Provable and Robust Wavefront Sensing via Self-Reference Interferometry

Nebiyou Yismaw¹, Vishwanath Saragadam¹, Aswin C. Sankaranarayanan², M. Salman Asif¹

¹University of California, Riverside   ²Carnegie Mellon University

Overview

Conventional interferometric approaches like phase-shifting interferometry (PSI) can recover phase information, but they rely on a stable reference beam that is difficult to realize in practical settings. We propose a self-reference framework that instead interferes an incoming wavefront with spatially shifted copies of itself, producing pairwise phase differences between shifted pixels. These differences are propagated across a connected graph to recover the complete phase profile, with co-prime shifts proven to guarantee full connectivity and bound worst-case error accumulation.

This repository contains the core phase-recovery algorithm, a simulator for generating synthetic coprime-shift measurements, and scripts to produce results.

Installation

git clone git@github.com:CSIPlab/coprime-psi-code.git
cd coprime-psi-code
pip install -r requirements.txt

Requires Python >= 3.9. Sample images can be found in data/div2k_samples/.

Quick start

The pipeline is three scripts: generate measurements, recover phase, then summarize results across shift sets.

# 1. Simulate coprime-shift PSI measurements (writes to ./measurements/simulated/)
python gen_simulated_data.py --phase-types peak --shifts 0,1,16,17

# 2. Recover phase from those measurements (writes figures/results to ./results/)
python recover_phase.py --phase-types peak --shift-groups "1;16,17"

# 3. Compose a comparison grid across shift sets (recovered phase per shift
#    set, ground truth rightmost, measurement SNR in the title)
python summarize_results.py --phase-types peak --shift-groups "1;16,17"

For additional details, run any of them with --help.

Code structure

• recover_phase.py: main entry point. Loads measurements, runs coprime-shift phase recovery (BFS phasor propagation + least-squares refinement), and saves the figures described in Outputs below.
• summarize_results.py: run after recover_phase.py; composes a comparison grid across shift sets from the results it already saved.
• recovery_algorithms.py: the recovery algorithms themselves. Two BFS phasor-propagation implementations of Algorithm 1 in the paper are included:
  • integrate_coprime_bfs_v3: the vectorized/parallel formulation used by recover_phase.py, where every visited pixel propagates to its neighbors simultaneously via tensor ops each iteration (matches the paper's "efficient parallel implementation" of Algorithm 1).
  • integrate_coprime_bfs_v2: a sequential, one-pixel-at-a-time queue implementation matching Algorithm 1's pseudocode directly. Kept as a readable reference, not called at runtime (its least-squares tail is unfinished/non-functional).
• gen_simulated_data.py: simulated coprime-shift PSI measurement generation (4f optical system + SLM phase encoding).
• psi_least_sqaures.py: closed-form Fourier-domain least-squares phase refinement (Algorithm 1's refinement step).

Outputs

Running recover_phase.py writes figures and data for each (experiment, shift set) combination to {results_dir}/{exp_name}/. By default only the main output is generated:

File	What it shows
summary_{shifts}.png	Ground truth phase and recovered phase side by side (recovered phase re-referenced to the ground truth's global phase), with MAE and phasor error in the title. Start here.
U0_recovered_{shifts}.npz, U0_recovered_LS_{shifts}.npz	Recovered complex field (amplitude + phase), before/after least-squares refinement.

{results_dir}/{base_exp_name}_{noise}_error_analysis.csv collects MAE/MSE/circular-MAE/phasor error across every shift set tried for that experiment and noise setting. summarize_results.py additionally writes all_shifts_summary.png per experiment.

Pass --debug to also save a larger set of per-shift diagnostic figures (phase differences, hop-count error curves, recovered-phase-only plots, etc).

Results

Recovery quality improves with more coprime shifts, for both phase types and at both SNR levels. Suboptimal shift sets, such as a single shift ([1]), increase the number of hops needed to reach each pixel and lead to poorer reconstruction quality. Each additional shift contributes an independent phase-difference measurement per pixel, giving the BFS graph more redundancy to average over and shortening the typical hop distance to the reference pixel, both of which reduce phasor error.

Citation

If you find this work useful, please cite it. We will update this citation once the ECCV proceedings version is available.

@article{yismaw2026provable,
  title   = {Provable and Robust Wavefront Sensing via Self-Reference Interferometry},
  author  = {Yismaw, Nebiyou and Saragadam, Vishwanath and Sankaranarayanan, Aswin C and Asif, M Salman},
  journal = {arXiv preprint arXiv:2604.03564},
  year    = {2026}
}

License

MIT. See LICENSE.