# Phase-Coded and Noise-Based Brillouin Optical Correlation-Domain Analysis
## 1 Introduction
In the first approach, the Brillouin pump and signal waves are jointly phase-modulated by high-rate binary sequences. The spatial extent of the correlation peaks scales with the duration of a single bit in the sequence. At the same time, the periodicity of the cross-correlation function is determined by the length of the sequence, which may by arbitrarily long. Consequently, _phase-coded B-OCDA_ removes the constraint between measurement range and resolution. A first demonstration of this technique was provided in a joint work of the [PERSON] group of Bar-Ilan University, and the [PERSON] group at the Ecole Polytechnique Federale de Lausanne (EPFL) [18]. The first experiments addressed 4000 resolution points with a 1-cm resolution [18]. The performance of phase-coded B-OCDA was since enhanced to successfully address 440,000 resolution points [19], and a system with over 2 million potential resolution points was demonstrated as well [20]. In Section 2 of this paper, the principle of phase-coded B-OCDA is introduced, and several extensions of the concept are discussed. These include the employment of carefully constructed phase codes for stronger suppression of the off-peak SBS interactions [21]; the overlay of pump pulses for addressing a large number of resolution points in a single trace [20; 22]; use of double-pulse acquisition [23]; elimination of frequency scanning through transient analysis of Brillouin gain [24]; and the combination of amplitude codes alongside phase sequences in the same protocol [19; 25]. Lastly, the application of phase-coded B-OCDA in structural health monitoring [26; 27; 28], and towards the mapping of acoustic waves along micro-fibers [29; 30], is presented as well. Another new variant of B-OCDA aims to remove the restrictions on modulation bandwidth. Rather than degrade the coherence of narrowband light sources through modulation, one may draw the Brillouin pump and signal waves from broadband, incoherent amplified spontaneous emission (ASE). The bandwidth of ASE sources can reach, in principle, several THz. Based on this concept, [PERSON] et al. demonstrated _ASE B-OCDA_ over a small-core, commercially available fiber with a spatial resolution of 4 mm [31]. The main challenge associated with this sensing protocol is low signal-to-noise ratios (SNRs)due to the weak SBS amplification over ultra-short segments and the inherent intensity fluctuations of ASE [32]. Despite this difficulty, the technique was successfully implemented in distributed Brillouin analysis along photonic integrated circuits in chalcogenide glass [33]. A record-breaking spatial resolution of 800 \(\upmu\)m has been achieved [33]. Section 3 of the paper presents the ASE B-OCDA concept and includes previously unpublished analysis of a standard fiber with a spatial resolution of 2 mm. The recent application of the protocol to planar waveguides is addressed [33], and a related concept of B-OCDA based on a chaotic laser source [34; 35] is noted as well. The vast majority of the results discussed below are already published in multiple separate papers by several groups. References are provided for complete details. This review aims to give a unified perspective on the development process and the state of the art of these two analysis protocols, which find increasing roles in applications of Brillouin sensors. Concluding remarks are given in Section 4.