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Relative motion of structured optical illumination with respect to an object and far-field measurement of intensity are presented as a means to obtain far-subwavelength spatial resolution with a direct imaging arrangement. The principle behind this approach is that the variable interaction of an object with a background field generates information about nanometer-scale features that is encoded in the propagating plane wave spectrum, allowing far-field data that is modulated with motion according to the nanostructure. Information theory supports this new super-resolution mechanism and illustrates sensitivity with respect to the illumination and detection arrangements. Simulations indicate that available lasers and detectors would enable a resolution of lambda/1000 with modest signal-to-noise requirements and single-pixel detection. Relative motion in structured fields is shown to enhance spatial resolution achievable using data inversion with constraints. Importantly, far-subwavelength sensitivity is shown to be achievable even when the illuminating field is unknown. These results suggest applications that include material defect detection and unlabeled protein sensing, and direct extensions to estimating geometrical features at unprecedented spatial resolution become possible.