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Significance: By incorporating multiple overlapping functional near-infrared spectroscopy (fNIRS) measurements, high-density diffuse optical tomography (HD-DOT) images human brain function with fidelity comparable to functional magnetic resonance imaging (fMRI). Previous work has shown that frequency domain high-density diffuse optical tomography (FD-HD-DOT) may further improve image quality over more traditional continuous wave (CW) HD-DOT. Aim: The effects of modulation frequency on image quality as obtainable with FD-HD-DOT is investigated through simulations with a realistic noise model of functional activations in human head models, arising from 11 source modulation frequencies between CW and 1000 MHz. Approach: Simulations were performed using five representative head models with an HD regular grid of 158 light sources and 166 detectors and an empirically derived noise model. Functional reconstructions were quantitatively assessed with multiple image quality metrics including the localization error (LE), success rate, full width at half maximum, and full volume at half maximum (FVHM). All metrics were evaluated against CW-based models. Results: Compared to CW, localization accuracy is improved by >40% throughout brain depths of 13 to 25 mm below the surface with 300 to 500 MHz modulation frequencies. Additionally, the reliable field of view in brain tissue is enlarged by 35% to 48% within an optimal frequency of 300 MHz after considering realistic noise, depending on the dynamic range of the system. Conclusions: These results point to the tremendous opportunities in further development of high bandwidth FD-HD-DOT system hardware for applications in human brain mapping.