We describe techniques used to measure straightness errors of precision machines. These measurements employ a dimensionally stable mechanical reference surface that is sampled with a laser interferometer-hence the term optical straightedge. The figure error of the reference surface and the straightness error motion of a coordinate measuring machine carriage in a horizontal plane are each measured with an estimated accuracy of 0.5 un. (13 nm) over 40 in. (1 m) of travel. When measuring straightness error in a vertical plane, the results are complicated by deformation of the reference surface by gravitational forces. We use a computational algorithm, based upon simple beam theory, to correct straightness data for this distortion. While inadequate for accuracies better than about 2 un. (50 nm), we believe that the algorithm, which may be tested using an uncalibrated straightedge, may be improved using finite-element calculations of gravitational sag.