# Inversion of ϕ-OTDR Spatial Windowing Effects Using Wiener Deconvolution for Improved Acoustic Wavefield Reconstruction

## TL;DR

This paper improves the spatial resolution of ϕ-OTDR by using Wiener deconvolution to correct windowing effects, leading to more accurate acoustic wavefield reconstructions.

## Contribution

A novel Wiener deconvolution method is introduced to invert spatial windowing effects in ϕ-OTDR for better acoustic sensing.

## Key findings

- The spatial windowing effect is modeled as a point spread function validated with a fiber-coupled tuning fork.
- Wiener deconvolution effectively enhances spatial resolution and reconstructs 2D wavefront geometry.
- The method reduces systematic errors in SRP-PHAT spatial spectrum estimation for acoustic field analysis.

## Abstract

The spatial response of rectangular pulse heterodyne phase-sensitive optical time-domain reflectometry (ϕ-OTDR) to an acoustic event is characterized by a windowing function rather than a point-like sensitivity. This effect degrades the system’s spatial resolution and introduces systematic errors in array signal processing. This work presents modeling analysis and a mitigation strategy for this fundamental limitation. The spatial windowing effect is modeled as a point spread function (PSF) derived from physical mechanisms and system parameters, including the pulse width, gauge length, and intra-pulse intensity dynamics. The PSF model is validated against measurements under near-ideal conditions using a fiber-coupled tuning fork. A Wiener filter-based deconvolution method is utilized to invert the windowed spatial response towards a point-like response. The effectiveness of this inversion is demonstrated through enhanced spatial resolution and accurate reconstruction of two-dimensional wavefront geometry. Furthermore, the impact of this effect on array signal processing is quantitatively evaluated. The results demonstrate that the proposed method effectively suppresses systematic errors in wavefield analysis, and specifically enhances the accuracy and confidence of steered response power—phase transform (SRP-PHAT) spatial spectrum estimation. This study provides a systematic framework for understanding, quantifying, and inverting the spatial response in ϕ-OTDR, enabling accurate and interpretable acoustic field sensing.