A speckle readhead includes a light source that outputs light towards an optically rough surface. Light scattered from this surface contains speckles. The scattered light is imaged onto an image detector, captured and stored. Subsequently, a second image is captured and stored. The two images are repeatedly compared at different offsets in a displacement direction. The comparison having the highest value indicates the amount of displacement between the readhead and the surface that occurred between taking the two images. An optical system of the readhead includes a lens and an aperture. The aperture can be round, with a diameter chosen so that the average size of the speckles is approximately equal to, or larger than, the dimensions of the elements of the image detector. The dimension of the aperture in a direction perpendicular to the direction of displacement can be reduced. Thus, the imaged speckles in that direction will be greater than the dimension of the image detector elements in that direction. Such a readhead is relatively insensitive to lateral offsets. The lens can be a cylindrical lens that magnifies the relative motion along the direction of displacement but does not magnify relative motions in the direction perpendicular to the direction of displacement. The optical system can also be telecentric. Thus, the readhead is relatively insensitive to both separation and relative motions between the readhead and the surface. The light source can be modulated to prevent smearing the speckles across the image detector. The light source can be strobed to freeze the image.