The internal shape and alignment of accelerator discs is crucial for efficient collider operation at the future compact linear collider (CLIC). We applied a calibrated custom-made Fourier-domain short coherence interferometer to measure the height of 40 and ultraprecisely turned steps (surface roughness , flatness ) on an oxygen-free electronic copper disc. The step heights were quantified to be and . The uncertainties are quoted at 95% confidence level and include contributions from calibration, refractive index of air, cosine error, surface roughness, and thermal expansion in comparison to standard temperature of 20°C. The results were verified by measuring the same steps using a commercial white light interferometer Veeco—NT3300. Our instrument can ensure that the accelerator discs of the CLIC are aligned within the tolerance required for efficient collider operation.