Single-photon Micro-scanning Imaging with SPAD Arrays Utilizing a Piezoelectrically Actuated Tilt Mirror

：Single-photon imaging has garnered significant attention in advanced photonic research due to its unparalleled capabilities in ultra-weak light detection and high-precision three-dimensional imaging. The Single Photon Avalanche Diode （SPAD）with Time Correlated Single Photon Counting （TCSPC）function excel in extracting scene distance information，their spatial resolution remains constrained by inherent limitations in data processing efficiency and the physical pixel density of SPAD arrays. To address these challenges，this study proposes an innovative integration of piezoelectric micro-scanning technology with a super-resolution reconstruction algorithm. By introducing sub-pixel-level displacement via a piezoelectrically actuated tilt mirror and applying advanced computational methods，this approach aims to transcend the physical resolution barriers of SPAD detectors，thereby enhancing both spatial resolution and depth discrimination capabilities. A dedicated micro-scanning imaging system was engineered for SPAD with TCSPC function arrays，incorporating a piezoelectrically actuated tilt mirror as the core scanning component. To mitigate photon scattering artifacts from intense illumination，the system adopted a non-coaxial optical architecture with spatially separated illumination and detection paths. The experimental setup utilized a Photon Force PF32 silicon SPAD array （32×32 pixels） and a PicoQuant picosecond pulsed laser （central wavelength： 532 nm， pulse width： ~70 ps）. A systematic “2×2” four-step micro-scanning protocol was implemented，generating 0.5-pixel displacements of the image plane through precise angular adjustments of the piezoelectric mirror. This sub-pixel scanning strategy acquired four complementary Low-Resolution （LR）frames，each containing unique spatial information. Based on the Point Spread Function （PSF），an enhancement to the traditional Projection Onto Convex Sets （POCS）algorithm is proposed. The improved PSF template involves stretching a Gaussian PSF along the edge direction，thereby simulating the anisotropic characteristics of the optical system. In conjunction with an edge detection operator，the enhanced PSF template is applied to the detected edge regions while retaining the Gaussian PSF in smooth areas. Compared with the conventional POCS method， the proposed algorithm suppresses blurring effects during the iterative process by leveraging the directional properties of edge regions. This approach not only preserves edge information but also enhances the detail resolution of the image. To ensure sub-pixel accuracy in micro-scanning displacements，a hybrid calibration method combining frequency-domain registration and iterative trial-number optimization was devised，achieving trajectory alignment errors below 0.01 pixels. The system Instrument Response Function （IRF） was modeled， and the pixel cross-correlation method was used to analyze the time-correlated photon distribution histograms to achieve sub-millimeter depth resolution. Two-dimensional and three-dimensional imaging experiments were performed using the USAF 1951 resolution target，white plastic bottles，and multi-structured pen holders. The superiority of the enhanced POCS algorithm over other methods was quantitatively assessed by analyzing the intensity variation curves of local details. Additionally，the Root Mean Square Error （RMSE）was employed as an objective evaluation metric to quantitatively assess the performance of three-dimensional super-resolution imaging. The imaging experiment was conducted in the darkroom utilizing the proposed single-photon micro-scanning imaging system. The results indicate that： 1） The micro-scanning trajectory closely approximates a standard vertical quadrilateral with a micro-displacement error of only 0.01 pixels；2）By reconstructing four frames of 32×32 pixel LR images into a single 64×64 pixel Super-Resolution （SR） image，the limit resolution is improved by 41.42%， surpassing both the bilinear interpolation method and the inter-frame difference method （25.99%）；3）In 3D depth imaging，the system achieves a depth resolution of 16.5 mm，reducing the RMSE in straight cross-sections by 14.12% and in curved cross-sections by 7.40%. The SPAD array micro-scanning single-photon imaging method based on piezoelectrically actuated tilt mirror，as proposed in this study，successfully overcomes the inherent resolution limitations of small-scale SPAD detectors. By preserving the high sensitivity characteristic of single-photon detection，this system not only enhances the spatial resolution for two-dimensional intensity imaging but also improves the detail resolution capability for three-dimensional depth imaging. Future extensions could explore larger-scale scanning configurations （e. g.，3×3 or 4×4 micro-displacements） to further amplify resolution gains，albeit with increased computational demands. Integration of deep learning architectures with the POCS framework may enable real-time processing for dynamic scenes，while miniaturization of the piezoelectric scanning module could facilitate deployment in portable imaging systems. The methodology presents potential for applications demanding simultaneous high spatial and temporal resolution，including quantum LiDAR，non-line-of-sight imaging，and in vivo fluorescence lifetime microscopy.