the fundamental B-OTDA technique is restricted to the order of 1 m or longer [3]. Over the last decade, much progress has been made in pushing the spatial resolution of B-OTDA towards a few centimeters using a variety of techniques [4; 5; 6; 7; 8; 9; 10; 11; 12]. Nevertheless, the resolution of distributed Brillouin analysis remains a significant and active area of research. In 1999 and 2000, Prof. [PERSON] and co-workers at the University of Tokyo proposed and demonstrated an alternative paradigm towards high-resolution Brillouin analysis [13; 14]. Theirproposition is based on the following property: The instantaneous electro-strictive driving force for the stimulation of the acoustic wave at a given fiber location is proportional to the inner product between the optical pump and signal fields at that particular point [15]. Consequently, one may show that the strength of the SBS process is closely related to the temporal cross-correlation function between the complex modulation envelopes of the two waves at a point of interest [13; 14]. Judicious, joint modulation of the two waves can confine their cross-correlation function to discrete locations, referred to as _correlation peaks_. The SBS interaction is largely restricted to these peaks, and it is strongly inhibited everywhere else [13; 14]. The spatial extent of the correlation peaks equals half the correlation length of the modulated common source of the pump and signal waves [13; 14]. Distributed sensing based on this principle came to be known as _Brillouin optical correlation-domain analysis_, or _B-OCDA_[13; 14]. The first realizations of B-OCDA involved joint frequency modulation of the two waves by sinusoidal waveforms [13; 14]. The spatial resolution of the analysis in this case improves with the magnitude of frequency modulation [13; 14]. The protocol provided distributed analysis with extremely high spatial resolution: up to 1.6 mm in a standard optical fiber [16]. At the time of writing, this resolution remains unmatched by time-domain Brillouin sensing protocols. One drawback, however, of the initial B-OCDA approach has been the periodicity of the cross-correlation function between pump and signal waves that are frequency modulated by a single sine-wave function. This periodicity restricted the spatial range of measurements that could be performed without ambiguity and limited the number of spatial resolution points to several hundred only [13; 14]. The number of resolution points was since extended using more elaborate frequency-modulation patterns involving multiple rates [17]. Nevertheless, frequency modulation provides only partial flexibility in the synthesis of the cross-correlation function between pump and signal. In addition, frequency modulation of a laser source is limited by practical considerations to a magnitude on the order of 50 GHz [16], corresponding to a spatial resolution of about 1.5 mm in a fiber [16]. The realization of higher modulation rates, and higher resolution, has proven challenging. This paper reviews two strategies that were proposed and demonstrated since 2012 as partial solutions to the above difficulties.