TRIShUL: Technique for Reconstructing magnetic Interstellar Structure Using starLight polarization

We present a novel technique for the decomposition of line-of-sight (LOS) stellar polarization as a function of distance, aimed at reconstructing 3D plane-of-sky magnetic structures in the interstellar medium. The method is based on the assumption that the observed polarization arises from discrete, thin dust layers located at varying distances along the LOS. Using a simple and intuitive frequentist framework, our method identifies structural changes in the distance-sorted cumulative Mahalanobis distance between Stokes parameters (q and u) to detect the locations of dust layers and estimates their associated physical properties (parallax and Stokes parameters) necessary for constructing 3D maps. We benchmarked the method using mock datasets representative of high-Galactic-latitude regions, incorporating realistic parallax uncertainties from Gaia and expected polarization measurements from the upcoming P<ns0:monospace>ASIPHAE</ns0:monospace> survey. Our tests show that the method reliably recovers the distances and polarization properties of dust clouds when the polarization signal exceeds 0.1%, and the effective fraction of background stars is greater than 10% in our tested samples with ∼345 stars. The effect of background star fraction on the performance becomes less critical with increasing amplitude of the polarization source field from the dust cloud. We applied our method to existing polarization data from two illustrative sight lines - one at intermediate-high Galactic latitude and one near the Galactic plane - with known tomographic solutions, finding excellent agreement with the literature and demonstrating its accuracy across both regions. We compare the performance of our method with that of the Bayesian method BISP-1. While both methods effectively recover dust cloud properties, our approach is prior-free and computationally more efficient in determining the optimal number of clouds along the LOS. These advantages make our method more flexible and broadly applicable for multilayer dust cloud reconstruction for the upcoming era of large-scale stellar polarization surveys.