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How to process phase singular points (SPs), or residues, is a difficult problem in a 2-D phase-unwrapping process to generate digital elevation maps (DEMs). Although the minimum-cost network-flow method is an effective and widely used technique, some problems still remain. That is, the method often generates spikes in high SP-density areas and long clifflike artifacts for isolated SPs. It also takes a long time to unwrap phase data that contain many SPs. In this paper, we propose a new unwrapping method, namely, singularity-spreading phase unwrapping (SSPU), which solves these problems. In this method, we spread the singularity at SPs around to make the closely located positive and negative SPs combine gently with each other or make the isolated SPs fade away. Experiments demonstrate that the spreading process compensates the distortion in phase values in the vicinities of SPs appropriately for landscape reconstruction. The SSPU generates high-quality DEMs with smaller calculation costs than the conventional method. Besides the simple SSPU, we also present weighted SSPU where we utilize amplitude information to improve the performance further. In addition, we discuss the relationship between landscape characteristics and SSPU performance.