We use optical Gabor-like filtering implemented with a digital micromirror device to achieve nanoscale sensitivity to changes in the size of finite and periodic objects imaged at low resolution. The method consists of applying an optical Fourier filter bank consisting of Gabor-like filters of varying periods and extracting the optimum filter period that maximizes the filtered object signal. Using this optimum filter period as a measure of object size, we show sensitivity to a 7.5 nm change in the period of a chirped phase mask with period around 1 microm. We also show 30 nm sensitivity to change in the size of polystyrene spheres with diameters around 500 nm. Unlike digital post-processing our optical processing method retains its sensitivity when implemented at low magnification in undersampled images. Furthermore, the optimum Gabor filter period found experimentally is linearly related to sphere diameter over the range 0.46 microm-1 microm and does not rely on a predictive scatter model such as Mie theory. The technique may have applications in high throughput optical analysis of subcellular morphology to study organelle function in living cells.