Efficient complex-field measurement in lens-free on-chip microscopy via lightweight state-space modeling

Efficient measurement of optical complex fields is a fundamental requirement in lens-free on-chip microscopy (LFOM) for applications in biomedical analysis, industrial inspection, and particle characterization. By recording only intensity distributions on image sensors, LFOM faces a severely ill-posed inverse problem in estimating the underlying complex field, further complicated by Hermitian-symmetry-induced twin-image artifacts and long-range diffraction coupling. In this work, we propose a lightweight state-space-enhanced computational framework, termed LMECNet, for high-fidelity complex-field measurement in LFOM. The framework integrates a bidirectional frequency-enhanced state-space fusion mechanism for long-range dependency aggregation with a dual-path residual architecture that explicitly models real and imaginary components to strengthen complex-domain estimation. To further suppress twin-image artifacts, a twin-artifact discrimination loss is introduced to improve reconstruction stability from a measurement perspective. Experimental results on high-resolution biological tissue datasets demonstrate that LMECNet consistently achieves the best reconstruction fidelity across the evaluated tissue test sets, while reducing model complexity by over 90% and delivering multi-fold gains in inference throughput relative to prior transformer-based baselines. These results highlight the potential of state-space modeling as an effective and practical paradigm for computational measurement in lens-free microscopic systems.