Harmonic-assisted illumination-parameter estimation in binary-harmonic incoherent structured illumination microscopy

Non-interferometric structured illumination microscopy (SIM) is widely used for super-resolution imaging. However, in digital micromirror device (DMD)-based SIM, the modulation depth often decreases rapidly at high spatial frequencies, which degrades illumination-parameter estimation (wavevectors and phases) and consequently limits reconstruction quality. Here, we propose binary-harmonic incoherent SIM (BH-iSIM), a harmonic-assisted framework for the estimation of illumination parameters and reconstruction of images. BH-iSIM exploits the higher-order components generated by binary DMD patterns by tuning the illumination period so that both the strong first-order component and the weaker third-harmonic component lie within the optical passband. The first-order peak is robustly localized using principal component analysis (PCA), and the third-harmonic location and corresponding illumination parameters are inferred through the harmonic relationship, avoiding direct detection of strongly attenuated high-frequency peaks. BH-iSIM is validated using resolution-target simulations across a range of super-resolution ratios, additional simulations under varying sampling conditions (i.e., pixel size), and an experimental microtubule dataset against a reference reconstruction. BH-iSIM maintains stable wavevector-estimation in high-frequency regimes with peak-localization errors below 0.05 pixels. These results indicate that binary-pattern illumination design combined with harmonic-assisted estimation improves parameter-estimation stability and practical resolution gains in non-interferometric DMD-SIM without additional hardware modifications.