Evaluation of Fourier-inspired single-pixel holography under photon-limited conditions

Phase imaging under photon-limited conditions remains a fundamental challenge across many imaging applications, where excessive illumination can cause sample damage or structural degradation. Single-pixel detectors (SPDs), such as photomultiplier tubes (PMTs), offer high sensitivity and low noise, making them particularly suitable for low-light imaging. By integrating SPDs with digital holography, single-pixel holography (SPH) enables phase-sensitive measurements with high detection sensitivity, making it particularly attractive for photon-limited imaging scenarios. Among various SPH approaches, Fourier-inspired single-pixel holography (FISH) combines Fourier single-pixel imaging with off-axis holography, allowing the direct acquisition of phase-carrying spectral components of the hologram through structured modulation with Fourier basis patterns. While this configuration suggests potential advantages in photon utilization efficiency, its effectiveness for phase imaging under photon-limited conditions has not been systematically investigated. In this work, we establish a photon-level numerical simulation framework incorporating a realistic PMT noise model to quantitatively evaluate the performance of FISH under low-light conditions. The imaging performance of FISH is compared with raster scanning, Hadamard, and random modulation schemes for both amplitude and phase objects. The results show that, due to its selective frequency-domain sampling strategy, FISH achieves improved reconstruction fidelity and enhanced robustness in photon-starved regimes. Furthermore, we introduce a physics-constrained single-layer neural network guided by the PMT noise model to adaptively optimize the sampling region of FISH under photon-limited conditions, leading to additional performance gains.